Fairfield Meeting (October 28-29)- Page 614 San Luis Obispo Meeting (November 11-12)-Page 622 Evanston Meeting (November 11-12)-Page 630

Notices of the American Mathematical Society

October 1983, Issue 228 Volume 30, Number 6, Pages 569- 712 Providence, Rhode Island USA ISSN 0002-9920 Calendar of AMS Meetings

THIS CALENDAR lists all meetings which have been approved by the Council prior to the date this issue of the Notices was sent to press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the Ameri· can Mathematical Society. The meeting dates which fall rather far in the future are subject to change; this is particularly true of meetings to which no numbers have yet been assigned. Programs of the meetings will appear in the issues indicated below. First and second announcements of the meetings will have appeared in earlier issues. ABSTRACTS OF PAPERS presented at a meeting of the Society are published in the journal Abstracts of papers presented to the American Mathematical Society in the issue corresponding to that of the Notices which contains the program of the meet· ing. Abstracts should be submitted on special forms which are available in many departments of mathematics and from the office of the Society in Providence. Abstracts of papers to be presented at the meeting must be received at the headquarters of the Society in Providence, Rhode Island, on or before the deadline given below for the meeting. Note that the deadline for ab· stracts submitted for consideration for presentation at special sessions is usually three weeks earlier than that specified below. For additional information consult the meeting announcement and the list of organizers of special sessions. MEETING ABSTRACT NUMBER DATE PLACE DEADLINE ISSUE 806 October 28-29, 1983 Fairfield, Connecticut AUGUST 23, 1983 October 807 November 11-12, 1983 San Luis Obispo, California AUGUST 25, 1983 October 808 November 11-12, 1983 Evanston, Illinois AUGUST 29, 1983 October 809 january 25-29, 1984 Louisville, Kentucky NOVEMBER 2, 1983 january {90th Annual Meeting) 1984 April 6-7, 1984 Notre Dame, Indiana August 16-19, 1984 Eugene, Oregon November 2-3, 1984 Minneapolis, Minnesota November 9-10, 1984 San Diego, California january 9-13, 1985 Anaheim, California {91 st Annual Meeting) March 22-23, 1985 Chicago, Illinois january 7-11, 1986 New Orleans, Louisiana {92nd Annual Meeting) january 21-25, 1987 San Antonio, Texas {93rd Annual Meeting)

DEADLINES: Advertising (November Issue) October 6, 1983 Uanuary 1984 Issue) December 1, 1983 News/Special Meetings: (November Issue) September 19,1983 Uanuary 19841ssue) November9, 1983

Other Events Soonsored by the Society january 23-24, 1984, AMS Short Course: Mathematics of Information Processing, Louisville, Kentucky. This issue, page 645. April 2-5, 1984, AMS-SIAM Symposium on Pseudodifferential Operators and Fourier Integral Operators with Applications to Partial Differential Equations, University of Notre Dame, Notre Dame, Indiana. May 1984, Symposium on Some Mathematical Questions in Biology, DNA Sequence Analysis, New York, New York. June-July 1984, AMS-SIAM Summer Seminar on Nonlinear Systems of PDE in Applied Mathematics. june 10- August 18, 1984 Joint Summer Research Conferences in the Mathematical Sciences, Bowdoin College, Brunswick, Maine. This issue, page 663. july 16-August 3, 1984, AMS Summer Research Institute on Geometric Measure Theory and the Calculus of Variations. Subscribers' changes of address should be reported well in advance to avoid disruption of service: address labels are prepared four to six weeks in advance of the date of mailing. Requests for a change of address should always include the member or subscriber code and preferably a copy of the entire mailing label. Members are reminded that U. S. Postal Service change-of­ address forms are not adequate for this purpose, since they make no provision for several important items of information which are essential for the AMS records. Suitable forms are published from time to time in the Notices (e.g. June 1980, page 378). Send change. of address notices to the Society at Post Office Box 6248, Providence, Rl 02g40. (Notices is published eight times a year (January, February, April, June, August, October, November, December) by the American Mathematical Society at 201 Charles Street, Providence, RI 02904. Second class postage paid at Providence, RI and additional mailing offices. POSTMASTER: Send address change notices to Membership and Sales Department, American Mathematical Society, Post Office Box 6248, Providence, RI 02940.] Publication here of the Society's street address, and the other information in brackets above, is a technical requirement of the U. S. Postal Service. The street address should never be used by correspondents, unless they plan to deliver their messages by hand. Members are strongly urged to notify the Society themselves of address changes (in the manner described above), since (as explained above) reliance on the postal service change-of-address forms is liable to cause delays in processing such requests in the AMS office. Notices of the American Mathematical Society

Volume 30, Number 6, October 1983

EDITORIAL COMMITTEE Paul F. Baum, Ralph P. Boas 571 The 1983 Warsaw Congress of IMU, Raymond L. johnson, Mary Ellen Rudin G. W. Mostow Bertram Walsh, Daniel Zelinsky Everett Pitcher (Chairman) 574 1983 Steele Prizes awarded in Albany MANAGING EDITOR 580 Nation at risk Lincoln K. Durst 591 Reports from the Mathematics Research Institutes ASSOCIATE EDITORS Hans Samelson, Queries 598 Queries Ronald L. Graham, Special Articles 600 Letters to the Editor SUBSCRIPTION ORDERS Subscription for Vol. 30 (1983): 606 News and Announcements $39 list, $20 member. The subscription 610 NSF News & Reports price for members is included in the annual dues. Subscriptions and orders 614 Future Meetings of the Society for AMS publications should be Fairfield, October 28-29, 614 addressed to the American Mathematical Society, P. 0. Box 1571, Annex Station, San Luis Obispo, November 17-12, 622 Providence, Rl 02901. All orders must Evanston, November 11-12, 630 be prepaid. Louisville, january 25-29, 641 ORDERS FOR AMS BOOKS AND Mathematical Sciences Employment Register, 657 INQUIRIES ABOUT SALES, SUBSCRIP­ Synopses, Short Course on Mathematics of TIONS, AND DUES may be made by Information Processing, 661 calling Carol-Ann Blackwood at joint Summer Research Conference Series, 663 800-556-7774 (toll free in U.S.) between 8:00a.m. and 4:15p.m. eastern time, Invited Speakers and Special Sessions, 666 Monday through Friday. 669 Special Meetings CHANGE OF ADDRESS. To avoid 674 New AMS Publications interruption in service please send address changes four to six weeks in 683 Miscellaneous advance. It is essential to include the Personal Items, 683; Deaths, 683; member code which appears on the AMS Reciprocity Agreements (Supplement), 684 address label with all correspondence Visiting Maths (Supplementary Lists), 685; regarding subscriptions. Application Deadlines, 687 INFORMATION ABOUT ADVERTISING in the· Notices may be obtained from 689 AMS Reports & Communications Wahlene Siconio at 401-272-9500. Recent Appointments, 689 CORRESPONDENCE, including changes Reports of Past Meetings: Albany Business of address should be sent to American and Council Meetings, 689 Mathematical Society, P.O. Box 6248, 692 Advertisements Providence, Rl 02940. ElMS Subscription Forms, 697, 698 Second class postage paid at Providence, Rl, and additional mailing 708 Preregistration Forms offices. Copyright © 1983 by the Employment Register, 708, 709, 710 American Mathematical Society. Louisville Preregistration and Housing, 711, 712 Printed in the United States of America. The Mathematical Heritage of , HENRI POINCARE Felix Browder, Editor

PART 1 § 1. Geometry Shing-Shen Chern J un-Ichi lgusa John Milnor Ngaiming Mok and Shing-Tung Yau Alan Weinstein §2. Topology J. Frank Adams William P. Thurston §3. Riemann surfaces, discontinuous groups and Lie groups Lipman Bers Wilfried Schmid Dennis Sullivan §4. Several complex variables Michael Beals, Charles Fefferman and Robert Grossman Phillip A. Griffiths Roger Penrose R. 0. Wells, Jr.

PART 2 §5. Topological methods in nonlinear problems Raoul Bott Haim Brezis Felix Browder L. Nirenberg §6. Mechanics and dynamical systems Jean Leray David Ruelle Steve Smale PROCEEDINGS OF SYMPOSIA § 7. Ergodic theory and recurrence IN PURE MATHEMATICS Volume 39 Harry Furstenberg Y. Katznelson and D. Ornstein PSPUM/39.1: Part 1, x + 439 pages. List $40, Institutional §8. Historical material member $30, Individual member $20 PSPUM/39.2: Part 2, vi + 470 pages. List $40, Institutional P. S. Aleksandrov member $30, Individual member $20 Henri Poincare PSPUM/39: Two volume set. List $75, Institutional member Jacques Hadamard $56, Individual member $38 Lettre de M. Pierre Boutroux a Prepayment is required for all AMS publications M. Mittag-Leffler Order from AMS, PO Box 1571, Annex Station, Bibliography of Henri Poincare Providence, Rl 02901, or call 800-55 6-7774 Books and articles about Poincare to charge with VISA or MasterCard. The 1983 Warsaw Congress of IMU by G. D. Mostow Chairman, U.S. National Committee for Mathematics

The Warsaw Mathematical Congress, originally not appear. Three of the Soviet invitees did not scheduled by the International Mathematical receive permission to appear, despite the vigorous Union {IMU) for 1982, took place as rescheduled efforts of the USSR National Committee to gain on August 16-24, 1983. In advance, there permission for them; in two cases, the absent was widespread speculation about its attendance, Soviet lecturers had their papers read by Soviet tenor, and success. colleagues. Its attendance turned out as follows: Ap­ The American presence was gratifying to the proximately 2,300 mathematicians registered of entire congress, including Polish mathematicians whom 600 were from Poland, 350 from the USSR, imprisoned for activities in support of Solidarity 100 from the USA, and 50 each from France and released after the formal lifting of martial and Great Britain. By comparison, about 3,000 law. mathematicians registered at the 1978 Helsinki There was wide consensus that, scientifically, Congress, of whom 600 were from the USA; the Congress was a success. Western participation generally was very visibly Inextricably linked with the scientific activities reduced. was the concern (at least among the Western At the opening ceremony Fields medals were participants) for the security and moral freedom awarded to A. Connes of France, W. Thurston of of the Polish colleagues on the one hand and the USA, S. Yau of the USA, and the Nevanlinna reluctance to grant tacit approval to martial law Prize to R. Tarjan of the USA. (See the October on the other. We were much relieved to learn 1982 Notices, pages 498-502.) upon arrival in Warsaw that all mathematicians Overall the arrangements, both physical and had been released from prison and internment. scientific, were very efficiently organized. The At the opening ceremonies, welcome was lectures took place at the monolithic Palace of extended to the Congress by its appointed Patron, Culture in large air-conditioned rooms supplied Professor Aleksander Gieysztor, President of the with overhead projectors but with skimpy low Polish Academy of Sciences. The Patron, an blackboards. The latter resulted in frustration historian, began by recalling that Poland is the for all but the front rows in rooms having no country in which World War II began, and podium, when the speakers declined the use of the that Warsaw is the city of the Ghetto uprising overhead projector. against the Nazis. Thereafter he recounted The caliber of the invited speakers, selected the history of science generally and mathematics by the IMU Program Committee, was excellent, particularly in Poland. The complete absence of the level of exposition was generally high, and any further political nuances in his speech was the coverage of all mathematical areas was much appreciated by those participants anxious to comprehensive. avoid tacit approval of martial law imprisonments. Apart from the scheduled lectures, the infor­ About twenty French, American, and English mal interchanges between mathematicians who invited speakers joined in a French initiative normally cannot meet was substantial. A num­ of dedicating lectures to Polish mathematicians interned or imprisoned after the imposition of ber of the very best USSR mathematicians who previously had not been permitted to attend con­ martial law. The individual dedications were gresses, did come to Warsaw. On the other hand, a varied but in the spirit expressed, for example, by leading mathematician from an Eastern European Teissier at the beginning of his lecture: country offered me his compliments on the high I am very pleased to lecture in Warsaw not only average caliber of the American attendees. because of the great mathematics tradition here, In the list of invited speakers on the next but also because I am in debt to our courageous page, the • indicates speakers who accepted the Polish colleagues who taught us how to stand up invitation to speak at some point prior to June with dignity when their rights were challenged. I 30, 1983, but who did not attend. dedicate this lecture to Boleslaw Gleichgewicht. Of the scheduled speakers on the list, 44 He then wrote the name Boleslaw Gleich- are from the USA. Fourteen from the USA gewicht on the blackboard and it remained there cancelled their lectures after June 30 or did throughout his lecture. These dedications were

571 Mathematicians Invited to Address the Warsaw Congress

One-hour Plenary 4- Geometry 9. Real and June- K. Osterwalder Addresses: S. Y. Cheng tional analysis 0. Ladyzenskaja V.I. Arnold W. Miiller R. Askey L. A. Takhtajan C. Hooley • E. B. Vmberg T. Figiel 14. Control theory and V. P. Maslov N. J. Hitchin Y. Meyer optimization A. Pelczynski L. Simon D. Voiculescu R. W. Brockett M. Sato • 0. Ja. Viro J. Bourgain P.-L. Lions • R. Thorn A. G. Hovansky B.S. Kasin H. W. Knobloch P. Erdos • R. M. Schoen B.S. Pavlov • R. T. Rockafellar Wu-Chung Hsiang • K. K. Uhlenbeck B. E. J. Dahlberg A. B. Kudanskil B. Mazur 5. Topology G. Kasparov J. Zabczyk • M. Rabin G. Pisier • S. Shelah F. R. Cohen 15. Numerical W. H. Fleming • M. H. Freedman 10. Probability and methods P. D. Lax • J. I. Shaneson mathematical B. Engquist R. D. MacPherson R. L. Cohen statistics G. H. Golub D. Ruelle • S. P. Kerkhoff D. R. Brillinger M. J. D. Powell Yum-Tong Siu H. Torunczyk P. Malliavin Feng Kang S. K. Donaldson s.-watanabe Ju. A. Kuznetsov D. M. Chibisov R. Glowinski 45-minute Addresses Wen-Hsuing Lin in Sections: 6. Algebraic geometry P. Mandl C. A. Micchelli 1. Mathematical logic A. Beilinson H. Kesten 16. Combinatorics and foundations of s. Iitaka D. W. Stroock and mathematical mathematics A. Ogus 11. Partial differential programming G. L. Cherlin • W. Fulton equations D. Foata R. A. Shore V. A. Iskovskih A. Ambrosetti J. H. van Lint J.-Y. Girard B. Teissier • L. A. Caffarelli R. L. Graham A. 0. Slisenko • J. Harris T. Iwaniec L. Lovasz P. A. Loeb S. Mori V. Zaharov • L. G. Khachiyan B. I. Zil'ber 7. Complex analysis J.-M. Bony 17. Computer and 2. Algebra W. Barth G. Eskin information sciences G. M. Henkin S. Klainerman R. Karp R. L. Griess, Jr. V. S. Buslaev • A. Joseph • J. E. Fornaess R. E. Tarjan P. W. Jones E. De Giorgi A. A. Letichevsky C. Soule • A. Majda • M. Gromov R. Harvey • L. G. Valiant A. Yu. Ol'sanski1 S. I. Pincuk 12. Ordinary differ- G. Plotkin R. P. Stanley 8. Lie groups and ential equations and 18. New applications J. C. Jantzen representations dynamical systems of mathematics C. M. Ringel J.Arthur • A. Katok N. Kopell E. I. Zel'manov P. van Moerbeke M. Misiurewicz B. B. Mandelbrot 9. Number Theory A. B. Venkov A. Lasota Ju. M. Svirezev G. R. Sell R. S. Ismagilov 19. History and A. N. Andrianov R. Mane D. W. Masser T. Oshima education 19. Mathematical J.-L. Waldspurger M. Vergne H. Freudenthal physics and J.-M. Fontaine • G. Lusztig A. V. Pogorelov mechanics K. A. Ribet R. Parthasarathy J. B. Serrin D. R. Heath-Brown M. Aizenman • W. M. Schmidt T. Nishida S. Woronowicz J. M. Ball

572 warmly applauded by the audience, especially the the 1978 Helsinki Congress, Western participation Poles. was drastically reduced. This was of course The Polish mathematicians spoke quite openly anticipated and very much noticed. However, of their concerns about the poor management instead of the absences of the 14 invited speakers of their economy, the prospects for academic from the USA being interpreted as a deliberate freedom in the future, the abolition of tenure, moral protest, the absences were attributed to and the preparation of blacklists intended to ban the block placed on federal travel grants by the young active supporters of Solidarity from entry U.S. Government (in reaction to the imposition of to the University. martial law in Poland). Although very many Polish mathematicians had That explanation won wide currency at the mixed feelings prior to the decision last November Congress, since it seemed so plausible. In point of whether to convene the Congress, all seemed to of fact, it is not correct. Indeed, on March be deeply gratified that the Congress had taken 23, 1983, I wrote to all us invitees (see the box place and that most American speakers attended. below) on behalf of the US National Committee for It should be added that many of the Poles who Mathematics advising them to obtain travel funds were delighted that most American speakers came from their own universities, in order to enable also drew comfort from the fact that a noticeable each invitee to attend or not attend the Congress number did not come-thereby calling attention as a matter of conscience rather than economic to the abnormalities in Poland. constraint. Thereby the us National Committee As far as I could determine, the American averted what might have been the major scandal participants were glad they had come to the of the USA wrecking an IMU Congress by heavy­ Congress. In retrospect, the decision made by the handed intervention. IMU Executive Committee in November 1982 to Our government's block on travel has set hold the Congress turned out to be a fortunate an unfortunate example of meddling in science. one. Scientists everywhere must try to dissuade any One aspect of the Congress was, however, country, including our own, from repeating that unfortunate for us. Compared with attendance at precedent.

NATIONAL ACADEMY OF SCIENCES

March 23, 1983

To U.S. INVITED LECTURERS AT THE WARSAW CONGRESS: The us National Committee on Mathematics has on several occasions expressed concern to the Executive Committee of the International Mathematical Union about the convening of the Warsaw Congress. At the same time, we have repeatedly affirmed that in the USA, the decision to attend or not is decided by each individual acting independently. I write on behalf of the USNCM to inform you that the us Travel Grants Program, which normally defrays the travel expenses of invited lecturers to the Congress, is not functioning normally for travel to Warsaw. Since January 1982 there has been a block on the use of federal funds for travel to scientific meetings in Warsaw, despite recommendations by the National Academy of Sciences and by scientists in government service to lift the block. Accordingly, the USNCM advises you to make plans as if you could not count on the us travel grant (although some of us still hope that the block will be lifted). If you have accepted the invitation to speak at the Congress and still wish to go, your declining to attend for financial reasons would reflect poorly on the independence of us mathematicians, and contradict our repeated assertions that individual decisions are based on conscience. We urge you to bring this problem to the attention of your university and request non-federal funds for travel. We sincerely hope that your university will comprehend the issue involved. If, on the other hand, you prefer not to attend the Congress, we hope that nevertheless you will support our view that attendance at the Congress should not be deterred by the withholding of travel funds. Sincerely, G. D.Mostow Chairman, USNCM

573 1983 Steele Prizes Awarded in Albany

A bequest from the estate of Leroy P. Steele, His articles on how to write, talk and publish a graduate of Harvard College in the class of mathematics have helped all mathematicians 1923, has provided funds for prizes awarded to communicate their ideas and results more by the Society each summer in honor of George effectively. David Birkhofl', Wilfuim Fogg Osgood and William Response. Not long ago I ran across a reference Caspar Graustein. to a publication titled A method of taking votes on At the Summer Meeting in Albany three prizes, more than two issues. Do you know, or could you each worth fifteen hundred dollars, were awarded guess, who the author is? What about an article in the following categories: titled On automorphisms of compact groups? Who (1) For a book or substantial expository paper. wrote that one? The answer to the first question This award was made to PAUL R. HALMOS for is C. L. Dodgson, better known as Lewis Carroll, his many graduate texts in mathematics and for and the answer to the second question is Paul his articles on how to write, talk and publish Halmos. mathematics. Lewis Carroll and I have in common that we (2) For a paper, whether recent or not, which both called ourselves mathematicians, that we has proved to be of fundamental importance both strove to do research, and that we both took in its field, or a model of important research. very seriously our attempts to enlarge the known STEPHEN C. KLEENE received this award for three body of mathematical truths. To earn his living, important papers published in 1955 which formed Lewis Carroll was a teacher, and, just for fun, the basis for later developments in generalized because he loved to tell stories, he wrote Alice's recursion theory and descriptive set theory. (3) For the cumulative influence of the total mathematical work of the recipient, high level of research over a period of time, particular influence on the development of a field, and influence on mathematics through Ph.D. students. The 1983 recipient is SHITNG-SHEN CHERN. These prizes were awarded by the Council of the American Mathematical Society, acting on the recommendations of the Committee on Steele Prizes. The members of the Steele Prize Com­ mittee were Stuart Antman, H. Jerome Keisler, Martin D. Kruskal, Yiannis N. Moschovakis, Louis Nirenberg, Alex Rosenberg (Chairman), Max M. Schiffer, Edwin H. Spanier and Gail S. Young, Jr. The text which follows includes, for each of these awards, the Committee's citation, the recipient's response on the presentation of the prize, and a brief biographical sketch of the recipient.

Paul R. Halmos Citation for Expository Writing. The award for a book or substantial survey or research­ expository paper is made to PAUL R. HALMOS for his many graduate texts in mathematics, dealing with finite dimensional vector spaces, measure theory, ergodic theory and Hilbert space. Many of these books were the first systematic presentations of their subjects in English. Their felicitous style and content has had a vast influence on the teaching of mathematics in North America. Paul R. Halmos

574 adventures in wonderland. To earn my living, I've 1978 when he was professor at the University been a teacher for almost fifty years, and, just of California in Santa Barbara. He has held for fun, because I love to organize and clarify, visiting positions for one or more terms at Tulane I wrote Finite dimensional vector spaces. And University (1951), University of Montevideo (1951- what's the outcome? I doubt if as many as a 1952), University of Washington (1959), University dozen readers of these words have ever looked of Miami (1965-1966}, University of Edinburgh at either A method of taking votes . . . or On (1973), and University of Western Australia (1975). automorphisms ... , but Lewis Carroll is immortal Professor Halmos has been a member of the for the Alice stories, and I got the Steele Prize Council of the Society, off and on, for over thirty for exposition. I don't know what the Reverend years, in a wide variety of positions: as member-at­ Mr. C. L. Dodgson thought about his fame, but, large of the Council (1950 to 1952, 1957 to 1959, as for me, I was brought up with the Puritan and 1983}, as vice president in 1981 and 1982, and ethic: if something is fun, then you shouldn't get as a member of the following editorial committees: recognized and rewarded for doing it. As a result, Proceedings (1958 to 1963), Mathematical Reviews while, to be sure, I am proud and happy, at the (1964 to 1969), Mathematical Surveys (1973 to same time I can't help feeling just a little worried 1975), Bulletin (1974 to 1979; Chairman, 1977, and guilty. 1978). He has been elected to four terms on the I enjoy studying, learning, coming to under­ Executive Committee of the Council (1959-1960, stand, and then explaining, but it doesn't follow 1965, 1974, 1983). In addition, he has served on that communicating what I know is always easy; more than a score of AMS committees. it can be devilishly hard. To explain something He has also served on the editorial boards you must know not only what to put in, but also of several journals. Currently he is Editor what to leave out; you must know when to tell of the American Mathematical Monthly and on the whole truth and when to get the right idea the board of the Indiana University Mathematics across by telling a little white fib. The difficulty in Journal and Journal fur die Reine und Angewandte exposition is not the style, the choice of words­ Mathematik (Crelle's Journal). He has been it is the structure, the organization. The words an editor of Ergebnij/e der Mathematik, and are important, yes, but the arrangement of the currently he is on the editorial board of Graduate material, the indication of the connections of Texts in Mathematics, Undergraduate Texts in its parts with each other and with other parts Mathematics, and Problem Books in Mathematics. of mathematics, the proper emphasis that shows Professor Halmos has given invited addresses what's easy and what deserves to be treated with at AMS meetings in Chicago (November 1948) caution-these things are much more important. and East Lansing (September 1960). He spoke But there I go again being expository-or at Special Sessions on Operator Theory at the should I say meta-expository? Enough of this Annual Meetings in Atlanta (January 1978) and foolishness; I think I had better stop now and go Biloxi (January 1979), and on C*-Algebras and prove a theorem about automorphisms of compact Operator Theory at the Annual Meeting in San groups. Antonio (January 1980). He also organized Biographical Sketch the Special Session on Compact Perturbations Paul Richard Halmos was born March 3, 1916, of Operators at the Annual Meeting in Dallas in Budapest, Hungary. He received a B.S. in (January 1973), and spoke at the Symposium 1934, an M.S. in 1935, and a Ph.D. in 1938, all on Lattice Theory in Monterey, California (April from the University of lllinois. In 1980 he received 1959). an honorary D. Sc. degree from the University of Professor Halmos held a Guggenheim Memorial St. Andrews. He was instructor of mathematics Foundation Fellowship at the Institute for Ad­ at the University of lllinois in 1938-1939. He vanced Study in 1947-1948. In 1947 he was then went to the Institute for Advanced Study, awarded the Chauvenet Prize for mathematical first as a fellow (1939-1940), then as an assistant exposition by the Mathematical Association of (1940-1942). He returned to the University of America, and he received the Lester R. Ford lllinois as an associate in mathematics for 1942- Award for mathematical exposition twice, in 1970 1943. From 1943 to 1946 he was assistant and in 1977. He was a member of the staff of professor at Syracuse University. In 1946 he the Radiation Laboratory at the Massachusetts became assistant professor at the University of Institute of Technology in 1945. He has been Chicago, advancing to the rank of professor in the AMS representative to the Division of Physical 1956. From 1961 to 1968 he was a professor at Sciences of the National Research Council (1958 the University of Michigan, then spent the year to 1961}, AMS representative on the Conference 1968-1969 as professor and department chairman Board of the Mathematical Sciences (1958 and at the University of Hawaii. In 1969 he became 1959), and AMS representative to the Conference a professor at Indiana University at Bloomington, in Washington on the Gilliland Report (1963). He where, except for a two-year interruption, he is a member of the Mathematical Association of has been Distinguished Professor of Mathematics America, a fellow of the Royal Society of Edin­ since 1970. The interruption was from 1976 to burgh and a member of the Hungarian Academy of

575 Science. His major research interests are ergodic developments-one has had the fortune to have theory, algebraic logic, and operators on Hilbert been working in a context in which such space. developments were implicit. I was lucky enough to have been at the right place mathematically at Stephen C. Kleene the right time. For this I am indebted first of all to Alonzo Citation for Important Works. The award for Church, whose set of postulates for the foundation a paper, whether recent or not, which has proved of logic (1932 and 1933) included as a subsystem to be of fundamental or lasting importance in the A-calculus, in terms of which the fertile idea its field, or a model of important research, is of A-definability was distilled by Church and me. presented to Stephen C. Kleene for the following Furthermore, it was he who first had the courage series of papers: to propose that the A-definable functions provide Arithmetical predicates and function quantifiers, an exact characterization of the class of the Transactions of the American Mathematical number-theoretic functions which are "effectively Society 79(1955), pages 312 to 340. calculable", or in other words for which there are On the forms of the predicates in the theory "algorithms" in the somewhat vague sense which of constructive ordinals (second paper}, American has come down through over two thousand years Journal of Mathematics 77(1955), pages 405 to of mathematical history. This became famous as 428. . "Church's thesis", first published by him in 1936. Hierarchies of number-theoretic predicates, Bulletin Later and independently, Alan Turing (1937) of the American Mathematical Society 61(1955), reached the thesis with another characterization, pages 193 to 213. the "Turing computable functions". These papers have had a profound influence on Secondly, I am indebted to Kurt Godel, for mathematical logic for three decades and form introducing me in 1931 to the primitive recursive the basis for two of the most active areas of functions (which had been around since Dedekind current research: generalized recursion theory and and Peano) with an exact description of his own, descriptive set theory. and then to the general recursive functions which Response. When one does work that turns he defined in 1934 modifying a 1931 suggestion out to be seminal-to lead to far-reaching of Jacques Herbrand. Godel held back from accepting Church's thesis until after Turing's version of it had appeared in 1937. (I showed in 1936 that the general recursive functions are coextensive with the A-definable functions, and Turing showed in 1937 that the latter are coextensive with his computable functions.) After Godel's introduction in 1934 of the general recursive functions, I found them to provide a happy format in which to develop the theory of the effectively calculable functions. Thirdly, I am indebted to L. E. J. Brouwer. His intuitionism (extending perceptions of Kronecker and Poincare) constituted a different and older manifestation of constructivism than the theory of general recursive (or A-definable or Turing computable) functions. Actually, it was in my 1950 International Congress paper, Recursive functions and intuitionistic mathematics, written in pursuit of my continuing project (begun in 1941) for relating these two manifestations of constructivism, that I took the step of generalizing recursiveness to allow type-1 variables, which forms the subject of the first of the papers cited now. In both the second and third of those papers (though they are quite classical, in contrast to intuitionistic), I used a construction that I mined from Brouwer's work. Indeed, one speaks now of "the Brouwer-Kleene ordering" . You will perhaps be amused by some recollec­ tions of mine from the time of writing the three papers. The paper cited second has the words "(second Stephen C. Kleene paper)'' concluding its title. What was the first

576 paper under that title? It was a 1944 paper of the third paper cited now for my Steele Prize. perpetrating a mammoth mathematical mistake, As I remember it, one Monday I said to myself, I think the only such in my career. (Of course, "If I don't solve the problem this week, I won't I have also made some flea-sized mistakes.) That waste any more time on it." Whether I would mistake has been compared to a mistake of have lived with this resolve I don't know. But as Lebesgue, who in his classic paper of 1905 on the it turned out, it was just before supper on the last theory of definability obtained a noteworthy result day of the week that I had an idea, which, when I by an argument which has since been described as tried it out after supper and in the next few days, "simple, short but false". The wrong step in his provided the solution. proof was hidden in a lemma taken as trivial. Ten I will conclude with reminiscences about a very years later, the error was spotted by Suslin, then uninhibited and outspoken graduate student I had a student of Lusin at Moscow. in those years. When he arrived in Madison, I My chagrin at having made a fundamental put him to work reading the first printer's proof mistake was diminished by my having been the of my book Introduction to metamathematics. one to recognize it as a mistake half a dozen He absolutely gloated when he found something years later. As Yiannis Moschovakis said on page wrong in it. I feigned humility, figuring that 444 of his 1980 book Descriptive set theory (from the more pleasure it gave him to correct me, the page 2 of which I have taken my information harder he would search for other errors. At that about Lebesgue's mistake), "Kleene was his own time, I had not been very productive of research Suslin." Thus my first paper On the forms of the papers, as the book had been taking up my time. predicates in the theory of constructive ordinals One day he said to me, "Kleene, you know (don't had got by the American Journal's referee. I you?) that there is such a thing as a mathematical could name several prominent American logicians menopause!" In the next couple of years I put who had heard me present my result in seminars, in his hands, for reading, the manuscripts of the and one who had made it the subject of a three papers now being cited for this Steele Prize. seminar talk of his own, without perceiving any Thank you very much! error. Andrzej Mostowski in his 1947 paper had Biographical Sketch developed independently of my 1943 paper the Stephen Cole Kleene was born January 5, 1909, arithmetical hierarchy, into which my 1944 paper in Hartford, Connecticut. He received an A. B. proposed to fit the predicates in question. After from Amherst College in 1930 and a Ph.D. from I informed him that the result I had claimed to Princeton University in 1934 for a thesis written have in 1944 was not proved, he wrote me from under the direction of Alonzo Church. He received Warsaw on Christmas day in 1952, "I was very an honorary Sc.D. degree from Amherst College astonished to learn that there is a flaw in your in 1970. After spending the spring semester of paper on the form of the predicates in the theory 1933-1934 and the year 1934-1935 as a research of constructive ordinals. I have read the paper assistant in mathematics at Princeton University, very carefully /as it then seemed to me/ and did Professor Kleene went to the University of not remark anything suspicious .... It seems to me Wisconsin, Madison, first as an instructor and that problems treated in your paper in question then as an assistant professor. From 1941 to may be of vital importance ... for certain plans of 1942 he was an associate professor at Amherst scientific work which I hope to start ... soon ...." College. After service in the U.S. Navy (which The situation was subtler than I had supposed included directing an applied mathematics group in 1944; and in the second paper under the same at the Naval Research Laboratory, 1943-1945), title (1955) a deeper and more interesting result­ he returned to the University of Wisconsin in 1946 shall I say a seminal result-was substituted for as associate professor of mathematics, becoming the result claimed in the first paper. professor in 1948. He served as chairman of the I will tell you that, when I submitted that second department (1957-1958, 1960-1962), as chairman paper to the American Journal, its referee gave of the Department of Numerical Analysis (1962- me a very rough time. Here was a complicated 1963), and as acting director of the Mathematics paper by an author who was admitting that his Research Center (1966-1967). In 1964 he was previous paper in the Journal was wrong-not named Cyrus Colton MacDuffee Professor of all wrong (as much of the work in it was still Mathematics; in 1974 "and Computer Sciences" used), but wrong in one crucial step and in its was added to this title. During this time he main result, based on that step. It seemed to me also served as dean of the College of Letters the referee was determined that this second paper and Science (1969-1974). Since 1979 he has been should not get into print. But he couldn't quite Emeritus Professor of Mathematics and Computer pin down a mistake in the new paper, try as he Science and Emeritus Dean of Letters and Science would-nor has anyone since. at the University of Wisconsin, Madison. What keeps a mathematician working at Professor Kleene gave invited addresses at problems until, if he is lucky, he solves them? I AMS meetings in Chicago (April-May 1954), the had worked unsuccessfully off and on for a year on published text of which is the third of the papers the problem whose solution forms the key result cited for this Steele Prize, and at Kenosha,

577 Wisconsin (October 1980). He also gave a 60- My appreciation of the prize goes further. minute talk at the 1958 International Congress Looking at the distinguished list of past recipients, of Mathematicians in Edinburgh. Between 1948 I wonder whether it makes sense for the Society to and 1983, he gave a dozen invited addresses at publish a book on the Steele Prizes. It could in­ international meetings of logicians, philosophers clude, among other materials, the autobiographies and computer scientists. or biographies of the recipients who receive the Professor Kleene held a Guggenheim Memorial prizes for their cumulative works and articles on Foundation Fellowship in 1949-1950, residing at the developments initiated by the seminal papers Amsterdam during the spring semester. He was a for which the prizes are given. I believe such a member of the Institute for Advanced Study (1939- book will be of both mathematical and historical 1940, 1965-1966), a visiting professor at Princeton interest. University (1956-1957), and held a National Biographical Sketch Science Foundation Grant at the University of Shiing-Shen Chern was born October 26, 1911, Marburg in 1958-1959. He was a member of the Mathematics Division of the National Research in Kashing, China. He received a B.S. degree Council (1957-1958) and was chairman designate from Nankai University in 1930, an M.S. from of its Division of Mathematical Sciences (1969- Tsing Hua University in 1934, and a D.Sc. from 1972), continuing one more year as a member the University of Hamburg in 1936. His honorary (1972-1973). degrees include LL.D. from the Chinese University He was vice president of the Association for of Hong Kong (1969), D. Sc. from the University Symbolic Logic (1942, 1947 -1949) and president of Chicago (1969), D. Sc. from the University (1956-1958), and consulting editor of the Journal of Hamburg (1971) and D.Math. from the of Symbolic Logic (1936-1942, 1946-1949) and Eidgenossische Technische Hochschule in Ziirich editor (1950-1962). (1982). From 1937 to 1943, he was professor of He was president both of the International mathematics at Tsing Hua University in China. Union of History and Philosophy of Science (1961) He served as professor of mathematics at the and of its Division of Logic, Methodology and Academia Sinica from 1946 to 1948, then at the Philosophy of Science (1960-1962). University of Chicago from 1949 to 1959. In 1960 he became professor at the University of Professor Kleene was elected to the National Academy of Sciences (1969), and to the American Academy of Arts and Sciences (1980). His major research interest is recursive func­ tions, but he has also contributed to proof theory and to the theory of finite automata. Shiing-Shen Chern Career Citation. The award for cumulative influence of the total mathematical work of the recipient is made to Shiing-Shen Chern who, for half a century, has been a leader in the field of differential geometry. His work is both deep and elegant, a typical example being his intrinsic proof of the Gauss-Bonnet Theorem. Professor Chern has extremely broad interests and has made very important contributions to such diverse areas as web geometry, integral geometry, complex manifolds, minimal submanifolds and characteristic classes. He is also an outstanding teacher. He has directed about fifty doctoral theses, first in China, then at the University of Chicago and, from the early sixties to the present, at the University of California, Berkeley. Many of his students have gone on to become famous in their own right. His research and teaching have exerted a deep and lasting influence on mathematics. Response. I am very grateful to be awarded a Steele Prize for my cumulative work. Such a prize is by definition given to an old mathematician. I think it appropriate because old mathematicians need encouragement. Shiing-Shen Chern

578 California, Berkeley, where he served until 1980. Professor Chern gave invited hour addresses He is now Professor Emeritus at Berkeley. Since at the Summer Meeting in New Brunswick, 1982 he has been Director of the Mathematical New Jersey (September 1945) and at the Annual Sciences Research Institute in Berkeley. Meeting in Houston (December 1955). He gave Professor Chern served the American Mathe­ one-hour talks at two International Congresses: in matical Society as vice president in 1963 and Cambridge, Massachusetts in 1950 and in Nice in 1964. In addition he has been active on many 1970, and a thirty-minute talk in the Congress AMS committees, including the Committee on at Edinburgh in 1958. He spoke at the Summer Summer Institutes (1953-1956; 1975-1976); the Institute on Entire Functions and Related Parts of Proceedings Editorial Committee (1956-1958); Analysis (San Diego, June 1966) and at the Special the Transactions and Memoirs Editorial Com­ Session on Entire Functions and Related Parts mittee (1957 -1959); the Selection Committee of Analysis (Annual Meeting, Houston, January for Expository Articles in the Bulletin (1962- 1967). He also delivered the Colloquium Lectures 1966); the Invitations and Organizing Committee at the Summer Meeting of the Society in East for the Summer Institute (1962 and 1963); the Lansing in September 1960. Committee to Select Hour Speakers for Annual Professor Chern held Guggenheim Memorial and Summer Meetings (1963 and 1964); the Com­ Foundation Fellowships in 1954-1955 and in 1967 mittee to Award the Veblen Prize (Chairman, and was an AMS representative to the Editorial 1966; 1976); the Organizing Committee on Board of the Duke Mathematical Journal (1953- the 1968 Summer Institute on Global Analysis; 1955). He was awarded the Chauvenet Prize of the Committee on Steele Prizes (1970-1972); the Mathematical Association of America in 1970 the Colloquium Editorial Committee, 1972-1977 and the National Medal of Science in 1976. He is (Chairman, 1974); the Organizing Committee for a member of the National Academy of Sciences, the 1973 Summer Research Institute (Chairman); the American Academy of Arts and Sciences, the Committee on Summer Institutes (1976); and the Mathematical Association of America, and the AMS Subcommittee of the AMS-IMS Committee the Academia Sinica. The areas of his major on Translations from Russian and Other Foreign research interest include differential geometry, Languages (1979-1981). integral geometry, and topology.

CONTENTS Paul Baum and Ronald G. Douglas, Index theory, bordism, and K-homology Joel M. Cohen and Leonede De-Michele, The radical Fourier-Stieltjes algebra of free groups David Handelman, Reducible topological Markov chains via K0-theory and Ext OPERATOR ALGEBRAS AND K-THEORY W. C. Hsiang and H. D. Rees, Miscenko's work on edited by Ronald G. Douglas and Claude Schochet Novikov's conjecture In the last twenty years there has been more and Jerome Kaminker, Pseudo-differential operators and more interplay between functional analysis and alge­ differential structures braic topology, and, more specifically, between oper­ Henri Moscovici, L 2-index on elliptic operators on ator algebras and K-theory. This interplay has led locally symmetric spaces of finite volume already to the index theorem for elliptic operators, William L. Paschke, K-theory for actions of the cir­ the classification of essentially normal operators, the cle group on C*-algebras index theorem f'Jr foliations, as well as a host of Marc A. Rieffel, Connes' analogue for crossed prod­ other related results. ucts of the Thom isomorphism A Special Session in Operator Algebras and K­ Jon athan Rosen berg, The role of K-theory in non­ Theory was held at the annual AMS meeting in San commutative algebraic topology Francisco on january 7-8, 1981. The present volume Norberto Salinas, Some remarks on the classification represents nearly all of the talks given, one extra of essentially n-normal operators paper by an honorary participant, and a list of prob· A Selection of Problems, edited by Edward G. Effros lems edited by Edward G. Effros. 1980 Mathematics Subiect Classifications: 46 LOS, 55 N15. The book is intended for mathematicians and graduate students. Several of the articles are partially or totally expository in nature, requiring a very Contemporary Mathematics modest background. Others are research articles for Volume 10, vii + 204 pages (soft cover) the specialist. These papers delineate a new field of List price $14, institutional member $11, individual member $7 study and describe various directions of new research. ISBN 0-8218-5011·3; LC 82-4094 They should make it possible for others to enter the Publication date: May 1982 field. To order, please specify CONMI10N Prepayment is required for all AMS publications. Order from AMS, P.O. Box 1571, Annex Station, Providence, Rl 02901, or call toll free 800-556-7774 to charge with Visa or MasterCard.

579 A Nation at Risk: The Imperative for Educational Reform

Introduction • defining problems which must be faced and Secretary of Education T. H. Bell created the overcome if we are successfully to pursue the course National Commission on Excellence in Education of excellence in education. on August 26, 1981, directing it to examine the The Commission's charter directed it to pay quality of education in the United States and to particular attention to teenage youth, and we have make a report to the Nation and to him within 18 done so largely by focusing on high schools. Selective months of its first meeting. In accordance with the attention was given to the formative years spent Secretary's instructions, this report contains practical in elementary schools, to higher education, and to recommendations for educational improvement and vocational and technical programs. We refer those fulfills the Commission's responsibilities under the interested in the need for similar reform in higher terms of its charter. education to the recent report of the American The Commission was created as a result of the Council on Education, To Strengthen the Quality of Secretary's concern about "the widespread public Higher Education. perception that something is seriously remiss in our In going about its work the Commission has relied educational system." Soliciting the "support of all in the main upon five sources of information: who care about our future," the Secretary noted • papers commissioned from experts on a variety of that he was establishing the Commission based on educational issues; his "responsibility to provide leadership, constructive • administrators, teachers, students, representatives criticism, and effective assistance to schools and of professional and public groups, parents, business universities." leaders, public officials, and scholars who testified The Commission's charter contained several specific at eight meetings of the full Commission, six public changes to which we have given particular attention. hearings, two panel discussions, a symposium, and a These included: series of meetings organized by the Department of • assessing the quality of teaching and learning in Education's Regional Offices; our Nation's public and private schools, colleges, and • existing analyses of problems in education; universities; •letters from concerned citizens, teachers, and • comparing American schools and colleges with administrators who volunteered extensive comments those of other advanced nations; on problems and possibilities in American education; • studying the relationship between college admis­ and sions requirements and student achievement in high • descriptions of notable programs and promising school; approaches in education. •identifying educational programs which result in To these public-minded citizens who took the notable student success in college; trouble to share their concerns with us-frequently • assessing the degree to which major social and at their own expense in time, money, and effort-we educational changes in the last quarter century have extend our thanks. In all cases, we have benefited affected student achievement; and from their advice and taken their views into account; how we have treated their suggestions is, of course, EDITORS' NoTE. The accompanying report, A our responsibility alone. In addition, we are grateful Nation at Risk: The Imperative for Educational Reform, to the individuals in schools, universities, foundations, was issued earlier this year by The National business, government, and communities throughout Commission on Excellence in Education. General the United States who provided the facilities and information on the Commission and its charter will staff so necessary to the success of our many public be found in the Introduction to the report on this functions. page. On the following pages, the main body of The Commission was impressed during the course the report is reprinted, in response to a growing of its activities by the diversity of opinion it received concern within the mathematical community for the regarding the condition of American education and problems confronting education in the mathematical by conflicting views about what should be done. In sciences. Readers of the Notices will recall Edward many ways, the membership of the Commission itself printed in the February issue Knapp's Denver talk, reflected that diversity and difference of opinion in which he called on research (pages 140 to 144), during the course of its work. This report, mathematicians and their professional societies to nevertheless, gives evidence that men and women active roles in the "restoration take more direct and of good will can agree on common goals and on ways of the quality" of instruction, especially at the to pursue them. precollege level.

580 A Nation at Risk

Our Nation is at risk. Our once unchallenged the malignant problems of older civilizations. The preeminence in commerce, industry, science, and world is indeed one global village. We live among technological innovation is being overtaken by com­ determined, well-educated, and strongly motivated petitors throughout the world. This report is competitors. We compete with them for international concerned with only one of the many causes and standing and markets, not only with products but also dimensions of the problem, but it is the one that with the ideas of our laboratories and neighborhood undergirds American prosperity, security, and civility. workshops. America's position in the world may We report to the American people that while we can once have been reasonably secure with only a few take justifiable pride in what our schools and colleges exceptionally well-trained men and women. It is no have historically accomplished and contributed to the longer. United States and the well-being of its people, the The risk is not only that the Japanese make educational foundations of our society are presently automobiles more efficiently than Americans and have being eroded by a rising tide of mediocrity that government subsidies for development and export. It threatens our very future as a Nation and a people. is not just that the South Koreans recently built the What was unimaginable a generation ago has begun world's most efficient steel mill, or that American to occur-others are matching and surpassing our machine tools, once the pride of the world, are educational attainments. being displaced by German products. It is also If an unfriendly foreign power had attempted that these developments signify a redistribution of to impose on America the mediocre educational trained capability throughout the globe. Knowledge, performance that exists today, we might well have learning, information, and skilled intelligence are the viewed it as an act of war. As it stands, we have new raw materials of international commerce and are allowed this to happen to ourselves. We have even today spreading throughout the world as vigorously squandered the gains in student achievement made as miracle drugs, synthetic fertilizers, and blue jeans in the wake of the Sputnik challenge. Moreover, did earlier. If only to keep and improve on the slim we have dismantled essential support systems which competitive edge we still retain in world markets, helped make those gains possible. We have, in effect, we must dedicate ourselves to the reform of our been committing an act of unthinking, unilateral educational system for the benefit of all-old and educational disarmament. young alike, affiuent and poor, majority and minority. Our society and its educational institutions seem Learning is the indispensable investment required for to have lost sight of the basic purposes of schooling, success in the "information age" we are entering. and of the high expectations and disciplined effort Our concern, however, goes well beyond matters needed to attain them. This report, the result of such as industry and commerce. It also includes 18 months of study, seeks to generate reform of our the intellectual, moral, and spiritual strengths of our educational system in fundamental ways and to renew people which knit together the very fabric of our the Nation's commitment to schools and colleges of society. The people of the United States need to know high quality throughout the length and breadth of that individuals in our society who do not possess our land. the level of skill, literacy, and training essential to That we have compromised this commitment is, this new era will be effectively disenfranchised, not upon reflection, hardly surprising, given the multitude of often conflicting demands we have placed on our Members of the National Commission Nation's schools and colleges. They are routinely called on to provide solutions to personal, social, on Excellence in Education and political problems that the home and other The members of the National Commission on institutions either will not or cannot resolve. We Excellence in Education are DAVID P. GARDNER, must understand that these demands on our schools University of Utah and University of California, and colleges often exact an educational cost as well YvONNE W. LARSEN, San Diego City School Board, as a financial one. WILLIAM 0. BAKER, Bell Telephone Laboratories, On the occasion of the Commission's first meeting, ANNE CAMPBELL, State of Nebraska, EMERAL President Reagan noted the central importance of A. CROSBY, Northern High School, CHARLES A. education in American life when he said: "Certainly FosTER, JR., Foundation for Teaching Economics, there are few areas of American life as important to NORMAN C. FRANCIS, Xavier University of our society, to our people, and to our families as Louisiana, A. BARTLETT GIAMATTI, Yale Univer­ our schools and colleges." This report, therefore, is sity, SHIRLEY GoRDON, Highline Community Col­ as much an open letter to the American people as lege, RoBERT V. HADERLEIN, National School it is a report to the Secretary of Education. We Boards Association, GERALD HOLTON, Harvard are confident that the American people, properly University, ANNETTE Y. KIRK, Kirk Associates, informed, will do what is right for their children and MARGARET S. MARSTON, Virginia State Board for the generations to come. of Education, ALBERT H. QurE of Minnesota, The Risk FRANCISCO D. SANCHEZ, JR., Albuquerque Public Schools, GLENN T. SEABORG, University of Califor­ History is not kind to idlers. The time is long nia, Berkeley, JAY SoMMER, New Rochelle High past when America's destiny was assured simply by School, and RICHARD WALLACE, Lutheran High an abundance of natural resources and inexhaustible School East. human enthusiasm, and by our relative isolation from

581 simply from the material rewards that accompany Nearly 40 percent cannot draw inferences from written competent performance, but also from the chance to material; only one-fifth can write a persuasive essay; participate fully in our national life. A high level and only one-third can solve a mathematics problem of shared education is essential to a free, democratic requiring several steps. society ,and to the fostering of a common culture, • There was a steady decline in science achievement especially in a country that prides itself on pluralism scores of U.S. 17-year olds as measured by national and individual freedom. assessments of science in 1969, 1973, and 1977. For our country to function, citizens must be able •Between 1975 and 1980, remedial mathematics to reach some common understandings on complex courses in public 4-year colleges increased by 72 issues, often on short notice and on the basis of percent and now constitute one-quarter of all conflicting or incomplete evidence. Education helps mathematics courses taught in those institutions. form these common understandings, a point Thomas •Average tested achievement of students graduat­ Jefferson made long ago in his justly famous dictum: ing from college is also lower. I know no safe depository of the ultimate powers • Business and military leaders complain that of the society but the people themselves: and if they are required to spend millions of dollars on we think them not enlightened enough to exercise costly remedial education and training programs in their control with a wholesome discretion, the such basic skills as reading, writing, spelling, and remedy is not to take it from them but to inform computation. The Department of the Navy, for their discretion. example, reported to the Commission that one­ quarter of its recent recruits cannot read at the Part of what is at risk is the promise first made ninth grade level, the minimum needed simply to on this continent: All, regardless of race or class or understand written safety instructions. Without economic status, are entitled to a fair chance and remedial work they cannot even begin, much less to the tools for developing their individual powers complete, the sophisticated training essential in much of mind and spirit to the upmost. This promise of the modern military. means that all children by virtue of their own efforts, competently guided, can hope to attain the mature These deficiencies come at a time when the demand for higher skilled workers in new fields is accelerating and informed judgment needed to secure gainful rapidly. For example: employment and to manage their own lives, thereby serving not only their own interests but also the • Computers and computer-controlled equipment progress of society itself. are penetrating every aspect of our lives-homes, factories, and offices. Indicators of the Risk • One estimate indicates that by the turn of the The educational dimensions of the risk before us century millions of jobs will involve laser technology have been amply documented in testimony received and robotics. by the Commission. For example: • Technology is radically transforming a host of • International comparisons of student achievement, other occupations. They include health care, medical completed a decade ago, reveal that on 19 academic science, energy production, food processing, construc­ tests American students were never first or second tion, and the building, repair, and maintenance of and, in comparison with other industrialized nations, sophisticated scientific, educational, military, and were last seven times. industrial equipment. • Some 23 million American adults are functionally Analysts examining these indicators of student illiterate by the simplest tests of everyday reading, performance and the demands for new skills have writing, and comprehension. made some chilling observations. Educational •About 13 percent of all 17-year olds in the researcher Paul Hurd concluded at the end of a United States can be considered functionally illiterate. thorough national survey of student achievement that Funtional illiteracy among minority youth may run within the context of the modern scientific revolution, as high as 40 percent. ''We are raising a new generation of Americans that •Average achievement of high school students on is scientifically and technologically illiterate." In a most standardized tests is now lower than 26 years similar vein, John Slaughter, a former Director of the ago when Sputnik was launched. National Science Foundation, warned of "a growing chasm between a small scientific and technological • Over half the population of gifted students do elite and a citizenry ill-informed, indeed uninformed, not match their tested ability with comparable on issues with a science component." achievement in school. But the problem, does not stop there, nor do all • The College Board's Scholastic Aptitude Test observers see it the same way. Some worry that (SAT) demonstrate a virtually unbroken decline from schools may emphasize such rudiments as reading and 1963 to 1980. Average verbal scores fell over 50 points computation at the expense of other essential skills and average mathematics scores dropped nearly 40 such as comprehension, analysis, solving problems, points. and drawing conclusions. Still others are concerned • College Board achievement tests also reveal that an overemphasis on technical and occupational consistent declines in recent years in such subjects as skills will leave little time for studying the arts and physics and English. humanities that so enrich daily life, help maintain • Both the number and proportion of students civility, and develop a sense of community. Knowledge demonstrating superior achievement on the SATs of the humanities,they maintain, must be harnessed (i.e., those with scores of 650 or higher) have also to science and technology if the latter are to remain dramatically declined. creative and humane, just as the humanities need to • Many 17 -year olds do not possess the "higher be informed by science and technology if they are order" intellectual skills we should expect from them. to remain relevant to the human condition. Another

582 analyst, Paul Copperman, has drawn a sobering of mathematics and science. This movement is conclusion. Until now, he has noted: but a start on what we believe is a larger and Each generation of Americans has outstripped its more educationally encompassing need to improve parents in education, in literacy, and in economic teaching and learning in fields such as English, attainment. For the first time in the history of our history, geography, economics, and foreign languages. country, the eduational skills of one generation We believe this movement must be broadened and will not surpass, will not equal, will not even directed toward reform and excellence throughout approach, those of their parents. education. It is important, of course, to recogni2!e that the Excellence in Education average citizen today is better educated and more We define "excellence" to mean several related knowledgeable than the average citiillen of a generation things. At the level of the individual learner, it means ago-more literate, and exosed to more mathematics, performing on the boundary of individual ability in literature, and science. The positive impact of this ways that test and push back personal limits, in fact on the well-being of our country and the lives school and in the workplace. Excellence characteriilles of our people cannot be overstated. Nevertheless, a school or college that sets high expectations and the average graduate of our schools and colleges today goals for all learners, then tries in every way possible is not as well-educated as the average graduate of to help students reach them. Excellence characterizes 25 or 35 years ago, when a much smaller proportion a society that has adopted these policies, for it of our population completed high school and college. will then be prepared through the education and The negative impact of this fact likewise cannot be skill of its people to respond to the challenges of a overstated. rapidly changing world. Our Nation's people and its Hope and Fruatration schools and colleges must be committed to achieving Statistics and their interpretation by experts show excellence in all these senses. only the surface dimension of the difficulties we We do not believe that a public commitment to face. Beneath them lies a tension between hope and excellence and educational reform must be made at frustration that characteriilles current attitudes about the expense of a strong public commitment to the education at every level. equitable treatment of our diverse population. The We have heard the voices of high school and twin goals of equity and high-quality schooling have college students, school board members, and teachers; profound and practical meaning for our economy and of leaders of industry, minority groups, and higher society, and we cannot permit one to yield to the education; of parents and State officials. We could other either in principle or in practice. To do so hear the hope evident in their commitment to qualify would deny young people their chance to learn and education and in their descriptions of outstanding live according to their aspirations and abilities. It programs and schools. We could also hear the would also lead to a generali2!ed accommodation to intensity of their frustration, a growing impatience mediocrity in our society on the one hand or the with shoddiness in many walks of American life, creation of an undemocratic elitism on the other. and the complaint that this shoddiness is too often Our goal must be to develop the talents of all to reflected in our schools and colleges. Their frustration their fullest. Attaining that goal requires that we threatens to overwhelm their hope. expect and assist all students to work to the limits of What lies behind this emerging national sense of their capabilities. We should expect schools to have frustration can be described as both a dimming of genuinely high standards rather than minimum ones, personal expectations and the fear of losing a shared and parents to support and encourage their children vision for America. to make the most of their talents and abilities. The search for solutions to our educational On the personal level the student, the parent, and the caring teacher all perceive that a basic promise problems must also include a commitment to life­ long learning. The task of rebuilding our system of is not being kept. More and more young people learning is enormous and must be properly understood emerge from high school ready neither for college and taken seriously: Although a million and a half nor for work. This predicament becomes more acute new workers enter the economy each year from our as the knowledge base continues its rapid expansion, schools and colleges, the adults working today will the number of traditional jobs shrinks, and new jobs still make up about 75 percent of the workforce in the demand greater sophistication and preparation. year 2000. These workers, and new entrants into the On a broader scale, we sense that this undertone of workforce, will need further education and retraining frustration has significant political implications, for if they-and we as a Nation-are to thrive and it cuts across ages, generations, races, and political prosper. and economic groups. We have come to understand that the public will demand that educational and The Learning Society political leaders act forcefully and effectively on In a world of ever-accelerating competition and these issues. Indeed, such demands have already change in the conditions of the workplace, of ever­ appeared and could well become a unifying national greater danger, and of ever-larger opportunities for preoccupation. This unity, however, can be achieved those prepared to meet them, educational reform only if we avoid the unproductive tendency of some should focus on the goal of creating a Learning to search for scapegoats among the victims, such as Society. At the heart of such a society is the the beleaguered teachers. commitment to a set of values and to a system of On the postive side is the significant movement education that affords all members the opportunity by political and educational leaders to search for to stretch their minds to full capacity, from early solutions-so far centering largely on the nearly childhood through adulthood, learning more as the desperate need for increased support for the teaching world itself changes. Such a society has as a basic

583 foundation the idea that education is important not • the persistent and authentic American dream that only because of what it contributes to one's career superior performance can raise one's state in life and goals but also because of the value it adds to the shape one's own future; general quality of one's life. • the dedication, against all odds, that keeps Also at the heart of the Learning Society are teachers serving in schools and colleges, even as the educational opportunities extending far beyond the rewards diminish; traditional institutions of learning, our schools and • our better understanding of learning and teaching colleges. They extend into homes and workplaces; and the implications of this knowledge for school into libraries, art galleries, museums, and science practice, and the numerous examples of local centers; indeed, into every place where the individual success as a result of superior effort and effective can develop and mature in work and life. In our view, dissemination; formal schooling in youth is the essential foundation • the ingenuity of our policymakers, scientists, for learning throughout one's life. But without State and local educators, and scholars in formulating life-long learning, one's skills will become rapidly solutions once problems are better understood; dated. • the traditional belief that paying for education In contrast to the ideal of the Learning Society, is an investment in ever-renewable human resources however, we find that for too many people education that are more durable and flexible than capital plant means doing the minimum work necessary for the and equipment, and the availability in this country of moment, then coasting through life on what may sufficient financial means to invest in education; have been learned in its first quarter. But this • the equally sound tradition, from the Northwest should not surprise us because we tend to express Ordinance of 1787 until today, that the Federal our educational standards and expectations largely Government should supplement State, local, and in terms of "minimum requirements." And where other resources to foster key national educational there should be a coherent continuum of learning, we goals; and have none, but instead an often incoherent, outdated patchwork quilt. Many individual, sometimes heroic, • the voluntary efforts of individuals, businesses, examples of schools and colleges of great merit and parent and civic groups to cooperate in do exist. Our findings and testimony confirm the strengthening educational programs. vitality of a number of notable schools and progams, These raw materials, combined with the unparal­ but their very distinction stands out against a vast leled array of educational organizations in America, mass shaped by tensions and pressures that inhibit offer us the possibility to create a Learning Society, in systematic academic and vocational achievement for which public, private, and parochial schools; colleges the majority of students. In some metropolitan and universities; vocational technical schools and areas basic literacy has become the goal rather than institutes; libraries; science centers, museums, and the starting point. In some colleges maintaining other cultural institutions; and corporate training and enrollments is of greater day-to-day concern than retraining programs offer opportunities and choices maintaining rigorous academic standards. And the for all to learn throughout life. ideal of academic excellence as the primary goal of The Publie's Commitment schooling seems to be fading across the board in Of all the tools at hand, the public's support for American education. education is the most powerful. In a message to a Thus, we issue this call to all who care about National Academy of Sciences meeting in May 1982, America and its future; to parents and students; to President Reagan commented on this fact when he teachers, administrators, and school board members; said: to colleges and industry; to union members and This public awareness-and I hope public ac­ military leaders; to governors and State legislators; to the President; to members of Congress and other tion-is long overdue ... This country was built on public officials; to members of learned and scientific American respect for education ... Our challenge societies; to the print and electronic media; to now is to create a resurgence of that thirst for concerned citizens everywhere. America is at risk. education that typifies our Nation's history. We are confident that America can address this The most recent (1982) Gallup Poll of the Public's risk. If the tasks we set forth are initiated now and Attitudes Toward the Public Schools strongly supported a our recommendations are fully realized over the next theme heard during our hearings: People are steadfast several years, we can expect reform of our Nation's in their belief that education is the major foundation schools, colleges, and universities. This would also for the future strength of this country. They even reverse the current declining trend-a trend that considered education more important than developing stems more from weakness of purpose, confusion of the best industrial system or the strongest military vision, underuse of talent, and lack of leadership, force, perhaps because they understood education as than from conditions beyond our control. the cornerstone of both. They also held that education is "extremely important" to one's future success, and The Tools at Hand that public education should be the top priority It is our conviction that the essential raw materials for additional Federal funds. Education occupied needed to reform our educational system are waiting first place among 12 funding categories considered in to be mobilized through effective leadership: the survey-above health care, welfare, and military • the natural abilities of the young that cry out defense, with 55 percent selecting public education to be developed and the undiminished concern of as one of their first three choices. Very clearly, parents for the well-being of their children; the public understands the · primary importance of •the commitment of the Nation to high retention education as the foundation for a satisfying life, an rates in schools and colleges and to full access to enlightened and civil society, a strong economy, and education for all; a secure Nation.

584 At the same time, the public has no patience with • This curricular smorgasboard, combined with undemanding and superfluous high school offerings. extensive student choice, explains a great deal about In another survey, more than 75 percent of all those where we find ourselves today. We offer intermediate questioned believed every student planning to go to algebra, but only 31 percent of our recent high school college should take 4 years of mathematics, English, graduates complete it; we offer French I, but only history /U. S. government, and science, with more than 13 percent complete it; and we offer geography, but 50 percent adding 2 years each of a foreign language only 16 percent complete it. Calculus is available in and economics or business. The public even supports schools enrolling about 60 pecent of all students, but requiring much of this curriculum for students who do only 6 percent of all students complete it. not plan to go to college. These standards far exceed • Twenty-five percent of the credits earned by the strictest high school graduation requirements of general track high school students are in physical and any State today, and they also exceed the admission health education, work experience outside the school, standards of all but a handful of our most selective remedial English and mathematics, and personal colleges and universities. service and development courses, such as training for Another dimension of the public's support offers adulthood and marriage. the prospect of constructive reform. The best term Findings Regarding Expectations. We define ex­ to characterize it may simply be the honorable word pectations in terms of the level of knowledge, abilities, "patriotism." Citizens know intuitively what some of and skills school and college graduates should possess. the best economists have shown in their research, that They also refer to the time, hard work, behavior, education is one of the chief engines of a society's self-discipline, and motivation that are essential for material well-being. They know, too, that education high student achievement. Such expectations are is the common bond of a pluralistic society and helps expressed to students in several different ways: cultures around the globe. Citizens tie us to other • by grades, which reflect the degree to which United also know in their bones that the safety of the students demonstrate their mastery of subject matter; States depends principally on the wit, skill, and spirit graduation of a self-confident people, today and tommorrow. • through high school and college It is, therefore, essential-especially in a period of requirements, which tell students which subjects are long-term decline in educational achievement-for most important; government at all levels to affirm its responsibility for • by the presence or absence of rigorous examina­ nurturing the Nation's intellectual capital. tions requiring students to demonstrate their mastery And perhaps most important, citizens know and of content and skill before receiving a diploma or a believe that the meaning of America to the rest of degree; the world must be something better than it seems to • by college admissions requirements, which rein­ many today. Americans like to think of this Nation as force high school standards; and the preeminent country for generating the great ideas • by the difficulty of the subject matter students and material benefits :or all mankind. The citizen confront in their texts and assigned readings. is dismayed at a steady 15-year decline in industrial Our analysis in each of these areas indicate notable productivity, as one great American industry after deficiencies: another falls to world competition. The citizen wants • The amount of homework for high school seniors the country to act on the belief, expressed in our has decreased (two-thirds report less than one hour hearings and by the large majority in the Gallup Poll, a night) and grades have risen as average student that education should be at the top of the Nation's achivement has been declining. agenda. • In many other industrialized nations, courses Findings in mathematics (other than arithmetic or general physics, and We conclude that declines in educational perfor­ mathematics), biology, chemistry, mance are in large part the result of disturbing geography start in grade 6 and are required of inadequacies in the way the educational process it­ all students. The time spent on these subjects, based self is often conducted. The findings that follow, on class hours, is about three times that spent by culled from a much more extensive list, reflect four even the most science-oriented U.S. students, i.e., important aspects of the educational process: content, those who select 4 years of science and mathematics expectations, time, and teaching. in secondary school. Findings Regarding Content. By content we mean •A 1980 State-by-State survey of high school the very "stuff" of education, the curriculum. Because diploma requirements reveals that only eight States of our concern about the curriculum, the Commission require high schools to offer foreign language examined patterns of courses high school students instruction, but none requires students to take the took in 1964-1969 compared with course patterns courses. Thirty-five States require only 1 year of in 1976-1981. On the basis of these analyses we mathematics, and 36 require only 1 year of science conclude: for a diploma. • Secondary school curricula have been • In 13 States, 50 percent or more of the units homogenized, dilluted, and diffused to the point required for high school graduation may be electives that they no longer have a central purpose. In effect, chosen by the student. Given this freedom to choose we have a cafeteria-style curriculum in which the the substance of half or more of their education, appetizers and desserts can easily be mistaken for the many students opt for less demanding personal service main courses. Students have migrated from vocational courses, such as bachelor living. and college preparatory programs to "general track" • "Minimum competency" examinations (now re­ courses in large numbers. The proportion of students quired in 37 States) fall short of what is needed, as taking a general program of study has increased from the "minimum" tends to become the "maximum," 12 percent in 1964 to 42 percent in 1979. thus lowering educational standards for all.

585 • One-fifth of all 4-year public colleges in the United preparation programs need substantial improvement; States must accept every high school graduate within that the professional working life of teachers is on the the State regardless of program followed or grades, whole unacceptable; and that a serious shortage of thereby serving notice to high school students that teachers exists in key fields. they can expect to attend college even if they do not • Too many teachers are being drawn from the follow a demanding course of study in high school or bottom quarter of graduating high school and college perform well. students. • About 23 percent of our more selective colleges • The teacher preparation curriculum is weighted and universities reported that their general level heavily with courses in "educational methods" at the of selectivity declined during the 1970s, and 29 expense of courses in subjects to be taught. A survey percent reported reducing the number of specific high of 1,350 institutions training teachers indicated that school courses required for admission (usually by 41 percent of the time of elementary school teacher dropping foreign language requirements, which are candidates is spent in education courses, which now specified as a condition for admission by only reduces the amount of time available for subject one-fifth of our institutions of higher education). matter courses. • Too few experienced teachers and scholars are • The average salary after 12 years of teaching is involved in writing textbooks. During the past decade only $17,000 per year, and many teachers are required or so a large number of texts have been ''written to supplement their income with part-time and down" by their publishers to ever-lower reading levels summer employment. In addition, individual teachers in response to perceived market demands. have little influence in such critical professional •A recent study by Education Products Informa­ decisions as, for example, textbook selection. tion Exchange revealed that a majority of studies • Despite widespread publicity about an over­ [sic] were able to master 80 percent of the material population of teachers, severe shortages of cer­ in some of their subject-matter texts before they had tain kinds of teachers exist: in the fields of even opened the books. Many books do not challenge mathematics, science, and foreign languages; and the students to whom they are assigned. among specialists in education for gifted and •Expenditures for textbooks and other instruc­ talented,language minority, and handicapped stu­ tional materials have declined by 50 percent over the dents. past 17 years. While some recommend a level of • The shortage of teachers in mathematics and spending on texts of between 5 and 10 percent of the science is particularly severe. A 1981 survey of 45 operating costs of schools, the budgets for basal texts States revealed shortages of mathematics teachers in and related materials have been dropping during the 43 States, critical shortages of earth sciences teachers past decade and a half to only 0.7 percent today. in 33 States, and of physics teachers everywhere. Findings Regarding Time. Evidence presented to • Half of the newly employed mathematics, science, the Commission demonstrates three disturbing facts and English teachers are not qualified to teach these about the use that American schools and students subjects; fewer than one-third of U.S. high schools make of time: (1) compared to other nations, American offer physics taught by qualified teachers. students spend much less time on school work; (2) Reeommendations time spent in the classroom and on homework is In light of the urgent need for improvement, both often used ineffectively; and (3) schools are not doing immediate and long term, this Commission has agreed enough to help students develop either the study skills required to use time well or the willingness to on a set of recommendations that the American people can begin to act on now, that can be implemented spend more time on school work. over the next several years, and that promise lasting • In England and other industrialized countries, it reform. The topics are familiar; there is little mystery is not unusual for academic high school students to about what we believe must be done. Many schools, spend 8 hours a day at school, 220 days per year. In districts, and States are already giving serious and the United States, by contrast, the typical school day constructive attention to these matters, even though lasts 6 hours and the school year is 180 days. their plans may differ from our recommendations in • In many schools, the time spent learning how to some details. cook and drive counts as much toward a high school We wish to note that we refer to public, private, diploma as the time spent studying mathematics, and parochial schools and colleges alike. All are English, chemistry, U.S. history, or biology. valuable national resources. Examples of actions •A study of the school week in the United States similar to those recommended below can be found in found that some schools provided students only 17 each of them. hours of academic instruction during the week, and We must emphasize that the variety of student the average school provided about 22. aspirations, abilities, and preparation requires that •A California study of individual classrooms found appropriate content be available to satisfy diverse that because of poor management of classroom needs. Attention must be directed to both the time, some elementary students received only one­ nature of the content available and to the needs of fifth of the instruction others received in reading the particular learners. The most gifted students, comprehension. for example, may need a curriculum enriched and • In most schools, the teaching of study skills accelerated beyond even the needs of other students of is haphazard and unplanned. Consequently, many high ability. Similarly, educationally disadvantaged students complete high school and enter college students may require special curriculum materials, without disciplined and systematic study habits. smaller classes, or individual tutoring to help them Findings Regarding Teaching. The Commission master the material presented. Nevertheless, there found that not enough of the academically able remains a common expectation: We must demand the students are being attracted to teaching; that teacher best effort and performance from all students, whether

586 they are gifted or less able, affluent or disadvantaged, of both ancient and contemporary ideas that have whether destined for college, the farm, or industry. shaped our world; (c) understand the fundamentals of Our recommendations are based on the beliefs that how our economic system works and how our political everyone can learn, that everyone is born with an system functions; and (d) grasp the difference between urge to learn which can be nurtured, that a solid high free and repressive societies. An understanding of school education is within the reach of virtually all, each of these areas is requisite to the informed and and that life-long learning will equip people with the committed exercise of citizenship in our free society. skills required for new careers and for citizenship. 5. The teaching of computer science in high Recommendation A: Content school should equip graduates to: (a) understand the computer as an information, computation, and We recommend that State and local high school communication device; {b) use the computer in the graduation requirements be strengthened and that, at a study of the other Basics and for personal and work­ minimum, all students seeking a diploma be required to related purposes; and {c) understand the world of lay the foundations in the Five New Basics by taking the computers, electronics, and related technologies. following curriculum during their 4 years of high school: In addition to the New Basics, other important (a) 4 years of English; {b) 9 years of mathematics; (c) curriculum matters must be addressed. 9 years of science; (d) 9 years of social studies; and (e) 6. Achieving proficiency in a foreign language one-half year of computer science. For the college-bound, ordinarily requires from 4 to 6 years of study 2 years of foreign language in high school are strongly and should, therefore, be started in the elementary recommended in addition to those taken earlier. grades. We believe it is desirable that students Whatever the student's educational or work achieve such proficiency because study of a foreign objectives, knowledge of the New Basics is the language introduces students to non-English-speaking foundation of success for the after-school years cultures, heightens awareness and comprehension of and, therefore, forms the core of the modern one's native tongue, and serves the Nation's needs in curriculum. A high level of shared education in commerce, diplomacy, defense, and education. these Basics, together with work in the fine and 7. The high school curriculum should also provide performing arts and foreign languages, constitutes the students with programs requiring rigorous effort in mind and spirit of our culture. The following subjects that advance student's personal, educational, Implementing Recommendations are intended as and occupational goals, such as the fine and illustrative descriptions. They are included here performing arts and vocational education. These to clarify what we mean by the essentials of a strong areas complement the New Basics, and they should curriculum. demand the same level of performance as the Basics. Implementing Recommendations. 8. The curriculum in the crucial eight grades 1. The teaching of English in high school should leading to the high school years should be specifically equip graduates to: (a) comprehend, interpret, designed to provide a sound base for study in those evaluate, and use what they read; {b) write well­ and later years in such areas as English language organized, effective papers; (c) listen effectively and development and writing, computational and problem discuss ideas intelligently; and (d) know our literary solving skills, science, social studies, foreign language, heritage and how it enhances imagination and ethical and the arts. These years should foster an enthusiasm understanding, and how it relates to the customs, for learning and the development of the individual's ideas, and values of today's life and culture. gifts and talents. 2. The teaching of mathematics in high school 9. We encourage the continuation of efforts by should equip graduates to: (a) understand geometric groups such as the American Chemical Society, the and algebraic concepts; {b) understand elementary American Association for the Advancement of Science, probability and statistics; (c) apply mathematics in the Modern Language Association, and the National everyday situations; and {d) estimate, approximate, Councils of Teachers of English and Teachers of measure, and test the accuracy of their calculations. Mathematics, to revise, update, improve, and make In addition to the traditional sequence of studies available new and more diverse curricular materials. available for college-bound students, new, equally We applaud the consortia of educators and scientific, demanding mathematics curricula need to be devel­ industrial, and scholarly societies that cooperate to oped for those who do not plan to continue their improve the school curriculum. formal education immediately. Recommendation B: 3. The teaching of science in high school should Standards and Expectations provide graduates with an introduction to: (a) the concepts, laws, and processes of the physical and We recommend that schools, colleges, and universities biological sciences; {b) the methods of scientific adopt more rigorous and measurable standards, and inquiry and reasoning; (c) the application of scientific higher expectations, for academic performance and student knowledge to everyday life; and (d) the social conduct, and that 4-year colleges and universities raise and environmental implications of scientific and their requirements for admission. This will help students technological development. Science courses must be do their best educationally with challenging materials revised and updated for both the college-bound and in an environment that supports learning and authentic those not intending to go to college. An example accomplishment. of such work is the American Chemical Society's Implementing Recommendations. "Chemistry in the Community" program. 1. Grades should be indicators of academic achieve­ 4. The teaching of social studies in high school ment so they can be relied on as evidence of a should be designed to: (a) enable students to fix their student's readiness for further study. places and possibilities within the larger social and 2. Four-year colleges and universities should raise cultural structure; {b) understand the broad sweep their admissions requirements and advise all potential

587 applicants of the standards for admission in terms 4. The time available for learning should be of specific courses required, performance in these expanded through better classroom management and areas, and levels of achievement on standardized organization of the school day. If necessary, additional achievement tests in each of the five Basics and, time should be found to meet the special needs of where applicable, foreign languages. slow learners, the gifted, and others who need more 3. Standardized tests of achievement (not to be instructional diversity than can be accommodated confused with aptitude tests) should be administered during a conventional school day or school year. at major transition points from one level of schooling 5. The burden on teachers for maintaining dis­ to another and particularly from high school to cipline should be reduced through the development college or work. The purposes of these tests would be of firm and fair codes of student conduct that are to: (a) certify the student's credentials; (b) identify enforced consistently, and by considering alternative the need for remedial intervention; and (c) identify classrooms, programs, and schools to meet the needs the opportunity for advanced or accelerated work. of continually disruptive students. The tests should be administered as part of a 6. Attendance policies with clear incentives and nationwide (but not Federal) system of State and sanctions should be used to reduce the amount of local standardized tests. This system should include time lost through student absenteeism and tardiness. other diagnostic procedures that assist teachers and 7. Administrative burdens on the teacher and students to evaluate student progress. related intrusions into the school day should be 4. Textbooks and other tools of learning and reduced to add time for teaching and learning. teaching should be upgraded and updated to assure 8. Placement and grouping of students, as well more rigorous content. We call upon university as promotion and graduation policies, should be scientists, scholars, and members of professional guided by the acedemic progress of students and their societies, in collaboration with master teachers, to instructional needs, rather than by rigid adherence to help in this task, as they did in the post-Sputnik era. age. They should assist willing publishers in developing Reeommmendation D: Teaching the products or publish their own alternatives where Thil recommendation consists of seven parts. Each there are persistent inadequacies. is intended to improve the preparation of teachers or to 5. In considering textbooks for adoption, States make teaching a more rewarding and respected profession. and school districts should: (a) evaluate texts and Each of the seven stands on its own and should not be other materials on their ability to present rigorous considered solely as an implementing recommendation. and challenging material clearly; and (b) require 1. Persons preparing to teach should be required to publishers to furnish evaluation data on the material's meet high educational standards, to demonstrate an effectiveness. aptitude for teaching, and to demonstrate competence 6. Because no textbook in any subject can be in an academic discipline. Colleges and universities geared to the needs of all students, funds should offering teacher preparation programs should be be made available to support text development in judged by how well their graduates meet these "thin market" areas, such as those for disadvantaged criteria. students, the learning disabled, and the gifted and 2. Salaries for the teaching profession should be talented. increased and should be professionally competitive, 7. To assure quality, all publishers should furnish market-sensitive, and performance-based. Salary, evidence of the quality and appropriateness of promotion, tenure, and retention decisions should be textbooks, based on results from field trials and tied to an effective evaluation system that includes credible evaluations. In view of the enormous numbers peer review so that superior teachers can be rewarded, and varieties of texts available, more widespread agerage ones encouraged, and poor ones either consumer information services for purchasers are improved or terminated. badly needed. 3. School boards should adopt an 11-month 8. New instructional materials should reflect the contract for teachers. This would ensure time for most current applications of technology in appropriate curriculum and professional development, programs curriculum areas, the best scholarship in each for students with special needs, and a more adequate discipline, and research in learning and teaching. level of teacher compensation. 4. School boards, administrators, and teachers Reeommendation C: Time should cooperate to develop career ladders for teachers We recommend that significantly more time be devoted that distinguish among the beginning instructor, the to learning the New Basics. This will require more experienced teacher, and the master teacher. effective use of the existing school day, a longer school 5. Substantial nonschool personnel resources day, or a lengthened school year. should be employed to help solve the immediate problem of the shortage of mathematics and science Implementing Recommendations. teachers. Qualified individuals including recent 1. Students in high schools should be assigned far graduates with mathematics and science degrees, more homework than is now the case. graduate students, and industrial and retired scien­ 2. Instruction in effective study and work skills, tists could, with appropriate preparation, immediately which are essential if school and independent time begin teaching in these fields. A number of our leading is to be used efficiently, should be introduced in the science centers have the capacity to begin educating early grades and continued throughout the student's and retraining teachers immediately. Other areas of schooling. critical teacher need, such as English, must also be 3. School districts and State legislatures should addressed. strongly consider 7-hour school days, as well as a 200- 6. Incentives, such as grants and loans, should be to 220-day school year. made available to attract outstanding students to

588 the teaching profession, particularly in those areas of America Can Do It critical shortage. Despite the obstacles and difficulties that inhibit 7. Master teachers should be involved in designing the pursuit of superior educational attainment, we teacher preparation programs and in supervising are confident, with history as our guide, that we can teachers during their probationary years. meet our goal. The American educational system Recommendation E: has responded to previous challenges with remarkable Leadership and Fiscal Support success. In the 19th century our land-grant colleges provided the research and training We recommend that citizens across the Nation hold and universities natural resources and educators and elected officials responsible for providing the that developed our Nation's of the American farm. leadership necessary to achieve these reforms, and that the rich agricultural bounty citizens provide the fiscal support and stability required to From the late 1800s through the mid-20th century, bring about the reforms we propose. American schools provided the educated workforce needed to seal the success of the Industrial Revolution hnplementing Recommendations. and to provide the margin of victory in two world 1. Principals and superintendents must play a wars. In the early part of this century and continuing crucial leadership role in developing school and to this very day, our schools have absorbed vast community support for the reforms we propose, and waves of immigrants and educated them and their school boards must provide them with the professional children to productive citizenship. Similarly, the development and other support required to carry out Nation's Black colleges have provided opportunity their leadership role effectively. The Commission and undergraduate education to the vast majority of stresses the distinction between leadership skills college-educated Black Americans. goals and developing involving persuasion, setting More recently, our institutions of higher education community consensus behind them, and managerial have provided the scientists and skilled technicians are and supervisory skills. Although the latter who helped us transcend the boundaries of our planet. school boards must necessary, we believe that In the last 30 years, the schools have been a major develop leadership skills at the school consciously vehicle for expanded social opportunity, and now we propose are to be and district levels if the reforms graduate 75 percent of our young people from high achieved. school. Indeed, the proportion of Americans of college board 2. State and local officials, including school age enrolled in higher education is nearly twice that of members, governors, and legislators, have the primary Japan and far exceeds other nations such as France, schools, responsibility for financing and governing the West Germany, and the Soviet Union. Moreover, in and should incorporate the reforms we propose when international comparisons were last made a fiscal planning. their educational policies and decade ago, the top 9 percent of American students 3. The Federal Government, in cooperation with compared favorably in achievement with their peers States and localities, should help meet the need of key in other countries. such as the gifted and talented, groups of students In addition, many large urban areas in recent disadvantaged, minority and the socioeconomically years report that average student achievement in language minority students, and the handicapped. elementary schools is improving. More and more In combination these groups include both national schools are also offering advanced placement programs resources and the Nation's youth who are most at and programs for gifted and talented students, and risk. more and more students are enrolling in them. 4. In addition, we believe the Federal Government's of a past that gives us every role includes several functions of national consequence We are the inheritors reason to believe that we will succeed. that States and localities alone are unlikely to be able to meet: protecting constitutional and civil A Word to Parents and Students rights for students and school personnel; collecting The task of assuring the success of our recommen­ data, statistics, and information about education dations does not fall to the schools and colleges alone. generally; supporting curriculum improvement and Obviously, faculty members and administrators, along research on teaching, learning, and the management with policymakers and the mass media, will play a of schools; supporting teacher training in areas of crucial role in the reform of the educational system. critical shortage or key national needs; and providing But even more important is the role of parents and student financial assistance and research and graduate students, and to them we speak directly. training. We believe the assistance of the Federal Government should be provided with a minimum of To Parents administrative burden and intrusiveness. You know that you cannot confidently launch your 5. The Federal Government has the primary children into today's world unless they are of strong responsibility to identify the national interest in character and well-educated in the use of language, education. It should also help fund and support efforts science, and mathematics. They must possess a deep to protect and promote that interest. It must provide respect for intelligence, achievement, and learning, the national leadership to ensure that the Nation's and the skills needed to use them; for setting goals; public and private resources are marshaled to address and for disciplined work. That respect must be the issues discussed in this report. accompanied by an intolerance for the shoddy and 6. This Commission calls upon educators, parents, second-rate masquerading as "good enough." and public officials at all levels to assist in bringing You have the right to demand for your children about the educational reform proposed in this report. the best our schools and colleges can provide. Your We also call upon citizens to provide the financial vigilance and your refusal to be satisfied with less support necessary to accomplish these purposes. than the best are the imperative first step. But your Excellence costs. But in the long run mediocrity costs right to a proper education for your children carries far more. a double responsibility. As surely as you are your

589 child's first and most influential teacher, your child's For not one can doubt that the United States is under ideas about education and its significance begin with challenge from many quarters. you. You must be a living example of what you expect Children born today can expect to graduate from your children to honor and to emulate. Moreover, you high school in the year 2000. We dedicate our report bear a responsibility to participate actively in your not only to these children, but also to those now in child's education. You should encourage more diligent school and others to come. We firmly believe that study and discourage satisfaction with mediocrity a movement of America's schools in the direction and the attitude that says "let it slide"; monitor called for by our recommendations will prepare these your child's study; encourage good study habits; children for far more effective lives in a far stronger encourage your child to take more demanding rather America. than less demanding courses; nurture your child's Our final word, perhaps better characterized as curiosity, creativity, and confidence; and be an active a plea, is that all segments of our population give participant in the work of the schools. Above all, attention to the implementation of our recommenda­ exhibit a commitment to continued learning in your tions. Our present plight did not appear overnight, own life. Finally, help your children understand that and the responsibility for our current situation is excellence in education cannot be achieved without widespread. Reform of our educational system will intellectual and moral integrity coupled with hard take time and unwavering commitment. It will require work and commitment. Children will look to their equally widespread, energetic, and dedicated action. parents and teachers as models of such virtues. For example, we call upon the National Academy of To Students Sciences, National Academy of Engineering, Institute You forfeit your chance for life at its fullest when of Medicine, Science Service, National Science Foun­ you withold your best effort in learning. When you dation, Social Science Research Council, American give only the minimum to learning, you receive only Council of Learned Societies, National Endowment the minimum in return. Even with your parents' best for the Humanities, National Endowment for the Arts example and your teachers' best efforts, in the end and other scholarly, scientific, and learned societies it is your work that determines how much and how for their help in this effort. Help should come well you learn. When you work to your full capacity, from students themselves; from parents, teachers, and you can hope to attain the knowledge and skills that school boards; from colleges and universities; from will enable you to create your future and control your local, State, and Federal officials; from teachers' and destiny. If you do not, you will have your future administrators' organizations; from industrial and thrust upon you by others. Take hold of your life, labor councils; and from other groups with interest in apply your gifts and talents, work with dedication and and responsibility for educational reform. self-discipline. Have high expectations for yourself It is their America, and the America of all of us, and convert every challenge into an opportunity. that is at risk; it is to each of us that this imperative is addressed. It is by our willingness to take up the A Final Word challenge, and our resolve to see it through, that This is not the first or only commission on America's place in the world will be either secured or education, and some of our findings are surely not forfeited. Americans have succeeded before and so we new, but old business that now at last must be done. shall again.

MEMOIRS OF THE AMS 1. Introduction 2. Decorations of the known simple groups The local Structure of Finite Groups 3. Local subgroups of the known simple groups 4. Balance and signalizers of Characteristic 2 type 5. Generational properties of K-groups Daniel Gorenstein and Richard lyons 6. Factorizations In this Memoir Gorenstein and Lyons study the 7. Miscellaneous general results and lemmas about generic finite simple group of characteristic 2 type K-groups whose proper subgroups are of known type. Their Appendix by N. Bt.Jrgoyne principal result (the Trichotomy Theorem) asserts Part II: The Trichotomy Theorem that such a group has one of three precisely deter­ 1. Odd standard form mined internal structures. (Simple groups with these 2. Signalizer functors and weak proper 2-generated structures have been classified by several authors.) p-cores The proof is completely local-theoretic and, in partie· 3. Almost strongly p-embedded maximal 2-local ular, depends crucially on signalizcr functor theory. subgroups It also depends on an inordinate number of proper· References tics of the known finite simple groups. The develop­ 1980 Mathematics Subject Classification: 20005 ment of some of these properties can be viewed as Memoirs of the American Mathematical Society a contribution to the general theory of the known Number 276, viii + 736 pages {soft cover) List price $49, institutional member $37, groups. individual member $25 Contents ISBN 0-8218-2276-4; LC 82-24354 Part 1: Properties of K-groups and Preliminary Publication date: March 1983 Lemmas. To order, please specify MEM0/276N Prepayment is required for all AMS publications. Order from AMS, P.O. Box 1571, Annex Station, Providence, Rl 02901, or call toll free 800-556-7774 to charge with Visa or MasterCard.

590 Reports from the Mathematics Research Institutes Berkeley and Minneapolis This section contains reports of activities of the two mathematics research institutes, MSRI, the Mathematical Sciences Research Institute, Inc., in Berkeley, California, and IMA, the Institute for Mathematics and its Applications in Minneapolis, Minnesota. Both institutes are funded by the National Science Foundation for a five-year interval. These reports cover programs of the first two years of their operation, as well as plans for the third year, 1984-1985, and other news of their activities. The reports on the mathematics institutes are supplemented by an article about the Theoretical Physics Institute in Santa Barbara, which has had its first five-year review and will have its funding extended by NSF for a second five years. Berkeley Kaplansky, chairman, Howard Garland, and Bertram Kostant). As an adjunct to the program in ergodic theory and dynamical systems there Report from Calvin C. Moore will be considerable activity devoted to the study of turbulence and its connection with dynamical 1982-1983 and 1983-1984 Programs systems. This will be supported in part by Each year two special programs provide a a $75,000 contract with the Air Force Office focus for a large part of the Institute's scientific of Scientific Research, which supplements the activities. A Program Committee is appointed Institute's core NSF operating grant. to oversee and coordinate the activities of As part of the two main programs the Institute each of these programs. The selection of the will sponsor a number of one-week workshops program topics and the appointment of program during the 1983-1984 year. committees is one of the major functions of Vertex Operators in Mathematics and Physics, the Scientific Advisory Council in collaboration November 10-15, 1983 with the Director and Deputy Director. During Coding and Isomorphisms in Ergodic Theory, the 1982-1983 year which has just concluded, December 8-13, 1983 the two special programs were Nonlinear Partial Turbulence, January 30-February 3, 1984 Differential Equations (Program Committee: I. Rational Maps, March 26-30, 1984 M. Singer, chairman, S. T. Yau, and Alexandre Chorin) and Mathematical Statistics (Program Infinite Dimensional Lie Groups, May 10-15, Committee: David Siegmund, chairman, Lucien 1984 LeCam, and Charles Stone). Geometry, Groups, and Ergodic Theory, May For the year just starting (1983-1984), the 24-June 1, 1984 two special programs are Ergodic Theory and The Topology and Geometry of Smooth Dynami­ Dynamical Systems (Program Committee: Jack cal Systems, June 4-8, 1984 Feldman, chairman, John Franks, Anatole Katok, Finally the Institute will host a special three-day Jiirgen Moser, and Roger Temam), and Kac­ conference, May 21-23, 1984, in honor of George Moody Algebras (Program Committee: Irving Mackey who will be visiting for the entire year. Lists of invited speakers for these conferences will be circulated shortly. People who are interested Physical Facilities in attending these workshops should contact the The Institute began full scientific operation in Deputy Director, for there is a small amount September 1982 in temporary quarters on the of money set aside for support of additional University of California Berkeley campus under participants. Preference will be given in allocating a lease agreement with the University. Progress this money to new and recent Ph.D.'s. on a permanent building for the Institute is Although a large majority of the Institute's well underway. A design/build competition resources are ordinarily devoted to the two special was concluded in June for the design and con­ programs each year, a substantial amount is struction of the building on University land in reserved for appointments covering all other parts the hills overlooking the campus and San Fran­ of the mathematical sciences. It is termed the cisco Bay. A contract has been awarded to a General Area as there is no planned overall joint venture team consisting of Shen/Glass Ar­ programmatic focus, and each year the Institute chitects and Amoroso Construction Company. has a substantial number of members who are not Groundbreaking will occur in the fall of 1983 formally associated with either of the two main with occupancy scheduled for November 1984. programs. The University of California will finance con­ struction of the building with a bank loan, 1984-1985 Programs and the Institute will in turn pay rent to the University sufficient to amortize construction, The two special programs for 1984-1985 will based on a 25-year repayment schedule. be devoted to Low Dimensional Topology and to the topic K-Theory, Index Theory, and Operator

591 Algebras. The Program Committee for the first Mathematical scientists interested in applying of these consists of Robert Edwards, chairman, for membership within either of the two programs Robion Kirby, and William Thurston. This or the general area should do so now. The program will focus on mathematics relating to deadline for completed applications is January 1, the topology and geometry of low dimensional 1984 (see advertisement at the back of this issue manifolds. Particular topics of interest in­ of the Notices). clude maps and automorphisms of surfaces, the 1985-1986 Programs geometry and geometries of 3- and 4-dimensional Programs for 1985-1986 have also been selected. manifolds, various kinds of structures on such There will be a program on Computational manifolds (e.g. foliations, laminations, handle body Complexity and a program in Mathematical structures, etc.), knots and links and submanifolds Economics; the latter of these will be only half in general, various representations of manifolds, the size of the Institute's usual programs. Plans group actions on low dimensional manifolds, and are pending whether to schedule an additional in general, progress toward the classification of program for 1985-1986 or whether to devote 3- and 4-dimensional manifolds. The interests of the remaining resources to a rather larger-than­ participants will range from classical to modern. normal general area with no particular overall The Program Committee for the second of the programmatic focus. Miniprograms similar to the two programs consists of Alain Connes, chairman, one in differential geometry in 1984-1985 are also Ronald Douglas, and Masamichi Takesaki. This possibilities. program will concentrate on recent important The Program Committee for the Computational advances concerning operator algebras, the for­ Complexity program consists of Richard Karp and mulation and proof of Atiyah-Singer type index Stephen Smale, cochairmen, and Ronald Graham, theorems for foliated spaces, and associated K­ with Shmuel Winograd as consultant. The homology and cohomology groups for these struc­ program will emphasize concrete computational tures. Measure theory is extended beyond its clas­ problems of importance either within mathematics sical framework by the theory of weights on non­ and computer science or in the applications of commutative von Neumann algebras. Measure these disciplines to operations research, numerical theoretic invariants of the transverse structure of computation, economics and other fields. The a foliation and their link with classification of von primary emphasis will be on the design and Neumann algebras form the first part of the pro­ analysis of efficient algorithms; attention will gram. Similarly the algebraic topology of locally also be given to lower bounds on the inherent compact spaces (in particular their K-theory), computational complexity of problems. once extended to non-commutative C* algebras The Program Committee for Mathematical becomes the natural framework of index theory. Economics will consist of Gerard Debreu, This allows one to treat untractable spaces such as chairman, Kenneth Arrow, and Andreu Mas­ the leaf space of a foliation. The main problems Colell. The rapid development of mathemati­ are the relations between the analytically defined cal economics during the last fifty years, and K-theoretical invariants and the usual invariants particularly after World War IT, has been charac­ of the "homotopy quotient", i.e. the classifying terized by 1) the solution of fundamental problems space of the graph of the foliation. These prob­ concerning among others the optimality, the exis­ lems also apply to the C* algebras of Lie groups tence, and the computation of various equilibrium or p-adic groups and will form the second main concepts, the structure of the set of equilibria, part of the program. Finally the links of the non­ the study of economies with a large number of agents, the study of preference relations and the commutative analogue of homology with algebraic properties of aggregate demand functions; 2) the K-theory, as well as eventual connections with introduction in economic theory of basic results mathematical physics will be discussed. and techniques borrowed from convex analysis, al­ In an attempt to give the general, or third, gebraic topology, measure theory, global analysis, area, outside the two programs, a modicum of etc. This development was powerfully helped additional structure for 1984-1985, the Institute by the interaction between economists and math­ will have a "miniprogram" in differential geometry ematicians. The 1985-1986 year at MSRI will as a small part of these general activities outside provide an exceptionally favorable environment of the two main programs. Christopher Croke for interaction between the two groups, especially and Andrzej Derdzinski will be at the Institute in the promising area that lies at the boundary of for the entire year. Chern will remain active economic theory and of complexity theory. The in the Institute's scientific program as Director main scientific direction of this small program Emeritus, and Marcel Berger, Jeffrey Cheeger, will be quite distinct from the 1983-1984 program Mikhael Gromov, and Blaine Lawson have each in mathematical economics at the Minnesota been invited to spend two months at the Institute Institute. with, it is hoped, staggered terms. Differential Plans for programs for 1986-1987 and beyond geometers wishing to spend some time at the are pending. Suggestions and proposals from Institute should apply for Institute membership the mathematical sciences community are most in the general area. welcome.

592 or recent Ph.D.'s is roughly Ph.D. age of five Kaplansky Appointed Director of MSRI years or less. For more senior and established The Board of Trustees of the Mathemati­ scholars, the usual mode of support is a fellowship cal Sciences Research Institute in Berkeley an­ stipend which supplements sabbatical leave or nounced in June that Irving Kaplansky of the other fellowship support. Only in very rare and University of Chicago will come to Berkeley compelling cases can full fellowship support be and assume the Directorship of the Institute, provided for senior people. Another mode of effective September 1, 1984. Kaplansky, age 66, support is partial or full expenses for visits to was born in Toronto and was the recipient of the Institute that can range from a few weeks to the first William Lowell Putnam Fellowship for several months and which may include attendance graduate study at Harvard in 1938. After receiv­ at one or more workshops that are usually scheduled in conjunction with the programs. ing his doctoral degree in 1941 from Harvard, he taught there for three years and subsequently The Institute operates year-round with activities distributed over all twelve months. The nominal joined the faculty at the University of Chicago in 1945 where he has been ever since. He held starting date of the program year is August 1, and full-year postdoctoral fellowships are nominally a Guggenheim Foundation Fellowship during for the period August 1 through the following the year 1948-1949. He was elected to the July 31, although there is considerable flexibility National Academy of Sciences in 1966 and was in these dates for individuals. For 1982-1983, appointed George Henry Mead Distinguished the overall magnitude of activity amounts to Service Professor of Mathematics at Chicago in 50 person-years, of which 31 are postdoctoral 1968. He has served on several AMS committees, has been a member of the Council (1951-1953) scholars. and the Board of Trustees (1968-1972), served Inquiries, applications, and suggestions for as Vice-President in 1975 and this year has been future programs should be addressed to Calvin C. nominated for the position of President-elect. Moore, Deputy Director, Mathematical Sciences Research Institute, 2223 Fulton Street, Room 603, Berkeley, California 94720. The Directorship The first Director of the Institute, Shiing-shen Chern, will conclude three years of service as Director; this is the term that he agreed to serve when the Institute became a reality in 1981. In February 1983 Chern reconfirmed to the Board of Trustees of the Institute at their annual meeting his wish to step down in 1984. The Board then appointed a Search Committee charged to conduct a nationwide search for a new director; this process culminated with the appointment of Kaplansky as the new Director. Calvin C. Moore, who has served as deputy director of the Institute since its inception, will continue in that capacity. I. M. Singer, who along with Chern and Moore formulated plans for the Institute, will continue as Associate Director for Development in the Institute. Singer has also served on the Institute's Scientific Advisory Council and will assume the chairmanship of that body on October 1, 1983 when the present Chairman, R. H. Bing, steps down. The Scientific Advisory Council is a small group that works closely with the Director and Deputy Director on formulating scientific policy, choosing programs, and in selecting members for Policies and Practices Regarding Support the Institute's programs. The six appointed The Mathematical Sciences Research Institute members serve staggered four-year terms and at places a very high priority on support, training, present the members are R. H. Bing, Dan Quillen, and encouragement of new and recent Ph.D.'s. David Siegmund, James Serrin, I. M. Singer, and At least 60% of the Institute's scientific budget Shmuel Winograd. On October 1, 1983, the is targeted for support of such scholars, usually terms of Bing and Siegmund will end, and Don in the form of yearlong postdoctoral fellowships. Burkholder and Barry Mazur will join the group. Half-year fellowships are also possible and are Ultimate legal and financial responsibility for the reasonably frequent. The definition of new Corporation, a nonprofit California corporation

593 (completely independent from the University of T. Davis, B. Hughes, and L. E. Scriven of the local California) which operates the Institute, is vested Department of Chemical Engineering, S. Prager in a 26-member Board of Trustees. of the Department of Chemistry, W. Halley of the Department of Physics, and B. Ninham of Minneapolis the Australian National University, who spent the year at the IMA. J. Hammersley was among the speakers. A constructive dialogue was estab­ Report from Hans F. Weinberger lished between pure and applied mathematicians, physicists, and engineers, including both academic The programs of IMA are selected by the and industrial, as well as theoretical and ex­ Board of Governors which normally meets perimental research workers. Another workshop in September of each year. The Board in the same spirit devoted to the subject of orient­ and the Directors of IMA strongly encourage ing polymers was organized by J. Ericksen. The individuals and groups of scientists to submit proceedings of these workshops will be published proposals for future programs. The present in the Springer Lecture Notes in Mathematics members of the Board of Governors are Felix series. Browder, Donald Burkholder, Wendell Fleming, The spring and summer were devoted to the Frederick Gehring, Ronald Graham, Shizuo foundations of phenomenological thermodynamics Kakutani, Joseph Keller, Daniel Kleitman, and thermomechanics, and to a renewed interest in Jiirgen Moser, and Stephen Smale. Hans the Korteweg theory of transitions. The program Weinberger is Director and George Sell is was coordinated by James Serrin. Visitors Associate Director of the IMA. included: Elias Aifantis, John Ball, Garrett Birkhoff, Haim Brezis, Bernard Coleman, Richard 1982-1983 and 1983-1984 Programs Ellis, Martin Feinberg, Mauro Fabrizio, Richard The first program of the IMA was on Continuum James, William Lawvere, George Mackey, Chi­ and Statistical Approaches to Phase Transition. Sing Man, Saunders MacLane, David Owen, The fall program, which was organized by Os­ Stephen Passman, Marshall Slemrod, Miroslav car Lanford, dealt with Statistical Mechanics Silhavy, Barry Simon, and Clifford Truesdell. and Dynamical Systems. A broad spectrum A highlight of this part of the year was a of physicists, engineers, and mathematicians col­ one-week workshop on the formulation of Con­ laborated on problems of common interest ranging tinuum Thermomechanics, including fourteen in­ from Ising models, renormalization groups, and vited hour addresses and a round-table discussion Hamiltonian systems for a large number of par­ session. This workshop emphasized a remark­ ticles to chaotic attractors, turbulence, and the able unity of method and approach, and an dynamics of rational mappings. One of the altogether new sense of mathematical clarity in early results of this collaboration was a new the understanding of the roles of heat, work, and simplified proof of the Oseledec theorem hotness, energy, and entropy in thermodynamics. discovered by R. Johnson and G. Sell. Particularly important developments which have arisen as a direct consequence of the IMA year KAM theory, thermodynamic limits, and other are a clarification of the position of Silhavy's new problems in statistical mechanics were discussed First Law of Thermodynamics, the possibility by G. Gallavotti, L. Gross, and E. Lieb. P. Collet, of energy unbalanced processes, the first solu­ J.-P. Eckmann, and C. Tresser considered the tion of the Korteweg equations for a dynamic dynamics of low-dimensional mappings. Closely phase transition, and a clear formulation of the related to this was a short period of concentra­ position of entropy in general thermodynamic tion on the theory of complex mappings of the structures. These developments will also appear plane during which A. Douady, J. Hubbard, in the Springer Lecture Notes. J. Milnor, and D. Sullivan visited IMA. C. Conley, In addition to the areas of special concentra­ 0. Lanford, and K. Meyer worked on resonance, tion noted above, the second half of the ther­ hyperbolicity and Lyapunov exponents in dynami­ modynamics year provided valuable additional cal systems. Many of these results and other opportunities for interchange and stimulation be­ research at IMA appear in the IMA Preprint Series. tween members working in related areas including The winter term was concerned with some ap­ chemical reaction theory, the theory of fading plications of statistical and continuum mechanics memory, nonlinear elasticity, second sound in to the properties of materials. During January materials, calculus of variations, the Gibbs phase a group of visitors including Frederick Almgren, rule, liquid crystal theory, percolation theory, John Cahn, Richard James, James Langer, Mar­ interfacial stability, and mathematical physics. shall Slemrod, Jean Taylor, and David Wollkind The Postdoctoral Members, Paul Blanchard, worked on problems of capillarity and crystal Ernest Dunn, Robert Hagan, James Kirkwood, surface growth. Luis Magalhaes, Milan Miklavcic, Scott Spector, A workshop on the Mathematics and Physics and C. Eugene Wayne provided a sense of of Disordered Media: Percolation, Random Walk, continuity and a spirit of adventure to the Modelling, and Simulation was organized by program.

594 During the 1983-1984 year the IMA is presently will be devoted to Equilibrium and Stability Con­ studying Mathematical Models for the Economics siderations, while the second half will concentrate of Decentralized Resource Allocation, a program on Dynamical and Evolutionary Features. organized by Leonid Hurwicz of the University The discussion during the first half will be of Minnesota. The basic problem is to design centered around equilibrium and stability ques­ a simple set of rules, sanctions, and incentives tions that arise in incompletely posed problems, with the property that when the various members transition of phase, and instability. The familiar of an economy, be they workers in a factory or theories such as elasticity, plasticity, and vis­ citizens of a country, act to maximize their own coelasticity, are not good enough to describe benefits, the overall equilibrium is good for the many interesting materials like liquid crystals, organization as a whole. The basic mathematical champagne, or heat-shrinking packaging. The tools are those of game theory, but many other wide variety of mathematical issues encountered mathematical ideas are needed. in addressing such problems includes: Long-term participants in this program include • Variational problems involving convex or C. A. Aliprantis, D. Artzner, G. Chichilnisky, nonconvex functionals, subject to constraints or S.-N. Chow, W. Harris, G. Heal, D. Heath, governed by auxiliary equations or inequalities, C. Johnson, Y. Kannai, W. Lucas, H. Moulin, •Relative minimum or saddle point problems, K. Mount, N. Noakes, S. Reichelstein, S. Reiter, • Singularities of solutions of possibly H. Rosenberg, D. Saari, C. Simon, D. Schmeidler, degenerate elliptic equations and systems, T. Suzuki, G. White, and W. Zame. In addition • Multiplicity of solutions and the identification nine Postdoctoral Members will participate. of distinguished manifolds which are especially The program opened with an introductory suitable to describe qualitative behavior of general workshop. In addition to several of the long­ solutions, term visitors, speakers included Thomas Marshak, • Homogenization as a theoretical and computa­ Lloyd Shapley, Martin Shubik, and Andrew tional method, Postlewaite. • Reliability of computational methods. A workshop on Price Dynamics Based on Entry, The Scientific Committee consists of Jerald Exit, and Quantity Adjustment organized by Hugo Ericksen and David Kinderlehrer, Program Coor­ Sonnenschein of Princeton University will be held dinators, together with Haim Brezis and Constan­ from October 24 to 28, 1983. tine Dafermos. Robert Aumann of the Hebrew University and Additional persons who have so far agreed Daniel Kleitman of the Massachusetts Institute of to be in residence for extended periods during Technology will be in residence for the month of this program include Charles Amick, John Ball, Janaury. Avner Friedman and Shizuo Kakutani Felix Browder, John Gianfranco Capriz, L. Craig will participate for four weeks during the year. Evans, Avner Friedman, M. Giaquinta, Enrico Further workshops, including some with more Giusti, Stefan Hildebrandt, Cornelius Horgan, direct applications, are being planned for the J. L. Lions, Jerry Marsden, Ingo Mueller, Vladimir winter, spring, and summer periods. Oliker, Joel Smoller, Joel Spruck, John Toland, G. Vergara-Caffarelli, and William Ziemer. 1984-1985 Program Postdoctoral and sabbatical support is available The topic of the third year of the IMA from to persons who wish to participate in the third September 1984 to August 1985 will be Continuum and fourth year programs. Core mathematicians Physics and Partial Differential Equations. The who are interested in studying applications are scope of continuum physics is the physics of the especially welcome. Further information may be world that we encounter in our daily lives, the obtained by writing: Hans Weinberger, Director, phenomena perceived through our ordinary senses Institute for Mathematics and its Applications, such as dough making, cracking eggs, and ice 514 Vincent Hall, 206 Church Street, S.E., cream making. The equations which model such Minneapolis, Minnesota 55455. The University of occurrences are typically partial differential equa­ Minnesota is an equal opportunity educator and tions. The close connection between experimental employer and specifically invites and encourages features of continua, qualitative properties of applications from women and minorities. differential equations, and methods of efficient 1985-1986 Program numerical computation makes these topics espe­ cially suitable fields for combined study. The fourth-year program from September 1985- August 1986 will deal with the topic of Stochastic The program is designed to encourage col­ Differential Equations and their Applications. The laboration among a broad spectrum of engineers, organizing committee consists of Daniel Stroock scientists, and mathematicians with interest in (Chairman), Wendell Fleming, Theodore Harris, continuum physics, partial differential equations, Pierre-Louis Lions, and Stephen Orey. or related areas. The first half of the program

595 the founding of This article, NSF adds five more years to Boris Kayser, who spearheaded physics division. The theory center on the Institute for Theoretical the institute within the NSF staff and visitors, who sometimes refer Physics is reprinted from the August 1983 issue institute's of Physics Today with the permission of the to themselves as "Santa barbarians," variously and publisher. The author is Irwin Goodwin, Senior describe the place as "lively," "stimulating" Associate Editor of Physics Today. Copyright "bushy-tailed." © 1983 by the American Institute of Physics. While NSF does not plan to increase its funding much beyond the current level of $1.4 million annually, the institute has attracted grants of Santa Barbara $25,000 for each of its first three years from mM and $10,000 per year from Xerox, as well as Theoretical Physics Institute smaller gifts from corporations and individuals. In addition, NASA is contributing $250,000 this In reviewing the first three years of the Institute year and intends to provide similar amounts for at for Theoretical Physics at Santa Barbara last fall, least another two years. When Caltech's William a panel of ten physicists reported to the National A. Fowler learned of NASA's support at a recent Science Board, the governing board of NSF, that meeting of the NSF Physics Advisory Committee, it is "strikingly successful ... even more so than he exclaimed: "It's significant for another Federal anticipated." The review group, headed by Peter agency to sponsor the institute. That's a rare Carruthers of Los Alamos National Laboratory, happening." commended the institute's leaders, faculty and According to Kohn, NASA's support is going to participants for developing a "unique atmosphere" help resolve an urgent need-access to computers. of "special excitement" and "high expectations" This was one of the high-priority problems in which new directions are explored across identified by the Carruthers panel last year. The disciplines by senior physicists working alongside theorists have been using University of California's postdoctoral fellows from the U.S. and abroad. VAX 780 computers and a Cray I at Los Alamos for Accordingly, the panel's recommendation came number crunching, but need additional computer as no surprise: "The reviewers enthusiastically time (Physics Today, May 1982, page 23). To support the proposed continuation of the institute ease the pressure, a VAX 750 will be delivered in for a second five-year period." In due course the next month or two. What's more, Kohn is last April, the Science Board reached the same negotiating with Glenn Culler of em Systems Inc. conclusion, meaning that NSF will continue to to acquire an array processor that will extend VAX sponsor the institute to 1989. computing power tenfold. The decision, says the institute's director, The Carruthers panel also suggested that the in­ Walter Kohn, is "extremely gratifying as a vote of stitute's advisory board "should be representative confidence in everyone associated with our way of of the entire physics community, including ex­ doing theoretical physics." Until the board acted, perimentalists." While the board has functioned there had been some anxiety on the top floor of well, the panel said, "we encourage wider com­ Ellison Hall on the campus of the University of munity participation in the selection of future California at Santa Barbara, where the institute members," with particular sensitivity to "the has been located since its start in September 1979. needs of subfields of physics, such as atomic and Doubts had been expressed within the physics nuclear physics and new areas which may arise in community about the wisdom and effectiveness of the future and may not be represented in the per­ a centralized theory center with a large proportion manent staff." One experimentalist, Richard A. of visitors, staying typically from a few months Muller of Lawrence Berkeley Laboratory, already to a year. The panel's report erased such doubts. is on the board. Moreover, accepting the panel's "In the few years of its existence," the report recommendation, Kohn wrote to Robert Marshak, said, "the institute has emerged as a leading in his capacity as president of the American Physi­ national facility with programs and research at cal Society, seeking nominations to the board. In the forefront of theoretical physics." It has September, when new members will be rotated achieved international recognition, with about onto the board, additional nontheorists are likely 40% of the 500 visitors who spend more than to be appointed. a month there coming from outside the U.S., Besides Kohn, the permanent staff now consists usually on their own money. of James Langer, who came from Carnegie­ The interdisciplinary nature of the institute, the Mellon University, Frank Wilczek from Princeton, panel observed, is "an instrument for expanding and J. Robert Schrieffer from the University of the conceptual scope of theoretical physics" and Pennsylvania, who spends one-third of his time accelerating the collaboration of physicists with at the institute. The latest addition is Douglas different specialities and diverse interests. Indeed, Eardley, an astrophysicist, from Harvard. Kohn the report went on, "unplanned interactions may and the board are now actively recruiting another turn out to be the most important feature of the staff member from the community of elementary­ institute." "Theorists thrive on interactions," says particle theorists. "We are going to maintain the

596 same high standards as in the past," Kohn said in commmittee sent a short list of six names to an interview, "even if it takes a little time." Richard Blankenbecler of SLAG, who is chairman Finally, the panel pointed out, "of critical of the institute's advisory board. Because the importance for continued success of the institute," institute's programs have to be formulated more is a successor to Kohn, who will step down than a year in advance, says Blankenbecler, the when the institute reaches its fifth birthday next board will try to decide on Kohn's replacement year. The panel calls for a new director with at its September meeting. "It is remarkable that "breadth of competence, experience and interest people are taking this so seriously," he says. "It in physics" -criteria used by a search committee means the institute, despite its youth, is a force under Paul C. Martin of Harvard. In June that in physics."

RECENT AMERICAN MATHEMATICAL SOCIETY PUBLICATION

CONFERENCE PROCEEDINGS OF THE CANADIAN MATHEMATICAL SOCIETY

Current Trends in Algebraic Topology Richard M. Kane, Stanley 0. Kochman, PaulS. Selick, and Victor P. Snaith, Editors Contents of Part 2 papers by P. Baum, Current trends in algebraic topology is the pro- ALGEBRAIC VARIETIES, with Harper and R. ceedings of a conference by the same name held at W. Browder and N. Katz, and). the University of Western Ontario, London, Ontario Mandelbaum by A. Assadi, H. from June 29 to July 10, 1981. It contains papers GROUP ACTIONS, with papers and I. Madsen, S. lllman, which were presented at the conference and some Dovermann, 1. Hambleton May and ) . E. McClure, related papers. s. Kahn, L. G. Lewis, ) . P. May and J. E. The book contains research papers in topology T.-Y. Lin, A. Liulevicius, ). P. ) . Tornehave, M. and so potential readers should be at least at the McClure, T. Petrie, R. Schultz, level of graduate students in topology. Since the Wang, and A. Zabrodsky ON MANIFOLDS, book is a collection of research papers from different MANIFOLDS AND STRUCTURES .-C. Hausmann, W.-C. areas, papers of interest to any individual will vary with papers by M. Frame, J and S. Wein- according to his or her research interests. Anyone Hsiang and B. )ahren, N. Levitt, doing research in topology is likely to find some berger H. Miller, H. Munkholm papers of interest. TRANSFER, with papers by Contents of_ Part 1 and E. Pedersen and H. Munkholm and A. ALGEBRAIC K-THEORY, w1th papers by R. Charney, R . k" ' ante 1 . . d V S . h V 18F25, M. Karoubl, E. Lluls-Puebla an · nalt ' ' 1980 Mathematics Subject Classifications: 55-06; Snaith (two papers), C. Soule, ) . Stienstra, R. 55 N2o, 55 N22, 55P35 & others. Waldhausen Thomason, and F. Conference Proceedings of the GENERALIZED HOMOLOGY AND COHOMOLOGY, Canadian Mathematical Society with papers by ) . Boardman, P. Landweber and Volume 2: Parts 1 and 2 (soft cover) (Part 1); xxiv + 484 pages (Part 2) Z. Yosimura, H. Miller and V. Snaith, D. Ravenel, xxiv + 516 pages Set: List price $42, AMS institutional member $32, and R. Seymour individual AMS or CMS member $21 HOMOTOPY THEORY, with papers by R. Bruner, ISBN 0-8218-6003-8; LC 82·13789 member $20, Cohen, D. Davis and M. Mahowald, ) . Neisen­ Part 1: List price $26, AMS institutional F. CMS member $13 P. Selick individual AMS or dorfer and P. Selick, and ISBN 0-8218·6001-1; LC 82·13789 H-SPACES, with papers by ) . Harper and R. Kane Part 2: List price $24, AMS institutional member $18, member $12 AND COHOMOLOGY, individual AMS or CMS ORDINARY HOMOLOGY ISBN 0·8218-6002-X; LC 82-13789 with papers by A. Bahri, A. Baker, S. Kochman, Publication date: October 1982 D. Kraines and T. Lad a, j. McCleary, S. Papastav­ To order, please specify (Set) CMSAMS/2N ridis, and D. Pengelley (Part 1) CMSAMS/2.1 N, (Part 2) CMSAMS/2.2N

Prepayment is required for all American Mathematical Society publications. Order from AMS, P.O. Box 1571, Annex Station, Providence, Rl 02901.

597 Queries Edited by Hans Samelson QUESTIONS ARE WELCOMED from AMS members regarding mathematical matters such as details of, or references to, vaguely remembered theorems, sources of exposition of folk theorems, or the state of current knowledge concerning published or unpublished conjectures. REPLIES from readers will, when appropriate, be edited into a composite answer and published in a subsequent column. All answers received will be forwarded to the questioner. QUERIES and RESPONSES should be typewritten if at all possible and sent to Professor Hans Samelson, American Mathematical Society, P. 0. Box 6248, Providence, Rhode Island 02940. Queries where X= e-a- b, Y =b-e-a, Z =a-b-e and r(x,y, ... ) = r(x)f(y)···. For a= b = e the 284. R. Gurevich (Maurice Thorez 33, Apt. above identity reduces to 205, Leningrad, 194223 USSR). Consider the 4Fa( -a, -a, -a, -a; -4a- 1, 1, 1; 1) Cauchy problem y' = f(x, y), y(xo) = Yo with a good (say elementary) function f defined on = (-1)a(4a + 2)B(a + 1, 3a + 2) {(x, y)Jg1 (x, y) > 0 & · · ·& gk(x, y) > 0} with good · 4Fa(3a + 2, -a, -a, -a; 1, 1, 1; 1). (say, elementary) functions Yi· Any ordinary differential equations textbook states that there I am unable to find this identity in the literature. is an interval (a, b) 3 x0 such that the solution I would appreciate an alternative mathematical exists on (a,b) but cannot be extended beyond proof for this identity. (a,b). How does (a,b) depend on f? (The answer is evident for f depending only on y.) Problem List In fact I'm interested in f(x,y, parameter) and want, say, differential equations for a(parameter), Value Distribution Theory b(parameter) with f's a bit more general than The following is a list of open questions and elementary. Mathematical and bibliographical conjectures introduced at a special session on information will be welcome. Value Distribution Theory and Its Applications 285. D. Gurarie (Department of Mathematics, organized by Chung-chun Yang and held at the Case Western Reserve University, Cleveland, Ohio AMS meeting in New York City, April14-15, 1983. 97331). I would like to have any reference to I.J'­ 1. (C. Yang). Let Ot and Et denote, respec­ theory of Hermit functions {Hn(x)}, n = 0,1, .... tively, the order and the exponent of convergence The following questions are of particular interest: of the zeros of a meromorphic function f(z). (a) Do they form a basis in I.J'(R)? What basis? Assume Ot < co. Then it can be shown: If (b) If {Hn} are £ 2-normalized, can one estimate max{E,,,Et} < Of, then Et, < Ot· Is it true products of I.J'-norms Cn =II Hn liP' (p' = pf(p-1)). that if max{E,,E1cn>} then E1ckl Is Cn = O(n"')? The answer may be important for where 1 < k < n? LP-spectral theory of the Hermit operator. 2. (C. Yang). Let P(z), Q(z) be two nonlinear 286. J. B. Wilker (Mathematics Department, polynomials with the same degree. It is conjec­ Scarborough College, University of Toronto, West tured that if P(z) = 0 -<* Q(z) = 0 and P(z) = Hill, Ontario M1C 1A4, Canada). Motivated 1 -<* Q(z) = 1, without counting multiplicities, by Euclid's proof that there are infinitely many then either P =Q or P + Q =1. It is known that primes we let Po be a finite set of primes and the conjecture is not true if deg P # deg Q. proceed by induction to define Pn+l as the union 3. (K. Niino). Let x : C--+ PnC be a holomor­ of Pn and all the prime factors of Nn = 1 + 1r{p : phic curve of lower order p,, x = (x 0 , x1. ..• , Xn) : p E Pn}· Does this procedure eventually generate c --+ cn+l- {0} its reduced representation, ).. all the primes? In particular, does it do so if its index of degeneracy, that is, ).. is the maxi­ Po= {2}? mum number of independent, linear relations with 287. K. Srinivasa Rao (MATSCIENCE, The In­ constant coefficients among the entire functions stitute of Mathematical Sciences, Madras-600 Xo,xl,···•xn, and A a finite system of PnC in 113, India). The following identity, satisfied by general position. Then we conjecture that Saalschutzian generalized hypergeometric func­ L 8(a):::; n + (>-. + 1)(1- sin 1rp,) tions of unit argument, has been derived while aEA studying the connection between special functions and angular momentum coefficients: when 1/2 < p, < 1. 4Fa(X,X,X,X;-2a-2b-1, 2e-2a+1, 2e-2b+1; 1) = (-1)xf(a+b+e+ 2,1-X,1-X,1-X,1-X,2e-2a+ 1,2e- 2b+ 1) f(2a+2b+ 2,1-X,1-¥,1- Z) ·4Fa(a + b + e + 2,X,Y,Z; 1,1,1; 1),

598 Responses 274. (Vol. 30, p. 302, April1983, Elvin Lee) What is the state of the conjecture that every prime The editor would like to thank all those who number divides at least one amicable number? Is sent in replies. it true that the number of distinct prime divisors 268. (Vol. 30, p. 11, January 1983, A. Wilansky) of an amicable number is unbounded (assuming For a l.c. Frechet space X is X' fully (= B-) there are infinitely many amicable numbers)? Does complete in the strong topology? Reply: The anybody have computer files of amicable numbers? strong dual of a countable product of copies of Re~ly: I have a computer file of, currently, 3978 amicable number pairs 1050 . Anyone who is the Banach space c0 is not B-complete. The same < question for Br-completeness is also negative: able to contribute one or more new pairs to this file will be rewarded with a print-out, or, if he consider the space c0 X I1~ 1 l 2 . Its strong dual likes, a copy-on-tape. I have made frequency 11 X EB;"' 12 is not Br-complete (Remark 2 of E. T. three Shavgulidze, Br-completeness, Functional Anal. counts which show that there are only 1000 which do not divide a member Appl. 9 (1975), 363-364) (this last result is given primes below 641, without proof). (Contributed by Pedro Perez of these 3978 amicable number pairs, viz., prime Carreras) 733 and 821. The largest number of distinct divisors of any amicable number in my file is ten. 272. (Vol. 30, p. 302, April 1983, Francis D. (Contributed by Herman J. J. te Riele) Lonergan) Is it known for which integer values of l, m, n, t the "generalized" binary polyhedral 278. (Vol. 30, p. 403, June 1983, M. S. Brandly) designs with certain groups, (l, m, n(tl), given by the group presenta­ The query concerns block parameters and additional matching requirements. tions generators: R, S, T, relations: R 1 = S'"' = = RSTt are or are not residually finite? Reply: Suppose that in addition to asking that rn which More generally, has anything been published or we have a design with block size four in twice as is much known about these groups? Reply: The all pairs occur once as partners and given generalized binary polyhedral groups in question opponents, we also ask that the blocks be Then the are Seifert fibre groups, that is, extensions of in classes which partition the points. an infinite cyclic group by a fuchsian group or arrangement is known as a Whist tournament. other two-dimensional group. It was proved in Whist tournaments were first studied by E. H. J. the Ph.D. thesis of A. B. Mamagani (Birmingham, Moore (Tactical memoranda, I-III, Amer. England, 1979, unpublished?) that all Seifert Math. 18 (1896), 264-303), and are now known 4) fibre groups are residually finite. Mamagani also to exist for any v congruent to 0 (mod Sixth proved that a Seifert fibre group is residually (R. D. Baker, Whist tournaments, Proc. Theory finite-soluble if and only if its associated fuchsian Southeast Conf. Combinatorics, Graph group is distinct from its derived group. Many and Computing (Florida Atlantic Univ., Boca of these groups are fundamental groups of the Raton, Fla., 1975), Congressus Numerantium, Utilitas Math., Winnipeg, Man., 1975, 3-manifolds known as Seifert fibre spaces, and No. XIV, in both as such have been extensively studied, the best pp. 89-100. Generalizations are discussed references. (Contributed by R. D. Baker and H. gene~al reference being Peter Orlik's book, Seifert manifolds, Lecture Notes in Math., Vol. 291, Hanani) Springer-Verlag, 1972. (Contributed by A. M. Macbeath)

Induction Theorems for Groups lian groups which is natural with respect to induction of Homotopy Manifold Structures and restriction for a covering projection of finite index Andrew J. Nicas (and more generally for fibrations with compact mani­ fold fiber). Dress induction and localization are applied The work of Sullivan and Wall, as extended by to obtain induction theorems for STop(M, oM). Kirby and Siebenmann, showed the existence of an exact sequence of pointed sets for the surgery theory 1980 Mathematics Subject Classifications: 57R67, 57R65, of a compact oriented manifold with boundary 18F25, 20C99. (Mm, oM), m;;;. 6: Memoirs of the American Mathematical Society Memoir Number 267, vi+ 108 pages (soft cover) List price $8, institutional member $6 individual member $4 ' ISBN 0·8218-2267-5; LC 82-11546 In this Memoir it is shown how to make this sequence Publication date: September 1982 and its extension to the left an exact sequence of abe- To order, please specify MEM0/267N

Prepayment is required for all AMS publications. Order from AMS, P. 0. Box 1571, Annex Station, Providence, Rl 02901, or call toll free 800-556-7774 to charge with Visa or MasterCard.

599 Letters to the Editor

Can Research be Expounded! were declared to be research-expository articles, The Bulletin of the American Mathematical and so were left-over invited addresses (if you Society has been on the losing side of popularity can't publish them one way, just call them contests for quite some time. "Why do I have something else), as well as Colloquium Lectures, to buy it?", many members complained. "I don't Gibbs Lectures, and many duplicates, blatantly need it and I don't read it; I'd rather do without reprinted from other current outlets. It is not it and have my dues lowered." Nevertheless, surprising that the quality was variable, to say the for reasons that are partly idealistic and partly least. financial, the governing bodies of the Society have Then there are those books (I don't know been loath to let the Bulletin die. They have what else to call them) that started appearing encouraged and welcomed one proposed alteration as research -expository articles; pieces of writing after another, hoping to find the one that will over 150 pages long, in one case 198 pages. stop the grumbling. There have been five of them; they constitute· One traditional source of many complaints about one third of the total number of pages. was the almost automatic publication of invited It is a priori unlikely that any such "book" addresses. It is an honor to be invited to give could possibly be a research -expository article; a one-hour address at a meeting of the Society, is anyone really going to sit down and read it, an honor frequently awarded to the people who all of it? The one closest to my own interests show promise of becoming the leaders of the next (Harmonic analysis ... , by Mackey, July 1980) is generation. They are likely to be just out of their an admirable accomplishment. It is a valuable mathematical youth; to make that description survey; I have read. in it, I have consulted it, and quantitative I'll guess that one's youth ends ten I am glad it exists. It cannot, however, be called years after the doctorate. Such people are often a research-expository article, not by any stretch prolific contributors to the research literature, but of the imagination. It is a survey, as are many it is a rare piece of luck when they turn out others, and that makes it a very different thing to be good expositors too. The written versions with a very different purpose. A survey tells the of the addresses were usually highly technical history of a subject, contains a detailed, scholarly presentations of the specialized research that the bibliography, and, in between, it defines, it states, speaker and his coreligionists had produced in the it proves, and it is mercilessly complete. A survey last two years. Few subscribers to the Bulletin is, in effect, a mini-encyclopedia. A good thing­ read them and even fewer liked them. As a result, yes, sometimes-but not for exposition, not for the Society decided to change policy; under the learning. new way the published invited addresses were to I was discussing the research-expository articles become as rare as the rejected ones used to be. with one of our leading mathematicians recently, The most recent lifesaving experiment was to one whose name (let's call him P) is known the establish in the Bulletin a new section called world over, an important figure in the AMS, a Research-Expository Articles. The idea was member of the National Academy. He confessed that although you work on partial differential that he cannot-in any event he does not­ equations, you are (should be?) curious about read the research-expository articles; he had read recent progress in the theory of the inverses pretty nearly the whole of one, but all the others of polynomials, and even if you don't work on he just glanced at and gave up on. In the course of anything at all, you are still intellectually alive our conversation another mathematician's name and would like to keep up with current research. arose, Q, let us say, one with at least equal Doesn't that sound good? The section was stature. I was told that Q hated the Bass-Connell­ officially started in January 1979, and so far, Wright article (September, 1982); he does not through May 1983, there have been 71 titles in know what a module is, and he thinks the level of it. Some people like the research-expository that piece is totally inappropriate. (I disagree; the articles very much and think that anyone who Bass-Connell-Wright article is one of the few that does not like them belongs to the great body of I could read three pages of and learn something the anti-intellectual unwashed. from.) The most revealing anecdote was told by I don't like them. another mathematician at the table, a slightly One reason I don't like them is that fewer than younger one, not so famous as P and Q, but an half of the ones that have appeared deserve the active research worker with a well-known name, at name, and I cannot think of a single one that one of the top six mathematics departments in the accomplishes the purpose the name was intended U.S. He, let's call him R, told about a colleague to describe. Since in the beginning there was, of his, S, who recently gave a talk on finite simple obviously, no backlog, the terminology began groups to the undergraduate mathematics club of by being less than completely honest; obituaries their university. My friend R attended S's talk,

600 and, he said happily, that was the first time he got journals which a mathematician in my position a glimmering of what all the fuss was about, what has the opportunity to see, as an individual the words meant, and what the breakthrough had member affiliated with an institutional member of really accomplished; what he had been needing all the Society. I believe that it would better serve along was a research-expository revelation aimed the mathematical community at large to reserve at undergraduates. I didn't make up any of this; this space in the CMP for title pages from journals under pressure I would be prepared to tell whoP, other than those of the AMS, which are so widely Q, R, and S are. disseminated anyway. Can bona fide research -expository articles Marlow Anderson really exist? Have there been any, anywhere, Colorado College any time? I feel that the answer must be yes, but EDITORS' NOTE. The MR Editorial Committee I cannot think of an example that everyone would and the Editors of MR. are pleased that Professor find convincing. Is van der Poorten's report on the Anderson finds CMP invaluable; they share his irrationality of ~(3) a possibility? (Mathematical desire to see the Tables of Contents from a Intelligencer, volume 1, number 4.) broader selection of journals in the pages of CMP. The main question is whether the mathematical To this end, a mailing has been sent to the editor community can produce articles such as were of each high-density journal (i.e., a journal which hoped for in sufficient number to achieve the MR. generally treats cover-to-cover) asking them to desired effect. I wonder. I am inclined to provide us copies of their table of contents, either be pessimistic. It is an almost impossible with page-proofs of their journal (to enable earlier editorial task to persuade experts to explain their coverage of the contents) or with a small payment subjects to non-experts approximately, roughly, to cover the marginal cost of the extra space non-technically, and not in great detail. An expert in CMP. To date, 39 journals have responded must, he thinks, always keep his fellow experts in affirmatively; the Tables of Contents section­ mind-what will they think of an approximate, now marked with a black corner on each page­ rough, non-technical explanation? And, anyway, should show a steady increase in coverage over the the expert says to himself, surely everyone in the next year. world knows what a Lie algebra is, or what the elementary properties of subharmonic functions Jose Luis Massera are; I cannot possibly take the time to explain that stuff. He is wrong; not ewry devotee of integral Having written approximately one year ago [to equations knows about Lie algebras, and very Uruguay] to request the release of Professor Jose few algebraic homologists know the elementary Luis Massera, currently imprisoned in Uruguay, I properties of subharmonic functions. They might have recently received the following formal reply, have heard them in a course once, but that was from Juan J. Sosa, dated April 26, 1983 at 10 or 15 or 20 years go, and by now they have Montevideo: regained their innocence. "In regard to your note to the Director That's the way things are. Others feel of Military Detention Establishment No. 1, differently, of course, but I am convinced that my in which you express an interest in the conclusions are those of the great majority, even if Uruguayan civilian Jose Luis Massera, cur­ that word is interpreted in its narrowest, highest, rently serving a sentence at the above named most elitist sense to refer to the majority of Establishment, I wish to inform you that: active research mathematicians. The "research­ The person in question is serving a twenty­ expository articles" as they now stand are a year sentence for charges of 'attempted failure. They should either be made expository, conspiracy against the constitution' and or, if that cannot be done, they should be 'subversive association' with special aggravat­ abandoned. ing circumstances. Paul R. Halmos He has exhibited some symptoms of arterial Indiana University, hypertension which have received adequate Bloomington medical treatment and he currently enjoys good health. Current Mathematical Publications The request which you make for his freedom Ail a mathematician engaged in research at lies in the responsibility of the competent an institution not' blessed with a full-scale judicial official. research library, I find Current Mathematical I trust I have satisfied your unease regarding Publications invaluable. I especially appreciate this prisoner." the opportunity to examine the title pages of Though the formal tone of this reply does journals I do not ordinarily see. This brings me not encourage additional correspondence, I have to my small complaint. Space in this section transmitted the following letter to Mr. Sosa: of CMP is regularly taken by title pages from "I am in receipt of your letter of April26, 1983, the Proceedings, the Transactions and even the concerning Professor Massera. A sentence of Bulletin of the AMS. These are exactly the twenty years for charges such as 'attempted

601 conspiracy' and 'subversive association,' im­ in the Soviet Union, Hebrew is a forbidden posed upon an elderly scholar, can hardly im­ language (de facto, but not de jure), and therefore prove Uruguay's image in the civilized world. Begun was tried and sentenced for "parasitism." I would like to suggest once more that by When he returned from his first exile to his acting in this way, Uruguay simply isolates home in Moscow, he was arrested and sentenced itself from the international family of scien­ again to exile for "violation of internal passport tists which is vital to its economic progress, regulations"(!) The third arrest came again and destroys the contribution which Professor without any legal basis, but only as harassment Massera could make to the mathematical de­ for Begun's past and present "crimes": applying velopment of Uruguay. Is it not plain that for emigration to Israel, and teaching Hebrew your country has more to gain from his release privately. than from his continued imprisonment?" The Israel Mathematical Union calls upon math­ Jacob T. Schwartz ematicians throughout the world to protest the New York University, harassment of Yosef Begun by Soviet authorities, Courant Institute of and to request that he be permitted to emigrate. Mathematical Sciences Shmuel Kantorovitz, PosT ScRIPT: The return address on Sosa's letter Chairman was O.C.I.P., Uruguay 972, Montevideo, Uruguay. Israel Mathematical Union

Soviet Mathematicians The Axiom of Choice Vladimir Albrekht, like numerous individuals In Gregory H. Moore's recent interesting book around the world, has had his human rights Zermelo 's axiom of choice one reads on page 80: violated. Albrekht, a Soviet mathematician, We must reject the claims of those historians was arrested in Moscow on April 2, 1983 for who, relying on the articles of Peano and the peaceful exercise of his right to freedom of Levi. .. , have asserted that one or both of them expression. He is accused of being the author of formulated the Axiom of Choice explicitly the legal aid pamphlet How to Conduct Yourself before Zermelo. What we can say is that Peano During a House-Search. Besides being active was the first to reject the use of infinitely many in raising support for the relatives of political arbitrary choices. Levi, probably influenced prisoners, he was secretary of the Moscow group by Peano, also endeavored to avoid proofs of Amnesty International from 1975 through 1981. that employed such arbitrary choices. Mathematicians can lend their support to Yet on page 79 Moore discusses Levi as follows. Albrekht by writing to President B. S. Kashin, If a set A is partitioned into a family S of The V. A. Steklov Institute of Mathematics, 42 disjoint non-empty sets s, then the cardinal Vavilova Street, Moscow, RSFSR, USSR. number of S is less than or equal to the Letters should express concern about the arrest cardinal number of A. After showing that and request Albrekht's immediate and uncondi­ [this] Partition Principle held whenever A was tional release. Letters written on departmental finite, Levi added that "this demonstration stationery might have more impact. is applicable without change to any case C. Herbert Clemens where all the s are well-ordered or else, more Hugo Rossi generally, where we can distinguish a unique University of Utah element in each s" [1902, 864]. However, he EDITORS' NoTE. A duplicate of the above letter did not regard his comment as grounds for was submitted for publication in the Notices by using the Partition Principle in general. Robert Carlson of Culver City, California. Since Levi's quote includes an explicit formulation of the Axiom of Choice as a workable hypothesis, Dr. Yosef Begun, a Jewish mathematician in Moore's ground for rejection of Levi's priority is the Soviet Union, was arrested in November 1982, based on the latter's negative attitude toward the and is to be tried on charges of "anti-Soviet Axiom. Such thinking is like denying Columbus propaganda," which carries a maximum sentence credit for having discovered America because he of seven years' imprisonment with an additional died believing he had landed in Asia. five years' exile. Dr. Begun has already served Both Fraenkel and Sierpir\.ski pointed out Levi's two sentences in Siberia, first for "parasitism," priority over Zermelo. E. W. Beth did so, too, and then for "gross violation of internal passport saying: regulations." His total sentence summed up In 1904 E. Zermelo succeeded in proving the to five years in exile. What was Begun's real well-ordering theorem. . . . In his proof he "crime"? In 1971, he applied for emigration to used the axiom of choice to which Erhard Israel. This was refused on grounds of "regime Schmidt had directed his attention. As early considerations," and Begun automatically lost his as 1890, this axiom had been stated and job. He subsisted by teaching Hebrew privately. applied incidentally by Peano, but only in While private teaching is a recognized profeseion 1902 was it seen, by Beppo Levi, to constitute

602 an independent principle of proof. (The as important. The audience in concert halls has foundations of mathematics, 1959, page 376.) as much part in the development of music as J. van Heijenoort also states: The Axiom of Choice the composers and players, A mathematically was "recognized as a new mathematical principle cultured person is essentially a sensitive listener by Beppo Levi." (From Frege to Godel, 1967, to the continuous mathematical symphony of the page 139.) time, whose interest and reactions help mold the None of these opinions in the least reduces shape of contemporary mathematics as much as Zermelo's accomplishments. After all, most of the work of mathematical producers. today's set theories are variations of Zermelo's 4. How can we encourage mathematical culture? system. But since one must go back to (a) By constantly pointing out in our courses Euclid's famous Fifth Postulate to find a principle the historical development of the subjects, their comparable to the Axiom of Choice for the goals and their relations with other subjects in significance of its consequences, I believe it is and outside mathematics. important to give appropriate credit to the person (b) By requiring students to take courses in the who first saw the Axiom as a workable hypothesis. history of mathematics. The evidence points clearly to Beppo Levi. (c) By offering special courses developing the F. G. Asenjo skill of writing mathematics. University of Pittsburgh, (d) In grading and evaluating tests, homework, Pittsburgh etc., attention should be paid not merely to correctness in the strict sense of the word, but Mathematically Civilized also to full understanding, clarity, motivation, 1. "Do you have gifted students?" "How aesthetic appeal and the like. many?" "In what subjects?" "In what level 5. A worthy piece of mathematics, whether a of mathematical development?" These are some new discovery or a presentation of a classical questions we are occasionally asked. But here is topic, when viewed superficially, may share some another question: How civilized, mathematically features with a bank statement. But when fully speaking, are your students? understood, one should be able to recognize it as What does it mean to be mathematically a piece of art. It is not easy to create new art; civilized (or cultured)? One cannot expect a but let us try, when transmitting mathematics, to sharp, precise, mathematical definition. But preserve its artistic content. this concept does have enough substance to be 0. Shisha definitely meaningful. University of Rhode Island 2. A mathematically civilized person is one who (a) has some, perhaps slight and superficial, Bineit University notion about all major areas of mathematics. The Council of the AMS, in tabling a resolution (b) has a thorough understanding of at least one criticizing Israel for closing Birzeit University on mathematical field, or subfield, or sub-subfield. the West Bank, has wisely chosen not to involve (c) in familiar areas, can tell when a given the Society in fundamentally political issues. It definition, theorem or proof makes sense and is is unfortunate that John Kelley chose to resign clear, and can point out when it is not. from the AMS because of the Council's decision (d) knows how to express mathematical ideas, [Notices, June 1983, page 402]. One of us was orally and in writing, correctly, rigorously and formerly a participant in Kelley's seminars who clearly. retains fond memories of his gracious treatment of graduate students and deeply regrets both (e) has a reasonably good knowledge of the Kelley's resignation and the issues history of mathematics. that divide us. But the Council decision was both right in (f) has a sense of proportion; knows, in a given principle and will serve to minimize resignations context, how much weight to give to a topic or and pointless dissension within the Society. argument. While the Council showed wisdom, the same (g) more generally, has good mathematical taste cannot be said for the AMS Human Rights and judgment; knows what is important and what Committee, whose resolution criticizing Israel for is not; enhances mathematical knowledge and resorting to "collective punishment" was tabled induces in listeners a feeling of aesthetic pleasure. by the Council. If "collective punishment" A mathematically civilized person is not neces­ meant sending people to jail without charging sarily a mathematical virtuoso, but is very similar or convicting them individually, we could all to a person having a deep appreciation of art. condemn it without reservation or detailed inquiry Why say "similar"? Such a person has a deep into circumstances. The "illegal acts" of Birzeit appreciation of the art of mathematics. students included planting bombs on buses, closing 3. Should we encourage mathematical eulture? highways and the killing and wounding of civilians, Of eourse. Why? and these actions were encouraged by members Mathematies develops not merely by the few of the Birzeit faculty and administration. While who create new theories. Their audience is just we can all regret that Israel closed a campus,

603 this decision was only made after numerous acts [1979]letter ends "Do we wish to ostracize Soviet of violence, repeated warnings and temporary scientists ... ? Must we join the ranks of the new closings that finally convinced Israel that Birzeit cold warriors? We think not." was so dominated by those seeking violent A human rights agenda may be a dangerous confrontations with the surrounding society as trap for the Society because some will use it to to be incapable of serving its educational goals. promote their own highly selective morality. If Many of us who live in a more secure society the Society cannot confine itself to protesting than Israel would still, if we were Israelis, protest against what the vast majority see as the most the closing of a campus, almost regardless of egregious violations of human rights and academic the provocation, and some Israelis are extremely freedom, it would be better to delete the question angry about their government's policy. But in a of human rights from the AMS agenda and for world in which human rights violations typically mathematicians to speak only as individuals. mean mass murder, torture, disappearance and Malcolm J. Sherman imprisonment without charges, it is farfetched to Boris Korenblum treat the closing of a campus that was a center SUNY, Albany of terrorism as a human rights issue. There is no reason to suppose that Israel's announced I was saddened to read in the June Notices of reasons for closing Birzeit were a pretext for J. L. Kelley's resignation from the AMS in reaction other motives. When the West Bank was to the Council's refusal to act on the Human under Jordanian occupation Birzeit was only a Rights Committee recommendation on the Israeli secondary school. Its expansion and upgrading closing of Birzeit University. to a university took place under and with the Kelley writes of ending his 44-year membership, encouragement of Israel. remembering how in the "early 1940s there were Those who, like John Kelley, most vehemently people who wanted to 'avoid controversy' and protest against the closing of Birzeit are fun­ others who wanted not to know." Kelley surely damentally objecting to the Israeli occupation does not mean to include himself in either of these itself, not to the particular policies that Israel groups, although he clearly did not resign in the is following. Few issues are less appropriate for early 1940s. Must we assume that he has grown the Society than the rights and wrongs of recent in wisdom, in political and ethical awareness, and Middle East history, and the circumstances that in commitment to humanity over the years? Or led to Israeli control over the West Bank. may the change in Kelley's stand be somehow Kelley's perspective is an especially offensive related to the reversal in the real-world position one. After stating that "the facts of the of the same people whose wives, children and Israeli occupation are generally well known," he elderly parents were being helplessly, brutally and "remember[s] with queasy horror that in the very systematically murdered "in the early 1940s" and early 1940s there were people who wanted to 'avoid who are now resisting, so far successfully, repeated controversy' and others who wanted not to know attempts at such annihilation? the facts about the occupied territories." Kelley Kelley is "at a loss to explain" the Coun­ thus compares the West Bank to Poland under cil's refusal "to apply its previous standards German occupation, and compares the Israelis to (concerning the welfare and academic freedom of Nazis. Kelley is echoing, whether consciously or mathematicians and mathematical programs) to not, Soviet-Arab propaganda equating Israel with the Israeli treatment of Birzeit." The difficulty Nazi Germany. {Most members of the AMS will in explaining this is seemingly compounded by recall that during the 1980 presidential campaign the Secretary's unsuccessful attempts to write a the United States, to its great embarrassment, summary of the arguments ''which is regarded as publicly repudiated its vote in the United Nations fair and accurate by all parties." Indeed, the issue in support of an Arab-Eastern Bloc-Third World is a highly complex one, which has proven highly resolution condemning Israel. What is less well perplexing recently to contemporary historians, known is the content of that resolution, which sociologists and political scientists. accused Israel of violating the Geneva convention Let me suggest briefly two of the many factors that outlawed genocidal occupational policies such which [I believe] go into an explanation of the as those followed by Hitler in Poland.) Council's inaction. Kelley is promoting a political agenda as First, the "facts of the Israeli occupation" which opposed to applying even-handed standards. In Kelley is so certain are "generally well known" the October 1979 Notices, page 398, Kelley was and "easily obtainable by any literate person with one of six mathematicians who objected to the access to a decent library" are far from being either conclusions and to the very publication of an of these. We mathematicians ought to know better article on Soviet anti-Semitism. Kelley and his than anyone the need to approach with suspicion colleagues conceded that there was a "prima facie "generally well known facts." Sometimes we case of anti-Semitic activity by a few Soviet seem to forget to apply our critical ability to mathematicians," but they denied that anti­ nonmathematical "facts" we would like to believe Semitism was an official Soviet policy. Kelley's for one reason or another. (This is true of

604 mathematical facts as well, but that is not the ... I hope Professor Kelley can understand and issue we are discussing.) Particularly in light of appreciate these issues, and that he will reconsider the by now well-documented falsification of facts, his resignation from the Society. figures, and even photographs which took place David Mescheloff in the popular press and the media only a year Moshav Hemed, Israel ago during the Israeli anti-terrorist campaign in Lebanon (see, for example, a report on the press Mathematics Research Journals which appeared in Newsweek), any truly literate The August 1983 issue of the Notices contains and aware person must know that what he reads the annual backlog survey of mathematics re­ derogatorily about Israel's actions must be read search journals. This survey, covering mostly critically. Please note-I am not suggesting that North American journals only, shows that ~ach Israel can do no wrong or should not be criticized. year we print 77,490+ pages of research mathe­ I only question the "well known" nature of the matics! What has our profession wrought? If one "facts" to which Kelley refers. assumes, generously, that 100 really significant In the case of Birzeit, the Human Rights mathematical results are obtained each year, the Committee was quite right in calling the closing system is set up so that one is expected to ''what appears from a distance" to be an unjust plough through about 775 pages of pedestrian collective punishment. Closer examination reveals mathematics to find one key result. that the other universities and colleges on the A. Bruce Clarke West Bank have not been closed down, for they Western Michigan engage in "the educational process." Birzeit has University been a hot-bed of radicalism which has attained symbolic status beyond the borders of Israel, has drawn over a third of its faculty from America and Europe, and whose leaders speak openly of being "drawn to Birzeit to support the Palestinian cause." Serious students are afraid or intimidated from speaking out against the PLO and its campus supporters, whose official aim is the destruction of Israel (see Israel's Birzeit University: A center for Palestinian Nationalism, by Staughton Clark, in Change magazine, July/August 1981, pages 50- 52). Student demonstrations may be generally ignored in the U.S., but Israel, where terrorist attacks are all too real, and which is still officially in a state of war with some twenty Arab states, can not permit organized support for the PLO. Thus rejection of the proposed resolution is not so hard to explain in terms of the "facts" alone. But a second factor plays a role here, too. There is a ... growth in popularity in intellectual Policy on Letters to the Editor liberal circles ... of a multi-faceted anti-Zionism. Letters submitted for publication in the Notices are While this is clearly different from the rightist reviewed by the Editorial Committee, whose task is anti-Semitism of decades ago, which has gone to determine which ones are suitable for publication. The publication schedule requires from two to four out of fashion, its denial of legitimacy to the months between receipt of the letter in Providence and Jewish state (remember, for example the U.N. publication of the earliest issue of the Notices in which resolution equating Zionism with racism!) is all it could appear. too reminiscent of the denial by anti-Semitic Publication decisions are ultimately made by majority ideology of the legitimacy of the existence of Jews vote of the Editorial Committee, with ample provision (see the proceedings of a symposium on Anti­ for prior discussion by committee members, by mail or at meetings. Because of this discussion period, some Semitism and Anti-Zionism, held last November letters may require as much as seven months before a by the International Center for the Study of Anti­ final decision is made. Semitism of the Hebrew University of Jerusalem, The committee reserves the right to edit letters. for further discussion of the relationships between The Notices does not ordinarily publish complaints these two phenomena). This similarly frightens about reviews of books or articles, although rebuttals Jews and others, who remember, as does Kelley, and correspondence concerning reviews in the Bulletin "the facts about the occupied territories in the of the American Mathematical Society will be considered early 1940s." Indeed, Kelley's terminology, which for publication. seems to be chosen so as to imply a moral equation Letters should be mailed to the Editor of the between the Nazis' brutal dehumanization and Notices, American Mathematical Society, Post Office Box 6248, Providence, Rhode Island 02940, and will be murder of Jews and Israel's actions, is of the same acknowledged on receipt. frightening kind.

605 News and Announcements

MacArthur Prize Fellows Fellowship for the twelve-month period beginning September 1, 1984. This Fellowship will be The John D. and Catherine T. MacArthur supported jointly by the American Mathematical Foundation has announced the selection of four­ Society, the Mathematical Association of America, teen new MacArthur Fellows. Richard Schoen, and the Society for Industrial and Applied Mathe­ University of California, Berkeley, and Karen matics; it is one of some thirty similar fellowships Uhlenbeck, University of Chicago, are the two supported by scientific societies in a program mathematical scientists in the present group. administered by the American Association for The appointments cover five years and carry the Advancement of Science. The 1984-1985 total stipends of $172,000 in Schoen's case and stipend for the AMS-MAA-SIAM Science Fellowship $204,000 in Uhlenbeck's (the awards va.rY with the is $26,000, which may be supplemented by a small age of the recipient and range from $24,000 to amount toward relocation and travel expenses, $60,000 per year). and possibly even by sabbatical salary or other Richard Schoen was born in Celina, Ohio on employer contributions. October 23, 1950. He earned his Ph.D. from Congressional Science Fellows spend their fel­ Stanford University in 1976. During 1978-1979 lowship year working on the staff of a member of he was at the Courant Institute of Mathematical Congress or on the staff of the Congressional Office Sciences, New York University. Schoen works of Technology Assessment. The AAAS collects in­ on global nonlinear partial differential equations formation on the availability of such positions with applications to differential geometry. He and, following an intensive two-week orientation collaborated with S. T. Yau in solving the positive program under the direction of the AAAS, each mass and action conjectures in relativity. He Fellow's assignment is worked out by the Fellow is currently working on regularity theorems for and the congressional office concerned. The AAAS harmonic maps. provides advice and assistance during the entire Karen Uhlenbeck was born in Cleveland, Ohio program, and communicates on a regular basis on August 24, 1942. She received her Ph.D. from with each Fellow throughout the year. Detailed Brandeis University in 1968. She was previously information on the program is available from affiliated with the University of illinois, Chicago AAAS Congressional Science Fellow Program, 1776 (1976-1983), the University of illinois, Urbana­ Massachusetts Avenue, N.W., Washington, D.C. Champaign (1971-1975), and was a member of 20036; 202-467-4475. The Institute for Advanced Study (1979-1980). The AMS-MAA-SIAM Congressional Science Fel­ Uhlenbeck has contributed to geometry and to lowship was held by EDMUND GREGORY LEE partial differential equations. Her work has in 1978-1979 (Dr. Lee worked on the staff of had applications to the foundations of high­ the Subcommittee on the Environment and the energy theoretical physics and to topology in four Atmosphere of the House Committee on Science dimensions. and Technology), by RoBERT T. SMYTHE in 1979-1980 (Dr. Smythe worked on the staff of London Mathematical Society congressman George E. Brown, D-Calif., then Awards 1983 Prizes chairman of the Subcommittee on Science, Re­ search and Technology of the House Committee The London Mathematical Society has an­ on Science and Technology), and in 1980-1981 nounced the following awards: by CHERYL G. TROPF (Dr. Tropf worked on the The De Morgan Medal is awarded to K. F. Roth majority staff of the Subcommittee on Science, for his contributions to and influence on number Technology and Space of the Senate Committee theory. on Commerce, Science and Transportation). The AMS-MAA-SIAM Fellowship was vacant in 1981- The Junior Berwick Prize is awarded to D. H. 1982. JoHN T. CHu held the Fellowship in 1982- Hamilton for his work in function theory. 1983 and worked on the staff of Senator Daniel K. Junior Whitehead Prizes are awarded to J. B. Inouye, D-Hawaii. The 1983-1984 Fellowship has Paris for his work in set theory and to A. A. been awarded to CHARLES G. BIRD of the General Ranicki for his work in algebraic topology. Motors Research Laboratories (as reported in the June 1983 Notices, page 394). AMS-MAA-SIAM These fellowships are awarded, without regard Congressional Science Fellowship to age, sex, race, or citizenship, to mathematical 1984-1985 scientists who have received a doctoral degree. Handicapped persons and members of minority Applications are invited from candidates in the groups are encouraged to apply. The selection mathematical sciences for a Congressional Science is made by a panel of the AMS-MAA-SIAM Joint

606 Concerns Committee in Mathematics. Applicants universities and research institutes. Application should demonstrate exceptional competence in is open to citizens and permanent residents of some areas of the mathematical sciences, should the United States regardless of national origin, have a broad scientific and technical background sex, or religious affiliation. The number of grants and a strong interest in the uses to which depends on available funding. The Program has mathematics and other sciences may be put for three components; application should be made to the solution of societal problems; in addition, they the Graduate Program, the Research Program, should be articulate, literate, flexible and able to or to the Distinguished Scholar Exchange Pro­ work effectively with a wide variety of people. gram. Inquiries should be addressed to the An application should contain a statement CSCPRC, National Academy of Sciences, 2101 describing the applicant's reasons for wanting to Constitution Avenue, N.W., Washington, DC be a Congressional Science Fellow, a summary 20418. Postmark/mailing deadline for applica­ of the applicant's qualifications, and should be tions is November 7, 1983. accompanied by a detailed resume. In addition, each applicant should ask three people, who AMS Massera Fund are informed about the candidate's competence and suitability for the award, to send letters of A delegation from the Societe Mathematique recommendation. de France, the Sociedad Matematica Mexicana, Applications should be sent to the Con­ and the American Mathematical Society plans to ference Board of the Mathematical Sciences, 1529 visit Uruguay in an effort to secure the freedom of Eighteenth Street, N.W., Washington, D.C. 20036. Jose Luis Massera, a professor of mathematics of The deadline for receipt of completed applications distinction who has been imprisoned since 1975, (including letters of reference) is January 1, 1984. apparently for political reasons. (See Notices, The award is expected to be announced by February 1981, page 165.) The representative of February 15, 1984. the AMS is Professor Mary Gray. The Society is paying part of her expenses and is soliciting Karel deLeeuw Memorial Fund contributions from individuals to pay the rest. The order of magnitude of anticipated expenses The summer of 1983 marks the fifth anniversary is $3,000. Contributions should be made to the of the tragic murder of Karel deLeeuw. In Society and sent to the AMS Massera Fund c/o order to honor his memory and to carry on Dr. W. J. LeVeque, P. 0. Box 6248, Providence, in his tradition, a Memorial Fund was set Rhode Island 02940. Please write "Massera Fund" up. The fund has already been used for on the check. It is believed that the contributions several purposes, including a teaching award are tax deductible. for graduate students and support for innovative approaches to undergraduate teaching. This year National Research Council the Karel deLeeuw Memorial Lecture Series was Minority Fellowships inaugurated. The lectures are not intended to be specialized or technical, but rather of broad Thirty-five minority scholars have been selected interest and accessibility. The first speaker was by the National Research Council to receive year­ Andre Weil of the Institute for Advanced Study long postdoctoral fellowships. They represent who gave a lecture entitled Euler and number the fourth group of recipients, now totaling theory. Anyone wishing to contribute to the 140, of the annual Postdoctoral Fellowships deLeeuw Memorial Fund should send a check for Minorities Program, sponsored by the Ford payable to Stanford University to the Department Foundation and administered by the National of Mathematics, Stanford University, Stanford, Research Council. One of the thirty-five awards California 94305, with a note that it is intended is in the mathematical sciences. for the deLeeuw Fund. The thirty-five were selected in a national competition from 183 minority citizens who are National Exchange Program with current or prospective university teachers. Panels the People's Republic of China of humanities scholars and scientists, convened by the Research Council, evaluated the applications. The Committee on Scholarly Communica­ Plans for the 1984 fellowship competition tion with the People's Republic of China are now under way. Further information and (CSCPRC) announces opportunities under the applications will be available after September National Program for Advanced Study, Re­ 1, 1983, from the Fellowship Office, National search, and Scholarly Exchange with the PRC Research Council, 2101 Constitution Avenue, for graduate students and postdoctoral scholars in N.W., Washington, DC 20418. the natural sciences, engineering, social sciences, The 1983 recipient in the mathematical sciences and humanities for 1984-1985. This Program is Alain A. Lewis of the University of Singapore makes possible long-term study and research, who will be studying at Cornell University. or lecturing and collegial dialogue at Chinese -NRC News Release

607 Smithsonian Opportunities in the course objectives, instructional modes, and lists of History of Science and Technology topics included. Each topic is weighted in terms of a suggested percent of time dedicated to the The Smithsonian Institution announces its pro­ subject. gram of research training in higher education in This publication is available for $7.50 for ACM the History of Science and Technology for 1984- members and $10.00 for nonmembers, prepaid, 1985. Smithsonian Fellowships are awarded to from ACM Order Department, P. 0. Box 64145, support independent research, in residence at the Baltimore, Maryland 21264, Order #201830. Smithsonian, related to research interests of the -ACM News Release Institution's professional staff and using the In­ stitution's collections, facilities, and laboratories. Fulbright Scholar-in-Residence Program Six to twelve month pre- and postdoctoral fellow­ ship appointments and ten-week graduate student The Scholar-in-Residence Program is part of appointments are awarded. Proposals for research the Fulbright Program, which is funded and may be made in fields in which the Institution has administered by the United States Information research strength: history of mathematics, physi­ Agency. The purposes of the program are cal sciences, medicine and pharmacy, engineering, to strengthen the international dimension of transportation, agriculture, air and space, electri­ teaching programs at institutions with limited cal technology, and the history of science in opportunities to receive foreign scholars, and to America. develop or enrich established area studies or Applications are due by January 15, 1984. international programs. Institutions with one Stipends supporting the awards are: $18,000 per of these goals in mind are invited to submit year plus allowances for postdoctoral fellows; a proposal for hosting a scholar from abroad $11,000 per year plus allowances for predoctoral as a visiting Fulbright Scholar-in-Residence for fellows; and $2,000 for graduate students for 1984-1985. the ten-week period of appointment. Pre- and Grants cover international travel for the scholar, postdoctoral stipends and allowances are prorated maintenance stipends of approximately $1,750 per on a monthly basis for periods of less than one month, limited funds for books and educational year. materials, and basic medical insurance. Appoint­ Awards are based on merit. Smithsonian ments may be for one quarter, a semester, or a Fellowships are open to all qualified individuals full academic year. without reference to race, color, religion, sex, There will be two separate competitions, ac­ national origin, age, or condition of handicap of cording to the type of institution: Those which any applicant. For more information and applica­ have not had frequent opportunities to receive tion forms, please write: Office of Fellowships scholars from abroad as lecturers and researchers and Grants, 3300 L'Enfant Plaza, Smithsonian and are introducing programs with an interna­ Institution, Washington, D.C. 20560. Please indi­ tional perspective on their campuses, including cate the particular area of the proposed research four-year liberal arts and community colleges; and give the dates of degrees received or expected. those which have established an international or area studies program and are developing or Infonnation Systems enriching their program. In their proposals in­ Curriculum Recommendations stitutions can document their past activities and current planning. The Association for Computing Machinery has The Council for International Exchange of published a new set of curriculum recommenda­ Scholars (CIES) assists the United States Informa­ tions for colleges and universities entitled Infor­ tion Agency in the administration of the part of mation systems curriculum recommendations for the Fulbright Program which provides grants for the 80s: Undergraduate and graduate programs. senior scholars and lecturers. The deadline for The recommendations are based on a report of receipt of completed proposals at CIES is October the ACM Curriculum Committee on Information 15, 1983. Proposal forms and further details may Systems, chaired by Jay F. Nunamaker of the be obtained from CIES, 11 Dupont Circle, Suite University of Arizona. 300, Washington, D.C. 20036. The report is an update of ACM's 1972 and 1973 curriculum recommendations for bachelor's, Institute for Retraining master's, and doctoral level programs in infor­ in Computer Science mation systems based on advances in the field over the past ten years. The report emphasizes Under the auspices of the Joint ACM/MAA the continuing need for education related to Committee on Retraining for Computer Science, the definition, analysis, design, construction and a Summer Institute for retraining college faculty management of in~ormation systems in organiza­ members to teach Computer Science has been tions. The structures of bachelor's and master's established at Clarkson College. The first class level programs are described with course outlines, began in June 1983 and new classes are planned

608 for 1984. The retraining program consists of to perform research on problems largely of two summers in residence at Clarkson plus a their own choosing yet compatible with the large programming project to be completed at research interests of the supporting laboratory. the home institution during the intervening year. Initiated in 1954, the Associateship Programs In addition, participants are expected to teach have contributed to the career development of a Computer Science course during that year. over 3,800 scientists ranging from recent Ph.D. The curriculum emphasizes modern methods of recipients to distinguished senior scientists. structured programming and top-down design plus Approximately 250 new full-time associateships a strong exposure to the fundamental concepts in will be awarded on a competitive basis in the growing field of Computer Science. Course 1984 for research in chemistry, engineering, and syllabi take full advantage of the Mathematics mathematics, and in the earth, environmental, background of the participants. physical, space, and life sciences. Most of the The faculty consists of established Computer programs are open to both U.S. and non-U.S. Scientists with solid research records who are nationals, and to both recent Ph.D. degree holders outstanding teachers. Among the faculty mem­ and senior investigators. bers teaching in 1983 and/or 1984 are M. Clancy Awards are made for one or two years; senior (University of California, Berkeley), S. Drysdale applicants who have held the doctorate at least (Dartmouth College), M. Furst (Carnegie-Mellon five years may request shorter tenures. Stipends University), J. Gilbert (Cornell University), D. for the 1984 program year will range from $24,500 Gries (Cornell University), G. Levin (Arizona a year for recent Ph.D.'s up to approximately State University), M. Sipser (Massachusetts In­ $50,000 a year for senior associates. A stipend stitute of Technology), and D. Wall (DEC Re­ supplement up to $5,000 may be available to search). regular (not senior) awardees holding recognized At the end of the first summer, participants doctoral degrees in those disciplines wherein the are qualified to teach a two-semester introductory number of degrees conferred by U.S. graduate sequence in Programming and Computer Science, schools is significantly below the current demand. including some material on Data Structures. Mter In the 1983 program year these areas have the full program, they will be qualified to teach been engineering, computer science, space-related about half of the ACM Core Curriculum in Com­ biomedical science, and petroleum-related earth puter Science (ACM Curriculum '78, Communica­ sciences. tions of the ACM, March 1979, pages 147-166). Applications to the National Research Council This includes most of the material for a Computer must be postmarked no later than January 15, Science minor in a mathematics department as 1984. Initial awards will be announced in March recommended in the 1981 CUPM Report, Recom­ and April followed by awards to alternates later. mendations for a General Mathematical Sciences Information on specific research opportunities Program, MAA, 1981. Also they will have learned a and federal laboratories, as well as application considerable amount of Computer Science beyond materials, may be obtained from Associateship this level. Programs, Office of Scientific and Engineering Participants are expected to have some Personnel, JH 608-D3, National Research Council, familiarity with programming and a personal 2101 Constitution Avenue, N.W., Washington, commitment to continue in college teaching. D.C. 20418; 202-334-2760. -NRC News Release The first class was supported by a grant from the Alfred P. Sloan Foundation. Additional funding is being sought to partially defray the cost for participants in the new class. For more information and application forms write to Ed Dubinsky, Department of Mathe­ matics and Computer Science, Clarkson College, Potsdam, New York 13676.

NRC Senior and Postdoctoral Research Assoeiateships

The National Research Council (NRC) has announced the 1984 Postdoctoral, Resident, and Cooperative Research Associateship Programs for research in the sciences and engineering to be conducted in behalf of nineteen federal agencies or research institutions, whose laboratories are located throughout the United States. The programs provide Ph.D. scientists and engineers of unusual promise and ability with opportunities

609 National Science Foundation News & Reports

The Role of NSF in Precollege state of precollege education in mathematics Mathematics, Science, science,.~~ .technology, and in view of the special and Technology Education responsibilities of the NSF for science education at alll~vels, it is incumbent upon the NSF to develop The National Science Board recently adopted specific programs as a regular, consistent part a statement concerning the role of the NSF in of NSF activity directed at improving precollege science education at the precollege level. Under science education. These programs should draw upon the experience and expertise possessed by the National Science Foundation Act the NSF has specific responsibility ''to initiate :md support the NSF. ... programs to strengthen ... science education The NSB expects the NSF to provide leadership ... at all levels." Accordingly the National to the Nation in precollege science education S~ience Board hereby affirms 'that precollege by (1) developing new and productive means of improving precollege science education with scie~ce edu~ation is a high-priority activity of the NatiOnal Science Foundation. the strong involvement of classroom te~chers· (2) communicating those methods to other in~ The NSF has an important role in precollege terested parties; (3) conducting appropriate re­ mathematics and science education because of search programs to improve understanding of the its special responsibilities for the vitality of processes of teaching, learning, and evaluating American science and engineering. The following in sc~e~ce education; (4) regularly evaluating the ch~~c~eris.tics should guide the NSF in selecting conditiOn of precollege science education in our actiVIties m precollege science education: NSF Nation's sc~ools; (5) advising appropriate govern­ s~ould ma~e _use of its unique relationship ~ent a~encie~ of that condition and disseminating ~th the scien~Ific community in any precollege Its findmgs Widely; and (6) operating certain pro­ science educatiOn program it undertakes; NSF grams that are appropriate to the Foundation's should select projects and activities in precollege position, expertise, experience, and resources. education on the basis of the principles of -National Science Board excellence and should not administer formula or other forms of grant programs that might preclude NSF, Turkish Research Council application of these principles; NSF should seek to use its resources in ways that exert high leverage. Sign Science, Technology Pact Examples of high leverage activities include The NSF and the Scientific and Technical selective teacher training programs and model Reseru:ch Council of the Republic of Turkey course content development in mathematics . d ' have signed a memorandum of understanding for science, an technology. collaboration in science and technology. The five­ -National Science Board year agreement is the first such mutual effort between the two countries. Program in Precollege Mathematics The cooperation will include projects of basic Science, and Technology ' and applied research of mutual interest and educa­ tion ~n science and technology. The agreement A program in precollege science education has also mcludes foreign visits and attendance at been recently adopted by the National Science intern~tional meetings, cooperation in the holding Board (NSB). It states that in view of the present of semmars and workshops on scientific and tech­ nological interest, and an exchange of information Acting Head of the Mathematical and scientists. The memorandum implements Sciences Section ll: bilateral agreement in science and technology fu July Judith S. Sunley was appointed Acting signed between the two countries in Ankara on Head of the Mathematical Sciences Section of February 21, 1983. -NSF News Release the Division of Mathematical and Computer Sciences of the National Science Foundation. u.s.-China Cooperative Seienee Program Dr. Sunley was educated at the University of Michigan and received her Ph.D. from the The annual meeting of the U. S.-China Joint University of Maryland. Her research interests Working Group for Cooperation in the Basic are algebra and number theory. fu 1971 Sciences wa:s held in May 1983. The NSF she joined the department of mathematics of and its three Chinese cooperating organizations :unerican University as an assistant professor, (the Chinese Academy of Sciences, the Chinese m 1975 she was promoted to associate professor. Academy of Social Sciences, and the Ministry of Education) have agreed to further expand

610 the scope of the U. S.-China Cooperative Science These changes are announced in NSF's Impor­ program. tant Notice No. 90. A copy of the Notice and The program will continue to emphasize NSF's revised Grant General Conditions. and an cooperative research projects. It will also support explanatory brochure entitled The NSF Grant a limited number of jointly organized seminars Relationship may be ordered on the Publica­ and short-term visits by U.S. scientists to China tions Order Form. Questions concerning NSF's for the purpose of completing cooperative research redefined grant relationship and associated grantee proposals. responsibilities should be directed to NSF's Divi­ Fields of science in which proposals may be sion of Grants and Contracts; 202-357-7842. submitted are: plant sciences; earth sciences; -NSF Bulletin engineering sciences (heat transfer and fluid mechanics); information science (artificial in­ Number of New Seienee, Engineering telligence, pattern recognition, basic computer Ph.D.'s Increased in 1981 sciences); international studies; archaeology and paleoanthropology; astronomy; chemistry of A nine-year decline in science and engineering natural products; linguistics; materials sciences; doctorate production ended in 1981 when the system analysis. number increased 400 from the previous year Proposals may be submitted at any time. to 17,600, according to a new report by the Further details, guidelines and information on the NSF. Preliminary data for 1982 show the number current scope of the program may be obtained of science and engineering degrees virtually from Pierre Perrolle or Alexander DeAngelis, unchanged from 1981. Division of International Programs; 202-357-7393. -NSF Bulletin The report, titled Science and Engineering Doctorates, 1960-1981, also found that the number of science and engineering doctorates Cooperative Research with Eastern Europe granted to women has increased yearly, from 400 NSF's Eastern Europe Cooperative Science in 1960 to 4,000 in 1981. Women doctorates were programs seek to foster and support scientific concentrated in the life and social sciences. and technological cooperation between the U.S. The report provides such information as sex, and Bulgaria, Hungary, and Romania. race and citizenship of new doctorates as well The program offers financial support for three as their postgraduate plans. Also included types of activities: cooperative research projects, are rank-ordered lists of the 100 institutions seminars and workshops, and scientific visits for that awarded the most science and engineering planning purposes. Proposals for joint research doctorates during the 1960-1981 period and the should be submitted at least nine months before 300 baccalaureate institutions with the largest the requested starting date; for seminars twelve number of science and engineering doctorate­ months, and for short-term visits, six months. holding alumni. Copies of the report (NSF 83- Further information may be obtained from 309) are available from the Division of Science Deborah Wince, Division of International Pro­ Resources Studies, National Science Foundation, grams; 202-357-9516. -NSF Bulletin Washington, DC 20550; 202-634-4622. -NSF News Release Changes in Administration of NSF Grants Swiss National Seienee NSF is implementing significant changes in Foundation Fellowships policies and procedures for administering NSF grants. These changes are the result of a The Swiss National Science Foundation (SNSF) redefinition of the NSF-grantee relationship to annually awards a few International Postdoctoral emphasize grantee responsibilities and to minimize Fellowships for tenure in Switzerland, normally NSF involvement in the management of grant­ for one year, to American scientists working supported activities. in the mathematical, physical, astronomical, Under the new NSF-grantee relationship, atmospheric, earth, or engineering sciences. grantees will be given authority to approve Recipients must be under the age of 36 years at many actions and expenditures previously requir­ the beginning of fellowship tenure. ing approval by NSF. In order to exercise this authority, grantees must establish an Organiza­ Applications for fellowships with tenure begin­ tional Prior Approval System which complies with ning between September 1, 1984, and April 1, certain standards. This redefinition concept in­ 1985, must be completed and returned to NSF by volves changes which supplement and in some October 3, 1983. Applicants can expect to learn instances supersede certain provisions of Grants of decisions directly from the SNSF in July 1984. for Scientific and Engineering Research (NSF 81- Application forms may be obtained from 79) and the NSF Grant Policy Manual (NSF 77-47, Warren Thompson, Division of International as revised). Programs; 202-357-9700. -NSF Bulletin

611 NSF Awards to Purchase Scientific Corporate Support Computing Research Equipment of Academic Research Higher than Generally Believed The National Science Foundation (NSF) has an­ nounced the award of approximately $850,000 for Corporate support of academic research in the purchase of computing equipment to twenty­ the U.S. is significantly higher than generally is two institutions having graduate programs in believed, and there has been a 10-year upward mathematics, applied mathematics and statistics. trend in this activity, the National Science Board The awards are made to enhance the quality (NSB) said in a report to the President and the and productivity of research activities by provid­ Congress just released. The 25-member NSB is ing access to appropriate computing equipment. the policymaking body of the National Science They continue an effort that began last year under Foundation. The report said these findings are all supervision of the NSF's Mathematical Sciences the more remarkable because of several downturns Section. in the business climate during this period. A broad-based panel of mathematics scientists The 33-page report, University-industry re­ helped the NSF review and evaluate the proposals. search relationships: Myths, realities and poten­ The number of proposals that could receive tials, states that ties between industry and educa­ support was expanded considerably because many tional institutions have been numerous and con­ of the awardees received significant contributions structive since the turn of the century. from other government agencies, institutional In most recent public discussions of industry­ sources and, in a substantial number of cases, university relationships, a base figure of between manufacturers of computing equipment. three and four percent of academic research and The following institutions will receive awards: development is attributed to industrial sources, University of Alabama, Huntsville; University the report states. However, the study found of Arizona; Brown University; University of that this significantly underestimates industrial California, Los Angeles; City University of New support for academic research and graduate York, City College; City University of New student support. York, Graduate School and University Center; If universities move closer to a partnership with Clarkson College of Technology; Cornell Univer­ industry, more resources can become available, but sity; Harvard University (2 awards); University the university may relinquish some of its unique of Houston; Louisiana State University; Mas­ capabilities for unrestricted exploratory research sachusetts Institute of Technology; New Mexico and freedom of action, according to the report. State University; Princeton University; Purdue The primary requirement is not so much increased University; Rensselaer Polytechnic Institute; Rice partnership, but increased understanding of each University; University of South Carolina; Univer­ other's role. That is the ultimate basis for a sity of Virginia; University of Washington; and healthy strengthening of university and industry Yale University. -NSF News Release cooperation, the report concludes. Single copies of this report may be obtained Robotics and Automated Manufacturing from the U.S. Government Printing Office, Washington, D.C. 20402. -NSF News Release The Office of Interdisciplinary Research (OIR) in the Directorate for Engineering is coordinating Grants for Experimental a Program Announcement to encourage the Computer Science Research submission of proposals dealing with issues in robotics and automated manufacturing. The National Science Foundation (NSF) has Research issues include computers, sensors awarded grants totalling more than $13.1 million and controls, production research, mechanical to four universities to provide long-term support systems, systems problems, integrated systems for experimental computer science research in the design, multiple robot systems, and flexible United States. manufacturing systems. Interdisciplinary research The grants, made through NSF's Mathematical and systems oriented proposals are especially and Computer Sciences Division, are made to encouraged. address concerns about the shortage of computer OIR will coordinate the efforts of a number science Ph.D.'s available to industry and academia of current NSF programs which support robotics­ as well as the deterioration of U.S. facilities for related research. There are no deadlines for experimental computer science research. Over proposal submission. The Program Announce­ the next five years, the grants will support ment (NSF 83-34) may be requested from the university efforts to buy or upgrade computing Forms and Publications Unit. Further information equipment, provide professional and technical may be obtained from George Brosseau, Office of support staff, defray graduate student salaries Interdisciplinary Research; 202-357-9707. and cover other costs involved in maintaining -NSF Bulletin experimental computer research facilities.

612 The University of Maryland received a Projects will be supported through nationwide $4,547,577 grant to study, analyze and de­ competition in these areas: Models and Demonstra­ velop new procedures for solving problems in tions of programs for the continuing education image processing, numerical computation, and of teachers; Development of Materials, teaching knowledge-based systems which will exploit the aids, computer programs, software and systems capabilities of a special highly parallel multi­ and television based-materials, etc., to improve processor machine developed by university re­ science and mathematics teaching; Analysis of the .searchers. The University of Pennsylvania has precollege science and mathematics educational received $3,838,546 to enhance its capabilities in system; Dissemination of ideas and materials major research thrusts related to artificial intel­ for sustaining high quality precollege science ligence and robotics. A natural language research and mathematics teaching; and Applied Research group works very closely with a database group aimed at understanding how the processes of and is supported by a cognitive sciences center. A teaching and learning of precollege science and . newly developed robotics group is building on ex­ mathematics can be more effective. isting expertise in image processing and computer Eligible disciplines are limited to mathematics, graphics. engineering, the natural sciences (including biol­ Duke University, which has been awarded ogy, chemistry, atmospheric, earth and ocean $1,724,503, and the University of North Carolina, sciences, physics and astronomy) and computer which will get $3,048,000, plan the development science. of a joint center for Very Large Scale Integrated Proposals may be submitted at any time (VLSI) circuit research. They propose to work and should be prepared in accordance . with closely with a newly formed Microelectronics Cen­ the guidelines contained in Grants for Scientific ter of North Carolina and with local industry to and Engineering Research (NSF 81-79). This examine VLSI research issues from the level of publication is available from the NSF Forms and basic physical interaction through to the fabrica­ Publications Unit, National Science Foundation, tion of new special and general purpose architec­ 1800 G Street, N.W., Washington, D.C. 20550. tures. The two campuses will concentrate their re­ search on computer-aided design/computer-aided Current Program Direetors of the manufacturing (CAD/CAM) systems for VLSI design Mathematieal Seienees Seetion and on VLSI-based architectures. The grant also will enhance activities in computer graphics at Classical Analysis JACKRYFF the University of North Carolina. Modem Analysis FRANK GILFEATHER -NSF News Release Geometric Analysis Su-SHING CHEN Materials Development for Preeollege Topology & Foundations RALPH KRAUSE Seienee and Mathematies Algebra & Number Theory BERNARD McDoNALD The Materials Development for Precollege Applied Mathematics MELVYN CIMENT Science and Mathematics program addresses the JACK LAGNESE need to develop teacher capabilities in the critical Statistics & Probability JERRY SACKS areas of mathematics and science and improve Special Projects Program ALVIN THALER their instruction of students. Projects will be Drs. Ryff, Krause, and Thaler are permanent considered for teachers and instruction at all members of the staff; the others are referred precollege levels, from kindergarten through the to as rotators since they spend two or three twelfth grade. years at the Foundation and then return to their The program has a Fiscal Year 1983 budget of permanent positions. Dr. Ciment in on leave $12 million. The Fiscal Year 1984 budget will be from the National Bureau of Standards and the announced as soon as it is determined. others are all from universities: Dr. Gilfeather, Projects proposed under this program should University of Nebraska; Dr. Chen, University of support its objective of enlisting the best scientists Florida; Dr. McDonald, University of Oklahoma; and science educators to develop new or improved Dr. Lagnese, Georgetown University; and Dr. science and mathematics instruction materials Sacks, Northwestern University. and to perform related applied research, analysis and dissemination of materials and information.

613 Fairfield, October 28-29, 1983, Fairfield University Program for the 806th Meeting

The eight hundred and sixth meeting of the Michael Saks, Edward R. Scheinerman, Richard American Mathematical Society will be held at P. Stanley, and Herbert S. Wilf. Fairfield University in Fairfield, Connecticut, on Approximation theory and numerical analysis, Friday and Saturday, October 28 and 29, 1983. JoHN A. RouLIER, University of Connecticut. Invited addresses will be held in the auditorium The speakers include R. P. Gosselin, Myron of Gonzaga Hall. Sessions on Friday afternoon S. Henry, Andras Kro6, James T. Lewis, D. F. will be held in the Faculty Office Building and McAllister, Harry W. McLaughlin, Dennis D. Canisius Hall. Saturday sessions will be held in Pence, T. J. Rivlin, John A. Roulier, Oved Bannow Science Center and the School of Nursing. Shisha, Roy L. Streit, and D. Zwick. Topics in complex analysis, DoROTHY B. SHAFFER, Fairfield University. The speakers Invited Addresses include Roger W. Barnard, Louis Brickman, By invitation of the Committee to Select Hour B. A. Case, Peter Duren, Walter Hengartner, Y. J. Speakers for Eastern Sectional Meetings, there Leung, T. H. MacGregor, Peter A. McCoy, E. P. will be three invited one-hour addresses. The Merkes, David Minda, George Piranian, J. R. speakers, their affiliations, the titles of their talks, Quine, Maxwell 0. Reade, Burton Rodin, Glenn and the dates and times of presentation are as Schober, Herb Silverman, Evelyn M. Silvia, Ted follows: J. Suffridge, and Anna Tsao. JoHN L. HARER, University of Maryland, Contributed Papers College Park, The homology of the moduli space of curves, Saturday, 1:00 p.m. There will also be sessions for contributed ten­ JOHN HUBBARD, Cornell University and Har­ minute papers on Friday and Saturday afternoon. vard University, Dynamics of rational maps, Registration Saturday, 10:30 a.m. DANIEL J. KLEITMAN, Massachusetts Institute The meeting registration desk will be located of Technology, Independence and minimum in the Lobby of Gonzaga Hall, and will be open generating sets for collections of intervals, Friday from 12:30 p.m. to 5:30 p.m. on Friday, and from 1:15 p.m. 8:30 a.m. to 1:30 p.m. on Saturday. The registration fees are $10 for members, $16 for Special Sessions nonmembers, and $5 for students or unemployed mathematicians. By invitation of the same committee, there will be five special sessions of selected twenty-minute Petition Table papers. The topics of these special sessions, A petition table will be set up in the registration the names and affiliations of the mathematicians area. Additional information can be found in a arranging them, and the final lists of speakers are: box in the Louisville meeting announcement in Theory of infinite groups, BEN FINE, Fairfield this issue. University. The speakers include Robert Bieri, Richard Goldstein, R. C. Lyndon, John G. Accommodations Ratcliffe, Dennis Spellman, Carol Tretkoff, Marvin Rooms have been blocked at the Fairfield Tretkoff, Peter Waterman, and Kenneth Weston. Motor Inn. Individuals should have made Surfaces and three-manifolds, WILLIAM their own reservations, and identified themselves GoLDMAN, Massachusetts Institute of Technol­ as participants in the American Mathematical ogy and the University of Maryland, and JOHN L. Society's meeting at Fairfield University. The HARER. The speakers include William Abikoff, cut-off date for reservations was August 15, after Robert Brooks, R. Charney, Tim D. Cochran, which rooms were to be assigned on a space­ David Gabai, Jane Gilman, William M. Goldman, available basis. The rates listed below are subject Linda Keen, Irwin Kra, Larry Lok, Howard to possible change and do not include applicable Masur, John D. McCarthy, Lee Mosher, Patricia taxes. L. Sipe, and Scott Wolpert. Fairfield Motor Inn (1.6 Iniles) Combinatorics, DANIEL J. KLEITMAN. The 417 Post Road, Fairfield 06430 speakers include Michael 0. Albertson, Kenneth Telephone: 203-255-0491 Baclawski, Douglas Bauer, Kenneth A. Berman, Single $50.50 Double $60.50 Seth Chaiken, F. R. K. Chung, Paul H. Edelman, Ira Gessel, R. L. Graham, Curtis Greene, Joan P. Although rooms have not been blocked at Hutchinson, J. Kahn, Howard Kleiman, Jeffrey C. the following motels, they are included here for Lagarias, David R. Richman, Gian-Carlo Rota, information purposes.

614 FAIRFIELD UNIVERSITY CAMPUS

1. Faculty Office Building 3. Bannow Science Center 2. Canisius Hall 4. School of Nursing 5. Campus Center

FROM MERRITT PARKWAY- Take Exit 44 (Black Rock Turnpike); turn R. on Stillson Rd.; bear L. into N. Benson Rd. CONN. TURNPIKE FROM NEW HAVEN- Take Exit 22; turn R. on N. Benson Rd. CONN. TURNPIKE FROM NEW YORK- Take Exit 22; turn L. on Round Hill Rd.

Merritt Parkway Motor Inn-, ~

To New lla••en

615 Merritt Parkway Motor Inn (5 miles) For those driving to the meeting, Fairfield Black Rock Turnpike, Fairfield 06430 University is very close to Exit 22 of the Telephone: 203-259-5264 Connecticut Turnpike, and is about 10 minutes 44 Single or Double $43 from Exit of the Merritt Parkway. Since there is no scheduled airline service to Pequot Motor Inn (4.5 miles) Fairfield, participants are advised to obtain flights 3471 Post Road, Fairfield 06430 into LaGuardia or Kennedy Airports in New Telephone: 203-259-7885 York. From there, the Connecticut Limousine Single or Double $48 service is a reliable company whose cars and buses (The Pequot Motor Inn has a few family suites at depart from both these airports at intervals not $65 per night, which can accommodate groups of exceeding one hour. The ride to Fairfield takes four.) approximately 90 minutes. The cost is $18 one way or $35 round trip. Upon request, passengers Inn Westport New Englander (5 miles) are delivered to the Fairfield Motor Inn or to the 1595 Post Road East, Westport 06880 Westport New Englander Inn. Telephone: 203-259-5236 Food Single or Double $75 A list of restaurants located within easy driving Parking distance of the campus will be available at the Ample free parking will be available at several meeting registration desk. lots scattered about the campus. On Saturday, a popular cafe-style buffet brunch will be available to participants in the Campus Travel Center Dining Room for a cost of $3.85, payable The Metropolitan Transit Authority provides at the door. Participants should arrive between frequent commuter service between Grand Central 11:30-11:50 a.m. The scientific sessions have Station in New York City and New Haven, Con­ been scheduled to accommodate these boundary necticut, with Fairfield as an intermediate stop. conditions. The train station in Fairfield is approximately 1.5 Social Event miles from campus, and economical taxi service is available. Many trains on Amtrak's Northeast The Local Arrangements Committee has or­ corridor service (operating between Boston and ganized a beer party on Friday evening from 8:30 Washington) stop at Bridgeport, which is about p.m. to 11:00 p.m. in the Faculty Lounge in five miles from the Fairfield University campus. Bannow Science Center. Tickets are $4. The Taxi service is available from the station. Amtrak Committee requests that tickets be purchased tickets to Bridgeport are sold only from locations upon registration; however, tickets will be avail­ south of New York or east of New Haven. able at the door.

Presenters of Papers Numbers following the names indicate the speakers' positions on the program. •Invited one-hour lecturer *Special session speaker

*Abikoft', W., 75 *Goldstein, R., 65 *MacGregor, T. H., 80 * Saks, M., 62 *Albertson, M. 0., 12 Gordon, G., 87 *Masur, H., 70 * Scheinerman, E. R., 56 *Baclawski, K., 59 *Gosselin, R. P., 14 *McAllister, D. F., 52 *Schober, G., 19 *Barnard, R. W., 18 *Graham, R. L., 63 *McCarthy, J.D., 5 * Shisha, 0., 51 *McCoy, P. A., 42 Shiskowski, K., 26 *Bauer, D., 11 *Greene, C., 9 *Silverman, H., 84 *Berman, K. A., 8 •Harer, J. L., 55 *McLaughlin, H. W., 79 *Silvia, E. M., 43 *Bieri, R., 68 *Hengartner, W., 44 *Merkes, E. P., 45 *Sipe, P. L., 50 Boivin, A., 91 *Henry, M. S., 53 Mihram, G. A., 94 *Spellman, D., 35 *Brickman, L., 47 •Hubbard, J., 54 *Minda, D., 81 Spencer, D. E., 30 *Brooks, R., 6 *Hutchinson, J.P., 41 *Mosher, L., 49 *Stanley, R. P., 57 Brown, T. C., 86 *Kahn, J., 58 Moulis, E. J. Jr., 92 *Streit, R. L., 76 *Case, B. A., 85 *Keen, L., 73 Pearce, K., 90 * Suffridge, T. J., 22 *Chaiken, S., 38 Kidwell, M., 25 *Pence, D. D., 15 Temkin, B., 88 *Charney, R., 48 *Kleiman, H., 10 *Piranian, G., 82 Traldi, L., 28 * Tretkoft', C., 66 eKleitman, D. J., 1 *Quine, J. R., 23 *Chung, F. R. K., 40 * Tretkoft', M., 67 Rassias, G. M., 29 *Cochran, T. D., 4 *Kra, 1., 71 * Tsao, A., 24 Connor, A. C., 31 *Kro6, A., 17 *Ratcliffe, J. G., 64 *Waterman, P., 33 *Duren, P., 21 *Lagarias, J. C., 36 *Reade, M. 0., 46 *Weston, K., 32 *Edelman, P. H., 39 *Leung, Y. J., 20 *Richman, D. R., 61 * Wilf, H. S., 37 * Gabai, D., 3 *Lewis, J. T., 16 *Rivlin, T. J., 78 *Wolpert, S., 69 * Gessel, I., 60 *Lok, L., 72 *Rodin, B., 83 Zaidman, S., 93 *Gilman, J., 74 Lonergan, F. D., 27 *Rota, G.C., 7 Zimmerman, J., 89 *Goldman, W. M., 2 *Lyndon, R. C., 34 *Roulier, J. A., 13 *Zwick, D., 77

616 Program of the Sessions

The time limit for each contributed paper in the AMS general 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 AMS sessions at this meeting will be found in the October 1983 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.

Friday, October 28, 1983, 1:15 p.m. Invited Address Gonzaga Auditorium 1:15- 2:15 (1) Independence and minimum generating sets for collections of ~'ntervals. DANIEL J. KLEITMAN, Massachusetts Institute of Technology (806-05-70)

Friday, October 28, 1983, 2:30p.m. Special Session on Surfaces and Three-manifolds, I Faculty Office Building, Room 350 2:30- 2:50 (2) Local properties of representation spaces of surface groups. Preliminary report. WILLIAM M. GoLDMAN, Massachusetts Institute of Technology and the University of Maryland, College Park (806-99-89) 3:00- 3:20 (3) Detecting fibred links in 8 3. DAVID GABAI, University of Pennsylvania (806-57-38) 3:30- 3:50 (4) Geometric invariants of link cobordism. Preliminary report. TIM D. COCHRAN, Massachusetts Institute of Technology (806-57-01) 4:00- 4:20 (5) Automorphisms of surface mapping class groups-A recent theorem of N. Ivanov. Preliminary report. JOHN D. McCARTHY, Massachusetts Institute of Technology (806-99-93) 4:30- 4:50 (6) Branched coverings of 3-manifolds and the modular group. RoBERT BROOKS, Courant Institute of Mathematical Sciences, New York University, and University of Maryland, College Park (806-53-16)

Friday, October 28, 1983, 2:30p.m. Special Session on Combinatorics, I Canisius Hall, Room 107 2:30- 2:50 (7) Witt vectors and the algebra of necklaces. GrAN-CARLO ROTA, Massachusetts Institute of Technology (806-05-76) 3:00- 3:20 (8) Telephone problems with failures. KENNETH A. BERMAN* and MICHAEL HAWRYLYCZ, Wesleyan University (806-05-49) 3:30- 3:50 (9) Staircase Young tableaux and maximal chains in weak Bruhat orders. CuRTIS GREENE, Haverford College (806-05-80) 4:00- 4:20 (10) An improved algorithm for obtaining a hamilton circuit in a directed graph. Preliminary report. HowARD KLEIMAN, Queensborough Community College, City University of New York (806-05-17) 4:30- 4:50 (11) Extremal non-bipartite regular graphs of girth 4. DOUGLAS BAUER, Stevens Institute of Technology (806-05-28) 5:00- 5:20 (12) Homomorphisms of 3-chromatic graphs. Preliminary report. MICHAEL 0. ALBERTSON, Smith College (806-05-46)

Friday, October 28, 1983, 2:30 p.m. Special Session on Approximation Theory and Numerical Analysis, I Faculty Office Building, Room 348 2:30- 2:50 (13) Convex surface interpolation to grid data. JOHN A. RouLJER, University of Connecticut, Storrs (806-65-13) 3:00- 3:20 (14) On some non-linear spaces of approximating functions. R. P. GossELIN, University of Connecticut, Storrs (806-41-07) 3:30- 3:50 (15) Three dimensional elastica and splines. Preliminary report. DENNIS D. PENCE, University of Vermont (806-41-25) 4:00- 4:20 (16) On best partial bases. Preliminary report. JAMES T. LEWIS* and OVED SHISHA, University of Rhode Island (806-41-19) 4:30- 4:50 (17) On Chebyshev subspaces in the space of differentiable functions. Preliminary report. ANDRAS KRo6, Mathematical Institute of the Hungarian Academy of Sciences, Hungary (806-41-21) (Introduced by Myron S. Henry)

617 Friday, October 28, 1983, 2:30p.m. Special Session on Topics in Complex Analysis, I Faculty Office Building, Room 349 2:30- 2:50 (18) Criteria for local 'Variations for slit mappings. Preliminary report. RoGER W. BARNARD, Texas Tech University (806-30-36) 3:00- 3:20 (19) Coefficient estimates for the class I:. GLENN ScHOBER, Indiana University, Bloomington (806-30-61) 3:30- 3:50 (20) An elementary remark on the geometry of the coefficient regions for schlicht functions. Y. J. LEUNG, Indiana University, Bloomington and University of Delaware (806-30-57) 4:00- 4:20 (21) 1hlncation of support points for uni'Valent functions. LoUis BRICKMAN, State University of New York, Albany, and PETER DUREN*, University of Michigan, Ann Arbor (806-30-52) 4:30- 4:50 (22) Extreme points in the family of typically real polynomials. TED J. SuFFRIDGE, University of Kentucky (806-30-55) 5:00- 5:20 (23) Circular symmetrization and the star-function. J. R. QuiNE, Florida State University (806-30-78) 5:30- 5:50 (24) On a coefficient problem for typically real functions. JOHNNY E. BROWN, Purdue University, West Lafayette, and ANNA TsAo*, Texas Tech University (806-30-60)

Friday, October 28, 1983, 2:30p.m. Session on Geometry and Topology Faculty Office Building, Room 331 2:30- 2:40 (25) The primary kneading cycles of unimodal functions. MARK KIDWELL, United States Naval Academy (806-58-18) 2:45- 2:55 (26) Euler-Poincare characteristic. C. C. HsiUNG, Lehigh University, and KEN SHISKOWSKI*, Eastern Michigan University (806-53-68) 3:00- 3:10 (27) Three 3-dimensional manifolds with the same infinite fundamental group. Prelhninary report. FRANCIS D. LONERGAN, Webster, Massachusetts (806-55-06) 3:15- 3:25 (28) Milnor's in'Variants and the completions of link modules. Prelhninary report. LORENZO TRALDI, Lafayette College (806-57-26) 3:30- 3:40 (29) Recent ad'Vances on the applications of topology to the n-body problem of mechanics. GEORGE M. RAssiAS, Southeastern College, Boston University, and Athens, Greece (806-99-92) 3:45- 3:55 (30) Classsification of co'Variant deri'IJati'IJes of higher order tensors. MARTIN K. ALBERT and DoMINA EBERLE SPENCER*, University of Connecticut, Storrs (806-53-04) 4:00- 4:10 (31) The uni'Verse is a sphere, an alternati'Ve proof ANDREW CLAYTON CoNNOR, Auburn, Alabama (806-57-05) (Introduced by Ralph Ford)

Saturday, October 29, 1983, 8:30a.m.

Special Session on Theory of Infinite Groups, I Bannow Science Center, Room 139 8:30- 8:50 (32) On a correspondence between ring and group presentations. Preliininary report. PETER KENNE and M. NEWMAN, Australian National University, and KENNETH WESTON*, University of Wisconsin, Parkside (806-20-67) 9:00- 9:20 (33) Fuchsian groups and algebraic number fields. Preliminary report. PETER WATERMAN*, Temple University, and COLIN MACLACHLAN, Aberdeen University, Scotland (806-20-02) 9:30- 9:50 (34) The word problem for cocompact groups. W. J. FLOYD, Virginia Polytechnic Institute and State University, A. H. M. HoARE, University of Birmingham, England, and R. C. LYNDON*, University of Michigan, Ann Arbor (806-20-65) 10:00-10:20 (35) Are some groups more discriminating than others?Preliminary report. ANTHONY M. GAGLIONE, United States Naval Academy, and DENNIS SPELLMAN*, Sacred Heart University (806-99- 86)

Saturday, October 29, 1983, 8:30a.m. Special Session on Combinatoric&, II Bannow Science Center, Room 124 8:30- 8:50 (36) Tiling regions with polyominoes and combinatorial group theory. Preliminary report. JOHN H. CONWAY, University of Cambridge, England, and JEFFREY C. LAGARIAS*, Bell Laboratories, Murray Hill (806-05-33) 9:00- 9:20 (37) Bar:ktrack: An 0(1) a'Verage time algorithm for the graph colonng problem. HERBERT S. WILF, University of Pennsylvania (806-05-84) 9:30- 9:50 (38) The Thtte polynomial of a ported matroid. Preliminary report. SETH CHAIKEN, State University of New York, Albany (806-05-50) 10:00-10:20 (39) The acyclic sets of an oriented matroid. PAUL H. EDELMAN, University of Pennsylvania (806-05-45)

618 10:30-10:50 (40) Edge-colored complete graphs with precisely colored subgraphs. Preliminary report. F. R. K. CHUNG, Bell Laboratories, Murray Hill (806-05-54) 11:00-11:20 (41) A five-color theorem for graphs on surfaces. JOAN P. HuTCHINSON, Smith College (806-05-41)

Saturday, October 29, 1983, 8:30a.m. Special Session on Topies in Complex Analysis, II School of Nursing, Room 214 8:30- 8:50 (42) On the Dirichlet problem for harmonic functions on the unit sphere. Preliminary report. PETER A. McCoY, United States Naval Academy (806-30-15) 9:00- 9:20 (43) On partial sums of convex functions of order a. Preliminary report. EVELYN M. SILVIA, University of California, Davis (806-30-10) 9:30- 9:50 (44) On a conjecture of Bombieri. DAOUD BSHOUTY, Technion, Israel, and WALTER HENGARTNER*, Universite Laval (806-30-58) (Introduced by J. J. Gervais) 10:00-10:20 (45) On univalence of an integral transform. E. P. MERKES, University of Cincinnati, Cincinnati (806-30-62) 10:30-10:50 (46) On the univalence of rational functions. MAXWELL 0. READE*, University of Michigan, Ann Arbor, HERB SILVERMAN, College of Charleston, and PAVEL G. ToDOROV, Paissij Hilendarski University, Bulgaria (806-30-14) 11:00-11:20 (47) On certain support points of the class S. Lours BRICKMAN*, State University of New York, Albany, and STEPHAN RuSCHEWEYH, Wiirzburg University, Federal Republic of Germany (806-30-59)

Saturday, October 29, 1983, 9:00a.m. Special Session on Surfaees and Three-manifolds, II Bannow Science Center, Room 131 9:00- 9:20 (48) On the cohomology of the moduli space of stable curves. R. CHARNEY* and R. LEE, Yale University (806-57-53) 9:30- 9:50 (49) Combinatorial invariants of pseudo-Anosovs. LEE MOSHER, Barnegat Light, New Jersey (806-57-83) 10:00-10:20 (50) Some finite quotients of the mapping class group of a surface. PATRICIA L. SIPE, Smith College (806-57-51)

Saturday, October 29, 1983, 9:00a.m. Special Session on Approximation Theory and Numerieal Analysis, II School of Nursing Auditorium 9:00- 9:20 (51) On the convergence ofL.,';:=l np-l E~(!). MAURICE HASSON, Emory University, Atlanta, and OVED SHISHA *, University of Rhode Island (806-41-12) (Introduced by John A. Roulier) 9:30- 9:50 (52) Methods for shape preserving interpolation of bivariate functions. Preliminary report. G. YATES FLETCHER and D. F. McALLISTER*, North Carolina State University (806-41-29) (Introduced by John A. Roulier) 10:00-10:20 (53) Local Lipschitz constants. Preliminary report. JAMES A. ANGELOS, MYRON S. HENRY*, EDWIN H. KAUFMAN, JR., and TERRY D. LENKER, Central Michigan University (806-41-20)

Saturday, October 29, 1983, 10:30 a.m. Invited Address Gonzaga Auditorium 10:30-11:30 (54) Dynamics of rational maps. JOHN HUBBARD, Cornell University and Harvard University

Saturday, October 29, 1983, 1:00 p.m. Invited Address Gonzaga Auditorium 1:00- 2:00 (55) The homology of the moduli space of curves. JOHN L. HARER, University of Maryland, College Park (806-57-81)

Saturday, October 29, 1983, 1:00 p.m.

Speeial Session on Combinatories, ill Bannow Science Center, Room 124 1:00- 1:20 (56) Intersection classes of graphs and multiple intersection parameters. Preliminary report. EDWARD R. SCHEINERMAN, Princeton University (806-05-32) 1:30- 1:50 (57) Unimodal sequences and Lie superalgebras. RICHARD P. STANLEY, Massachusetts Institute of Technology (806-05-40) 2:00- 2:20 (58) Balancing poset extensions. J. KAHN* and M. SAKS, Rutgers University, New Brunswick (806-05-71)

619 2:30- 2:50 (59) Some combinatorial algorithms for group representations. KENNETH BACLAWSKI, Northeastern University (806-05-72) 3:00- 3:20 (60) Binomial determinants. IRA GESSEL*, Massachusetts Institute of Technology, and GERARD VIENNOT, Universite de Bordeaux, France (806-05-48) 3:30- 3:50 (61) The degree of trace (xt). Preliminary report. DAVID R. RICHMAN, University of South Carolina and Massachusetts Institute of Technology (806-05-27) 4:00- 4:20 (62) Every poset has a central element. NATHAN LINIAL, Hebrew University, Israel, and MICHAEL SAKS*, Rutgers University, New Brunswick (806-05-73) 4:30- 4:50 (63) Isometric embeddings of graphs. Preliminary report. R. L. GRAHAM*, Bell Laboratories, Murray Hill, and P.M. WINKLER, Emory University, Atlanta (806-99-90)

Saturday, October 29, 1983, 2:15p.m. Special Session on Theory of Infinite Groups, II Bannow Science Center, Room 139 2:15- 2:35 (64) On the one-relator groups xaybxcyd = 1. JOHN G. RATCLIFFE, University of Illinois, Urbana-Champaign (806-20-23) 2:45- 3:05 (65) Numerical invariants of words. Preliminary report. RICHARD GoLDSTEIN* and EDWARD TURNER, State University of New York, Albany (806-20-79) 3:15- 3:35 (66) Algorithms, permutations and complex variables. CAROL TRETKOFF*, Brooklyn College, City University of New York, and MARVIN TRETKOFF, Institute for Advanced Study (806-20-66) 3:45- 4:05 (67) Applications of the Bass-Serre theory to subgroup separability. MARVIN TRETKOFF*, Institute for Advanced Study, and CAROL TRETKOFF, Brooklyn College, City University of New York (806-20-64) 4:15- 4:35 (68) A theorem on finitely presented groups. Preliminary report. RoBERT BIERI*, University of Frankfurt, Federal Republic of Germany, WALTER D. NEUMANN, University of Maryland, College Park, and RALPH STREBEL, University of Heidelberg, Federal Republic of Germany (806-20-22)

Saturday, October 29, 1983, 2:15p.m. Special Session on Surfaces and Three-manifolds, III Bannow Science Center, Room 131 2:15- 2:35 (69) Characteristic classes of the Teichmiiller curve. ScoTT WoLPERT, University of Maryland, College Park (806-30-34) (Introduced by John L. Harer) 2:45- 3:05 (70) Ergodic actions of the mapping class group. HowARD MASUR, University of Illinois, Chicago (806-32-85) 3:15- 3:35 (71) Moduli for Riemann surfaces (especially ton). Preliminary report. IRWIN KRA, State University of New York, Stony Brook (806-30-39) 3:45- 4:05 (72) A theorem of Weil and deformations of Kleinian groups. LARRY LoK, Columbia University (806-57-47) 4:15- 4:35 (73) Relating parametrizations of Teichmuller spaces. LINDA KEEN, Herbert H. Lehman College, City University of New York (806-99-91) 4:45- 5:05 (74) Characterizing finite subgroups of the mapping-class group. JANE GILMAN, Rutgers University, Newark (806-32-63) 5:15- 5:35 (75) Conformal and quasiconformal mappings. Preliminary report. WILLIAM ABIKOFF, University of Connecticut, Storrs (806-99-87)

Saturday, October 29, 1983, 2:15 p.m. Special Session on Approximation Theory and Numerical Analysis, III School of Nursing Auditorium 2:15- 2:35 (76) An algorithm for Chebyshev approximation of complex valued functions on finite domains with constraints on the coefficients. RoY L. STREIT, Naval Underwater Systems Center, New London (806-41-09) (Introduced by John A. Roulier) 2:45- 3:05 (77) B-splines, divided differences and n-convex functions. R. F ARWIG, University of Bonn, Federal Republic of Germany, and D. ZWICK*, University of Vermont (806-41-75) 3:15- 3:35 (78) The best strong uniqueness constant for a multivariate Chebyshev polynomial. T. J. RIVLIN, IBM T. J. Watson Research Center (806-41-30) 3:45- 4:05 (79) Shape preserving surface interpolation. Preliminary report. HARRY W. McLAUGHLIN, Rensselaer Polytechnic Institute (806-52-7 4)

Saturday, October 29, 1983, 2:15p.m. Special Session on Topics in Complex Analysis, III School of Nursing, Room 214 2:15- 2:35 (80) Radial growth of the derivative of univalent functions. J. G. CLUNIE, Open University, Milton Keynes, England, and T. H. MACGREGOR*, State University of New York, Albany (806-30-42)

620 2:45- 3:05 (81) Properties of the hyperbolic metric. Preliminary report. DAVID MINDA, University of Cincinnati, Cincinnati (806-30-37) 3:15- 3:35 (82) Blaschke products and boundary trees. Preliminary report. RoBERT D. BERMAN, Wayne State University, and GEORGE PIRANIAN*, University of Michigan, Ann Arbor (806-30-08) 3:45- 4:05 (83) Intrinsic rotations of simply connected regions. BuRTON RoDIN, University of California, San Diego (806-30-77) 4:15- 4:35 (84) Extremal properties for a family of a-convex functions. HERB SILVERMAN, College of Charleston (806-30-11) 4:45- 5:05 (85) Polygonal Bazilevic functions. Preliminary report. B. A. CASE* and J. R. QuiNE, Florida State University (806-99-88)

Saturday, October 29, 1983, 2:15p.m. General Session for Contributed Papers School of Nursing, Room 212 2:15- 2:25 (86) Common transversals for partitions of a finite set. T. C. BROWN, Simon Fraser University (806-05-31) 2:30- 2:40 (87) Constructing infinitely many prime-field planar configurations. GARY GoRDON, Williams College (806-05-43) 2:45- 2:55 (88) Farey series partition. BHARTI TEMKIN, Berkeley Heights, New Jersey (806-10-82) 3:00- 3:10 (89) Countable torsion FC-groups as automorphism groups. JAY ZIMMERMAN, Michigan State University (806-20-24) 3:15- 3:25 (90) Omitted area for starlike functions. KENT PEARCE, Texas Tech University (806-30-44) 3:30- 3:40 (91) Meromorphic tangential approximation. Preliminary report. ANDRE BOIVIN, Universite de Montreal (806-30-69) 3:45- 3:55 (92) Some results on the radius of starlikeness for certain classes of analytic functions. Preliminary report. E. J. MouLis, JR., United States Naval Academy (806-30-35) 4:00- 4:10 (93) Asymptotic expansions of linear operators in some vector spaces. SAMUEL ZAIDMAN, Universite de Montreal (806-34-03) (Introduced by L. K. Durst) 4:15- 4:25 (94) Is not relativity theory becoming an international shame? Preliminary report. G. ARTHUR MrHRAM, Princeton, New Jersey (806-83-56)

W. Wistar Comfort Middletown, Connecticut Associate Secretary

Fixed Points and Ronald E. Bruck, Asymptotic behavior of nonexpan- Nonexpansive Mappings sive mappings Robert c. Sine, Editor Frank Deutsch, A survey of metric selections David ). Downing, Some aspects of nonlinear map- A nonexpansive mapping is a natural generaliza- ping theory and equivalent renormings tion of a contraction mapping of Banach fixed point ). Elton, Pei-Kee Lim, E. Odell and S. Szarek, theorem fame. The asymptotic behavior and invari- Remarks on the fixed point problem for nonex- ant structure which can arise with nonexpansive map- pansive maps pings offers a wide variety of interesting behavior in W. A. Kirk, Fixed point theory for nonexpansive contrast to that of a Banach contraction. mappings. II The subject has grown out of work in the 30s on Tech-Cheong Lim, Asymptotic centers in c0, c and m metric geometry and research in the early 60s on William 0. Ray, Normally solvable nonlinear opera- problems in nonlinear analysis. At the present time tors interest stems from applications to POE, functional Simeon Reich, Convergence, resolvent consistency, DE's, approximation theory and theoretical numeri­ and the fixed point property for nonexpansive cal ana lysis. mappings These lectures grew out of special sessions at the Robert Sine, Recurrence of nonexpansive mappings annual AMS meeting in Cincinnati in January of in Banach spaces 1982. While the specialist will find much of interest, S. Swami nathan, Normal structure in Banach spaces many of the lectures of the special sessions have and its generalisations been reworked for this volume to be surveys which Ricardo Torrejon, Some remarks on nonlinear func­ will be accessible to any mathematician or graduate tional equations student either wishing to acquaint himself with this T. E. Williamson, A geometric approach to fixed area or wishing to prepare himself to add to the re­ points of non-self mappings T: D ---> X search literature. The required background for a Contemporary Mathematics great deal of the exposition is a modest knowledge Volume 18, viii+ 256 pages (soft cover) of metric spaces and analysis. List price $20, institutional member $15, The extensive bibliographies of several of the sur­ individual member $10 veys will prove to be of considerable value to both ISBN 0-8218-5018-0; LC 83-6077 Publication date: May 1983 the specialist and the novice. There are a total of To order, please specify CONM/18N 575 bibliographic references for all these papers.

621 San Luis Obispo, November 11-12, 1983, California Polytechnic State University Program for the 807th Meeting

The eight hundred and seventh meeting of the speakers will include Randolph E. Bank, R. C. Y. American Mathematical Society will be held at Chin, Gerald W. Hedstrom, Dennis Jespersen, California Polytechnic State University in San Mark Kac, Randall J. LeVeque, Stanley Osher, Luis Obispo, California, on Friday and Saturday, Roland A. Sweet, and H. C. Yee. November 11 and 12, 1983. This meeting will Automorphic forms, AuDREY A. TERRAS, be held in conjunction with a meeting of the University of California, San Diego. The speakers Mathematical Association of America (MAA). will include Dorothy Wallace Andreoli, Avner Invited Addresses Ash, Daniel Bump, Bernd Dreseler, Isaac Efrat, Helaman Rolfe Pratt Ferguson, Paul Garrett, By invitation of the Committee to Select Hour Paul Gerardin, Jeffrey Hoffstein, Pei Hsu, Martin Speakers for Far Western Sectional Meetings, L. Karel, Neal Koblitz, Phil Kutzko, Wen-Ch'ing there will be two invited one-hour addresses. The Winnie Li, Carlos Julio Moreno, Steve Rallis, speakers, their affiliations, and the titles of their Kenneth A. Ribet, Peter Sarnak, Peter Stiller, talks, are as follows: Audrey Terras, llan Vardi, Joseph A. Wolf, David PETER B. GILKEY, University of Oregon, J. Wright, and Don Zagier. Applications of analysis to topology, 5:00 p.m. Partial differential equations, theory and ap­ Friday. plication, AHMED I. ZAYED, California Polytech­ T. Y. LAM, University of California, Berkeley, nic State University. The speakers will include The arithmetic of fields, 11:00 a.m. Saturday. Freddy F. Brackx, James L. Buchanan, Deborah Special Sessions Tepper Haimo, Ralph E. Kleinman, Mark A. Kon, Peter A. McCoy, Louise A. Raphael, Walter By invitation of the same committee, there will Schempp, Franc;ois Treves, Gilbert G. Walter, be six special sessions of selected twenty-minute Joseph Wiener, and Ahmed I. Zayed. papers. The topics of these special sessions and the names and affiliations of the mathematicians Contributed Papers arranging them, are: There will also be sessions for contributed ten­ Geometric methods for partial differential equa­ minute papers. tions, IAN M. ANDERSON, Utah State Univer­ MAAProgram sity. The speakers will include Judith M. Arms, The MAA program will include two invited David Bao, Charles Boyer, Dennis DeThrck, speakers. IvAN NIVEN of the University of Tom Duchamp, David J. Eck, Dominic G. B. Oregon will deliver a one-hour address titled, Edelen, Mark J. Gotay, James Isenberg, N. Some peculiarities of rational and irrational Ka1nran, Marek Kossowski, Joseph P. S. Kung, numbers. JuDITH V. GRABINER of California Boris A. Kuperschmidt, Jerrold Marsden, Richard State University, Dominguez Hills, will deliver an Montgomery, Peter J. Olver, William F. Shad­ address titled, The Newton-Liebniz controversy. wick, Chehrzad Shakiban, J~;drzej Sniatycki, A panel discussion, moderated by C. CoLEMAN Stanly Steinberg, Alexander P. Stone, and Philip of Harvey Mudd College, will take place on B. Yasskin. Friday afternoon. The tentative title is Should Singular perturbations, E. CouTSIAS, University there be an undergraduate specialization in applied of New Mexico and JAMES R. MuELLER, Califor­ mathematics? nia Polytechnic State University. The speakers Registration will include S. C. Anco, E. A. Coutsias, Pat Hagan, William L. Kath, J. Kevorkian, P. A. The meeting registration desk will be located at Lagerstrom, and C. G. Lange. the Cal Poly Theatre, and will be open from 8:00 The lower division curriculum in mathematics, a.m. until3:00 p.m. on Friday, and from 8:00 a.m. including calculus, MARTIN E. FLASH MAN, Hum­ until 10:30 a.m. on Saturday. The registration boldt State University. The speakers will include fees are $6 for members of the AMS or MAA, $8 for Robert Borrelli, Donald Bushaw, Philip C. Curtis, nonmembers, and $2 for students or unemployed Jr., Marjorie Enneking, James K. Finch, Martin mathematicians. Coffee and doughnuts will be E. Flashman, Grant A. Fraser, Roland H. Lam­ provided adjacent to the registration area. berson, Philip S. Marcus, Robert Osserman, and Petition Table Sherman K. Stein. A petition table will be set up in the registration Numerical solutions of partial differential equa­ area. Additional information can be found in a tions, WLODEK PROSKUROWSKI and RICHARD box in the Louisville meeting announcement in SANDERS, University of Southern California. The this issue.

622 Accommodations Social Events San Luis Obispo has a large number of motels Lunch on Friday can be purchased at the Vista within a two-kilometer radius of campus. In Grande Restaurant on the campus. A banquet view of the large tourist business, early reserva­ will be held at 7:00p.m. on Friday in the Garden tions are advised and encouraged. Participants Room at the Madonna Inn; the cost will be $13 should make their own reservations directly with per person. Preceding the banquet, there will also the motels and should identify themselves as par­ be a no-host cash bar at the Madonna fun. The ticipants at the AMS-MAA mathematics meeting. featured speaker at the banquet will be announced Some hotels have offered a special rate. For addi­ at the meeting. There will be a luncheon in the tional information or help with accommodations, Faculty Dining Hall at 12:15 p.m. on Saturday. write to H. Arthur DeKleine, Department of Math­ Tickets for the Friday banquet and Saturday ematics, California Polytechnic State University, luncheon will be available at the registration San Luis Obispo, CA 93407, or telephone him at desk. Since the number of tickets will be limited, 805-546-2206. advance reservations are requested. They may be Campus Motel obtained by calling Euel Kennedy of California 404 Santa Rosa Polytechnic State University at 805-546-2245. Telephone: 805-544-0881 Travel and Local Information Single $34 up Double $38 up San Luis Obispo is approximately half-way Discovery Motor Inn between Los Angeles and San Francisco on 1800 Monterey Street the coast (about 375 kilometers south of San Telephone: 805-544-8600 Francisco, and 300 kilometers north of Los Angeles). The area is served daily by Greyhound Single $40-45 up Double $45-50 up Bus, Amtrak, and Wings West Airline from either Suite $60-80 up San Francisco or Los Angeles. The train ride Howard Johnson's along the coast is very scenic and popular, and U. S. 101 South early reservations are advised for both Amtrak Telephone 805-544-5300 and Wings West Airline. Local bus service is Single $32 up Double $37 up excellent and buses operate between the campus and the Greyhound and Amtrak terminals. Taxis Lamplighter Motel operate between the airport and the campus. 1604 Monterey Street Persons driving south to San Luis Obispo Telephone 805-543-3709 via Highway 101 should take the Monterey exit Single $32 up Double $36 up to Grande Avenue, then turn right on Grande Madonna Inn (Mrs. Billie Long) Avenue and continue to the campus. Persons driving north to San Luis Obispo via Highway 100 Madonna Road 101 should take the Grande Avenue exit, then Telephone: 805-543-3000 turn left on Grande Avenue and continue to the Single $60 up Double $65 up campus. In order to proceed to Monterey Street Motel6 (where several motels are located), turn right on 1433 Calle Joaquin Grande Avenue, instead of left. Telephone: 805-544-8400 The central coast of California frequently has moderate weather during early November, with a Single $15.95 Double $19.95 daily temperature range of 5°C to 300C. Rainfall Triple or Quad $22.95 is infrequent, but is possible. Peaeh Tree Several attractions of scenic or historical impor­ 2001 Monterey Street tance exist in the local area and include Mission Telephone: 805-543-3170 San Luis Obispo de Tolosa, Hearst San Simeon Single $30 up Double $32 up State Historical Monument (65 kilometers) and Royal Oak Montana de Oro State Park. 214 Madonna Road Telephone_: 805-544-4410 Single $42 up Double $50-56 up

623 Presenters of Papers Numbers following the names indicate the speakers' positions on the program. •Invited one-hour lecturer •Special session speaker

•Anco, S. C., 70 •Enneking, M., 33 •Kleinman, R. E., 45 *Rallis, S., 14 •Andreoli, D. W., 9 •Ferguson, H. R. P., 76 •Koblitz, N., 40 •Raphael, L.A., 47 •Arms, J. M., 51 •Finch, J. K., 32 •Kon, M.A., 85 •Ribet, K. A., 75 •Ash, A., 12 •Flashman, M. E., 91 •Kossowski, M., 8 * Sarna.k, P., 38 •Bank, R. E., 55 •Fraser, G. A., 94 Kubelka, R. P., 20 •Schempp, W., 48 •Shadwick, W. F., 7 •Bao, D., 67 •Garrett, P., 11 •Kung, J.P. S., 2 * Sha.kiban, C., 3 Bhatt, B. S., 22 •Gerardin, P., 17 • Kupershmidt, B. A., 4 * Sniatycki, J., 50 *Borrelli, R., 35 •Gilkey, P. B., 25 •Kutzko, P., 77 Stein, S. K., 18 •Boyer, C., 6 * Gotay, M. J., 61 •Lagerstrom, P. A., 26 *Stein, S. K., 34 •Brackx, F. F., 43 Grone, R. D., 21 •Lam, T. Y., 59 * Steinberg, S., 66 •Buchanan, J. L., 84 •Hagan, P., 29 •Lamberson, R. H., 93 *Stiller, P., 72 •Bump, D., 10 •Haimo, D. T., 44 •Lange, C. G., 27 •Stone, A. P., 53 •Bushaw, D., 92 •Hedstrom, G. W., 86 •LeVeque, R. J., 87 *Sweet, R. A., 58 *Chin, R. C. Y., 54 * Hoffstein, J., 36 •Li, W.-C. W., 16 * Terras, A., 13 * Coutsias, E. A., 71 •Hsu, P., 79 •Marcus, P. S., 30 •Treves, F., 83 •Curtis, P. C., Jr., 31 •Isenberg, J., 68 •Marsden, J., 60 • Vardi, I., 78 *Walter, G. G., 80 •DeTurck, D., 1 Janos, L., 19 •McCoy, P. A., 46 *Wiener, J., 82 Dombroski, M., 23 *Jespersen, D., 89 •Montgomery, R., 62 *Wolf, J. A., 39 •Dreseler, B., 74 •Kac, M., 57 •Moreno, C. J., 37 *Wright, D. J., 15 •Duchamp, T., 63 •Kamran, N., 52 Muses, C., 24 •Yasskin, P. B., 49 * Eck, D. J., 5 •Karel, M. L., 42 *Olver, P. J., 65 * Yee, H. C., 88 •Edelen, D. G. B., 64 •Kath, W. L., 28 •Osher, S., 56 • Zagier, D., 73 • Efrat, I., 41 •Kevorkian, J., 69 * Osserman, R., 90 •Zayed, A. I., 81

AMS SHORT COURSE LECTURE NOTES A Subseries in Proceedings of Symposia in Applied Mathematics

CONTENTS Lawrence A. Shepp, Scope of pure and applied tomography Kennan T. Smith, Reconstruction formulas in com­ Computed Tomography puted tomography Lawrence A. Shepp, Editor Oleh ]. Tretiak, Attenuated and exponential Radon transforms This book is composed of the lecture notes from Allan M. Cormack, Computed tomography: Some an AMS Short Course on Computed Tomography history and recent developments given in Cincinnati, january 1982. It reviews (for F. Alberto Griinbaum, The limited angle reconstruc­ both pure and applied mathematicians) the algo­ tion problem rithms and mathematics of computed tomography Sigurdur Helgason, Ranges of Radon transforms (CT). It presents one particularly important (med­ johann Radon, Uber die Bestimmung von Funk­ ically, financially, scientifically) example of applied tionen durch ihre lntegra/werte fangs gewisser mathematics, illustrating the general applied mathe­ Mannigfaltigkeiten (reprinted from Berichte iJber matical approach of problem solving and problem die Verhandlungen der Koniglich Siichsischen posing through modelling-an approach not often Gesel/schaft der Wissenschaften zu Leipzig 69 taught in pure mathematics programs. New problems (1917), 262-277). in emission CT and nuclear magnetic resonance CT arc posed and new research frontiers defined, e.g., 1980 Mathematics Subject Classification: 42820 estimation of errors in limited angle CT; correction Proceedings of Symposia in Applied Mathematics Volume 27, x + 86 pages (hard cover and soft cover) for attenuation in emission CT; Radon transform Soft cover prices: List $14, institutional member $11, range spaces in homogeneous space CT. individual member $7 An individual who reads this book can expect to Hard cover prices: List $20, institutional member $15, gain a feel for experimental or nondeductive meth­ individual member $10 ods through the use of computers in applied prob­ ISBN 0-8218-0033-7; LC 82-18508 Publication date: january 1983 lems, i. c., simulation, large scale computation, nu­ To order, please specify PSAPM/27N (hard cover) merical techniques, and imaging methods. PSAPMS/27N (soft cover) Prepayment is required for all AMS publications. Order from AMS, P. 0. Box 1571, Annex Station, Providence, Rl 02901, or call toll free 800-556-7774 to charge with Visa or MasterCard.

624 Program of the Sessions

The time limit for each contributed paper in the AMS general 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 AMS sessions at this meeting will be found in the October 1983 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.

Friday, November 11, 1983, 1:00 p.m. Special Session on Geometrie Methods for Partial Differential Equations, I Fisher Science Hall, Room 287 1:00- 1:20 (1) Exploiting the invariance of differential systems. DENNIS DETURCK, University of Pennsylvania (807 -35-29) 1:30- 1:50 (2) Invariant theory and linear differential equations. JOSEPH P. S. KuNG, North Texas State University (807-35-25) 2:00- 2:20 (3) Conservation laws and invariant theory. CHEHRZAD SHAKIBAN, College of St. Thomas (807-35-30) (Introduced by Peter J. Olver) 2:30- 2:50 (4) Discrete groups, classical mechanics, and noncommutative calculus of variations. BORIS A. KuPERSHMIDT, University of Tennessee Space Institute (807-49-40) 3:00- 3:20 (5) Natural sheaves and natural differential operators. DAVID J. EcK, State University of New York, Buffalo (807-53-12) 3:30- 3:50 (6) Group theory and the twistor method for self-dual Einstein spaces. Preliminary report. CHARLES BoYER, Clarkson College of Technology (807-35-63) 4:00- 4:20 (7) The Carlan equivalence problem for multiple integral variational problems. Preliminary report. WILLIAM F. SHADWICK, University of Waterloo (807-35-18) 4:30- 4:50 (8) Special points on a first order PDE and the associated qualitative properties of solutions. Preliminary report. MAREK KossowsKI, Rice University (807-35-26)

Friday, November 11, 1983, 1:00 p.m. Speeial Session on Automorphie Forms, I Fisher Science Hall, Room 289 1:00- 1:20 (9) The Selberg trace formula for SL(3, Z) \ SL(3, R)/S0(3, R) DoROTHY WALLACE ANDREOLI, Florida International University (807-10-58) 1:25- 1:45 (10) A Kronecker limit formula for cubic fields. DANIEL BUMP* and DORJAN GOLDFELD, University of Texas, Austin (807-10-20) (Introduced by Audrey A. Terras) 1:50- 2:10 (11) Explicit Fourier expansion of non-holomorphic Eisenstein series. PAUL GARRETT, University of Minnesota, Minneapolis (807-10-71) 2:15- 2:35 (12) Congruences between automorphic forms. Preliminary report. AVNER AsH, Ohio State University, Columbus (807-22-22) 2:40- 3:00 (13) The Poisson summation formula and automorphic forms for GL(n, Z). AuDREY TERRAS, University of California, San Diego (807-10-13) 3:05- 3:25 (14) Rankin integral representations of £-functions. STEVE RALLIS, Ohio State University, Columbus (807-10-76) (Introduced by Audrey A. Terras) 3:30- 3:50 (15) The adelic zeta function associated with the space of binary cubic forms. DAVID J. WRIGHT, Massachusetts Institute of Technology (807-10-10) 3:55- 4:15 (16) On local correspondence of representations of GL(2) and quaternions. PAUL GERARDIN, Universite Paris Vll, France, and Pennsylvania State University, University Park, and WEN-CH1ING WINNIE LI*, Pennsylvania State University, University Park (807-10-61) 4:20- 4:40 (17) On root numbers of degree two representations of local Weil groups. Preliminary report. PAUL GERARDIN*, Universite Paris vn, France, and Pennsylvania State University, University Park, and WEN-CH1ING WINNIE LI, Pennsylvania State University, University Park (807-10-62)

Friday, November 11, 1983, 2:30 p.m. Session on Contributed Papers Science North, Room 202 2:30- 2:40 (18) Packing certain star bodies and abelian groups. Preliminary report. SHERMAN K. STEIN, University of California, Davis (807-52-05) 2:45- 2:55 (19) A partial converse to the "swelling lemma." LuDVIK JANOS, California State University, Fullerton (807 -54-57)

625 3:00- 3:10 (20) The transfer and the failure of a mock Riemann-Roch theorem. RicHARD P. KuBELKA, San Jose State University (807-55-82) 3:15- 3:25 (21) An algorithm for the second immanant. RoBERT D. GRONE*, Auburn University, Auburn, and RusSELL MERRIS, California State University, Hayward (807-65-56) 3:30- 3:40 (22) Slow rotation of a porous sphere. B. S. BHATT, University of the West Indies, Trinidad (807-76-91) (Introduced by Hugo Rossi) 3:45- 3:55 (23) A space-time quantum mathematics: Empirical Chebyshev-Root phase orders. MicHAEL DOMBROSKI, Los Angeles City College (807-81-24) 4:00- 4:10 (24) The Mendelian binomial distribution and its generalization. C. MusE:s, Centre de Mathematique, France (807-92-67) (Introduced by K. Demys)

Friday, November 11, 1983, 5:00 p.m. Invited Address Fisher Science Hall, Room 286 5:00- 6:00 (25) Applications of analysis to topology. PETER B. GILKEY, University of Oregon (807-58-79)

Friday, November 11, 1983, 7:00p.m. Banquet Garden Room of the Madonna Inn 7:00- Banquet

Saturday, November 12, 1983, 8:00 a.m. Special Session on Singular Perturbations, I Science North, Room 206 8:00- 8:50 (26) Ideas and techniques in matched asymptotic expansions. P. A. LAGERSTROM, California Institute of Technology (807-41-73) 9:00- 9:30 (27) Bifurcation analysis of nonlinear turning point problems. C. G. LANGE, University of California, Los Angeles (807-41-72) 9:35-10:15 (28) Slowly varying phase planes and boundary layer theory. WILLIAM L. KATH, California Institute of Technology (807-41-34) (Introduced by James R. Mueller) 10:20-10:50 (29) Steady currents in materials with thin inclusions. PAT HAGAN, Exxon Research and Engineering, Linden, New Jersey (807-41-74) (Introduced by James R. Mueller)

Saturday, November 12, 1983, 8:00 a.m.

Special Session on The Lower Division Curriculum in Mathematics, Including Calculus, I Science North, Room 213 8:00- 8:25 (30) College credit for remedial arithmetic. PHILIP S. MARcus* and RoN GREEK, Eureka College (807-98-04) 8:30- 8:55 (31) Problems of student preparation and attempts to deal with them. Preliminary report. PHILIP C. CURTIS, JR., University of California, Los Angeles (807-98-77) 9:00- 9:25 (32) Using computers in lower division mathematics courses. JAMES K. FINCH, University of San Francisco (807-98-75) 9:30- 9:55 (33) Teacher training programs. MARJORIE ENNEKING, Portland State University (807-98-83) 10:00-10:25 (34) The hidden curriculum. SHERMAN K. STEIN, University of California, Davis (807-98-06) 10:30-10:55 (35) The proiect approach in applied mathematics education. RoBERT BORRELLI, Harvey Mudd College (807-98-36) (Introduced by Martin E. Flashman)

Saturday, November 12, 1983, 8:00 a.m. Special Session on Automorphic Forms, II Fisher Science Hall, Room 289 8:00- 8:20 (36) Eisenstein series of half-integral weight and the average value of quadratic L-series. JEFFREY HoFFSTEIN*, University of Rochester, and DoRIAN GOLDFELD, Harvard University and University of Texas, Austin (807-10-65) (Introduced by Audrey A. Terras) 8:25- 8:45 (37) Automorphic forms for GL(n) and the associated Euler products. CARLOS JuLio MoRENO, University of illinois, Urbana-Champaign (807-99-93) 8:50- 9:10 (38) Mean values of L-functions. Preliminary report. PETER SARNAK, Courant Institute of Mathematical Sciences, New York University (807-10-66) 9:15- 9:35 (39) Automorphic cohomology and singular unitary representation theory. JosEPH A. WOLF, University of California, Berkeley (807-99-92) 9:40-10:00 (40) p-adic modular forms of half integer weight. Preliminary report. NEAL KOBLITZ, University of Washington (807-12-01) 10:05-10:25 (41) Cusp forms in higher rank. IsAAC EFRAT, Massachusetts Institute of Technology (807-10-46)

626 10:30-10:50 (42) Automorphic forms on tube domains. Preliminary report. MARTIN L. KAREL, Rutgers University, Camden (807-10-64)

Saturday, November 12, 1983, 8:00 a.m. Special Session on Partial Differential Equations, Theory and Application, I Science North, Room 201 8:00- 8:20 (43) Two Hartog's theorems for nullsolutions of overdertermined Cauchy-Riemann systems in Euclidean space. Preliminary report. FREDDY F. BRACKX* and WILLY PINCKET, Rijksuniversiteit Gent, Belgium (807-35-35) 8:30- 8:50 (44) Inversion of the dual Weierstrass-Laguerre transform. DEBORAH TEPPER HAIMO, University of Missouri, St. Louis (807-35-50) 9:00- 9:20 (45) On constructing the Green's function for exterior boundary value problems for the Helmholtz equation. RALPH E. KLEINMAN, Applied Mathematics Institute, University of Delaware (807-35-03) 9:30- 9:50 (46) Interpolation and approximation methods for a class of heat functions. Preliminary report. PETER A. McCoY, United States Naval Academy (807-35-09) 10:00-10:20 (47) Equisummability of eigenfunction expansions under analytic multipliers. LOUISE A. RAPHAEL, Howard University (807-35-39) 10:30-10:50 (48) Reconstructing holomorphic functions. Preliminary report. WALTER SCHEMPP, University of Siegen, Federal Republic of Germany (807-41-28)

Saturday, November 12, 1983, 8:30a.m. Special Session on Geometric Methods for Partial Dift'erential Equations, II Fisher Science Hall, Room 287 8:30- 8:50 (49) Einstein-Dirac dynamics: Fields and symmetries on a principal bundle. PHILIP B. YASSKIN*, Texas A&M University, College Station, DAVID BAo, University of California, Berkeley, and JAMES IsENBERG, University of Oregon (807-83-27) 9:00- 9:20 (50) On quantization of gauge fields. Preliminary report. J~DRZEJ SNIATYCKI, University of Calgary (807-81-41) 9:30- 9:50 (51) Conservation laws and formal power series solutions for field equations. Preliminary report. JuDITH M. ARMs*, University of Washington, and IAN M. ANDERSON, Utah State University (807-35-55) 10:00-10:20 (52) Symmetry operators and separation of variables for the massless Dirac equation on Lorentzian manifolds. N. KAMRAN, University of Waterloo (807-53-11) 10:30-10:50 (53) A differential geometric approach to electromagnetic lens design. ALEXANDER P. STONE, University of New Mexico (807-53-47)

Saturday, November 12, 1983, 8:30a.m. Special Session on Numerical Solutions of Partial Dift'erential Equations, I Science North, Room 202 8:30- 8:50 (54) General considerations for solving multiple scale problems. R. C. Y. CHIN, Lawrence Livermore National Laboratory (807-35-17) (Introduced by Wlodek Proskurowski) 9:00- 9:20 (55) Multi-level iterative methods. RANDOLPH E. BANK, University of California, San Diego (807-65-42) (Introduced by Wlodek Proskurowski) 9:30- 9:50 (56) Entropy condition satisfying approximations for the full potential equations of transonic flow. STANLEY OsHER, University of California, Los Angeles (807-65-88) 10:00-10:20 (57) Discretization as an aid in understanding. MARK KAC, University of Southern California (807-65-45) 10:30-10:50 (58) Fast, direct methods for the solution of separable elliptic equations. RoLAND A. SWEET, National Bureau of Standards, Boulder (807-65-43) (Introduced by Wlodek Proskurowski)

Saturday, November 12, 1983, 11:00 a.m. Invited Address Fisher Science Hall, Room 286 11:00-12:00 (59) The arithmetic of fields. T. Y. LAM, University of California, Berkeley (807-12-86)

Saturday, November 12, 1983, 12:15 p.m. Luncheon Faculty Dining Hall 12:15- Luncheon

Saturday, November 12, 1983, 1:30 p.m. Special Session on Geometric Methods for Partial Differential Equations, ill Fisher Science Hall, Room 287 1:30- 1:50 (60) Hamiltonian structures and nonlinear stability in fluids and plasmas. JERROLD MARSDEN, University of California, Berkeley (807-76-08)

627 2:00- 2:20 (61) Poisson reduction and quantization for the n+1 photon. MARK J. GoTAY, University of Calgary (807-53-33) (Introduced by Richard C. Churchill) 2:30- 2:50 (62) Canonical formulations of a classical particle in a Yang-Mills field and Wong's equations. RICHARD MONTGOMERY, University of California, Berkeley (807-70-23) 3:00- 3:20 (63) The Carathedory theory t'n the calculus of variations. Preliminary report. ToM DucHAMP, Thlane University (807-53-59) 3:30- 3:50 (64) Isovectors for partial differential equations on extended symplectic product manifolds. DOMINIC G. B. EDELEN, Lehigh University (807-35-07) (Introduced by Ian M. Anderson) 4:00- 4:20 (65) Differential hyperforms. PETER J. OLVER, University of Minnesota, Minneapolis (807-58-31) 4:30- 4:50 (66) Computer symbol manipulation and nonlinear differential equations. STANLY STEINBERG, University of New Mexico (807-35-49) 5:00- 5:20 (67) The linearization stability of supergravity. DAVID BAo, Institute for Advanced Study (807-58-16) 5:30- 5:50 (68) Supergravity as a well-posed Cauchy problem. JAMES ISENBERG, University of Oregon (807-83-48)

Saturday, November 12, 1983, 1:30 p.m. Special Session on Singular Perturbations, II Science North, Room 206 1:30- 2:20 (69) Multiple-scale expansions, passage through resonance, and adiabatic invariants. J. KEVORKIAN, University of Washington (807-41-69) (Introduced by James R. Mueller) 2:30- 3:20 Discussion 3:30- 4:00 (70) Linearization and autonomization of ODE. S. C. ANco*, R. S. CHIVUKULA and P. A. LAGERSTROM, California Institute of Technology (807-41-70) 4:10- 4:40 (71) Resonance in the scattering of an electron beam by a standing laser wave. E. A. CoUTSIAS* and J. K. McivER, University of New Mexico (807-41-89) (Introduced by D. A. Sanchez)

Saturday, November 12, 1983, 1:30 p.m. Special Session on Automorphic Forms, m Fisher Science Hall, Room 289 1:30- 1:50 (72) Special values of Dirichlet series, monodromy, and the periods of automorphic forms. PETER STILLER, Texas A&M University, College Station (807-14-38) (Introduced by Audrey A. Terras) 1:55- 2:15 (73) Non-holomorphic Eisenstein series and zeta-functions of non totally real fields. Preliminary report. DoN ZAGIER, University of Maryland, College Park, and Max-Planck-Institut fiir Mathematik, Federal Republic of Germany (807-10-60) (Introduced by Audrey A. Terras) 2:20- 2:40 (74) Norms of zonal spherical functions and Fourier series on compact symmetric spaces. BERND DRESELER, University of Siegen, Federal Republic of Germany (807-43-68) (Introduced by Ahmed I. Zayed) 2:45- 3:05 (75) Systematic congruences between modular forms. KENNETH A. RrBET, University of California, Berkeley (807-12-51) 3:10- 3:30 (76) Zeros of Mellin transforms of cusp forms. HELAMAN ROLFE PRATT FERGUSON, Brigham Young University, Provo (807-10-84) 3:35- 3:55 (77) On the local Langlands correspondence in prime dimension. PHIL KuTZKo*, University of Iowa, and ALLEN MoY, Yale University (807-20-90) 4:00- 4:20 (78) Relations between Kloosterman sums and Dedekind sums. Preliminary report. ILAN V ARDI, Stanford University (807-99-95) 4:25- 4:45 (79) Analytic continuation of Eisenstein series for SL(3, Z). Preliminary report. PEr Hsu, Stanford University (807-99-94)

Saturday, November 12, 1983, 1:30 p.m. Special Session on Partial Dift'erential Equations, Theory and Application, II Science North, Room 201 1:30- 1:50 (80) Real singularities of singular Sturm-Liouville expansions. Preliminary report. GILBERT G. WALTER*, University of Wisconsin, Milwaukee, and AHMED ZAYED, California Polytechnic State University (807-34-14) 2:00- 2:20 (81) On the singularities of singular Sturm-Liouville expansions and an associated class of elliptic PDEs. AHMED I. ZAYED*, California Polytechnic State University, and GILBERT G. WALTER, University of Wisconsin, Milwaukee (807-35-15) 2:30- 2:50 (82) Distributional and entire solutions of partial differential equations (PDE} Preliminary report. JOSEPH WIENER, Pan American University (807-35-78) 3:00- 3:20 (83) Approximation of solutions to overdetermined systems defined by complex vector fields. FRANQOIS TREVES, Rutgers University, New Brunswick (807-35-52)

628 3:30- 3:50 (84) Boundary value problems for Pascali systems. JAMES L. BuCHANAN, United States Naval Academy (807-35-80) 4:00- 4:20 (85) Schriidinger operators with boundary conditions. MARK A. KoN, Boston University (807-35-81)

Saturday, November 12, 1983, 2:00 p.m. Speeial Session on Numerieal Solutions of Partial Dilferential Equations, II Science North, Room 202 2:00- 2:20 (86) A moving-grid method for gas dynamics. GERALD W. HEDSTROM, Lawrence Livermore National Laboratory (807-65-32) 2:30- 2:50 (87) A large time step generalization of Godunov's method for systems of conservation laws. Preliminary report. RANDALL J. LEVEQUE, University of California, Los Angeles (807-65-54) 3:00- 3:20 (88) On a class of TVD schemes for gas dynamic calculations. H. C. YEE* and R. F. WARMING, NASA Ames Research Center, Moffett Field (807-65-87) (Introduced by Richard Sanders) 3:30- 3:50 (89) A multigrid algorithm for the steady Euler equations. Preliminary report. DENNIS JESPERSEN, NASA Ames Research Center, Moffett Field (807-65-44) (Introduced by Wlodek Proskurowski)

Saturday, November 12, 1983, 2:30p.m. Special Session on The Lower Division Currieulum in Mathematics, lneluding Caleulus, II Science North, Room 213 2:30- 2:55 (90) Unified calculus. RoBERT OssERMAN, Stanford University (807-98-21) 3:00- 3:25 (91) Suggestions for implementing a thematic approach in the calculus curriculum. Preliminary report. MARTIN E. FLASHMAN, Humboldt State University (807-98-37) 3:30- 3:55 (92) Discrete mathematics. DONALD BusHAW, Washington State University (807-98-02) 4:00- 4:25 (93) The VisUMAP project. ROLAND H. LAMBERSON, Humboldt State University (807-98-19) (Introduced by Martin E. Flashman) 4:30- 4:55 (94) The role of abstract algebra in the lower division mathematics curriculum. GRANT A. FRASER, California State University, Los Angeles (807-98-53) 5:00- 5:25 Discussion Hugo Rossi Salt Lake City, Utah Associate Secretary

growing theoretical developments in structural and mechanical design problems_ L. E. Payne, On the stabilization of ill posed Cauchy problems In nonlinear elasticity ]ames Moseley, A nonlinear eigenvalue problem with an exponential nonlinearity CONTEMPORARY MATHEMATICS Erich Miersemann, Eigenvalue problems for varia­ (ISSN 0271-4132) tional Inequalities George H. Knightly and D. Sather, Regularity and symmetry properties of solutions of the john shell equations for a spherical shell Kyung K. Choi and Edward ]. Haug, Repeated PROBLEMS OF ELASTIC STABILITY eigenvalues in mechanical optimization problems AND VIBRATIONS Vadim Komkov and Edward]. Haug, Effects of edited by Vadim Komkov some nonlinear terms on the buckling of elastic The articles collected in this volume are enlarged bodies versions of the talks presented in one of the special Raymond H. Plaut, Vibrations and stability of shal­ sessions at the spring meeting of the American Math­ low elastic arches ematical Society held in Pittsburgh in May 1981 1980 Mathematics Subject Classifications: 73H05, 73H10, All papers are directly related to problems in sta­ 73030. bility or eigenvalue problems arising in considera­ Volume 4, vii + 137 pages (soft cover) tions of elastic stability or elastic vibrations. A mul­ List price $9, institutional member $7 individual member $5 ' titude of papers has appeared in the five years pre­ ISBN 0-8218-5005-9; LC 81-12833 ceding this meeting in various aspects of elastic sta­ Publication date: September 1981 bility and elastic vibrations because of the rapidly To order, please specify CONM/4N Prepayment is required for all AMS publications. Order from AMS, P.O. Box 1571, Annex Station, Providence, Rl 02901, or call toll free 800-556-7774 to charge with Visa or MasterCard.

629 Evanston, November 11-12, 1983, Northwestern University Program for the 808th Meeting

The eight hundred and eighth meeting of the Perkins, Eric Todd Quinto, Haskell P. Rosenthal, American Mathematical Society will be held at Daniel W. Stroock, Srinivasa Varadhan, and Joel Northwestern University, Evanston, illinois, on Zinn. Friday and Saturday, November 11 and 12, 1983. Approximation theory, STEPHEN D. FISHER, The sessions on Friday will be held in the Norris Northwestern University. The speakers include University Center, while the sessions on Saturday Sheldon Axler, James E. Brennan, Rong-Qing Jia, will be held in Leverone Hall. Dmitry Khavinson, Theodore Kilgore, Paul Nevai, Invited Addresses and Joel H. Shapiro. By invitation of the 1982 Committee to Select Harmonic analysis and its applications to Hour Speakers for Central Sectional Meetings, partial differential equations, CARLOS E. KENIG, there will be four invited one-hour addresses. The University of Minnesota, Minneapolis. The speakers, their affiliations, their titles, and the speakers include Patricia Bauman, Michael Beals, scheduled times of presentation are as follows: William Beckner, Michael Christ, R. Coifman, EncHI BANNAI, Ohio State University, Colum­ Bjorn Dahlberg, Robert Fefferman, G. B. Folland, bus, Orthogonal polynomials and algebraic com­ C. Robin Graham, Allan Greenleaf, David binatorics, 11:00 a.m. Friday. Jerison, Jeff E. Lewis, Walter Littman, Alexander BuRGESS J. DAVIS, Purdue University, Nagel, Yoram Sagher, Peter A. Tomas, Gregory Brownian motion and analytic functions, 1:45 Verchota, Stephen Wainger, Guido Weiss, Richard p.m. Friday. L. Wheeden, T. Wolff, and Jang Mei Wu. EuGENE B. F ABES, University of Minnesota, Volterra integral and integra-differential equa­ Minneapolis, Harmonic analysis and properties tions, JOHN A. NOHEL, University of Wisconsin, of solutions of partial differential equations with Madison. The speakers include T. A. Burton, C. nonsmooth coefficients, 11:00 a.m. Saturday. Corduneanu, Hans P. Engler, Ronald Grimmer, REINHARD E. ScHULTZ, Purdue University, Kenneth B. Hannsgen, Melvin L. Heard, Klaus Nonlinear analogs of linear actions on spheres, Hiillig, William Hrusa, J. J. Levin, Stig-Olof 1:45 p.m. Saturday. Londen, R. C. MacCamy, Reza Malek-Madani, Victor J. Mizel, Simeon Reich, Michael Renardy, Special Sessions Olof Staffans, Robert L. Wheeler, and Marvin By invitation of the same committee, there will Zeman. be nine special sessions of selected twenty-minute Connections between codes and designs, VERA papers. The topics of these special sessions, the PLESS, University of illinois at Chicago Circle. names of the organizers, and lists of speakers are The speakers include E. F. Assmas, Jr., A. R. as follows: Calderbank, Marshall Hall, Jr., W. Cary Huffman, Local fields in number theory and algebraic Vera Pless, Harold N. Ward, and Richard M. geometry, ALAN ADoLPHSON, Oklahoma State Wilson. University. The speakers include Richard M. Algebraic topology, STEWART B. PRIDDY, Crew, Jack Diamond, D. S. Dummit, Mike Northwestern University. The speakers include Fried, David Goss, William E. Lang, John Myron A. K. Bousfield, F. R. Cohen, Karl Heinz Dover­ Masley, Diane Meuser, Warren M. Sinnott, Steven Liulevicius, Harvey Sperber, Lawrence C. Washington, and Rodney mann, Mark Feshbach, Arunas I. Yager. Margolis, C. A. McGibbon, Stephen A. Mitchell, J. A. Neisendorfer, Paul Selick, Bruce Williams, Operator theory in classical function spaces, and John W. Wood. EARL R. BERKSON, University of illinois, Urbana­ Champaign. The speakers include Constantin As a supplement to this special session, the Apostol, Richard Askey, Hari Bercovici, Carl C. Midwest Topology Seminar will meet on Sunday, Cowen, T. A. Gillespie, Jerome A. Goldstein, November 13 in Leverone Hall. Further details P.R. Halmos, William B. Johnson, B. F. Logan, may be obtained by contacting Professor Mark Daniel Luecking, Barbara D. MacCluer, Allen A. Mahowald of Northwestern University. Shields, Mitchell Taibleson, A. Torchinsky, and Commutative algebra, JUDITH D. SALLY, Guido Weiss. Northwestern University. The speakers include Probability and related parts of analysis, Luchezar Avramov, Paul M. Eakin, E. Graham DoNALD L. BuRKHOLDER, University of il­ Evans, Jr., Robert Fossum, Eloise Hamann, Wil­ linois, Urbana-Champaign. The speakers include liam J. Heinzer, Craig Huneke, Melvin Hochster, M. T. Barlow, K. L. Chung, J. L. Doob, Richard Ebert Matlis, Stephen McAdam, T. T. Moh, Chris­ Durrett, Marjorie G. Hahn, William B. Johnson, tel Rotthaus, Avinash Sathaye, Bernd Ulrich, and H. Jerome Keisler, Terry R. McConnell, Edwin Wolmer V. Vasconcelos.

630 Contributed Papers 8:15a.m. and 7:35p.m. Participants may call312- There will also be five sessions for contributed 454-7800 for information, or check at the ground ten-minute papers. transportation desk in the baggage area in the American or United Airlines terminals. The trip Registration to the Holiday Inn or Orrington Hotel in Evanston The meeting registration desk will be located on takes approximately one hour; the one-way fare is the second floor of the Norris University Center $7.20 per person. Groups of three or more may on Friday and in the lobby of Leverone Hall on prefer to call Northshore Taxi (864-7500) upon Saturday. The desk will be open from 8:00a.m. arrival at O'Hare Airport. Return bus service to 3:30 p.m. on Friday and from 8:00 a.m. to from Evanston to O'Hare is available; however, 11:00 a.m. on Saturday. The registration fees are participants are advised to obtain a schedule for $10 for members, $16 for nonmembers, and $5 for the return airport trip, since service is limited on students or unemployed mathematicians. Saturday and Sunday. Petition Table Amtrak offers direct train service from many points to Union Station in Chicago. Two blocks A petition table will be set up in the registration north of Union Station is the Chicago and area. Additional information can be found in a Northwestern Station, from which there is direct box in the Louisville meeting announcement in commuter train service to Davis Street Station this issue. in Evanston. The Davis Street Station is two Accommodations long blocks from the Holiday Inn and Orrington The following two hotels are holding blocks of Hotel, and is about seven blocks from the Norris rooms until October 27: Center. For those coming by car, the following easy access to the campus: Holiday Inn three options afford (1) Follow illinois Route 42 (Sheridan Road), a 1501 Sherman Avenue, Evanston 60201 generally north-south route within a few blocks Telephone: 312-491-6400 of Lake Michigan, which skirts the Northwestern (7 blocks southwest of Norris Center) campus on the west. The parking entrance to Single $46 Double/Twin $53 Northwestern at the south end of the campus (the Triple $59 Quadruple $65 point at which northbound traffic on Sheridan Orrington Hotel Road makes a sharp left turn) leads directly to 1710 Orrington Avenue, Evanston 60201 the parking lot adjacent to the Norris Center. Telephone: 312-866-8700 (2) Follow the Edens Expressway (Interstate 94) at the eastbound Skokie-Evanston (5 blocks southwest of Norris Center) and leave it exit, which leads into Dempster Street. Continue Single $50 Double $60 east on Dempster Street (Illinois Route 58) until it In order to obtain the rates listed above, intersects Sheridan Road. Turn left on Sheridan participants should be sure to mention the Road and proceed as in (1). American Mathematical Society's meeting when (3) Follow the Tri-State Tollway (Interstate 294) making their reservations. and leave it at the eastbound Dempster Street Food Service exit. Continue east on Dempster Street, turn left on Sheridan Road, and proceed as in (1). A large cafeteria is located on the ground floor at the Norris Center; it will be open all day on Parking Friday and Saturday. Parking permits may be obtained at the meeting Travel and Local Information registration desk at no charge on Friday and Saturday. Participants are advised that a permit The Continental Air Transport Company must be displayed, or cars will be ticketed. The provides bus service to Evanston from Chicago's most convenient place to park is in the large lot O'Hare Airport on a periodic schedule between adjacent to the Norris Center.

631 Presenters of Papers Numbers following the names indicate the speakers' positions on the program. •Invited one-hour lecturer *Special session speaker

*Apostol, C., 32 Erber, T., 92 *Kilgore, T., 14 *Rotthaus, C., 57 *Askey, R., 114 Evans, A. B., 84 Kimura, K., 86 *Sagher, Y., 60 *Assmus, E. F., Jr., 45 *Evans, E. G., Jr., 97 Krueger, W. M., 37 * Sathaye, A., 93 *Avramov, L., 56 •Fabes, E. B., 126 *Lang, W. E., 52 • Schultz, R. E., 127 •Bannai, E., 42 *Fefferman, R., 59 deLaubenfels, R. J., 87 * Selick, P., 142 *Barlow, M. T., 123 *Feshbach, M., 116 *Levin, J. J., 16 *Shapiro, J. H., 64 *Bauman, P., 6 Fisher, E., 22 *Lewis, J. E., 131 *Shields, A., 30 *Beals, M., 98 *Folland, G. B., 100 *Littman, W., 101 *Sinnott, W. M., 25 *Beckner, W., 58 *Fossum, R., 95 *Liulevicius, A., 78 *Sperber, S., 26 Beder, J. H., 21 *Fried, M., 49 *Logan, B. F., 115 * Staffans, 0., 18 *Bercmici, H., 31 *Gillespie, T. A., 72 *Londen, S.-0., 17 * Stroock, D. W., 34 Bhatt, B. S., 91 *Goldstein, J. A., 74 *Luecking, D., 29 * Taibleson, M., 70 *Bousfield, A. K., 117 *Goss, D., 51 *MacCamy, R. C., 134 *Tomas, P. A., 102 *Brennan, J. E., 11 *Graham, C. R., 129 *MaeCluer, B. D., 75 * Torchinsky, A., 71 Brawn, T. C., 124 *Greenleaf, A., 130 *Malek-Madani, R., 66 *Ulrich, B., 1 *Burton, T. A., 20 *Grimmer, R., 106 *Margolis, H., 77 * Varadhan, S., 141 * Calderbank, A. R., 41 *Hahn, M. G., 138 *Masley, J. M., 108 *Vasconcelos, W. V., 5 *Christ, M., 128 *Hall, M., Jr., 44 *Mattis, E., 2 * Verchota, G., 9 *Chung, K. L., 120 *Halmos, P.R., 112 *McAdam, S., 55 * Wainger, S., 61 *Cohen, F. R., 118 *Hamann, E., 96 *McConnell, T. R., 82 *Ward, H. N., 48 Cohen, J., 85 *Hannsgen, K. B., 135 *McGibbon, C. A., 119 *Washington, L. C., 111 *Coifman, R., 7 Haruki, H., 89 *Meuser, D., 50 *Weiss, G., 62, 69 * Corduneanu, C., 137 *Heard, M. L., 104 *Mitchell, S. A., 143 * Wheeden, R. L., 63 *Cowen, C. C., 73 *Heinzer, W. J., 3 *Mizel, V. J., 136 *Wheeler, R. L., 19 *Crew, R. M., 28 *Hochster, M., 53 *Moh, T. T., 54 *Williams, B., 76 Daepp, U., 83 *Hrusa, Vt/., 65 *Nagel, A., 132 *Wilson, R. M., 47 *Dahlberg, B. E. J., 99 *Huffman, W. C., 40 *Neisendorfer, J. A., 145 *Wolff, T., 133 •Davis, B., 43 *Huneke, C., 94 *Nevai, P., 15 *Wood, J. W., 79 Davis, J. F., 39 *Hollig, K., 107 *Perkins, E., 122 Woods, D., 125 *Diamond, J., 27 Jardine, J. F., 36 *Pless, V., 46 * Wu, J.-M., 10 *Doob, J. L., 33 * Jerison, D., 8 Prather, C., 24 *Yager, R. I., 110 *Dovermann, K. H., 144 * Jia, R.Q., 12 Protter, P., 23 Zaidman, S., 88 *Dummit, D. S., 109 *Johnson, W. B., 81, 113 *Quinto, E. T., 140 *Zeman, M., 105 *Durrett, R., 121 Kahn, 8. M., 38 *Reich, S., 103 Zhang, B., 90 *Eakin, P.M., 4 *Keisler, H. J., 35 *Renardy, M., 67 *Zinn, J., 139 *Engler, H. P., 68 *Khavinson, D., 13 *Rosenthal, H. P., 80

CONTEMPORARY MATHEMATICS

Complex Representations of G L(2, K} representations, (11) The description of GL(2, K) for Finite Fields K by generators and relations, (12) Non-decomposable characters of [X, (13) Assigning cuspidal represen­ llya Piatetski-Shapiro tations to non-decomposable characters, (14) The This book is composed from lecture notes of a correspondence between v and Pv• (15) The small course given at Tel-Aviv University by Professor Weil group and the small reciprocity law. Piatetski-Shapiro, who holds the Cissie and Aaron 3. r-functions and Bessel functions. (16) Whittaker Beare Chair in Algebra and Number Theory at that models, (17) The r-function of a representation, institution. They were prepared for publication by (18) Determination of p by r , (19) The Bessel Moshe )arden. function of a representation, (20) A computation Contents of rp(w) for a non-cuspidal p, (21) A computa- 1. Preliminaries: Representation theory; the general tion of rp(w) for a cuspidal p, (22) The characters linear group. (1) Linear representations of finite of G. groups, (2) Induced representations, (3) The Schur 1980 Mathematics Subject Classification: 20G05 algebra, (4) The group GL(2, K), (5) The conju- Contemporary Mathematics gacy classes of GL(2, K). Volume 16, viii + 72 pages (soft cover) 2. The representations of GL(2, K). (6) The reprc- List price $13 , institutional member $10, sentations of P, (7) The representations of B, (8) individual member $7 ISBN 0-8218-5019-9; L.C 82-24484 Inducing characters from B toG, (9) The Schur Publication date: January 1983 algebra of lnd~tt, (10) The dimension of cuspidal To'order, please specify CONM/16N Prepayment is required for all AMS publications. Order from AMS, P.O. Box 1571, Annex Station, Providence, Rl 02901, or call toll free 800-556-7774 to charge with Visa or MasterCard.

632 Program of the Sessions The time limit for each contributed paper in the AMS general 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 AMS sessions at this meeting will be found in the October 1983 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.

Friday, November 11, 1983, 8:30a.m.

Special Session on Commutative Algebra, I Norris Center, Room 2F 8:30- 8:50 (1) Homological properties which are invariant under linkage. RAGNAR-0. BucHWEITZ, Brandeis University, and BERND ULRICH*, Northwestern University (808-13-44) 9:00- 9:20 (2) Commutative semi-coherent and semi-regular rings. Preliminary report. EBEN MATLIS, Northwestern University (808-13-08) (Introduced by Judith D. Sally) 9:30- 9:50 (3) Artinian modules and modules for which all proper submodv.les are finitely generated. WILLIAM J. HEINZER*, Purdue University, West Lafayette, and DAVID C. LANTZ, Colgate University and Purdue University, West Lafayette (808-13-69) 10:00-10:20 (4) Analytic extensions of commutative rings. Preliminary report. PAUL M. EAKIN, University of Kentucky (808-13-96) 10:30-10:50 (5) The homological rigidity of the conormal module. Preliminary report. WaLMER V. VASCONCELOS, Rutgers University, New Brunswick (808-13-38)

Friday, November 11, 1983, 8:30a.m. Special Session on Harmonie Analysis and its Applications to Partial Differential Equations, I Norris Center, Room 2G 8:30- 8:50 (6) Positive solutions of elliptic equations and their adioints. PATRICIA BAUMAN, Massachusetts Institute of Technology (808-35-31) 9:00- 9:20 (7) Applications of a theorem of Da'llid and Joume. R. COIFMAN*, Yale University, andY. MEYER, Ecole Polytechnique Paris, France (808-42-72) 9:30- 9:50 (8) Unique continuation and non-existence of positive eigenvalues for Schriidinger operators. Preliminary report. DAVID JERISON*, Massachusetts Institute of Technology, and CARLOS E. KENIG, University of Minnesota, Minneapolis (808-35-03) 10:00-10:20 (9) Layer potentials and boundary value problems for Laplace's equation on Lipschitz domains. Preliminary report. GREGORY VERCHOTA, California Institute of Technology (808-35-123) 10:30-10:50 (10) Comparison of harmonic measure and Hausdorff measure. JANG-MEI Wu, University of illinois, Urbana-Champaign (808-31-87)

Friday, November 11, 1983, 8:30 a.m. Special Session on Approximation Theory, I Norris Center, Room 1A 8:30- 8:50 (11) Analytic continuation and the overconvergence of sequences of analytic functions. JAMES E. BRENNAN, University of Kentucky (808-30-86) 9:00- 9:20 (12) On the controlled approximation order from certain spaces of smooth bivariate splines. RoNG-QING JIA, Mathematics Research Center, Madison (808-41-112) 9:30- 9:50 (13) Analytic measures and annihilators of the algebra R(X). Preliminary report. DMITRY KHAVINSON, University of Arkansas, Fayetteville (808-30-12) 10:00-10:20 (14) Optimization with incomplete polynomials. IT. THEODORE KILGORE, Ohio State University, Marion (808-41-81) (Introduced by Stephen D. Fisher) 10:30-10:50 (15) Mean convergence of Lagrange interpolation. PAUL NEVAI, Ohio State University, Columbus (808-42-13)

Friday, November 11, 1983, 8:30 a.m. Special Session on Volterra Integral and Integra-Differential Equations, I Norris Center, Room 2E 8:30- 8:50 (16) The asymptotic behavior of a system of Volterra equations. J. J. LEVIN, University of Wisconsin, Madison (808-45-50) 9:00- 9:20 (17) Asymptotic estimates for resolvents of some nonintegrable Volterra kernels. STIG-OLOF LONDEN, Helsinki University of Technology, Finland (808-45-70)

633 9:30- 9:50 (18) A Volterra integral equation with a monotone nonlinearity. OLaF STAFFANS, Helsinki University of Technology, Finland (808-45-45) 10:00-10:20 (19) Factorization of locally analytic matrices and applications to systems of convolution equations. Preliminary report. RoBERT L. WHEELER*, Virginia Polytechnic Institute and State University, (808-45-51) 10:30-10:50 (20) Periodic solutions of nonlinear Volterra equations. T. A. BURTON, Southern Dlinois University, Carbondale (808-45-63)

Friday, November 11, 1983, 8:30 a.m. Session on Statistics and Probability Norris Center, Room 2C 8:30- 8:40 (21) Maximum likelihood estimates for binomial parameters when both are unlcnown, with application to birth and death processes. Preliminary report. JAY H. BEDER, University of Wisconsin, Milwaukee (808-62-133) 8:45- 8:55 (22) A Skorokhod embedding and an invariance principle for weighted i.i.d. random variables. Preliminary report. EVAN FISHER, University of Santa Clara (808-60-110) 9:00- 9:10 (23) Approximations of solutions of stochastic differential equations driven by semimartingales. PHILIP PROTTER, Purdue University, West Lafayette (808-60-104) 9:15- 9:25 (24) Oscillations of derivatives of entire characteristic functions. Preliminary report. CARL PRATHER, Virginia Polytechnic Institute and State University (808-30-55)

Friday, November 11, 1983, 9:00a.m. Special Session on Local Fields in Number Theory and Algebraic Geometry, I Norris Center, Room 2A 9:00- 9:20 (25) The theorem of Ferrero and Washington. WARREN M. SINNOTT, Ohio State University, Columbus (808-99-143) 9:30- 9:50 (26) Newton polygons of certain exponential sums. STEVEN SPERBER, University of Minnesota, Minneapolis (808-14-64) 10:00-10:20 (27) Ratios of hypergeometric functions. Preliminary report. JACK DIAMOND, Queens College, City University of New York (808-12-127) 10:30-10:50 (28) A global monodromy theorem for overconvergent F-isocrystals. Preliminary report. RicHARD M. CREW, Boston University (808-99-140)

Friday, November 11, 1983, 9:00 a.m. Special Session on Operator Theory in Classical Function Spaces, I Norris Center, Room 2B 9:00- 9:20 (29) Representation of functions in Bergman spaces. DANIEL LUECKING, University of Arkansas, Fayetteville (808-47 -43) 9:30- 9:50 (30) The Bergman and Dirichlet spaces. LEON BROWN, Wayne State University, and ALLEN SHIELDS*, University of Michigan, Ann Arbor (808-30-26) 10:00-10:20 (31) A real variable restatement of Riemann's hypothesis. HARI BERCOVICI*, Massachusetts Institute of Technology, and CIPRIAN FOIA§, Indiana University, Bloomington (808-47-30) 10:30-10:50 (32) Operators dilated by the Bergman shift. Preliminary report. CONSTANTIN APOSTOL*, Arizona State University, and HARI BERCOVICI, Massachusetts Institute of Technology (808-47-122)

Friday, November 11, 1983, 9:30 a.m. Special Session on Probability and Related Parts of Analysis, I Norris Center, Room 2C 9:30- 9:50 (33) The domination principle in potential theory and in martingale theory. J. L. DooB, University of lllinois, Urbana-Champaign (808-60-138) 10:00-10:20 (34) Subellipticity, hypoellepticity, ergodicity, and what probabilists can say about them. DANIEL W. STROOCK, University of Colorado, Boulder (808-60-28) 10:30-10:50 (35) Laws of large numbers for stochastic processes with fast and slow components. Preliminary report. H. JEROME KEISLER, University of Wisconsin, Madison (808-60-103)

Friday, November 11, 1983, 9:30 a.m. Session on Algebraic Topology Norris Center, Room 2H 9:30- 9:40 (36) K-theory of algebraically closed fields via etale cohomology. Preliminary report. J. F. JARDINE, University of Chicago (808-18-22) 9:45- 9:55 (37) The 2-primary K-theory Adams spectral sequence. WARREN M. KRUEGER, New Mexico State University, Las Cruces (808-55-47) 10:00-10:10 (38) Orientable manifolds that fiber over 8 4 up to cobordism. STEVEN M. KAHN, Wayne State University (808-55-48)

634 10:15-10:25 (39) The homology space form problem. JAMES F. DAVIS*, University of Notre Dame, and SHMUEL WEINBERGER, Princeton University (808-57-56)

Friday, November 11, 1983, 10:00 a.m. Special Session on Connections Between Codes and Designs, I Norris Center, Louis Room South 10:00-10:20 (40) On automorphism groups of designs. W. CARY HUFFMAN, Loyola University, Chicago (808-05-78) 10:30-10:50 (41) On codes in the Hamming scheme Hn(q). A. R. CALDERBANK*, Bell Laboratories, Murray Hill, and J.-M. GOETHALS, Philips Research Laboratory, The Netherlands (808-05-91)

Friday, November 11, 1983, 11:00 a.m. Invited Address Norris Center, Louis Room South 11:00-12:00 (42) Orthogonal polynomials and algebraic combinatorics. EIICHI BANNAI, Ohio State University, Columbus (808-05-109)

Friday, November 11, 1983, 1:45 p.m. Invited Address Norris Center, Louis Room South 1:45- 2:45 (43) Brownian motion and analytic functions. BURGESS DAVIS, Purdue University, West Lafayette (808-60-11)

Friday, November 11, 1983, 3:00 p.m. Sepcial Session on Connections Between Codes and Designs, IT Norris Center, Room 2H 3:00- 3:20 (44) Relations between codes and designs. Preliminary report. MARSHALL HALL, JR., California Institute of Technology (808-05-71) 3:30- 3:50 (45) A Kirkman-Sylvester problem/or graphs. E. F. AssMUS, JR.*, Lehigh University, and CHESTER J. SALWACH, Lafayette College (808-05-92) 4:00- 4:20 (46) Duadic codes. JEFFREY LEON, JOHN MASLEY and VERA PLESS*, University of lllinois, Chicago (808-94-57) 4:30- 4:50 (47) Generalized preparata and Goethals codes. RICHARD M. WILSON, California Institute of Technology (808-05-101) (Introduced by VeraS. Pless) 5:00- 5:20 (48) Minimum weights of Abelian group codes. Preliminary report. HAROLD N. WARD, University of Virginia (808-94-116)

Friday, November 11, 1983, 3:00p.m. Special Session on Local Fields in Number Theory and Algebraic Geometry, IT Norris Center, Room 2A 3:00- 3:20 (49) L-series on a Galois stratification. MIKE FRIED, University of California, Irvine (808-12-18) (Introduced by Alan C. Adolphson) 3:30- 3:50 (50) On a Poincare series of two variables. Preliininary report. DIANE MEUSER, Boston University (808-10-130) 4:00- 4:20 (51) Some polynomials arising in the arithmetic theory of curves over a finite field. DAVID Goss, Ohio State University, Columbus (808-12-121) 4:30- 4:50 (52) Classical Enriques surfaces in characteristic two. Preliminary report. WILLIAM E. LANG, University of Minnesota, Minneapolis (808-14-139)

Friday, November 11, 1983, 3:00p.m. Special Session on Commutative Algebras, IT Norris Center, Room 2F 3:00- 3:20 (53) Matrix problems with applications to studying modules with finite free resolutions. Preliininary report. MELVIN HOCHSTER, University of Michigan, Ann Arbor (808-13-98) 3:30- 3:50 (54) The set-theoretic complete-intersection problem for algebroid curves. Preliininary report. T. T. MoH, Purdue University, West Lafayette (808-99-142) (Introduced by Judith D. Sally) 4:00- 4:20 (55) Grading sequences. Preliininary report. STEPHEN McADAM, University of Texas, Austin (808-13-20) 4:30- 4:50 (56) Homotopy Lie algebras for local rings and DG algebras. Preliminary report. LuCHEZAR AvRAMOV, University of lllinois, Urbana-Champaign (808-13-111) (Introduced by Robert Fossum) 5:00- 5:20 (57) Power series extensions and excellence property of local rings with Artin approximation. CHRISTEL RoTTHAus, University of Michigan, Ann Arbor, and University of Munster, Federal Republic of Germany (808-13-83) (Introduced by Judith D. Sally)

635 Friday, November 11, 1983, 3:00 p.m.

Special Session on Harmonic Analysis and its Applications to Partial Dift'erential Equations, IT Norris Center, Room 2G 3:00- 3:20 (58) Harmonic analysis, Sobolev inequalities and symmetrization. Preliminary report. WILLIAM BECKNER, University of Texas, Austin (808-42-05) 3:30- 3:50 (59) The atomic decomposition of HP functions on product spaces ROBERT FEFFERMAN, University of Chicago (808-42-107) (Introduced by Carlos E. Kenig) 4:00- 4:20 (60) A survey of recent results in interpolation theory. YORAM SAGHER, University of Illinois, Chicago (808-46-88) (Introduced by Carlos E. Kenig) 4:30- 4:50 (61) Recent progress on Hilbert transforms and maximal functions related to flat curves. STEPHEN WAINGER, University of Wisconsin, Madison (808-42-125) 5:00- 5:20 (62) A connection between partial differential equations and the theory of complex interpolation of Banach spaces. Preliminary report. RICHARD HOCHBERG and GUIDO WEISS*, Washington University (808-35-126) 5:30- 5:50 (63) Poincare and Sobolev inequalities with two weight functions. Preliminary report. RICHARD L. WHEEDEN*, Rutgers University, New Brunswick, and SAGUN CHANILLO, Indiana University, Bloomington (808-35-01) (Introduced by Carlos E. Kenig)

Friday, November 11, 1983, 3:00 p.m.

Special Session on Approximation Theory, n Norris Center, Room 1A 3:00- 3:20 (64) VMO, Alexander's area estimate, and Putnam's theorem. SHELDON AxLER and JOEL H. SHAPIRO*, Michigan State University (800-46-80) 3:30- 4:30 Problem session

Friday, November 11, 1983, 3:00p.m.

Special Session on Volterra Integral and Integro-dift'erential Equations, IT Norris Center, Room 2E 3:00- 3:20 (65) A semilinear hyperbolic-Volterra equation. WILLIAM HRUSA, Carnegie-Mellon University (808-35-131) 3:30- 3:50 (66) Formation of singularities for a conservation law with memory. REZA MALEK-MADANI*, United States Naval Academy, and JOHN A. NOHEL, University of Wisconsin, Madison (808-45-04) 4:00- 4:20 (67) A local existence and uniqueness theorem for a K-BK Z fluid. MICHAEL RENARDY, University of Wisconsin, Madison (808-76-65) 4:30- 4:50 (68) Stabilization of solutions for a class of partial integra-differential equations. Preliminary report. HANS P. ENGLER, University of Texas, Austin (808-45-90) 5:00- 6:00 Discussion and open problems

Friday, November 11, 1983, 3:00p.m.

Special Session on Operator Theory in Classical Function Spaces, n Norris Center, Room 2B 3:00- 3:20 {69) The weak-* completion of Bq and the characterization of bounded convolution operators on Bq. Preliminary report. YvEs MEYER, Ecole Polytechnique, Paris, and MITCHELL T AIBLESON and GuiDo WEiss*, Washington University (808-42-117) 3:25- 3:45 (70) A counterexample relevant to the study of intermediate spaces between Boo and L 2 . Prelhninary report. YvEs MEYER, Ecole Polytechnique, Paris, and MITCHELL TAIBLESON* and GuiDo WEISS, Washington University (808-42-118) 3:50- 4:10 (71) A Hardy-Littlewood embedding theorem. B. JAWERTH, Washington University, and A. TORCHINSKY*, Indiana University, Bloomington (808-47-119) (Introduced by Earl R. Berkson) 4:15- 4:35 (72) Spectral decompositions and AC functions on the circle. Preliminary report. E. R. BERKSON, University of lllinois, Urbana-Champaign, and T. A. GILLESPIE*, University of Edinburgh, Scotland (808-47-76) (Introduced by Earl R. Berkson) 4:40- 5:00 (73) Some subnormal Toeplitz operators. CARL C. CoWEN, Purdue University, West Lafayette (808-47-60)

5:05- 5:25 (74) The L2 and L1 theories of aujat = t::.u+cuf I X 12 . PIERRE BARAS, University of Grenoble, France, and JEROME A. GOLDSTEIN*, Tulane University (808-35-42) 5:30- 5:50 (75) Compact composition operators on HP(BN)· BARBARA D. MAcCLUER, University of Virginia (808-32-33)

636 Friday, November 11, 1983, 3:00 p.m.

Special Session on Algebraic Topology, I Norris Center, Room 2C 3:00- 3:20 (76) Equivariant algebraic K -theory. Preliminary report. BRUCE WILLIAMS, University of Notre Dame (808-55-113) 3:30- 3:50 (77) Periodic structure in stable homotopy theory. HARVEY MARGOLIS, Boston College (808-55-77) 4:00- 4:20 (78) Symmetric products of cycles. ARUNAS LIULEVICIUS, University of Chicago (808-55-19) 4:30- 4:50 (79) Some homotopy types which support a unique complex structure. Preliminary report. ANATOLY S. LIBGOBER and JoHN W. Woon*, University of illinois, Chicago (808-57-114)

Friday, November 11, 1983, 3:00p.m.

Special Session on Probability and Related Parts of Analysis, II Norris Center, Louis Room South 3:00- 3:20 Informal discussion 3:30- 3:50 (80) A new stopping-time Banach space. Preliminary report. HASKELL P. RoSENTHAL, University of Texas, Austin (808-60-99) 4:00- 4:20 (81) "Random embeddings" of finite dimensional normed spaces. Preliminary report. WILLIAM B. JoHNSON, Ohio State University, Columbus (808-60-128) 4:30- 4:50 (82) Littlewood-Paley inequalities for Banach-valued functions. TERRY R. McCONNELL, Cornell University (808-60-67) (Introduced by Donald L. Burkholder)

Saturday, November 12, 1983, 8:00a.m. Session on Commutative Rings Leverone Hall, Room G093 8:00- 8:10 (83) Openness and invariance results on generalized Cohen-Macaulay rings. Preliminary report. ULRICH DAEPP*, Bucknell University, and ALAN EVANS, Vassar College (808-13-62) 8:15- 8:25 (84) Algorithmic methods in affine semigroup rings. ALAN B. EVANS, Vassar College (808-13-102)

Saturday, November 12, 1983, 8:00 a.m. Session on Analysis and Applied Mathematics Leverone Hall, Room 1056 8:00- 8:10 (85) Stress potentials on C1 domains in the plane. JONATHAN COHEN*, University of Tennessee, Knoxville, and JoHN GossELIN, University of Georgia (808-35-53) 8:15- 8:25 (86) Kernels for the a-Neumann problem on the unit ball. KYOKO KIMURA, University of Toronto (808-35-46) 8:30- 8:40 (87) Well-behaved derivations on C(O, 1). RALPH J. DELAUBENFELS, Dartmouth College (808-47- 14) 8:45- 8:55 (88) Abstract differential equations with almost-periodic solutions. S. ZAIDMAN, Universite de Montreal (808-34-06) 9:00- 9:10 (89) On a functional equation for Jacobi's elliptic function cn(z; k). Preliminary report. HIROSHI HARUKI, University of Waterloo (808-39-75) 9:15- 9:25 (90) On the existence and uniqueness of random solutions to some nonlinear stochastic integral equations. BINGGEN ZHANG*, Shandong College of Oceanology, People's Republic of China, and University of South Carolina, Columbia, and W. J. PADGETT, University of South Carolina, Columbia (808-45-61) (Introduced by Robert M. Stephenson, Jr.) 9:30- 9:40 (91) The movement of single large liquid bubbles in vertical porous tubes. B. S. BHATT, University of the West Indies, Trinidad (808-76-134) (Introduced by Paul T. Bateman) 9:45- 9:55 (92) Urn models and pseudo-random number generators: the few-branch principle. W. DARSOW, T. ERBER* and M. FRANK, illinois Institute of Technology (808-82-36)

Saturday, November 12, 1983, 8:30a.m. Special Session on Commutative Algebra, III Leverone Hall, Room G093 8:30- 8:50 (93) Criteria for locally polynomial rings. Preliminary report. AviNASH SATHAYE, University of Kentucky (808-13-95) 9:00- 9:20 (94) Residual intersections. CRAIG HUNEKE, Purdue University, West Lafayette (808-13-82) 9:30- 9:50 (95) Formal group actions and Invariants. RoBERT FossuM, University of illinois, Urbana­ Champaign (808-13-68) 10:00-10:20 (96) R-algebras and R-reduced-algebras. ELOISE HAMANN, Elmhurst College (808-13-97) 10:30-10:50 (97) On Kth syzygies of rank K. Preliminary report. E. GRAHAM EVANS, JR.*, and PHILLIP A. GRIFFITH, University of illinois, Urbana-Champaign (808-13-66) (Introduced by Judith D. Sally)

637 Saturday, November 12, 1983, 8:30a.m. Special Session on Hannonic Analysis and its Applications to Partial Differential Equations, m Leverone Hall, Room G226 8:30- 8:50 (98) Propagation of smoothness for second order nonlinear hyperbolic equations. Preliminary report. MICHAEL BEALS, Rutgers University, New Brunswick (808-35-115) 9:00- 9:20 (99) Nonnegative solution of the porous medium equation. BJORN E. J. DAHLBERG*, University of Texas, Austin, and CARLOS E. KENIG, University of Minnesota, Minneapolis (808-35-100) 9:30- 9:50 (100) Some integral transforms related to the Fourier transform. Preliminary report. G. B. FOLLAND, University of Washington (808-42-89) 10:00-10:20 (101) Farfield patterns for solutions of PDEs in the complement of a proper cone. WALTER LITTMAN, University of Minnesota, Minneapolis (808-35-106) 10:30-10:50 (102) Systems of Stein- Weiss and Schmid, and representations of semisimple groups. Preliminary report. PETER A. ToMAS, University of Texas, Austin (808-42-54)

Saturday, November 12, 1983, 8:30 a.m. Special Session on Volterra Integral and Integro-dift'erential Equations, m Leverone Hall, Room G208 8:30- 8:50 (103) Asymptotic behavior of solutions to nonlinear Volterra integral equations in Banach spaces. SIMEON REICH, University of Southern California (808-45-02) 9:00- 9:20 (104) A class of integra-differential equations. Preliminary report. MELVIN L. HEARD, University of Dlinois, Chicago (808-45-21) 9:30- 9:50 (105) Quasilinear integra-differential equations and applications. RoNALD GRIMMER and MARVIN ZEMAN*, Southern Dlinois University, Carbondale (808-45-32) 10:00-10:20 (106) Regularity of solutions of linear Volterra integra-differential equations in Banach space. RoNALD GRIMMER* and MARIO MILMAN, Southern Dlinois University, Carbondale (808-45-07) 10:30-10:50 (107) A nonlinear integral equation occurring in a singular free boundary problem. KLAUS H6LLIG*, Texas A&M University, and JoHN A. NoHEL, University of Wisconsin, Madison (808-45-15)

Saturday, November 12, 1983, 8:30a.m. Special Session on Local Fields in Number Theory and Algebraic Geometry, m Leverone Hall, Room 1054 9:00- 9:20 (108) Local fields in number theoretic computations. JOHN MYRON MASLEY, University of Dlinois, Chicago (808-12-129) 9:30- 9:50 (109) A new classification of Demuskin groups. D. S. DuMMIT*, Macalester College, and J. LABUTE, McGill University (808-12-135) (Introduced by Alan C. Adolphson) 10:00-10:20 (110) p-adic measures on Galois groups. RoDNEY I. YAGER, Oklahoma State University, Stillwater (808-12-25) 10:30-10:50 (111) The simplest cubic fields: associated quartic fields and elliptic curves. LAWRENCE C. WASHINGTON, University of Maryland, College Park (808-12-132)

Saturday, November 12, 1983, 9:00 a.m. Special Session on Operator Theory in Classical Function Spaces, m Leverone Hall, Room G210 9:00- 9:20 (112) Subnormal suboperators and the subdiscrete topology. P. R. HALMOS, Indiana University, Bloomington (808-47-17) 9:30- 9:50 (113) On Banach spaces X for which K(X) is an M-ideal in L(X). Preliminary report. CHONG-MAN CHo and WILLIAM B. JOHNSON*, Ohio State University, Columbus (808-47-120) 10:00-10:20 (114) Orthogonal polynomials as solutions to some specific three term recurrence relations. Preliminary report. RICHARD AsKEY, University of Wisconsin, Madison (808-33-09) 10:30-10:50 (115) The norm of certain convolution transforms on Lp spaces of entire functions of exponential type. B. F. LoGAN, Bell Laboratories, Murray Hill (808-47-79) (Introduced by Earl R. Berkson)

Saturday, November 12, 1983, 9:00a.m. Special Session on Algebraic Topology, II Leverone Hall, Room G214 9:00- 9:20 (116) The Segal conjecture for compact Lie groups: Some corollaries. Preliminary report. MARK FESHBACH, University of Minnesota, Minneapolis (808-55-74) 9:30- 9:50 (117) Uniqueness of infinite loop structures on K-theoretically local spaces. Preliminary report. A. K. BousFIELD, University of Dlinois, Chicago (808-55-94) 10:00-10:20 (118) An analogue of the Kahn-Priddy theorem for the 3-sphere. Preliminary report. F. R. CoHEN, University of Kentucky (808-55-39)

638 10:30-10:50 (119) Homotopy groups of finite dimensional spaces. C. A. McGIBBON*, Wayne State University, and J. A. NEISENDORFER, Ohio State University, Columbus (808-55-27)

Saturday, November 12, 1983, 9:00a.m.

Special Session on Probability and Related Parts of Analysis, ill Leverone Hall, Room G113 9:00- 9:20 (120) Probabilistic approach to boundary value problems for Schrodinger's equation. K. L. CHUNG, Stanford University (808-60-24) 9:30- 9:50 (121) Curvature and the asymptotic behavior of Brownian motion. Preliminary report. RICHARD DuRRETT, University of California, Los Angeles (808-60-29) 10:00-10:20 (122) On singularities of the sample paths of Ito integrals. Preliminary report. MARTIN BARLOW, University of Cambridge, England, and EDWIN PERKINS*, University of British Columbia (808-60-137) (Introduced by Donald L. Burkholder) 10:30-10:50 (123) Martingale-type inequalities for optional processes at general times. M. T. BARLow* and S. JACKA, University of Cambridge, England, and M. YoR, Universite de Paris, France (808-99-144)

Saturday, November 12, 1983, 10:00 a.m. Session on Combinatorics and Number Theory Leverone Hall, Room 1056 10:00-10:10 (124) Monochromatic lines in finite vector spaces. T. C. BROWN, Simon Fraser University (808-05-41) 10:15-10:25 (125) A conjecture of Lee. Preliminary report. CAL GuTHRIE and DALE WooDs*, Central State University, Oklahoma (808-10-93)

Saturday, November 12, 1983, 11:00 a.m. Invited Address Leverone Hall, Room G226 11:00-12:00 (126) Harmonic analysis and properties of solutions of partial differential equations with nonsmooth coefficients. EuGENE B. F ABES, University of Minnesota, Minneapolis (808-35-84)

Saturday, November 12, 1983, 1:45 p.m. Invited Address Leverone Hall, Room G226 1:45- 2:45 (127) Nonlinear analogs of linear actions on spheres. REINHARD E. ScHULTZ, Purdue University, West Lafayette (808-57-85)

Saturday, November 12, 1983, 3:00p.m. Special Session on Hannonie Analysis and its Applications to Partial Differential Equations, IV Leverone Hall, Room G214 3:00- 3:20 (128) The Fefferman-Stein-Uchiyama decomposition of BMO on the Heisenberg group. MICHAEL CHRIST*, Princeton University, and DARYL GELLER, State University of New York, Stony Brook (808-43-10) 3:30- 3:50 (129) Some singular integrals arising in degenerate elliptic boundary problems. Preliminary report. C. RoBIN GRAHAM, Princeton University (808-35-108) 4:00- 4:20 (130) The first eigenvalue of a CR manifold. Preliminary report. ALLAN GREENLEAF, University of Rochester (808-58-52) 4:30- 4:50 (131) Parametrices for a class of characteristic Cauchy problems. JEFF E. LEWIS, University of Illinois, Chicago (808-35-49) 5:00- 5:20 (132) Metrics defined by vector fields. Preliminary report. ALEXANDER NAGEL, University of Wisconsin, Madison (808-35-59) 5:30- 5:50 (133) On a weighted inequality. Preliminary report. S.-Y. A. CHANG, University of California, Los Angeles, J. M. WILSON, University of Wisconsin, Madison, and T. WoLFF*, California Institute of Technology (808-26-124) (Introduced by Walter Craig)

Saturday, November 12, 1983, 3:00p.m. Special Session on Volterra Integral and Integra-differential Equations, IV Leverone Hall, Room G208 3:00- 3:20 (134) Mixed variational methods for time-dependent problems. R. C. MAcCAMY* and M. SuRI, Carnegie-Mellon University (808-45-16) 3:30- 3:50 (135) A series solution for a functional differential equation. Preliminary report. KENNETH B. HANNSGEN, Virginia Polytechnic Institute and State University (808-45-37) 4:00- 4:20 (136) Effect of noise on hereditary equations. VICTOR J. MIZEL *, Carnegie-Mellon University, and VICTOR TRUTZER, West Virginia University, Morgantown (808-45-23)

639 4:30- 4:50 (137) Two qualitative inequalities and their applications. Preliminary report. C. CORDUNEANU, University of Texas, Arlington (808-99-141)

Saturday, November 12, 1983, 3:00 p.m. Special Session on Probability and Related Parts of Analysis, IV Leverone Hall, Room G113 3:00- 3:20 (138) Compact, convex stable random sets of a Banach space. EVARIST GrNE, Texas A&M University, and MARJORIE G. HAHN*, Tufts University (808-60-40) 3:30- 3:50 (139) Limit theorems for empirical measures under combinatorial conditions. EvARIST GINE, Louisiana State University and Texas A&M University, College Station, and JOEL ZINN*, Texas A&M University, College Station (808-60-58) 4:00- 4:20 (140) Distances between measures from !-dimensional projections as implied by continuity of the inverse Radon transform. MARJORIE G. HAHN and ERic TODD QUINTO*, Tufts University (808-60-35) 4:30- 4:50 (141) Large deviations for Gaussian processes. SRINIVASA VARADHAN* and M. D. DONSKER, Courant Institute of Mathematical Sciences, New York University (808-99-145)

Saturday, November 12, 1983, 3:30p.m. Special Session on Algebraic Topology, m Leverone Hall, Room G226 3:30- 3:50 (142) The elements of PH*(O'[fS'[f;ZfpZ) annihilated by all Steenrod operations. PAUL SELICK, University of Western Ontario (808-55-136) 4:00- 4:20 (143) Some new finite complexes obtained from the Steinberg module. STEPHEN A. MITCHELL, Princeton University (808-55-34) 4:30- 4:50 (144) Smith equivalent representations for odd order cyclic groups. Preliminary report. KARL HEINZ DovERMANN*, Purdue University, West Lafayette, and TED PETRIE, Rutgers University, New Brunswick (808-57-105) 5:00- 5:20 (145) Some properties of 3-dimensional Moore spaces. J. A. NEISENDORFER, Ohio State University, Columbus (808-55-73)

Paul T. Batelllllll Urbana, lllinois Associate Secretary

and an inversion of the list showing LC numbers MATHFILE USER'S GUIDE and corresponding AMS classification codes. MATHFILE is the Society's new computer-search­ able version of Mathematical Reviews (the cumulative Index of terms occurring in the subject classification. index covering 1973 to 1979, as well as the contents Alphabetic listing of subject words from the 1980 of issues published in 1980 and since, including for Mathematics Subject Classification with the corre­ the latter texts of the reviews themselves). For infor­ sponding class numbers given for each. This list will mation on MATHFILE see the February 1982 Notices, be very helpful to searchers unfamiliar with the page 169. 1980 Mathematics Subject Classification. A user's guide has been prepared by the Society Title words of entries reviewed from 1973 to 1979, to make searching MATH Fl LE easier, more effective arranged alphabetically with class numbers under and faster. The Guide includes: which the entries occurred and frequency of occur­ Instructions. How to get started on the vendors' sys­ rence of each word in each section. tems, an explanation of the fife and suggestions on Inversion of the title word list, arranged by classifi­ search techniques. cation number, showing which title words occurred Abbreviations. Journal name abbreviations used by in each section and with what frequency. This will Mathematical Reviews, and the full titles as defined be useful in finding the right words to search on a by the Library of Congress, the ISSN, Coden, and specific subject. useful publishing information. Approximately 350 pages, Three-ring Binder Subject Classification Systems. A correlated four­ List price $55, institutional member $41, individual member $41 column display of the two (1970 and 1980) slightly ISBN 0-8218-0216-X different systems, the Library of Congress system, Publication date: May 1982 Prepayment is required for all AMS publications. Order from AMS, P.O. Box 1571, Annex Station, Providence, Rl 02901, or call toll free 800-556-7774 to charge with Visa or MasterCard.

640 Louisville Meetings, January 25-29, 1984 First Announcement

The January 1984 Joint Mathematics Meetings, 90th Annual Meeting of the AMS including the 90th Annual Meeting of the AMS January 25-28, 1984 and the 67th Annual Meeting of the Mathematical Association of America will be held January 25-29 (Wednesday-Sunday), 1984, in Louisville, Fifty-seventh Josiah Willard Gibbs Lecture Kentucky. The meetings will be preceded by the The 1984 Gibbs lecture will be presented at 8:30 AMS Short Course on January 23-24 (Monday­ p.m. on Wednesday, January 25, by HERBERT A. Thesday), 1984. Sessions will take place in the SIMON of Carnegie-Mellon University. Professor Commonwealth Convention Center and the Hyatt Simon will speak on Computer programs that Regency Louisville. model the process of scientific and mathematical The members of the Local Arrangements discovery. Committee are W. Wistar Comfort (ex-officio), Colloquium Lectures Roger H. Geeslin (publicity director), Thomas L. Holloman, William J. LeVeque (ex-officio), David There will be a series of four Colloquium P. O'Toole, David P. Roselle (ex-officio), Richard Lectures presented by BARRY MAZUR of Harvard Werle, and W. Wiley Williams (chairman). University. The title of this lecture series is On the arithmetic of curves. The lectures will be given WHERE TO FIND IT PAGE at 1:00 p.m. daily, Wednesday through Saturday, January 25-28. PREREGISTRATION AND HOUSING 642, 643 Bocher Prize ANNUAL MEETING OF THE AMS 641 Gibbs Lecture, Colloquium Lectures, Pri•es, The 1984 Bocher Memorial Prize will be Invited Addresses, Special Sessions, Contributed awarded at 4:00 p.m. on Thursday, January 26. Papers, Other AMS Sessions, Council and Business Meetings Invited Addresses AMS SHORT COURSE 645 By invitation of the Program Committee, there EMPLOYMENT REGISTER 657 will be eight invited one-hour addresses. The ANNUAL MEETING OF THE MAA 646 names of the speakers, their affiliations, the dates Retiring Presidential Address, Invited and times of their talks, and some of the titles Addresses, Minicourses, Other MAA Sessions, follow: Business Meeting, Board of Governors OTHER ORGANIZATIONS 647 A~,NAM,NSF,RMMC TIMETABLE 651 OTHER EVENTS OF INTEREST 648 Book Sales, Exhibits, MATHFILE, Petition Table ACCOMMODATIONS 648 Hotels REGISTRATION DESK 652 Fees, Dates and Times, Services MISCELLANEOUS INFORMATION 656 Child Care, Local Information, Parking, Social Event, Travel, Weather MAP 649

IMPORTANT DEADLINES AMS Abstracts, For consideration for special sessions October 12 Of contributed papers November 2 Employment Register (Applieanta & Employers) December 5 Preregistration and Housing Deeember 5 Motion• for AMS Buaineas Meeting December 27 Preregiatration eaneellationa (50% refund) January 22 Dues eredit for nonmembers/atudenta February 29

Herbert A. Simon, Gibbs Lecturer

641 Preregistration

Preregistration. Preregistration for these A $4 charge will be imposed for all invoices meetings must be completed by December 5, prepared when Preregistration/Housing forms are 1983. Those wishing to preregister must complete submitted without accompanying check(s) for the the form which appears at the back of this preregistration fee(s) and room deposits, or are issue and submit it together with the appropriate accompanied by an amount insufficient to cover preregistration fee(s) to the Mathematics Meetings the total fee(s). Preregistration/Housing forms Housing Bureau in Providence by December 5. received well before the deadline of December 5 which are not accompanied by correct payment will Preregistration fees do not represent an advance be returned to the participant with a request for deposit for lodgings. One must, however, preregister resubmission and full payment. for the meetings in order to obtain confirmed A 50 percent refund of the preregistration fee(s) hotel accommodations through the Mathematics will be made for all cancellations received in Meetings Housing Bureau, as outlined on the facing Providence no later than January 22. No page. refunds will be granted for cancellations As stated in the section titled Housing, all received after that date, or to persons who do requests for hotel accommodations must be ac­ not attend the meetings. companied by one night's room deposit for each The only exception to this rule is someone who room requested. A separate check made out preregisters for the Joint Mathematics Meetings to the Louisville Convention and Visitors Bureau only in order to attend an MAA Minicourse, and and/or a major credit card number for this deposit is too late to obtain a slot in the Minicourse. must accompany the Preregistration/Housing form In this case, full refunds will be made of the should housing be required. Joint Mathematics Meetings preregistration fee(s), provided the preregistrant has cheeked the box Checks for preregistration fees should be made on the Preregistration/Housing form that this was payable to the AMS. Canadian checks must be his or her intent. Individuals who preregister for marked for payment in U.S. funds. Those who both the Joint Meetings and a Minicourse and who preregister for the Joint Mathematics Meetings pay intend to attend the Joint Meetings, even if the fees which are 30 percent lower than those who Minicourse is not available, should, of course, not register at the meetings. The preregistration fees check the box on the Preregistration/Housing form. are as follows: In this case the Joint Meetings preregistration will AMS Short Course be processed. Those who wish to preregister for the Employ­ Student/Unemployed $ 5 ment Register should read carefully the special All Others $25 article titled "Mathematical Sciences Employment Joint Mathematics Meetings Register" which follows this announcement of the Member of AMS, MAA $47 Louisville meetings. The attention of applicants Emeritus Member of AMS, MAA $12 is particularly directed to the box regarding the Nonmember $71 December issue of Employment Information in Student/Unemployed $12 the Mathematical Sciences. Employer, Employment Register $50 Those who preregister for the AMS Short Course Applicant, Employment Register no charge will be able to pick up their badges and other MAA Minicourses (payable at meeting) $20 each material in Louisville after 11:00 a.m. on Monday, January 23, during the hours that the AMS Short There will be no extra charge for members of Course registration desk is open. the families of registered participants, except that Those who preregister for either the Joint all professional mathematicians who wish to attend Mathematics Meetings or the MAA Minicourses or sessions must register independently. both will be able to pick up their badges and All full-time students currently working toward other material in Louisville after 4:00 p.m. on a degree or diploma qualify for the student Tuesday, January 24, during the hours the Joint registration fees, regardless of income. Mathematics Meetings registration desk is open. The unemployed status refers to any person cur­ Please read the facing page titled Housing care­ rently unemployed, actively seeking employment, fully before completing the Preregistration/Housing form. and who is not a student. It is not intended to include any person who has voluntarily resigned or N.B.: Place your AMS or MAA mailing label retired from his or her latest position. on the Preregistration/Housing form where The emeritus status refers to any person who indicated. If you do not have a label has been a member of the AMS or MAA for twenty readily available, please supply complete name, years or more, and is retired on account of age from address, and AMS or MAA member code. his or her latest position.

642 Housing

Mathematics Meetings Housing Bureau. The Bureau, or give you a room outside of the block, Preregistration/Housing form for requesting hotel which may be at a higher rate. accommodations will be found at the back of The number of rooms being held by the Louisville this issue. Use of the services offered by the hotels at each rate is limited. Housing assignments Mathematics Meetings Housing Bureau requires are made on a first-come, first-served basis, so preregistration for the meetings. Persons desiring participants desiring low-cost accommodations are confirmed hotel accommodations should complete urged to get their housing requests in as early as the form, or a reasonable facsimile, and send it to possible. Participants should also be aware that the Mathematics Meetings Housing Bureau, Post the special rates being offered in the section titled Office Box 6887, Providence, Rhode Island 02940, Hotels may not be available after December 5. so that it will arrive no later than December 5, Housing requests received after the deadline of 1983. December 5 most surely cannot be honored. Please read carefully the section on Hotels before Participants are strongly urged to rank every completing the form. Forms sent to the wrong hotel on the housing form in the order of preference, address and thus incurring delay in delivery to the and circle the type of room and the rate desired. Housing Bureau until after the deadline cannot be Reservations will be made in accordance with accepted and will, therefore, be returned. preferences indicated on the reservation form insofar The Mathematics Meetings Housing Bureau as this is possible. Participants who rank only a has initiated a new policy whereby participants few of the hotels may find themselves assigned to requesting hotel accommodations in Louisville a hotel which is not satisfactory. If not all hotels are required to submit housing deposits when are ranked, and all rooms have been filled at the preregistering. Each deposit must be equal to ranked hotels, the assignment will be made at an the daily room rate for each room requested, and unranked hotel with the next lowest rate. may be submitted either by personal check (made Participants who are able to do so are urged to out to the Louisville Convention and Visitors share a room whenever possible as this procedure Bureau) and/or a major credit card as indicated in can be economically beneficial. The housing form the last column of the housing form. The method should be fully completed to ensure proper assign­ of payment differs with each of the participating ment of rooms. Participants planning to share hotels, and careful attention must be given to these accommodations should provide the name(s) of the requirements when submitting deposits. Please do person(s) with whom they plan to occupy a room. not include housing deposits in the same eheek Each participant should, however, complete a with preregistration fees. separate Preregistration/Housing form. In order to Since requirements vary from hotel to hotel, avoid confusion or disappointment, parties planning participants will be informed if there is a difference to share rooms should send their forms together in in the amount of the deposit submitted and the rate the same envelope. of the room actually assigned. N.B.: Participants Please make all changes to or cancellations of will receive an acknowledgement of their room hotel reservations with the Housing Bureau in deposits from the Louisville Convention and Providence before January 15, 1984, by ealling Visitors Bureau followed by a confirmation of 401-272-9500, extension 239. After that date, their room reservations from the hotel to which changes or cancellations should be made with they have been assigned. the Louisville Convention and Visitors Bureau by All reservation requests must be received in calling 502-584-2144. writing and be processed through the Housing Please read the facing page titled Preregis­ Bureau in Providence. Telephone requests will not tration carefully before completing the Preregistra­ be accepted. Please do not contact the hotels tion/Housing form. directly. Blocks of rooms and special rates have been set aside for the Housing Bureau, and the Please be sure to send housing deposits with hotel will either refer you back to the Housing preregistration/housing form. .------~------=~~ N.B.: Place your AMS or MAA mailing label on the Preregistration/Housing form where indicated. If you do not have a label readily available, please supply complete name, address, and AMS or MAA member code.

643 Incompressible fluid flow, J. THOMAS BEALE, Duke University, Wednesday, Friday, and Satur­ day afternoons. Ronald DiPerna, Ciprian Foia§, Jong Uhn Kim, Michael Renardy, and Bruce Turkington. Function theoretic operator theory, JoHN B. CONWAY, Indiana University, Wednesday morning and afternoon, and Thursday morning. Jim Agler, Sheldon Axler, Hari Bercovici, Scott Brown, John B. Conway, Carl Cowen, Jim Dudziak, Bill Helton, Thomas L. Kriete, III, C. R. Putnam, James E. Thomson, Tavan Trent, and Charles Voas. Random walks on finite groups, PERSI DIACONIS, Stanford University, Wednesday afternoon, Thursday morning, and Saturday afternoon. Ordered algebraic structures, ANDREW M. W. GLASS, Bowling Green State University, Thursday morning, Friday and Saturday afternoons. P. F. Conrad, M. Darnel, J. Dauns, T. Evans, A. W. Hager, M. Henriksen, M. Huss, S. Larson, J. T. Lloyd, J. J. Madden, J. Martinez, S. H. McCleary, F. Point, W. B. Powell, A. H. Rhemtulla, S. Steinberg, and C. Tsinakis. Vector field systems and control, HENRY HERMES, University of Colorado, Boulder and Barry Mazur, Colloquium Lecturer HECTOR SussMANN; Rutgers University, Wednes­ day morning and afternoon, and Friday afternoon. GuNNAR CARLSSON, University of Califor­ F. Albrecht, William Boothby, Alberto Bressan, nia, San Diego, Segal's Burnside ring conjecture, R. Brockett, M. Freeman, R. Gardner, K. Grasse, 2:15 p.m. Wednesday; PERSI DIACONIS, Stanford Robert Grossman, Henry Hermes, R. Hirschorn, University, Probability and group representations, R. Hunt, V. Jurdjevic, A. Krener, A. Lundell, 2:15 p.m. Friday; SIMON K. DoNALDSON, The Antonio Sanchez, E. Sontag, and H. Sussmann. Mathematical Institute, Oxford, England, The Partial differential operators, MARK A. KoN, Yang-Mills equations as a non-linear Hodge theory, Boston University, Wednesday morning and 9:00 a.m. Wednesday; ROBERT D. MACPHER­ afternoon, and Friday afternoon. Harold E. Ben­ SON, Brown University, Intersection homology and zinger, Thomas P. Branson, Rene Carmona, Paul some applications, 2:15p.m. Saturday; ANDREW R. Chernoff, Jeffrey M. Cooper, Allen Devinatz, MAJDA, University of California, Berkeley, Vor­ Jerome A. Goldstein, David Gurarie, Evans M. ticity and fluid dynamics, 9:00 a.m. Thursday; Harrell, Robert N. Hill, Rhonda J. Hughes, Ger­ M. SusAN MoNTGOMERY, University of Southern hard K. Kalish, Ian W. Knowles, Richard B. California, Group actions on rings and generalized Lavine, Stephen Paneitz, Alexander G. Ramm, inner automorphisms, 3:30 p.m. Friday; LEON and Clasine van Winter. SIMON, Australian National University, Some Partial differential equations and optimal control recent results concerning minimal surfaces, 3:30 problems, SuzANNE M. LENHART, University of p.m. Wednesday; and ROBERT E. TARJAN, Bell Tennessee, Wednesday, Friday, and Saturday Laboratories, Murray Hill, Design and analysis of afternoons. L. C. Evans. self-ad)"usting data structures, 10:15 a.m. Wednes­ Ring theory, M. SusAN MONTGOMERY, Univer­ day. sity of Southern California and LANCE SMALL, Special Sessions University of California, San Diego, Wednesday morning and afternoon and Thursday morning. By invitation of the same committee, there M. Cohen, J. Fisher, A. Heinicke, I. N. Herstein, will be twelve special sessions of selected twenty­ W. S. Martindale III, D. S. Passman, A. Regev, minute papers. The topics of these special M. K. Smith, R. Snider, R. Resco, and L. Malsar­ sessions, the names and affiliations of the mathe­ Limanov. maticians arranging them, and some partial lists Commutative algebra, IRA J. P APICK, Univer­ of anticipated speakers are as follows: sity of Missouri, Columbia, Wednesday morning Homotopy theory, DoNALD W. ANDERSON, and and afternoon and Thursday morning. Dan GuNNAR CARLSSON, University of California, Anderson, David Anderson, Luchezar Avramov, San Diego, Wednesday and Thursday morning, Doug Costa, Paul Eakin, E. Graham Evans, Jr., and Friday afternoon. E. Friedlander, Nick Kuhn, Richard Fedder, Robert Gilmer, Sarah Glaz, Wil­ Ben Mann, H. Miller, R. Thomason. liam Heinzer, Melvin Hochster, Evan Houston,

644 American Mathematical Society Short Course Series Introductory Survey Lectures on Mathematics of Information Processing Louisville, Kentucky, January 23-24, 1984

The American Mathematical Society, in conjunction with its ninetieth annual meeting, will present a one and one-half day short course titled Mathematics of Information Processing on Monday afternoon and Tuesday morning and afternoon, January 23 and 24, 1984, at the Hyatt Regency Louisville. The program is under the direction of Michael Anshel of CUNY, City College, and William Gewirtz of Bell Laboratories, Holmdel. The course will cover a number of areas in which mathematical techniques have led to a deeper understanding of Information Processing. The earliest applications of mathematics were in the design and analysis of algorithms and in the modeling of systems performance. Motivated by the challenge to use effectively the capabilities resulting from dramatically increased system capacity, multi-programming, parallel processing, and distributed computing environments, mathematics continues to play an important role in the design and analysis of computer systems. V\'hile mathematical logic and related disciplines have traditionally been intimately related to the foundations of computing, areas of more practical application have arisen in recent years. Specifically, in the area of database systems, both database languages and database design techniques have seen important applications of mathematical logic and related subjects. Synopses of the talks and accompanying reading lists appear in this issue of the Notices. The course will consist of six lectures. Fan R. K. Chung (Bell Laboratories, Murray Hill) will speak about the diameters of communication networks; Hector Garcia-Molina (Princeton University) about transaction management; Barry E. Jacobs (University of Maryland) about fundamental database issues; Victor S. Miller (IBM, Yorktown Heights) about compression algorithms; Avgustin Tuzhilin (CUNY, City College at Staten Island) about applications of category theory of structural sets to information systems and Moshe Y. Vardi (Stanford University) about the theory of data dependencies. Time will be allocated for summarizing and integrating the material presented in the lectures. The short course is open to all who wish to participate upon payment of the registration fee. There are reduced fees for students and unemployed individuals. Please refer to the boxes entitled Preregistration and Housing and Registration at the Meetings for details. The short course was recommended by the Society's Committee on Employment and Educational Policy, whose members are Lida K. Barrett, Lisl Novak Gaal, Irwin Kra, Robert W. McKelvey, Donald C. Rung (chairman), and Barnet M. Weinstock. The short course series is under the direction of the CEEP Short Course Subcommittee, whose members are Stefan A. Burr (chairman), Lisl Novak Gaal, Robert W. McKelvey, Cathleen S. Morawetz, Barbara L. Osofsky, and Philip D. Straffin, Jr.

645 James Huckaba, Craig Huneke, Andrew Kustin, to identify himself as a member of the Society. In David Lantz, David Rush, Bernd Ulrich, and further explanation, it is noted that each person Wolmer Vasconcelos. who is to vote at a meeting is thereby identifying fll-posed problems, WILLIAM L. PERRY, Texas himself as and claiming to be a member of the A & M University, Wednesday morning and American Mathematical Society. For additional afternoon and Friday afternoon. C. W. Groetsch, information on the Business Meeting, please refer D. Lee, H. A. Levine, M. Madych, M. Z. Nashed, to the box titled Committee on the Agenda for L. Payne, W. Rundell, R. Showalter, W. Symes, Business Meetings. F. A. Griinbaum, L.A. Shepp, and J. McLaughlin. Semigroup theory, W. WILEY WILLIAMS, 67th Annual Meeting of the MAA University of Louisville, Thursday morning, January 26-29, 1984 Friday and Saturday afternoon. D. R. Brown, K. E. Byleen, H. Cohen, M.P. Drazin, C. Eberhart, J. M. Howie, P.R. Jones, R. J. Koch, G. Lallement, Retiring Presidential Address K. D. Magill, B. Madison, R. Oehmke, M. S. RICHARD D. ANDERSON, Louisiana State Puchta, N. R. Reilly, B. M. Schein, J. Stepp, Y. University, Baton Rouge, will deliver his Retiring Kobayashi, and W. Williams. Presidential Address on Reflections of the mystique Most of the papers to be presented at these of R. L. Moore. special sessions will be by invitation; however, Invited Addresses anyone contributing an abstract for the meeting who feels that his or her paper would be There will be seven invited fifty-minute ad­ particularly appropriate for one of these sessions dresses. The list of speakers, their affiliations, and should indicate this clearly on the abstract, and their titles follow: should submit it by October 12, three weeks earlier than the normal deadline for contributed Committee on the Agenda for Business Meetings papers, in order that it may be considered for The Society has a Committee on the Agenda inclusion. for Business Meetings. The purpose is to make Contributed Papers Business Meetings orderly and effective. The There will be sessions for contributed papers committee does not have legal or administrative Wednesday morning and afternoon, Thursday power. It is intended that the committee morning, Friday afternoon, and Saturday after­ consider what may be called "quasi-political" noon. Abstracts should be prepared on the motions. The committee has several possible standard AMS form available from the AMS office courses of action on a proposed motion, includ­ in Providence or in departments of mathematics, ing but not restricted to and should be sent to the American Mathematical (a) doing nothing; Society, Post Office Box 6248, Providence, Rhode (b) conferring with supporters and opponents Island 02940, so as to arrive by the abstract to arrive at a mutually accepted amended deadline of November 2. Members are reminded version to be circulated in advance of the that a charge of $12 is imposed for retyping meeting; abstracts that are not in camera-ready form. (c) recommending and planning a format for Late papers will not be accepted. debate to suggest to a Business Meeting; Other AMS Sessions (d) recommending referral to a committee; (e) recommending debate followed by referral AMS Committee on Employment to a committee. and Educational Policy There is no mechanism that requires A panel discussion, moderated by LmA K. automatic submission of a motion to the com­ BARRETT, on the supply of mathematical science mittee. However, if a motion has not been researchers in the 1990's will be held from 4:30 submitted through the committee, it may be p.m. to 6:00p.m. on Friday, January 27. thought reasonable by a Business Meeting to Council Meeting refer it rather than to act on it without benefit The Council of the Society will meet at 2:00 of the advice of the committee. p.m. on Tuesday, January 24, in the Hyatt The committee consists of Everett Pitcher Regency Louisville. (chairman), Marian B. Pour-El, David A. Sanchez, and Guido L. Weiss. Business Meeting In order that a motion for the Business The Business Meeting of the Society will take Meeting of January 26, 1984 receive the service place immediately following the award of the offered by the committee in the most effective Bocher Prize at 4:00 p.m. on Thursday, January manner, it should have been in the hands of the 26. The secretary notes the following resolution of secretary by December 27, 1983. the Council: Each person who attends a Business Everett Pitcher, Secretary Meeting of the Society shall be willing and able

646 minicourse is full, full refund can be made of the Minicourses Joint Mathematics Meetings preregistration fees. Minicourse #1: Linear programming, Otherwise, the Joint Meetings preregistration will CHARLES E. IIAFF, University of Waterloo. be processed, and then be subject to the 50 Minicourse #2: Combinatorics, FRED S. percent refund rule. RoBERTS, Rutgers University and STEPHEN B. Other MAA Sessions MAURER, Swarthmore College. The Committee on Retraining for Computer Minicourse #3: Problem solving, ALAN H. Sciences will hold a panel discussion on Saturday, ScHOENFELD, University of Rochester. January 28. The moderator will be DoNALD Minicourse #4: Pasca~ HARLEY FLANDERS, L. KREIDER of Dartmouth College. The Florida Atlantic University. topic is Progress report on the Institute for Minicourse #5: Mathematics in industry, Retraining in Computer Science at Clarkson JEANNE L. AGNEW and MARVIN S. KEENER, College, conducted under the auspices of the Joint both of Oklahoma State University. ACM/MAA Committee on Retraining for Computer Minicourse #6: Computer graphics, JoAN Science. WYZKOSKI, Bradley University. Business Meeting Minicourse #7: CONDUIT microcomputer The Business Meeting of the MAA will take software, DAVID SMITH, Duke University. place at 10:00 a.m. on Sunday, January 29, at Minicourse #8: NonCONDUIT microcomputer which the 1984 Award for Distinguished Service, software, DAVID SMITH, Duke University. the Chauvenet Prize, and the Lester R. Ford Awards for expository writing will be presented. Beta and gamma functions from Euler to Selberg Board of Governors and beyond, RICHARD AsKEY, University of Wisconsin; Turning good mathematics into good The MAA Board of Governors will meet at 9:00 TV, Ross L. FINNEY and DoNALD BERMAN, both a.m. on Thursday, January 26. of COMAP; Non-expansive maps, ANDREW M. ACTMTIES OF OTHER ORGANIZATIONS GLEASON, Harvard University; The computer as a The Association for Women in Mathematics grader, MELVIN MARON, University of Louisville; (AWM) will sponsor a Panel Discussion at 11:15 Mathematics in industry-how do problems arise?, a.m. on Thursday, January 26, to be immediately HENRY 0. PoLLAK, Central Staff Organization followed by the AWM Business Meeting. for the Regional Bell Operating Companies; Some A party is being planned for Thursday evening, examples of combinatorial averaging, HERBERT S. January 26. WILF, University of Pennsylvania; Computational geometry: paradigms and applications, FRANCES The fifth annual AWM Emmy Noether Lecture will be given at 10:00 a.m. on Friday, January Y AO, Xerox Corporation. 27, by MARY ELLEN RuDIN. The title is Minicourses Paracompactness. The MAA will give eight Minicourses. Please The National Association of Mathematicians refer to the box titled Minicourses for titles and (NAM) will receive the William W. S. Claytor organizers. Lecture at 10:15 a.m. on Thursday, January The Minicourses are open only to persons 26, from A. T. BHARUCHA-REID, who will speak who have registered for the Joint Mathematics on Some notions and applications in probability Meetings and paid the Joint Meetings registration theory-numerical methods. fee. NAM will sponsor a panel discussion titled Some The Minicourses have separate registration fees approaches for providing computer literacy for of $20 each, and are limited to "30 participants students in small colleges and universities at 11:15 each. Payment of the fee(s) must be made to a.m. on Friday, January 27. The list of speakers the minicourse cashier at the meeting registration includes Melvis Atkinson, Samuel H. Douglas desk in Louisville two hours prior to the beginning (moderator), Henry L. Hardy, John Harris, and of the Minicourse or the reservation will be relin­ Nelloise Watkins. quished to someone on the waiting list. When The NAM Business Meeting will take place at making payment, the participant should present 1:30 p.m. on Friday, January 27. the confirmation to the cashier. "Standby" reser­ The National Science Foundation (NSF) will vation confirmations will be issued to participants sponsor an address on Thursday, January 26 at whose preregistration was received after the Mini­ 2:15 p.m. The speaker is JuDITH S. SuNLEY, course was filled. These individuals should check Acting Head of the Mathematical Sciences Section with the minicourse cashier one hour prior to the of NSF; her title is The Mathematical Sciences at Minicourse to see if any openings have occurred. the National Science Foundation. If the only reason for registering for the Joint The NSF will again be represented at a booth Meetings is to gain admission to a Minicourse, this in the exhibit area. NSF staff members will be should be indicated by checking the appropriate available to provide counsel and information on box on the preregistration form. Then, if the NSF programs of interest to mathematicians from

647 9:00 a.m. to 5:00 p.m., Thursday and Friday, desk. Those interested are invited to view the January 26-27. exhibition between 9:00 a.m. and 6:00 p.m., The Rocky Mountain Mathematics Consortium Wednesday through Friday. (RMMC) will sponsor a symposium on The mathematics of large scale simulation at 2:15 Petition Table p.m. on Friday, January 27. At the request of the AMS Committee on The RMMC Board of Directors will meet at 2:00 Human Rights of Mathematicians, a table will p.m. on Thursday, January 26. be made available in the meeting registration area at which petitions on behalf of named OTHER EVENTS OF INTEREST individual mathematicians suffering from human Book Sales rights violations may be displayed and signed by Books published by the AMS and MAA will be meeting participants acting in their individual sold for cash prices somewhat below the usual capacities. prices when these same books are sold by mail. Signs of moderate size may be displayed at These discounts will be available only to registered the table, but must not represent that the case participants wearing the official meeting badge. of the individual in question is backed by the VrsA and MASTERCARD credit cards will be Committee on Human Rights unless it has, in accepted for book sale purchases at the meeting. fact, so voted. Volunteers may be present at The book sales will be open the same days the table to provide information on individual and hours as the Joint Mathematics Meetings cases, but notice must be sent at least seven (7) registration desk (except on Saturday, January days in advance of the meeting to the Meetings 28, when they will close at 2:00 p.m.) and are Department in Providence (telephone 401-272- located in Exhibit Space C of the Commonwealth 9500). Since space is limited, it may also be Convention Center. necessary to limit the number of volunteers Exhibits present at the table at any one time. The Committee on Human Rights may delegate a The book and educational media exhibits are person to be present at the table at any or all located in Exhibit Space C of the Commonwealth times, taking precedence over other volunteers. Convention Center and will be open Wednesday, January 25, through Saturday, January 28. The Any material which is not a petition (e.g., exhibits will be open from 1:00 p.m. to 5:00 p.m. advertisements, resumes) will be removed by the on Wednesday; from 9:00 a.m. to 5:00 p.m. on staff. When registration closes, any material Thursday and Friday; and from 9:00 a.m. to noon on the table will be discarded, so individuals on Saturday. All participants are encouraged to placing petitions on the table should be sure to visit the exhibits during the meeting. Participants remove them prior to the close of registration. visiting the exhibits will be asked to display their meeting badge in order to enter the exhibit area. ACCOMMODATIONS MATHFll..E Hotels MATHFILE, the computerized version of Math­ ematical Reviews, will be demonstrated in the Please read the page on Housing carefully for exhibit area during regular registration hours. information on hotel deposits, which are now Sample literature searches on material published required. in MR since 1973 will be performed on request, with printed results available in minutes. The rates listed below are subject to a 5 MATHFILE is available through two U.S. on­ percent sales tax and a 4.2 percent occupancy line vendors, BRS and DIALOG. In addition, the European vendors SAMSOM Data Systemen and tax. The number after the name of the hotel the European Space Agency (ESA) will offer MATH­ is the number it carries on the map. The FILE, with access from the U.S. at comparable estimated walking distance from the hotel to the telecommunication rates. Commonwealth Convention Center is given in parentheses following the telephone number. Rare Book Exhibits Reservations at these hotels cannot be made by The University of Louisville (Belknap Campus) calling the hotel directly until after January 15, will mount an exhibition of rare books from 1984. Also, after that date, the rates below may the William Marshall Bullitt Collection of Math­ not apply. ematics and Astronomy in the Department of In all cases "single" refers to one person in Rare Books on the ground floor of the Ekstrom one bed; "double" refers to two persons in one Library. The library is approximately 20 blocks bed; "twin" refers to two persons in two single south of the Commonwealth Convention Center, beds; and "twin double" refers to two persons in off Third Street. Directions for reaching the two double beds. A rollaway cot for an extra university campus can be obtained at the Local person can be added to double or twin rooms Information Section of the meetings registration only; however, not all hotels are willing to do so.

648 1. Commonwealth Convention Center 6. Louisville TraveLodge 2. Galt House 7. Hyatt Regency Louisville 3. Rodeway Inn 8. Seelbach Hotel 4. Howard Johnson's 9. The Louisville Inn 5. Best Western-Midtown

649 Please make all changes to or cancellations of used, it must be accompanied by credit card hotel reservations with the Mathematics Meetings identification. Housing Bureau in Providence before January 15, The Louisville Inn {9) 1984. The telephone number in Providence is 120 West Broadway 401-272-9500 (extension 239). After that date, Louisville, Kentucky 40202 changes or cancellations should be made with Telephone: 502-582-2241 (15 minutes) the Louisville Convention and Visitors Bureau by Singles $38 calling 502-584-2144. Twin/Twin Double $46 Triples $52 Best Western-Midtown {5) Quads $58 200 E. Liberty Parlor /Bedroom $85 Louisville, Kentucky 40202 Transportation to the Commonwealth Conven­ Telephone: 502-589-6410 (11 minutes) tion Center will be available upon request at no Singles $25 charge. Twin Double $31 Personal cheeks and major credit cards will Triples $35 be accepted for room deposits and payment of Quads $39 balance due; however, if a personal cheek is Personal cheeks and major credit cards will used, it must be accompanied by credit card be accepted for room deposits and payment of identification. balance due; travelers' cheeks will also be accepted Rodeway Inn {3) at time of cheek-out. 101 East Jefferson Street Louisville, Kentucky 40202 Galt House {2) Telephone: 502-585-2200 (8 minutes) On the River at Fourth Louisville, Kentucky 40202 Singles $43 Telephone: 502-589-5200 (4 minutes) Double $49 Twin Doubles $49 Singles $40 Triples $49 Doubles $43 Quads $49 Twin Double $43 Transportation to the Commonwealth Conven­ Triples $46 tion Center will be available upon request at no Quads $48 charge. Parlor Suite $110 Personal cheeks and major credit cards will Personal cheeks and major credit cards will be accepted for room deposits and payment of be accepted for room deposits and payment of balance due; however, if a personal cheek or balance due; however, if a personal cheek will be travelers' cheek is used at time of cheek-out, it used at time of cheek-out, it must be cleared three must be accompanied by credit card identification. days prior to departure. Seelbach Hotel {8) Howard Johnson's {4) 500 Fourth Avenue 100 East Jefferson Street Louisville, Kentucky 40202 Louisville, Kentucky 40202 Telephone: 502-585-3200 (4 minutes) Telephone: 502-582-2481 (8 minutes) Singles $48 Singles $38 Doubles $54 Doubles $44 Twin/Twin Doubles $54 Twin Doubles $44 Triples $60 Triples $50 Quads $66 Quads $56 One-bedroom suite $100 Personal cheeks, travelers' cheeks, and major Two-bedroom suite $250 credit cards will be accepted for room deposits Personal cheeks, American Express and VIsA and payment of balance due. credit cards will be aeeepted in payment of room deposits; balance due is payable on cheek-out Hyatt Regency Louisville {7) in cash, major credit cards or travelers' cheeks. 320 West Jefferson Street Personal cheeks will be accepted at cheek-out Louisville, Kentucky 40202 subject to prior approval. Telephone: 502-587-3434 (2 minutes) Louisville TraveLodge (6) Singles $50 401 South Second Street Double $59 Louisville, Kentucky 40202 Twin/Twin Doubles $59 Telephone: 502-583-2841 (10 minutes) Triples $67 Singles $33 Quads $74 Doubles $38 Personal cheeks and major credit cards will Twin Doubles $43 be accepted for room deposits and payment of Triples $48 balance due; however, if a personal cheek is Quads $53 650 TIMETABLE

The parpose of this timetable is to provide assistance to registrants in the selection of arrival and departare dates. The program, as oatlined below, is based on information available at press time.

AMERICAN MATHEMATICAL SOCIETY SHORT COURSE SERIES

MONDAY, Janaary 23 MATHEMATICS OF INFORMATION PROCESSING 11:00 a.m. - 4:00 p.m. REGISTRATION 2:00p.m. - 3:00 p.m. Fandamental database issaes Barry E. Jacobs 3:30p.m. - 4:30 p.m. Theory of data dependencies Moshe Y. Vardi 4:45p.m. - 5:15 p.m. General Discassion

TUESDAY, Janaary 24 8:00a.m. - 2:00 p.m. REGISTRATION 9:00 a.m. - 10:00 a.m. The diameters of commanication networks Fan R. K. Chang 10:30 a.m. - 11:30 a.m. Compression algorithms Victor S, Miller 1:30 p.m. - 2:30 p.m. Applications of category theory of structaral sets to information systems Avgastin Tuzhilin 3:00p.m. - 4:00 p.m. Transaction management Hector Garcia-Molina 4:15 p.m. - 4:45 p.m. General Discassion

JOINT MATHEMATICS MEETINGS

TUESDAY, Janaary 24 American Mathematical Society Mathematical Association of America 2:00p.m. - 10:00 p.m. COUNCIL MEETINJ I 4:00 p, m, - 8:00 p. m, REGISTRATION 4:00 p. m, - 8:00 p.m. AMS BOOK SALE MAA BOOK SALE

Mathematical Association of America WEDNESDAY, Janaary 25 AMS and Other Organizations

8:00a.m. - 5:00p.m. REGISTRATION 8:00 a, m. - 5:00 p. m, AMS BOOK SALE MAA BOOK SALE morning Special Sessions Sessions for Contribated Papers 9:00a.m. - 10:00 a.m. INVITED ADDRESS The Yang-Mills equations as a non-linear Hodge theory Simon K. Donaldson 10:15 a, m. - 11:15 a. m, INVITED ADDRESS Design and analysis of self-adjasting data stractures Robert E. Tarjan 1:00 p. m, - 2:00 p.m. COLLOQUIUM LECTURE I On the arithmetic of carves Barry Mazar 1:00 p.m. - 5:00p.m. EXHIBITS afternoon Special Sessions Sessions for Contribated Papers

651 No personal cheeks will be accepted as payment or MASTERCARD credit card. Canadian checks for room deposit or balance of room charges; must be marked for payment in U.S. funds. however, all Irn\ior credit cards, money orders, There is no extra charge for members of the and travelers' cheeks will be honored. families of registered participants, except that all The AMS-MAA Joint Meetings Committee al­ professional mathematicians who wish to attend ways endeavors to obtain the lowest possible sessions must register independently. sleeping room rates for participants at annual All full-time students currently working toward meetings. The Committee is also responsible a degree or diploma qualify for the student for maintaining a sound fiscal position for these registration fees, regardless of income. meetings, and, until recently, has been able to The unemployed status refers to any person keep the deficits at a reasonable level, while still currently unemployed, actively seeking employ­ providing the very best meeting facilities available ment, and who is not a student. It is not intended to the participants. to include any person who has voluntarily resigned As the meetings have grown in scope and or retired from his or her latest position. complexity over the years, however, it has been Persons who qualify for emeritus membership in necessary to find larger facilities with more and either the Society or the Association may register more session rooms. For this reason, the meetings at the emeritus member rate. The emeritus status in Louisville will take place in the Commonwealth refers to any person who has been a member of Convention Center. Unfortunately, the cost of the AMS or MAA for twenty years or more, and is this excellent facility is higher than can be covered retired on account of age from his or her latest by the registration fees, and the Committee has position. arranged for most of the hotels in Louisville Nonmembers who register at the meetings to collect an extra $3 per room per night from and pay the $93 nonmember registration fee are participants, which will be used to offset the rental entitled to a discount of the difference between the cost of the Center. (The rates above include this member registration fee of $61 and the nonmember extra charge where applicable.) The Committee registration fee of $93 as a $32 credit against dues hopes that these extra funds will not be necessary in either the AMS or MAA or both, provided they at future annual meetings, and therefore chose apply for membership before February 29, 1984. this method over an increase in the registration Nonmember students who register at the fees. meetings and pay the $15 registration fee are entitled to a discount of the difference between the student preregistration fee of $12 and the Registration Desk registration fee of $15 as a $3 credit against dues in either the AMS or MAA or both, provided they Registration at the Meetings apply for membership before February 29, 1984. Meeting preregistration and registration fees Nonmembers and nonmember students who only partially cover expenses of holding meetings. thus qualify may apply for membership at the All mathematicians who wish to attend sessions meetings, or by mail afterward up to the deadline. are expected to register, and should be prepared Registration Dates and Times to show their meeting badge, if so requested. AMS Short Course The fees for Joint Meetings registration at the Prefunction Room, Regency Ballroom North meeting (listed below) are 30 percent more than Hyatt Regency Louisville the preregistration fees. Monday, January 23 11:00 a.m. to 4:00 p.m. Joint Mathematics Meetings Tuesday, January 24 8:00 a.m. to 2:00 p.m. Joint Mathematics Meetings Member of AMS, MAA, NCTM $61 [and MAA Minicourses (until ffiled)] Emeritus Member of AMS, MAA $15 Nonmember $93 Main Lobby, Commonwealth Convention Center Student/Unemployed $15 Tuesday, January 24 4:00 p.m. to 8:00 p.m. Employment Register Wednesday, January 25 8:00 a.m. to 5:00 p.m. Thursday, January 26, Employer $75 through 8:00 a.m. to 4:00 p.m. Applicant No charge Saturday, January 28 AMS Short Course Assistance and Information Desk Student/Unemployed $10 Main Lobby, Commonwealth Convention Center All Other Participants $30 Sunday, January 29 8:30 a.m. to 1:30 p.m. One-day Fee (Second Day Only) $15 MAA Minicourses #1 through #8 Please note that the Joint Mathematics Meet­ All Participants $20 each ings· registration desk will not be open on Sunday, January 29, and that the telephone message center Registration fees may be paid at the meetings will not be in operation. Other services provided in cash, by personal or travelers' check, or by VISA during the meeting at the registration desk will

652 TIMETABLE

Mathematical Association of America WEDNESDAY, January 25 AMS and Other Organizations 2:15p.m. - 3:15p.m. INVITED ADDRESS Segal's Burnside ring conjecture Gunnar Carlsson 3:30 p.m. - 4:30p.m. INVITED ADDRESS Some recent results concerning minimal surfaces Leon Simon 8:30p.m. - 9:30p.m. JOSIAH WILLARD GffiBS LECTURE Computer programs that model the process of scientific and mathema- tical discovery Herbert A. Simon

Mathematical Association of America THURSDAY, January 26 AMS and Other Organizations 8:00a.m. - 4:00p.m. REGISTRATION 8:00a.m. - 4:00p.m. AMS BOOK SALE MAA BOOK SALE morning Special Sessions Sessions for Contributed Papers 9:00a.m. - 10:00 a.m. INVITED ADDRESS Vorticity and fluid dynamics Andrew Majda 9:00a.m. - 4:00p.m. MAA - BOARD OF GOVERNORS MEETING 9:00a.m. - 5:00p.m. EXHIBITS 9:00a.m. - 9:30a.m. EMPLOYMENT REGISTER ORIENTATION SESSION 9:30 a.m. - 4:00p.m. EMPLOYMENT REGISTER REGISTRATION 10:15 a.m. - 11:15 a.m. National Association of Mathematicians William W. s. Claytor Lecture Some notions and applications in probability theory-numerical methods A. T. Bharucha-Reid 11:15 a.m. - 12:55 p.m. Association for Women in Mathematics Panel Discussion and Business Meeting 1:00 p.m. - 2:00p.m. COLLOQUIUM LECTURE IT On the arithmetic of curves Barry Mazur 2:00 p.m. - 4:00 p.m. Rocky Mountain Mathematics Consortium Board of Directors 2:15p.m. - 3:15p.m. The Mathematical Sciences at the National Science Foundation Judith S. Sunley, NSF 4:00p.m. - 6:00p.m. BOCHER PRIZE SESSION AND I BUSINESS MEETING 7:00 p.m. - 10:00 p.m. Joint Concerns Committee for Mathematics A National Meeting of Department Chairmen evening AWM -PARTY

Mathematical Association of America FRIDAY, January 27 AMS and Other Organizations

8:00a.m. - 4:00p.m. REGISTRATION 8:00 a.m. - 4:00 p.m. AMS BOOK SALE I MAA BOOK SALE 9:00a.m. - 5:00p.m. EXHIBITS 9:00a.m. EMPLOYMENT REGISTER DISTRffiUTION OF SCHEDULES 9:30 a.m. - 5:30 p.m. EMPLOYMENT REGISTER INTERVIEWS 10:00 a.m. - 11:00 a.m. A WM - Emmv Noether Lecture I Paracompactness Mary Ellen Rudin

653 Louisville Meetings SuperPhone Exclusive 800-556-6882 ~DELTA 'IS61R.

FLY TO LOUISVILLE WITH DELTA OR USAIR AND SAVE Delta and USAir, the two major carriers to Louisville, are making special round trip air fares available to the Joint Mathematics Meetings in Louisville, Kentucky, January 23-29, 1984. Delta is offering a 30 percent discount on full round-trip coach fares. This special fare requires departure between January 23 and 27. Reservations and ticketing must be done at least seven days in advance and a maximum stay of 15 days will be permitted. USAir is offering an unrestricted Super Saver fare to any participant purchasing tickets on its airline at least fourteen days in advance. Other fares will, of course, still be available after the fourteen-day limitation. These special offers are available ONLY through the Louisville Meeting SuperPhone Exclusive. Call SuperPhone toll-free today-800-556-6882-and save!!

(In Rhode Island and outside the Continental U.S. call 401-884-9500.) Hours of Operation: 9:00a.m. to 7:00p.m. EST, Monday through Thursday, Fridays until 6:00p.m. Where discounts exceed 30 percent, they will be provided automatically through SuperPhone's FARE CHECK system. also no longer be available (see section below on overhead projector and screen. Blackboards will not Registration Desk Services). There will, however, be available. be a small desk set up in the Main Lobby of Baggage and Coat Cheek the Commonwealth Convention Center, where local information will be available and where a Information on this service will be available later. staff member will provide limited assistance to Cheek Cashing participants. No registration or cash transactions The meeting cashier will cash personal or travelers' will be possible at this desk. checks up to $50, upon presentation of the official meeting registration badge, provided there is enough REGISTRATION DESK SERVICES cash on hand. Canadian checks must be marked for AMS /MAA Information payment in U.S. funds. Information on the publications and activities of Local Information both organizations may be obtained at this section of This section of the desk will be staffed by the registration desk. members of the Local Arrangements Committee and Assistance, Comments and Complaints other volunteers from the Louisville mathematical community. A log for registering participants' comments or complaints about the meeting is kept at the Trans­ Lost and Found parencies section of the registration desk. All See the meeting cashier. participants are encouraged to use this method of Mail helping to improve future meetings. Comments on all All mail and telegrams for persons attending the phases of the meeting are welcome. If a written reply meetings should be addressed to the participant, is desired, participants should furnish their name and c/o Joint Mathematics Meetings, Commonwealth address. Convention Center, 221 Fourth Avenue, Louisville, Participants with problems of an immediate nature Kentucky 40202. Mail and telegrams so addressed requiring action at the meeting should see the meeting may be picked up at the mailbox in the registration manager, who will try to assist them. area during the hours the registration desk is open. Audio-Visual Assistance U.S. mail not picked up will be forwarded after the meeting to the mailing address given on the A member of the AMS/MAA staff will be available participant's registration record. to advise or consult with speakers on their audio­ visual requirements. Personal Messages Rooms where special sessions and contributed Participants wishing to exchange messages during paper sessions will be held will be equipped with an the meeting should use the mailbox mentioned above.

654 TIMETABLE

Mathematical Association of America FRIDAY, January 27 AMS and Other Organizations

11:15 a.m. - 12:30 p.m. NAM - Panel Discussion Some approaches for providing computer literacy for students in small colleges and universities Melvis Atkinson Samuel H. Douglas (moderator) Henry L. Hardy John Harris Nelloise Watkins 1:00 p.m. - 2:00p.m. COLLOQUIDMLECTUREID On the arithmetic of curves Barry Mazur 1:30 p.m. - 2:30p.m. NAM - Business Meeting afternoon Special Sessions Sessions for Contributed Papers 2:15 p.m. - 3:15 p.m. INVITED ADDRESS Probability and group representations Persi Diaconis 2:15p.m. - 5:00p.m. RMMC - Symposium The mathematics of large scale simulation 3:30p.m. - 4:30p.m. INVITED ADDRESS Group actions on rings and generalized inner automorphisms M. Susan Montgomery 4:00p.m. - 6:00p.m. MAA - Section Officers Meeting 4:30p.m. - 6:00 p.m. Committee on Employment and Educational Policy Panel Discussion The supply of mathematical science researchers in the 1990's Lida K. Barrett (moderator) evening NO-HOST COCKTAIL PARTY

SATURDAY, January 28 AMS Mathematical Association of America 8:00 a.m. - 4:00 p.m. REGISTRATION 8:00a.m. - 4:00 p.m. AMS BOOK SALE I MAA BOOK SALE 9:00 a.m. - noon EXHIBITS 9:00a.m. EMPLOYMENT REGISTER DISTRIBUTION OF SCHEDULES 9:30a.m. - 5:30p.m. EMPLOYMENT REGISTER INTERVIEWS 1:00 p;m. - 2:00p.m. COLLOQUIDM LECTURE IV On the arithmetic of curves Barry Mazur afternoon Special Sessions Sessions for Contributed Papers 2:15 p.m. - 3:15 p.m. INVITED ADDRESS Intersection homology and some applications Robert D. MacPherson

SUNDAY, January 29 AMS Mathematical Association of America 8:30a.m. - 1:30 p.m. ASSISTANCE AND INFORMATION DESK 10:00 a.m. - 11:00 a.m. MAA - BUSINESS MEETING

655 Message pads and pencils are provided. It is regret­ of visitor interest will be available at the Local ted that such messages left in the box cannot be Information section of the registration desk. forwarded to participants after the meeting is over. Parking Telephone Messages Parking lots within a few blocks of the Common­ wealth Convention Center charge from 35 cents to A telephone message center is located in the 75 cents for one hour (50 cents median); twenty-four calls for registration area to receive incoming hour parking ranges from $1 to $3.50 ($3 median). participants. The center is open from January The Hyatt Regency has its own parking garage at 25 through 28 only, during the hours that the Third Street and River City Mall at a daily charge Joint Mathematics Meetings registration desk is of $3. This garage is also available for patrons of the open. Messages will be taken and the name of any Commonwealth Convention Center. individual for whom a message has been received will The Galt House has a 600-car parking lot which be posted until the message has been picked up at guests can use at no charge, with in and out the message center. The telephone number of the privileges. message center will be announced later. Social Events Transparencies The Local Arrangements Committee has arranged a no-host cocktail party for Friday, January 27, from Speakers wishing to prepare transparencies in 7:00 to 9:00 p.m., in the Regency Ballroom North at advance of their talk will find the necessary the Hyatt Regency Louisville. materials and copying machines at this section of the registration desk. A member of the staff will Travel assist and advise speakers on the best procedures and In January, Louisville is on Eastern Standard methods for preparation of their material. There is Time. There is regular airline service to Standiford Field by several major airlines. a modest charge for these materials. Please note The airport in Louisville is approximately four on Sunday, that this service will not be available miles from downtown and the trip takes about ten January 29. minutes. The airport limousine stops at the major Visual Index downtown hotels, and runs every forty-five minutes from 7:00 a.m. until 11:00 p.m. daily. Present cost An alphabetical list of registered participants, is $3.75 per person. A taxi from the airport to a including local addresses, arrival and departure dates, downtown hotel costs about $8.50, plus 30 cents for is maintained in the registration area. each additional passenger one way. There is bus service provided by Transit Authority of River City MISCELLANEOUS INFORMATION (TARC) on bus #2 from the airport to downtown, Child Care with the fare varying between 35 cents and 60 cents depending on the hour of the day. Most major car We Sit Better, Inc., offers professional babysitting rental agencies maintain desks at the airport. in hotel rooms. Day or evening service is available. Louisville can be reached by car via 1-65 from the Their present rate is minimum wage for a minimum North and South, 1-64 from the East and West, and of four hours, plus $3 carfare. Please notify them as 1-71 from the Northeast. far in advance as possible. For more information call There is no passenger train service into Louisville; 502-583-9618. Many of the listed hotels will arrange however, Greyhound and Trailways Bus Lines serve for a babysitter if given enough prior notice. the Louisville area. Local Information Weather Taxis presently cost $1.90 for the first mile and $1 Louisville is located on the south bank of the Ohio River. The climate, while continental in each additional mile. Each additional person is for type, is of a variable nature because of its position charged 30 cents extra, as long as they go from the in the midlatitudes. The winters are moderately same pickup point to the same destination. Fares cold with temperatures rarely below 0°F. The mean from the airport to downtown hotels should average temperature in January is 34°F while the average $9. The Transit Authority of River City (TARC) high temperature in January is 42°F and the average operates buses throughout the area. The fee is 60 low temperature is 26°F. On rare occasions the cents during peak hours (6:30-8:30 a.m. and 3:30- winters in Louisville are extreme both in temperature 5:30 p.m.) and 35 cents for nonpeak hours. and snowfall. A section of Fourth Avenue has been turned into a Galleria and pedestrian mall. Participants staying in W. Wistar Comfort downtown hotels will want to take advantage of the Middletown, Connecticut Associate Secretary many shops in this area. Louisville's museums include the J. B. Speed Art Museum, the Museum of History and Science, the Howard Steamboat Museum and the Kentucky Derby Museum at Churchhill Downs. The performing arts can be seen at Actors Theatre, Kentucky Center Important information on the Employment Reg­ for the Arts, Macauley Theatre, and the Louisville ister immediately follows. Palace. Information on these and other points

656 Mathematical Sciences Employment Register January Meeting in Louisville The Mathematical Sciences Employment Register, held annually at the Joint Mathematics Meetings in January, provides opportunities for mathematical scientists seeking professional employment to meet employers who have positions to be filled. Job listings (or descriptions) and resumes prepared by employers and applicants are displayed for the participants so that members of each group may determine which members of the other group they would like to have an opportunity to interview. A computer program assigns the appointments, matching requests to the extent possible, using an algorithm which maximizes the number of interviews which can be scheduled subject to constraints determined by the number of time periods available, the numbers of applicants and employers, and the pattern of requests. The report below outlines the operation of the register, indicating some of the procedures involved for the benefit of those not familiar with its operation. The Mathematical Sciences Employment Register is apparently unique among employment services offered by professional organizations in the sciences, engineering and the humanities. The computer programs used are constructed around a matching program, devised by Donald R. Morrison and based on an algorithm described in his paper "Matching Algorithms" in Journal of Combinatorial Theory, volume 6 (1969), pages 20 to 32; see also "Matching Algorithms" (abstract) Notices, August 1967, page 630. The number of interviews arranged by the program is significantly greater than the number possible at the employment registers of other organizations, in many cases greater by an order of magnitude. 1984 Employment Register in Louisville Saturday sessions must be submitted on Friday The Employment Register at the Louisville before 4:00 p.m. meeting will take place in the Commonwealth On Friday and Saturday mornings at 9 a.m. all Convention Center, Exhibit Hall C, on Thursday, schedules for applicants and employers for the day Friday, and Saturday, January 26, 27, and 28, (both the morning and afternoon sessions) will be 1984. A short (optional) orientation session will available for distribution in the Commonwealth be conducted by the AMS-MAA-SIAM Committee Convention Center, Exhibit Hall C. on Employment Opportunities at 9:00 a.m. on The Saturday afternoon session is the annual Thursday, January 26. The purpose of the "employers' choice" session. For this session orientation session is to familiarize participants interviews will be scheduled on the basis of with the operation of the Register and with the requests made by employers. Applicants do not various forms involved. Following orientation, submit specific interview requests for this session; participants of the Employment Register can pick but, in order to participate they must indicate up their interview request forms. Computer­ their availability for the session by filing the scheduled interviews will be held on Friday and Interview Request Form for Saturday, indicating Saturday, January 27 and 28. No interviews will that they will attend the afternoon session that be held on Thursday. day. Request Fonns for the "employers' choice" Fifteen-minute intervals are allowed for inter­ session must be submitted by 4:00 p.m. on Friday views, including two or three minutes between suc­ in order for the interviews to be scheduled for cessive interviews. The interviews are scheduled in Saturday afternoon. half-day sessions: Friday morning and afternoon, Applicants should be aware of the fact that and Saturday morning and afternoon, amounting interviews arranged by the Employment Register to four half-day sessions for interviews. There are represent only an initial contact with employers, ten time periods (9:30-11:45 a.m.) in which in­ and that hiring decisions are not ordinarily made terviews can be scheduled in the morning sessions during or immediately following such interviews. and fourteen time periods (1:15-5:00 p.m.) in the Applicants are advised to bring a number of copies afternoon sessions. It is possible that an applicant of their vitae or resumes so that they may leave or employer may be scheduled for the maximum them with prospective employers. number of interviews in a session. The scheduling All participants in the Employment Register program gives priority to your first six requests. are required to register for the Joint Mathematics The remaining requests will be accommodated Meetings. For applicants there is no additional depending on the availability of participants. The fee for participation in the Employment Register. scheduling program does not have a provision The preregistration deadline is December 5, allowing participants to specify particular times 1983. for interviews beyond the choice of session (day, For employers, additional fees for participation and morning or afternoon). Such requests cannot in the Employment Register are $50, if paid be accommodated. before the December 5 deadline for Joint Meetings Requests for interviews to take place during preregistration, or $75 if paid at the meeting. the two sessions on Friday must be submitted Employers who wish to participate in the on Thursday between 9:30 a.m. and 4:00 p.m. Register and who have neither preregistered Requests for interviews to take place during the nor paid the Employment Register fee must go

657 December Issue of Employment Information in the Mathematical Sciences

For several years the periodical Employment Preparation of Applicants' Resumes Information in the Mathematical Sciences (ElMS) for the Deeember issue of ElMS has published six issues per year listing open The December issue of ElMS will be printed using positions in academic, governmental and industrial photographic reproductions of Forms completed and organizations, primarily in North America, along submitted by applicants. For this reason, special with a few listings from countries in other parts care must be exercised by those who prepare the of the world. ElMS is a joint project of the American Mathematical Society, the Mathematical Forms in order to assure that the results are of good Association of America, and the Society for quality, and will be clear and legible after they have Industrial and Applied Mathematics. It is published been photographed, reduced in size, and printed. by the Society. Because an employer's first impressions of an The December issue of ElMS contains resumes of applicant are likely to be based on the appearance persons seeking professional positions in the math­ of the printed Form, applicants are strongly advised ematical sciences. Resumes of applicants taking to study the suggestions given below very carefully part in the January 1984 Mathematical Sciences before the forms are filled out, so that the original Employment Register at the Joint Mathematics copy will be neither marred nor damaged. Meetings in Louisville will be included in the The Forms must be carefully typed using a new December 1983 issue provided both that they are black ribbon. The best results are obtained by received before the December 5 deadline specified using a modern typewriter with a carbon-coated below and are in satisfactory condition. Other polyethylene film ribbon, but satisfactory results mathematical scientists who wish to be included may be obtained with a ribbon made of nylon or may have their resumes printed if the same deadline other woven fabric if suitable care is exercised. It is is observed and if the copy supplied meets the same important that the keys be clean and make a sharp technical requirements, described below. clear impression, which must be a uniform dark Copies of the December issue of ElMS will black; gray, blue, or other colors will not reproduce be distributed both to subscribers and to the and should, therefore, not be used. Do not use an employers who participate in the Mathematical eraser, as it will cause smudges which reproduce Sciences Employment Register at the Joint Mathe­ when photographed. Use a correcting typewriter, matics Meetings in Louisville in January 1984. Job or correction tape or fluid, if necessary. applicants planning to participate in the Employ­ Only an original copy of the Form should be ment Register in Louisville are therefore strongly submitted, a photocopy or xerographic reproduction urged to preregister so that their resumes can will not reproduce as well and may not be accepted appear in the December issue. for publication. It is therefore important to Applicants who will participate in the Employ­ exercise care in order to assure that the results are ment Register in Louisville and wish to have their satisfactory. The timetable for production of the resumes included in the December issue of Employ­ December issue will not permit poor copy received ment Information in the Mathematical Sciences should after the first week of December to be returned to complete both the special MSER Applicant Form applicants for correction or replacement. and the Preregistration and Housing Form at the Submission of copy of good quality is entirely back of this issue of the Notices. Both Forms must the responsibilty of the applicant. The Society be received in Providence by the December 5, 1983 (which will print this material) must be the final deadline. Forms received after the December 5 judge of what copy is capable of being reproduced deadline cannot be included in the printed booklet. adequately, and therefore of what is acceptable For details on registration and preregistration for for inclusion in the printed booklet. The Society the Louisville Joint Mathematics Meetings, please cannot undertake to correct or replace inadequate refer to the information on these subjects which copy, and cannot entertain requests to prepare may be found elsewhere in this issue of the Notices. original copy. In the event the quality of a Applicants for professional positions in the resume, submitted by an applicant participating mathematical sciences, who do not plan to attend in the Employment Register, does not meet the the meeting in Louisville and participate in the necessary conditions for inclusion in the December Employment Register there, may also submit issue, the resume will nonetheless be posted at resumes for publication in the December issue the Employment Register in Louisville, along with if they use the MSER Preregistration Form for those of the other participants. Applicants at the back of this issue of the Notices and observe the same deadline (December 5) as that for applicants who will be attending the meeting. (It is, of course, not necessary to preregister for the meeting if one is not going to attend the meeting. Resumes will not be posted if the participant is not attending the meeting.)

658 Preregistration Information for Mathematical Sciences Employment Register

MSER PREREGISTRATION- Employers indicate availability for the session in question, whether or not any specific interviews are to be Employers who plan to participate in the requested. Employment Register are urged to preregister for it. The MSER Preregistration Form for Employers MSER PREREGISTRATION - Applicants (which appears at the back of this issue of the Applicants planning to participate in the Employ­ Notices) should be submitted along with the Housing ment Register in Louisville are urged to preregister and Preregistration Form for the Joint Meetings. for it. The special Applicants Preregistration Form Deadline for receipt of both forms is December 5. for the Employment Register (which appears at Preregistration for the Employment Register, in the back of this issue of the Notices) should be addition to permitting inclusion in the printed lists, completed and submitted with the Housing and has the advantage of reduced fees and the services Preregistration Form for the Joint Mathematics of the Mathematics Meetings Housing Bureau, and Meetings prior to the deadline of December 5. has the further advantage of helping to reduce Applicants' resumes will be made available to waiting times at the meeting in Louisville. employers in printed form, so that they may Employers are encouraged to provide more than be studied carefully at leisure. The December one interviewer, when they are able to do so, in order issue of Employment Information in the Mathematical to increase the number of interviews which may be Sciences which will be printed a few weeks before scheduled. Please take care to indicate on the Form the Louisville meeting will contain photographic the number of interviewers for whom simultaneous reproductions of the resumes of applicants who interviews may be scheduled. (If all interviewers have preregistered by December 5. Forms not will be interviewing for the same position, or for received in time cannot be included in the issue. the same set of positions, only one form should be Applicants (as well as others planning to attend submitted and only one employer code number will the Joint Meetings) should note that those who be assigned; therefore, each interviewer would then preregister well in advance of the final deadline receive a separate computer schedule and separate have access to a wider selection of accomodations, table number.) More than one employer code will including, in particular, those in the lower price be required if some interviewers will not interview range, which (being in limited supply) tend to be for all positions. Thus, if there are two disjoint exhausted early in the preregistration process. sets of positions, two forms are required and two The deadline for receipt of applicant forms to be employer codes will be assigned. included in the December issue of ElMS is December A coded strip summarizes the information on 5. They must be accompanied by the Housing each Form; it appears at the bottom of the Form. and Preregistration Form, since registration for the Employers' job listings will be posted at the meeting, Joint Meetings is a prerequisite for registration for so that applicants may study them when choosing the Employment Register. The special forms for which employers they wish to interview. All the Employment Register, as well as the Housing employers are required to complete the Summary and Preregistration Form for the Joint Meetings, Strip. The strip provides an abbreviated version of appear at the back of this issue of the Notices. the information on the Form and is used to prepare Applicants who preregister for the Employment a computer-printed list of preregistered employers Register may pick up their MSER material anytime for distribution to the applicants, called the Winter after 9:30 a.m. on Thursday, January 26, 1984, List of Employers. in the Commonwealth Convention Center, Exhibit Employers who have preregistered must pick Hall C. Interview Request Forms must be submitted up their MSER material in the Commonwealth the day before interviews are to be scheduled; Convention Center, Exhibit Hall C, after 9:30 a.m. applicants who fail to submit the Form before the on Thursday, January 26, 1984, and must submit 4:00 p.m. deadline on the previous day, cannot an interview request form by 4:00 p.m. in order be included in the pool of participants available to receive a eomputer printed schedule for the for interviews on the day in question. The forms following day. This form is handed out at the are given out the day before the interviews to be meeting only. This is not the form that is submitted completed and returned. These are not the forms with preregistration. that are submitted with preregistration. In order for interviews to be scheduled on one day, the Employer's Interview Request Form must be submitted by the 4:00 p.m. deadline on the previous day; it will not be possible to assign any interviews to employers who do not submit the Request Forms in good time even if they choose not to identify particular applicants to be interviewed. Submission of the form is required in order to

659 to the Joint Mathematics Meetings registration List of Applicants. The resumes themselves will desk in the Main Lobby of the Commonwealth be posted at the site of the Register in addition to Convention Center in order to complete their the resumes of those who register at the meeting. registration. Registration for the Joint Meetings Additional copies of the December Issue of ElMS is required to use the Employment Register and both the summary Winter Lists (of Applicants facilities. (No provision will be made to and of Employers) will be available for sale at handle cash transactions at the site of the the AMS Book Sale at the meeting, as long as Employment Register in the Commonwealth supplies last. Prices at the meeting are $2 each for Convention Center, Exhibit Hall C.) the summary lists and $3 for the December issue. Employers and applicants who have completed Any copies remaining after the meeting will be registration for the Employment Register, and available from the Providence office of the Society employers and applicants who have preregistered, for $3 and $6, respectively. (Attention is called may pick up their MSER material after 9:30 a.m. to the fact that the December issue of ElMS will on Thursday, January 26, in the Commonwealth contain the Winter List of Applicants, but will Convention Center, Exhibit Hall C, where the not contain the Winter List of Employers.) Employment Register will be held. All who The Winter List of Employers consists of wish to have interviews scheduled for Friday or summaries of the position listings submitted by Saturday, must submit their Interview Request the employers who preregistered for the meeting; Forms on the preceding day by 4:00 p.m. Those it will be distributed without charge to the who fail to do so cannot be included in the applicants participating in the Register. Others pool of available participants when the matching may purchase the Winter List of Employers at program which schedules the interviews is run the AMS Book Sale at the meeting or from the on the computer that night. This applies both Providence office later, as long as the supply lasts. to preregistered employers and applicants, and to (See previous paragraph for prices.) those registering at the meeting. The Mathematical Sciences Employment These forms are given to participants at the Register is sponsored by the American Mathe­ meeting. These are not the forms that are matical Society, the Mathematical Association of completed with preregistration. America, and the Society for Industrial and Ap­ Employers who do not plan to attend the Em­ plied Mathematics; it is operated by members of ployment Register, but wish to display literature, the AMS staff under the general supervision of the may do so (subject to approval) at no charge, joint AMS-MAA-SIAM Committee on Employment provided all copies of the material to be displayed Opportunities. are received in the Providence Office (MSER, P. 0. Preregistration Information may be found in Box 6248, Providence, RI 02940) no later than an accompanying article in this issue of the December 5. Notices. Information on the December Issue of The MSER registration fee for employers covers Employment Information in the Mathematical the cost of a copy of the December Issue of Sciences, including specific suggestions for the Employment Information in the Mathematical proper preparation of material to be submitted Sciences (EIMS). This publication contains for publication in the December Issue, will also printed copies of the resumes of applicants who be found in a separate article in this issue of preregistered prior to the December 5 deadline; the Notices. it also contains a copy of the summary Winter

Homology and Dynamical Systems John M. Franks This book is an exposition of a number of results This book would be appropriate for a graduate level dealing with the connections between algebraic topol· course. Except for an assumed background in alge­ ogy and dynamical systems. For the most part proofs braic topology the material is largely self-contained. are included; where they are omitted a reference is There are numerous books on algebraic topology given. The topics covered include: Morse gradients, and many on dynamical systems. This is the only symbolic dynamics and subshifts of finite type, book devoted to the inter-relationships of these two Smale and Morse-Smale diffeomorphisms and flows, fields. and the zeta function and homology zeta function of a diffeomorphism. 1980 Mathematics Subject Classifications: 58F09; 57R50 The book is intended for graduate students or CBMS Regional Conference Series Number 49, vii + 120 pages (soft cover) researchers interested in the relationship between List price $14, individuals $7 topology and dynamical systems. It is especially ISBN 0-8218-1700-0; LC 82-8897 appropriate for persons with a background in topol- Publication date: September 1982 ogy who want to learn about dynamical systems. To order, please specify CBMS/49N Prepayment is required for all AMS publications. Order from AMS, P.O. Box 1571, Annex Station, Providence, Rl 02901, or call toll free 800-556-7774 to charge with Visa or MasterCard.

660 American Mathematical Society Short Course Series

Mathematics of Information Processing (January 23-24, 1984} Synopses and Reading Lists

Diameters of Communication Networks (F.R.K. 2. B. E. Jacobs and C. A. Walczak, A general­ Chung). When graphs are used to model the linkage ized query-by-example data manipulation language structure of communication networks, the diameter based on database logic, IEEE Transactions on of the graph corresponds to the maximum number Software Engineering SE-9, number 1 (January 1983), of links over which a message between two nodes 40-57. must travel. In cases where the number of links 3. B. E. Jacobs, On database logic, Journal of in a path is roughly proportional to the time delay the Association for Computing Machinery 29, (April or signal degradation encountered by messages sent 1982), 310-332. along the path, the diameter is often involved in the complexity analysis for the routing algorithms or the Applications of Category Theory of Structural performance of the networks. Sets to Information Systems (Avgustin Tuzhilin). A variety of interrelated diameter problems will The lecture consists of six sections. In the first section be discussed here, including: determining extremal we introduce a general model for the information graphs of bounded degrees and small diameters; system. We apply a general methodology of finding orientations for undirected or mixed graphs mathematical modelling based on the category theory to minimize diameters; and investigating diameter of structural sets for designing a model for some bounds for dynamically changing networks with processes in hospitals. We chose this system because possible node and link failures. it is very far from the traditional mathematical 1. B. Bollobas, Extremal graph theory, Academic practices, contains some main features of general Press, New York, 1978. systems, and specific methods should be designed for 2. S. Even, Graph algorithms, Computer Science investigating it. On the other hand, it is not difficult Press, Rockville, Maryland, 1979. to realize some processes in such systems. The Tran88.ction Management (Hector Garcia­ analysis of the model permits us to introduce main Molina). Database management systems must structures (in N. Bourbaki sense) for a mathematical guarantee that the user programs, called transactions, model of a vast class of information systems. This are executed as atomic units. This means that partial class contains, for example, relational data bases as a results from a transaction should not be observable by subclass. other transactions, even if transactions are executed Some results of the category theory of structural concurrently and if failures occur. The mechanism sets are described in the second section. The general for ensuring this are surveyed. Extensions of these notion of structural sets is introduced, which are mechanisms to a distributed computing system are a slight extension of N. Bourbaki structural sets. also discussed. Canonical morphisms between two objects of a given 1. C. J. Date, An introduction to database sys­ type (species) are introduced. These techniques tems, Volume II, chapters 1, 3, and 7, Addison-Wesley permit us to construct a category for every set of Publishing Company, Reading, Massachusetts, 1983. structural sets of a given type. Therefore, algebraic 2. J. D. Ullman, Principles of database systems, methods of the general category theory may be (second edition), chapters 11 and 12, Computer applied for investigation of structural sets. The Science Press, Rockville, Maryland, 1982. category representation of structural sets permits us to reformulate the notion of the information system Fundamental Database Issues (Barry E. Jacobs). The purpose of this talk is to show how many im­ in category terms. portant database issues can be framed and attacked In section three, we assume that all primitive using the recently developed tool called "database sets used for constructing structural sets are finite logic." These issues include external-to-conceptual (this is the case in traditional computer science) and mapping, view update, view integration and design, construct the universal query language for a given heterogeneous distributed query processing, database finite collection of primitive sets. A specific technique conversion, automatic program conversion and exter­ is developed for construction of the whole "world" of nal axiomatization. Underlying all of these issues is all objects-terms-on the basis of primitive objects the notion of "interpretation" in database logic which and specific sets of variables. The equivalence relation is a generalization of interpretation of first-order of this world permits us to introduce the set of all theories. relations including quantifier relations and "belong" 1. B. E. Jacobs, Applied database logic I: relations (primitive relation of the set theory). The Fundamental database issues, Prentice-Hall, notion of theorem is introduced. The set of all Englewoods Cliffs, New Jersey. relations appears to be a quantifier theory and holds

661 some axioms of the set theory. The universal query dencies. After the introduction, independently by language introduced is a basis for query languages of several researchers, of multivalued dependencies information systems. around 1976, the field became chaotic for a few Relations between information systems and general years in which researchers introduced many new systems are considered in section four. Some clas­ classes of dependencies. The situation has stabilized sical systems such as automata, Turing machines, since 1981 with the introduction, again independently difference schemes including G. von Neumann cellular by many researchers, of embedded implicational automata are considered. dependencies (eid's). Essentially, eid's are sentences In section five, a particular case of information in first-order logic stating that if some tuples, fulfilling systems and general systems called functional data certain equalities, exist in the database then either base and functional systems are considered. We some other tuples must also exist in the database formulate the problem of composition of data bases or some values in the given tuples must be equal. (general systems) and develop the technique for The class of eid's seems to contain most previously solving this composition problem for functional data studied classes of dependencies. bases (functional systems). Most of the papers in dependency theory deal In section six, another particular case of infor­ exclusively with various aspects of the implication mation systems called spaces of available states is problem, i.e., the problem of deciding for a given set considered. We define categories of spaces of available of dependencies ~ and a dependency u whether ~ states for different structures on element bases. By logically implies u. The reason for the prominence defining coproducts in these categories, we introduce of this problem is that an algorithm for deciding composition operations on spaces of (available) states. implication of dependencies enables us to decide We show applications of results obtained to modelling whether two given sets of dependencies are equivalent computer languages. or whether a given set of dependencies is redundant. A solution for the last two problems seems a 1. N. Bourbaki, Elements of mathematics, significant step towards automated database schema Theory of Sets, Addison-Wesley Publishing Company, design, which some researchers see as the ultimate Reading, Massachusetts, 1968. goal for research in dependency theory. 2. A. Tuzhilin, Category theory of structural sets The implication problem for eid's is by now fairly with application to mathematical modelling and well understood. It is known that in its full systems analysis, Mathematical Modelling (in print). generality the problem is recursively unsolvable, but 3. A. Tuzhilin, Category of spaces of available there is a large class of eid's, the class of full states with application to modelling computer implicational dependencies (fid's), for which the languages, Proceedings of Fourth International problem is solvable. The bad news is that this Conference on Mathematical Modelling, Zurich, 1983. solvability is not very practical, since the implication 4. M. Tausner and A. Tuzhilin, Modelling the problem for fid's is computationally intractable (it Apple II using categories of spaces of available requires exponential time). The good news is that states, Proceedings of Fourth International Con­ in many important cases the problem can be solved ference on Mathematical Modelling, Zurich, 1983. in polynomial time. There are still, however, some The Theory of Data Dependencies (Moshe Y. persistent open questions, like the case of embedded Vardi). In the relational database model, conceived multivalued dependencies. by Codd in the late 60s, one views the database An emerging application for the theory of depen­ as a collection of relations, where each relation is dencies is the universal relation model. This model a set of tuples over some domain of values. One aims at achieving data independence, which was the notable feature of this model is its being almost original motivation for the relational model. In the devoid of semantics. A tuple in a relation represents universal relation model the user views the data as if a relationship between certain values, but from the it is stored in one big relation. The data, however, mere syntactic definition of the relation one knows is not available in this form but rather in several nothing about the nature of this relationship, not smaller relations. It is the role of the database even if it is a one-to-one or one-to-many relationship. management system to provide the interface between One approach to remedy this deficiency is to the users' view and the actual data, and it is the devise means to specify the missing semantics. These role of the database designer to specify this interface. semantic specifications are often called semantic There have been different approaches to the question or integrity constraints, since they specify which of what this interface should be like, but they all use databases are meaningful for the application and dependencies as a specification language. which are meaningless. Of particular interest 1. Any standard textbook on first-order logic, are the constraints called data dependencies, or including the issue of recursive solvability. dependencies for short. 2. J. D. Ullman, Principles of database systems, The study of dependencies began in 1972 with chapter 7, Computer Science Press, Rockville, the introduction by Codd of the functional depen- Maryland, 1982.

662 Joint Summer Research Conferences in the Mathematical Sciences Bowdoin College, June 10 to August 18, 1984

The 1984 Joint Summer Research Conferences in The Joint Summer Research Conferences in the the Mathematical Sciences will be held at Bowdoin Mathematical Sciences is under the direction of College, Brunswick, Maine, between June 10 and the AMS-IMS-SIAM Committee on Summer Research August 18, 1984. It is anticipated that the series of Conferences in the Mathematical Sciences which week-long conferences will be supported by a grant includes: Benedict Gross, Malcolm R. Leadbetter, from the National Science Foundation. Angus J. Macintyre, Jerrold E. Marsden, James There will be ten one-week conferences in ten McKenna, Evelyn M. Nelson, Katsumi Nomizu, Julius different areas of mathematics. Each week par­ Shaneson, R. 0. Wells, Jr. (chairman), and Shmuel ticipants will arrive on Sunday and leave the follow­ Winograd. ing Saturday. The topics and organizers for the ten conferences were selected by the AMS-IMS-SIAM June 10 to June 16 Commmittee on Joint Summer Research Conferences New multivariate methods in statistics in the Mathematical Sciences. The selections were PETER HUBER (Harvard University), Chairman based on suggestions made by the members of the The past several years have seen a spate of renewed committee, by members of the Council of the AMS interest in multivariate analysis, departing in many and others. The committee considered it important ways from established paradigms. These activities that the conferences represent diverse areas of math­ range from "neoclassicist" developments based on ematical activity, with emphasis on areas currently second order properties (group theoretic models for especially active, and paid careful attention to sub­ covariance structure; mathematics of factor analysis) jects in which there is important interdisciplinary to revolutionary nonparametric and graphical ap­ activity at present. proaches (recursive partitioning; projection pursuit; The conferences will be similiar in structure to nonparametric regression and optimal transforma­ those held throughout the year at Oberwolfach. These tions; multi-dimensional scaling) and to new probabil­ conferences are intended to complement the Society's istic tools of relevance to the sampling theory of these program of annual Summer Institutes and Summer approaches (Vapnik-Cervonenkis classes). There are Seminars, which have much larger attendance and are obvious and not so obvious cross-connections between substantially broader in scope. The conferences are the various lines of development. We believe that a research conferences, and are not intended to provide gathering of experts should be most beneficial at this an entree to a field in which a participant has not point in time: it will lead to a clarification of the already worked. issues and will stimulate further advances. It is expected that funding will be available for Members of the Organizing Committee: Peter about thirty participants in each conference. Others, Bickel (University of California, Berkeley), Persi in addition to those funded, will be welcome, within Diaconis (Stanford University), and Jerry Friedman the limitations of the facilities of the campus. Up (Stanford University). to about seventy participants can be accommodated at each conference. Housing accommodations will June 17 to June 23 be available on campus for those attending the Random matrices and their applications conference, and daily meals will be served in a dining JOEL CoHEN (Rockefeller University), Chairman hall near the dormitories. A brochure describing The theory of random matrices and of products the facilities available at Bowdoin College will be of random matrics is developing actively, stimulated available from the AMS office in March 1984. The in part by many applications in statistics, physics, brochure will include information on firm room rates biology, and the behavioral sciences. The purposes of and the residence and dining hall facilities, as well as this conference are to bring together mathematicians local information and a reservation form to be used working in this area and to bring mathematicians for accommodations on campus. Each participant together with scientists involved in the applications of will pay a registration and social fee to cover the cost random matrices so that new questions may be asked of refreshments served at breaks and for social events. and answered. Those interested in attending one of the conferences Some of the topics that will be appropriate for this should request an application form from Carole conference are: Kohanski, Summer Research Conference Coordinator, American Mathematical Society, Post Office Box Generalizations and extensions of Wigner's semi­ 6248, Providence, RI 02940 (401-272-9500, extension circle theorem; 286), specifying which conference they wish to Subadditive ergodic theory, Oseledec's theorem, attend. Selection of the participants and approval of and strong and weak laws of large numbers for participant support will be made by the Organizing products of random matrices; Committee for each conference. Women and members Random difference equations; of minority groups are encouraged to apply and to Perturbation theory for products of random participate in these conferences. The deadline for matrices. receipt of applications is January 16, 1984. Those who Applications of the theory of products of random wish to apply for a grant-in-aid should so indicate matrices to the random Schrodinger equation, random on the application form; however, funds available for walks in random environments, Ising models of these conferences are limited and so individuals who disordered systems, age-structured populations with can obtain support from other sources should do so. random vital rates, ecological stability, exploration

663 and display strategies for high-dimensional data, is the cohomology of its fundamental group. Con­ continued fractions, neurophysiology, and power sequently, geometric techniques such as the Borel­ transmission in noisy cables. Serre compactification are useful in studying group Members of the Organizing Committee: Harry cohomology; in this case, for arithmetic groups. Also Kesten (Cornell University) and Charles M. Newman new developments about Teichmiiller space have been (University of Arizona). useful in studying the cohomology of the mapping class group. This is a sample of the many interesting June 24 to June 30 things which will be discussed at this conference. The mathematics of phase transitions Members of the Organizing Committee: Frank Raymond (University of Michigan, Ann Arbor). RICHARD DURRETT (University of California, Los Angeles), Chairman July 8 to July 14 In the last fifteen years, a number of results Group actions on rings have been proved about the phase transitions in SuSAN MONTGOMERY (University of Southern various systems, e.g. percolation, the Ising model, California), Chairman and related stochastic processes which describe the There has been great interest recently on the topic temporal evolution of nonequilibrium states. The of group actions on rings in a number of different results which have been obtained can be divided into areas, in particular in operator algebras, in invariant three more or less disjoint groups: Rigorous statistical theory, and in ring theory itself. The purpose of the mechanics, Percolation, and Infinite particle systems. conference is to bring together workers in these areas The problems in these areas are very similar but in order to share techniques and problems. unfortunately there has been little interaction between the mathematical physicists and the probabilists More specifically, the topics to be discussed will working on these problems. include: crossed products over rings, including von Neumann algebras and C*-algebras; Galois theory The aim of this conference is to remedy this of rings and the relationship between a ring and its situation by bringing together people who work in fixed subrings; classifying group actions on rings; and these fields so that they can talk about the past the relationship of ring theory to invariant theory, and future of these subjects. In keeping with this including non-commutative methods such as the use purpose the lecture time will be divided almost evenly of polynomial identities and generic matrix rings. between one-hour talks which survey the state of our knowledge concerning some of the basic models and The tentative format will consist of two one-hour shorter talks which describe current developments survey talks by the following speakers: 1) D. S. and open problems. Passman on group actions and crossed products of associative rings, 2) M. A. Rieffel on group actions Members of the Organizing Committee: Harry Kes­ on C*-algebras, 3) M. Hochster on invariant theory ten (Cornell University), Thomas L ggett (University of commutative rings, and 4) E. Formanek on non­ of California, Los Angeles), Barry El~non (California commutative invariant theory. In addition there will Institute of Technology), and Thomas Spencer be about 15 half-hour speakers on related topics. (Courant Institute of the Mathematical Sciences, New York University). Members of the Organizing Committee: Melvin Hochster (University of Michigan), Marc Rieffel July 1 to July 7 (University of California, Berkeley), and Robert Snider (Virginia Polytechnic Institute and State Aspherical complexes University). KENNETH BROWN (Cornell University), Co­ Chairman July 15 to July 21 F. T. FARRELL (University of Michigan, Ann Diophantine problems, including diophantine equations, Arbor), Co-Chairman diophantine approximation, and transcendency This topic is of particular interest to topologists, D. J. LEWIS (University of Michigan, Ann Arbor), differential geometers, and group theorists. A Co-Chairman topological space is aspherical if all its homotopy W. M. ScHMIDT (University of Colorado, Boulder), groups vanish except its fundamental group. Ellen­ Co-Chairman berg's obstruction theory shows that the homotopy In the last several years considerable and exciting type of an aspherical simplical complex is determined progress has been made in the areas of Diophan­ by its fundamental group. This suggests the follow­ tine equations, Diophantine approximations, and ing question. Does the fundamental group of a Transcendence theory, the subject matter of this closed aspherical manifold determine the manifold conference. In Diophantine equations the most up to homeomorphism? Mostow's rigidity theorem striking result has been the proof of the Mordell gives positive motivation that the answer is Yes. conjecture by Faltings. Also significant for its long­ A seemingly more tractable question, related to range potential has been the evolvement of analytic Novikov's conjecture, is the following: If two closed techniques to where they can be applied to general aspherical manifolds have isomorphic fundamental non-additive forms. In Diophantine approximation, groups, are their Cartesian products with Euclidean Pade approximation methods are leading to even bet­ 3-space homeomorphic? Another problem is to give ter effective estimates. Also ingeneous new estimates an effective way to decide when a given group can in uniform distribution have the potential to change be the fundamental group of a closed aspherical that theory. In transcendence theory the combining manifold. When it is, can one construct the manifold of commutative algebra with the analytic techniques from knowledge of the group? Aspherical complexes has led to results that supercede almost everything are intimately related to group cohomology; e.g., known a few years ago. The conference will enable the cohomology of the aspherical simplicial complex these developments to be presented by those working

664 at the frontier, and enable researchers to assess future particular, the problems of controlling linear time­ developments. invariant multivariable systems involve extensive use of linear algebraic tools; and also are emerging as rich July 22 to July 28 sources of new problems in linear algebra. Recent The Selberg trace formula and related topics developments in this area of interaction involve the AUDREY TERRAS (University of California, San geometric theory of multivariable control; the theory Diego), Chairman of polynomial and rational function matrices; and The Selberg trace formula is an analogue of algorithms for the computation of the objects of these the Poisson summation formula which applies to theories and for system design. fundamental domains for discrete groups acting on The purpose of this conference is to bring together symmetric spaces (e.g., the modular group SL(2,7) experts from systems theory as well as from linear acting on the Poincare upper half plane). Short algebra, both theoretical and numerical, to discuss expository accounts of the trace formula appear in recent research findings and to have a useful exchange Elstrodt [Jber. D. Dt. Math.-Verein. 83 (1981), 45-77], of ideas. Hejhal (Duke Math. J. 43 (1976), 441-482], Venkov Members of the Organizing Committee: Richard [Russian Math. Surveys 34 (1979), 79-153] and Terras A. Brualdi (University of Wisconsin, Madison), [S.I.A.M. Review 24 (1982), 159-193]. David Carlson (Oregon State University), Charles At the present there is a huge amount of work R. Johnson (University of Maryland), and Robert J. in progress, both on the development of the trace Plemmons (North Carolina State University). formula for higher rank symmetric spaces, as well August 5 to August 11 as on applications of the trace formula and another Integral geometry simpler analogue of the Poisson summation formula which is really Mercer's theorem. The aim of this RoBERT L. BRYANT (Rice University), Chairman conference is to consolidate this work. The point This conference will be devoted to integral geometry of view will be mostly that of classical real analysis and some of its recent ramifications. In addition and spectral theory, but we will also consider p-adic, to classical differential geometry, areas of recent adelic and discrete analogues of the real and complex applications include partial differential equations, theory. Another aim of the conference is to discuss group representations, tomography and mathematical the applications of the trace formula in number physics. The purpose of this conference is to explore theory, geometry, physics and applied mathematics, some of these applications and their relationships as and group representations. indicated by the topics listed below. The following are among the topics which should a) Classical integral geometry, measures on families be covered in the meeting: of geometric objects, and recent applications to differential geometric problems. I. The Theory b) The Radon transform and its generalizations. a) Eisenstein series, cusp forms, residual spectrum. Operational properties. b) Spectral decomposition of the invariant differen­ c) Applications of the Radon transform and its tial operators on L 2 (r \G/K); e.g., for G=SL (n,R) generalizations to analysis, in particular partial or Sp(n,R). differential equations, group representations, scatter­ c) conjugacy classes in r and associated orbital ing theory and holonomic systems. integrals. d) Integral geometry and mathematical physics. d) comparison of the theories for different groups. Members of the Organizing Committee: Victor e) the trace formula and simpler analogues of Guilleinin (Massachusetts Institute of Technology), Poisson summation, twisted versions. Sigurdur Helgason (Massachusetts Institute of Tech­ II. Applications nology), and R. 0. Wells, Jr. (Rice University). a) number-theoretic: units in number fields, Artin August 12 to August 18 L-functions, dimensions of spaces of automorphic Complex differential geometry and non-linear differential forms, circle problems, distribution of solutions of equations polynomial congruences. Y. T. Sm (Harvard University), Chairman b) geometric: asymptotics of eigenvalues of the In recent years new directions of research in Laplacian, length spectrum. complex differential geometry have been opened up c) group theoretic: multiplicities of representations. by the methods of non-linear differential equations d) applied mathematics: coherent states, Ising such as harmonic maps, minimal surfaces, and model, quantum statistical mechanics, fast trans­ complex Monge-Ampere equations. This conference forms. will focus on such methods and other closely related Members of the Organizing Committee: Dennis areas. The topics discussed will include the following: Hejhal (University of Minnesota, Minneapolis), and the application of harmonic maps to the theory of Peter Sarnak (Courant Institute of the Mathematical complex manifolds, the regularity results of Schoen­ Sciences, New York University). Uhlenbeck on harmonic maps, minimal surfaces of high codimension, the results of Taubes and July 29 to August 4 Uhlenbeck on Yang-Mills fields, the regularity of Linear algebra and its role in systems theory free boundary problems, complex Monge-Ampere BISWA NATH DATTA (Northern Dlinois University), equations, Einstein metrics for complex manifolds Chairman and stable holomorphic vector bundles. Linear algebra is a rapidly expanding field, whose Members of the Organizing Committee: L. concepts and techniques are used in virtually every Caffarelli (University of California, Berkeley) and area of mathematics and its applications. In R. Schoen (University of California, Berkeley).

665 Invited Speakers Barbara Cortzen, Ring theory Julia Knight, Model theory and Special Sessions N. Tenney Peck, Metric linear function spaces Invited Speakers at AMS Meetings April1984 Meeting Southeastern Section The individuals listed below have accepted invita­ Deadline for organizers: Expired tions to address the Society at the times and places Deadline for consideration: To be announced indicated. For some meetings, the list of speakers is incomplete. Spring 1984 Meeting Louisville, January 1984 Far Western Section Deadline for organizers: Expired Gunnar Carlsson M. Susan Montgomery Deadline for consideration: To be announced Persi Diaconis Herbert A. Simon Simon K. Donaldson (Gibbs Lecturer) Spring Meeting Robert D. MacPherson Leon Simon Eastern Section Andrew Majda Robert E. Tarjan Deadline for organizers: Expired Barry Mazur Deadline for consideration: To be announced (Colloquium Lecturer) August 1984 Meeting in Eugene Notre Dame, April1984 Associate Secretary: Frank T. Birtel Nigel J. Kalton Karel L. Prikry Deadline for organizers: November 15, 1989 Paul G. Nevai William Schetter Deadline for consideration: To be announced Minneapolis, November 1984 November 1984 Meeting in Minneapolis Deadline for organizers: February 15, 1984 Jerry L. Bona Naresh C. Jain Deadline for consideration: To be announced I. Martin Isaacs Stephen C. Milne Marian B. Pour-El, Logic Organizers and Topics Mareh 1985 Meeting in Chicago of Special Sessions Deadline for organizers: June 15, 1984 Deadline for consideration: To be announced The list below contains all the information about Special Sessions at meetings of the Society available Send Proposals for Special Sessions to the at the time this issue of the Notices went to the Associate Secretaries printer. The programs of sectional meetings are arranged by The section below entitled Infonnation for the Associate Secretary for the section in question: the timetable for announcing Organizers describes Far Western Section (Pacific and Mountain) the existence of Special Sessions. Hugo Rossi, Associate Secretary January 1984 Meeting in Louisville Department of Mathematics Institute for Advanced Study Associate Secretary: W. Wistar Comfort Princeton, NJ 08540 Deadline for organizers: Expired (Telephone 609-734-8157) Deadline for consideration: October 12, 1989 Central Section Donald W. Anderson and Gunnar Carlsson, Homo- Robert M. Fossum, Associate Secretary Presumptive topy theory Department of Mathematics J. Thomas Beale, Incompressible fluid flow University of lllinois John B. Conway, Function theoretic operator theory 1409 West Green Street Urbana, IL 61801 Persi Diaconis, Random walks on finite groups (Telephone 217-333-3975) Andrew M. W. Glass, Ordered algebraic structures Eastern Section Henry Hermes and Hector Sussmann, Vector field W. Wistar Comfort, Associate Secretary systems and control Department of Mathematics Mark A. Kon, Partial differential operators Wesleyan University differential equations Middletown, CT 06457 Suzanne M. Lenhart, Partial (Telephone 203-347-9411) and optimal control problems Southeastern Section M. Susan Montgomery and Lance Small, Ring theory Frank T. Birtel, Associate Secretary Ira J. Papick, Commutative algebra Department of Mathematics William L. Perry, fll-posed problems Thlane University W. Wiley Williams, Semigroup theory New Orleans, LA 70118 (Telephone 504-865-5646) April 1984 Meeting in Notre Dame As a general rule, members who anticipate organi~ing Central Section Special Sessions at AMS meetings are advised to seek Deadline for organizers: Expired approval at least nine months prior to the scheduled date Deadline for consideration: To be announced of the meeting. No Special Sessions can be approved to provide adequate advance notice to members . Theodore S. Chihara, Orthogonal polynomials and too late I. who wish to participate. 1. their applications

666 Information for Organizers Information for Speakers Special Sessions at Annual and Summer meetings A great many of the papers presented in Special are held under the general supervision of the Sessions at meetings of the Society are invited papers, Program Committee. They are administered by but any member of the Society who wishes to do the Associate Secretary in charge of the meeting with so may submit an abstract for consideration for staff assistance from the Society office in Providence. presentation in a Special Session, provided it is Some Special Sessions arise from an invitation to received in Providence prior to the special early a proposed organizer issued through the Associate deadline announced above and in the announcements Secretary. Others are spontaneously proposed by of the meeting at which the Special Session has been interested organizers or participants. Such proposals scheduled. are welcomed by the Associate Secretaries. Abstracts of papers submitted for consideration for The number of Special Sessions at a Summer or presentation at a Special Session must be received Annual Meeting is limited to twelve. Proposals, by the Providence office (Editorial Department, invited or offered, which are received at least American Mathematical Society, Post Office Box nine months prior to the meeting are screened for 6248, Providence, RI 02940) by the special deadline suitability of the topic and of the proposed list for Special Sessions, which is usually three weeks of speakers, and for possible overlap or conflict earlier than the deadline for contributed papers for with other proposals (specific deadlines for requesting the same meeting. The Council has decreed that no approval for Special Sessions at national meetings are paper, whether invited or contributed, may be listed given above). If necessary, the numerical limitation in the program of a meeting of the Society unless an is enforced. abstract of the paper has been received in Providence Proposals for Special Sessions should be submitted prior to the deadline. directly to the Associate Secretary in charge of the meeting (at the address given in the accompanying Call for Invitations box). If such proposals are sent to the Providence The undersigned Associate Secretary hereby office, addressed to the Notices, or directed to anyone solicits invitations from institutions interested in other than the Associate Secretary, they will have serving as host to a future meeting (Eastern Section) to be forwarded and may not be received before the of the Society. quota is filled. Among desirable characteristics for the site of a In accordance with an action of the Executive sectional meeting are: Committee of the Council, no Special Session may be arranged so late that it may not be announced in (a) Accessibility via public transportation; the Notices early enough to allow any member of the (b) Availability of inexpensive food and lodging Society, who wishes to do so, to submit an abstract on or near campus; for consideration for presentation in the Special (c) Minimal cost (normally nil) to the Society for Session before the deadline for such consideration. the use of classrooms and other facilities; and Special Sessions are effective at sectional meetings (d) A couple of energetic local mathematicians and can usually be accommodated. They are arranged willing to serve as an Arrangements Committee. by the Associate Secretary under the supervision of Planning for a sectional meeting begins ap­ the Committee to Select Hour Speakers for the proximately two years in advance of the meeting section. The limitation on the number of sessions itself. At the moment we seek sites for meetings in depends on the space and time available. The same the Spring and the Fall of 1985. Exact dates are restriction as for national meetings applies to the flexible and negotiable. deadline for announcing Special Sessions at sectional Exploratory correspondence may be addressed meetings: no Special Session may be approved too to W. W. Comfort, Associate Secretary, AMS, late for its announcement to appear in time to Department of Mathematics, Wesleyan University, allow a reasonable interval for members to prepare Middletown, Connecticut 06457. and submit their abstracts prior to the special early 1 deadline set for consideration of papers for Special Sessions.

667 ,...----NONLINEAR OSCILLATIONS IN BIOLOGY-----. Edited by F. C. Hoppensteadt

Contents with comments excerpted from a review by Robert Rosen, Dalhousie University, in Bulletin of Mathematical Biology, Volume 43, pp. 121-123.

"Taken together, the papers in this volume provide a marvellous introduction to their subject, and con­ vey the flavor of the most modem research activity at the interface between mathematics and biology. They fully show the symbiosis between the two areas; how biology gains from the mathematical formu­ lation of basic biologicai processes, and how mathematics gains by grappling with these formulations. The volume can be recommended most highly to all who are .interested in any aspect of these prolr /ems, the contributors and organizers, as well as the AMS and SIAM, can take a great deal of pride in it." LOUIS N. HOWARD, Nonlinear Oscillations "... contains a comprehensive discussion of linear and non-linear oscillators and their mathematical properties, with examples ranging from the harmonic oscillator and pendulum through limit-cycle sys­ tems such as the van der Pol osc;illator, the Brusse/ator, and the Oregonator. There is an extensive discus­ sion of propagation of oscillations and wave-trains, exemplified in properties of equations describing excitation in nerve (Nagumo's equation) and in the work on reaction diffusion equations carried out jointly by Howard and Nancy Kopel/. Also included is a brief but clear discussion of the Hopf Bifurca­ tion and its general significance in establishing the existence of periodic behavior."

CHARLES STEELE, Studies of the Ear "... contains a detailed physiological review of the structure of the ear and the problems arising from relating the basic problems of auditory perception to the known anatomy and physiology."

ARTHUR S. WINFREE, 24 Hard Problems About the Mathematics of 24 Hour Rhythms "... poses that number (24) of open problems directly bearing on circadian rhythms and biological clocks in general. About hair of these questions deal with phasing in individuaJ oscillators, and the rest with the understanding of populations of coupled oscillators and with entrainment. Sufficient back­ ground is given to make these questions intelligible to the non-specialist, and the exposition is remark­ ably clear." DONALD LUDWIG, Stochastic Modelling and Nonlinear Oscillations "... present only in a two-page abstract."

FRANK C. HOPPENSTEADT, Computer Studies of Nonlinear Oscillators "... indicative of a growing trend; namely, the employment of the computer as a legitimate research tool in analytical studies . .. In dynamical system theory, where explicit analytical solutions of nonlinear systems are few and far between, the computer provides an essential way of building insights into dy­ namical behavior which is the crucial guide to general understanding . .. Hoppensteadt deals with some questions involving harmonics in nonlinear systems, and with the study of chaotic behavior." OTTO E. ROSSLER, Chaotic Oscillations: An Example of Hyperchaos "... belongs to the study of 'strange attractors' and is full of interesting insights regarding the mani­ festation of chaotic properties in what we would consider 'simple' dynamical systems of dimension three and higher." JACK K. HALE, Nonlinear Oscillations in Equations with Delays "... The paper is entirely concerned with local problems, which are explored by means of bifurcation methods, using the lags themselves as bifurcation parameters. This procedure raises important formal problems, which are carefully discussed in the article." JOHN GUCKENHEIMER, A Brief Introduction to Dynamical Systems "... contains a good introduction to the modem theory of dynamical systems, emphasizing those properties which are of importance when such a system is regarded as a model for some real-world process. On its own terms, it is a masterpiece of concise and clear exposition, but it·is definitely not for the mathematically naive reader." viii +53 pages, Volume 17, Lectures in Applied Mathematics List price $40, institutional member $30, individual member $20 (ISBN Q-8218-1117-7; LC 79-26469. Publication date: November1979 ORDERS MUST BE PREPAID. To order, please specify LAM/17 American Mathematical Society P.O. Box 1571, Annex Station, Providence, Rhode Island 02901

668 Special Meetings

TIDS SECTION contains announcements of meetings of interest to some segment of the mathematical public, including ad hoc, local, or regional meetings, and meetings or symposia devoted to specialized topics, as well as announcements of regularly scheduled meetings of national or international mathematical organizations. (Information on meetings of the Society, and on meetings sponsored by the Society, will be found inside the front cover.) AN ANNOUNCEMENT will be published in the Notices if it contains a call for papers, and specifies the place, date, subject (when applicable), and the speakers; a second full announcement will be published only if there are changes or necessary additional information. Once an announcement has appeared, the event will be briefly noted in each issue until it has been held and a reference will be given in parentheses to the month, year and page of the issue in which the complete information appeared. IN GENERAL, announcements of meetings held in North America carry only date, title of meeting, place of meeting, names of speakers (or sometimes a general statement on the program), deadlines for abstracts or contributed papers, and source of further information. Meetings held outside the North American area may carry more detailed information. All communications on special meetings should be sent to the Editor of the Notices, care of the American Mathematical Society in Providence. DEADLINES for entries in this section are listed on the inside front cover of each issue. In order to allow participants to arrange their travel plans, organizers of meetings are urged to submit information for these listings early enough to allow them to appear in more than one issue of the Notices prior to the meeting in question. To achieve this, listings should be received in Providence SIX MONTHS prior to the scheduled date of the meeting.

Fall 1983. Special Semester in Hodge Theory: Valley 27-December 3. Mathematische Methoden zur VLSI, Geometry Seminar, Amherst College, Amherst, Mas­ Chairmen: M. Fischer, Seattle, M. Fontet, Paris, G. sachusetts; Mount Holyoke College, South Hadley, Mas­ Hotz, Saarbriicken. sachusetts; Smith College, Northampton, Massachusetts; December University of Massachusetts, Amherst, Massachusetts. 4-10. Nichtstandardanalysis, Chairmen: S. Albeverio, Program: There will be weekly lectures on Friday Bochum, D. Laugwitz, Darmstadt, W. A. J. Luxemburg, afternoons on topics from Hodge theory, including Pasadena. Torelli problems, infinitesimal variations of Hodge 11-17. Spez. Statistik: Asymptotic Statistics, Chairmen: J. structure, mixed Hodge theory, and applications to Pfanzagl, Koln, H. Strasser, Bayreuth. rational homotopy. 18-23. C*-Algebren, Chairmen: A. Connes, Paris, J. Cuntz, Speakers: Speakers will include E. Cattani, B. Friedman Heidelberg, R. Nagel, Tiibingen. and A. Kaplan. January 1984 Information: David Cox, Department of Mathematics, 2-7. Informationstheorie, Chairman: R. Ahlswede, Amherst College, Amherst, Massachusetts 01002. Bielefeld. 1983-1984. Academic Year Devoted to Problems on 8-14. Mathematische Theorien der Fluide, Chairmen: W. Iteration in Classical Real and Complex Analysis, The Burger, Karlsruhe, I. Miiller, Berlin. Mittag-Leffler Institute, Djursholm, Sweden. (February 15-21. Modelltheorie, Chairman: A. Prestel, Konstanz. 1983, p. 205) 22-28. Kombinatorik, Invariantentheorie und Darstel­ 1983. Special Year in Commutative Algebra and Al­ lungstheorie symmetrischer Gruppen, Chairmen: A. gebraic Geometry, University of Illinois, Urbana, lllinois. Kerber, Bayreuth, G.-C. Rota, Cambridge. (November 1982, p. 699) 29-February 4. Brauergruppen tiber Korpern, Chairmen: October 2, 1983-September 29, 1984. Matbematiaehea P. Draxl, Bielefeld, M.-A. Knus, Zurich. Forsehungsinstitut Oberwolfaeh (Weekly Conferences), February Federal Republic of Germany. 5-11. Nukleare Frechet-Rii.ume, Chairmen: E. Dubinski, Information: Martin Barner, Institute Director, Albert­ Potsdam, D. Vogt, Wuppertal. strasse 24, 7800 Freiburg i. Br., Federal Republic of 12-18. Funktionentheorie, Chairmen: G. Frank, Dortmund, Germany. St. Ruscheweyh, Wiirzburg, K. Strebel, Zurich. October 19-25. Mathematische Stochastik, Chairmen: W. Hazod, 2-8. Geometrie, Chairmen: D. Ferus, Berlin , K. Voss, Heidelberg, G. Neuhaus, Hamburg. Zurich. 26-March 3. Operationsresearch, Chairmen: K. Neumann, 9-15. Arbeitsgemeinschaft Geyer-Harder. Karlsruhe, D. Pallaschke, Karlsruhe. 16-22. Parametrische Optimierung und Approximation, March Chairmen: B. Brosowski, Frankfurt, F. Deutsch, Univer­ 4-10. Regelungstheorie, Chairmen: H. W. Knobloch, sity Park. Wiirzburg, M. Thoma, Hannover. 23-29. Mathematics in Industry, Chairman: H. Neunzert, 11-17. Linear operators and applications, Chairmen: I. C. Kaiserslautern. Gohberg, Tel Aviv, B. Gramsch, Mainz, H. H. Schaefer, 30-November 5. Komplexitatstheorie, Chairmen: C. P. Tiibingen. Schnorr, Frankfurt, A. Schonhage, Tiibingen, N. 18-24. Mathematische Spieltheorie, Chairmen: W. F. Strassen, Zurich. Lucas, Cornell, J. Rosenmiiller, Bielefeld, D. Schmeidler, November Tel Aviv. 6-12. Fortbildungslehrgang fiir Studienrii.te. 25-31. Order Statistics, Quantile Processes and Extreme 13-19. Microlokale Analysis und partielle Value Theory, Chairmen: R. Reiss, Siegen, W. R. van Dift'erentialgleichungen, Chairmen: G. Bengel, Munster, Zwet, Leiden. P. Shapira, Paris, J. Sjostrand, Paris. April 20-26. Singularities and Constructive Methods for their 1-7. Arbeitsgemeinschaft Geyer-Harder. Treatment, Chairmen: W. Wendland, Darmstadt, J. R. 8-14. Diophantische Approximation, Chairmen: P. Whiteman, Uxbridge. Bundschuh, Koln, R. Tijdeman, Leiden.

669 15-21. Rekursionstheorie, Chairmen: H.-D. Ebbinghaus, 8-9. The Fourteenth Midwest Partial Differential Equations Freiburg, G. H. Miiller, Heidelberg, G. E. Sacks, Seminar, Purdue University, West Lafayette, Indiana. Cambridge. (August 1983, p. 541) 22-28. Graphen, Gruppen und Kammernsysteme, 10-14. ICMI-JSME Regional Conference on Ma,thematical Chairmen: M. Aschbacher, Pasadena, D. Goldschmidt, Education, Tokyo, Japan. (June 1983, p. 437) Berkeley, F. G. Timmesfeld, Giessen. 29-May 5. Gruppentheorie, Chairmen: K. W. Gruenberg, 11-13. Conference on Phase Transformations and Material London, 0. Kegel, Freiburg. Instabilities in Solids, The Mathematics Research Center, May University of Wisconsin, Madison, Wisconsin. (June 1983, 6-12. Theorie, Numerik und Anwendung nichtlinearer p. 438) Eigenwertprobleme, Chairmen: H. B. Keller, Pasadena, 13-16. Conference in Algebraic Groups in Honor of K. Schmitt, Salt Lake City, H. 0. Peitgen, Bremen. Armand Borel, Institute for Advanced Study, Princeton 13-19. Geschichte der Mathematik, Chairmen: C. J. Scriba, University, Princeton, New Jersey. Hamburg, L. Navy, Prag. Program: Leading mathematicians in algebraic groups, 20-26. Gruppen und Geometrien, Chairmen: B. Fischer, number theory, topology (areas substantially influenced Bielefeld, D. G. Higman, Ann Arbor. by Professor Borel's work) will report on recent progress. 27-June 2. Algebraische K-Theorie, Chairmen: R. K. Principal Speakers: A. Borel, G. Harder, H. Jacquet, R. Dennis, Ithaca, U. Rehmann, Bielefeld. MacPherson, J. Millson, M. S. Raghunatuan, J. P. June Serre, C. Soule, T. Springer, D. Vogan, and A. Weil. 3-9. AG Algebra: Orders and their Applications, Chairmen: Information: N. R. Wallach, Department of Mathematics, K. W. Roggenkamp, Stuttgart, I. Reiner, Urbana. Rutgers University, New Brunswick, New Jersey 08903, 10-16. Gewebegeometrie, Chairmen: S. S. Chern, Berkeley, orR. Lee, Department of Mathematics, Yale University, V. V. Goldberg, Newark, K. Strambach, Bayreuth. New Haven, Connecticut 06520. 17-23. Integrierbare Hamiltonsche Systeme und al­ 17-21. NSF Conference on Asymptotic Behavior of Mass gebraische Geometrie, Chairmen: P. van Moerbecke, and Space-Time Geometry, Oregon State University, Waltham, H. Knorrer, Bonn. Corvallis, Oregon. (August 1983, p. 542) 24-30. Konstruktive Methoden zur praktischen Be­ handlung von Integralgleichungen, Chairmen: G. 18-21. Third Symposium on Microcomputer and Micro­ Hammelin, Miinchen, K. H. Hoffmann, Augsburg. processor Applications, Budapest, Hungary. (August 1983, July p. 542) 1-7. Integrierbare Hamiltonsche Systeme und algebraische 19-21. Ninth Annual Statistics Symposium on National Geometrie, Chairmen: P. van Moerbecke, Waltham, H. Energy Issues, Rockville, Maryland. Knorrer, Bonn. Topics: Methods for analyzing energy-rt;lated data, prob­ 8-14. Graphentheorie, Chairmen: W. Mader, Hannover, G. lems in probabilistic safety or risk analysis, analysis of Ringel, Santa Cruz. survival time data, techniques for resolution of health 15-21. Konvexe Korper, Chairmen: R. Schneider, Freiburg, issues, or solutions of specific practical statistics prob­ G. C. Shepard, Norwich. lems arising in energy studies. Applications include such 22-28. Potentialtheorie, Chairman: H. Bauer, Erlangen. energy fields as nuclear, fossil fuel, solar, geothermal, 29-August 4. Variationsrechnung, Chairmen: J. Frehse, etc. Bonn, W. Jager, Heidelberg, F. Tomi, Bonn. Information: Maurice C. Bryson, Statistics Group, MS August F600, Los Alamos National Laboratory, Los Alamos, 5-11. Algebraische Zahlentheorie, Chairmen: W. Jehne, New Mexico 87545, 505-667-3308. Koln, H. W. Leopoldt, Karlsruhe, P. Raquette, 21-22. Fifth Midwest Conference on Probability, Heidelberg. Northwestern University, Evanston, Illinois. (August 1983, 12-18. Topologie, Chairmen: D. Puppe, Heidelberg, L. p. 542) Siebenmann, Paris, C. B. Thomas, London. 19-25. Spez. Topologie: Algebraic K-Theory of Spaces 24-26. 1983 Annual Conference of Association for and Pseudo-isotropy Theory, Chairmen: D. Burghelea, Computing Machinery, Sheraton Centre Hotel, New York, Columbus, F. Waldhausen, Bielefeld. New York. (February 1983, p. 210) 26-September 1. Komplexe Analysis, Chairmen: W. Barth, Program: Plenary sessions will be presented by William Erlangen, H. Grauert, Gottingen, R. Remmert, Miinster. F. Miller (President, SRI International); Seymour September Papert (Massachusetts Institute of Technology); George Rittersbach (Peat, Marwick, Mitchell); Edith Martin; 2-8. Reelle algebraische Geometrie, Chairmen: E. and Irwin Jarett. The Educators Program will Becker, Dortmund, L. Brocker, Miinster, M. Knebusch, offer tutorials and panels by prominent educators Regensburg. and computer scientists focusing on the use of 9-15. Spez. Statistik: Robust Statistics, Chairmen: F. R. microcomputers in the classroom. Featured speakers Hampel, Ziirich, H. Rieder, Bayreuth. include Anthony Alvarado (Chancellor, New York City 16-22. Risikotheorie, Chairman: H. Biihlmann, Ziirich. Board of Education); Mary Alice White (Director, 23-29. Kombinatorische Geometrie, Chairmen: A. Dress, Electronic Learning Laboratory, Teachers College, Bielefeld, B. Griinbaum, Seattle. Columbia University); Alan Kay (Chief Scientific Officer, Atari Institute); Barbara Bowen (Director, Apple OCTOBER 1983 Foundation); and Fred Hechinger (President, New York Times Foundation). There will also be a luncheon 4-5. The Twenty-second Annual Army Operations Re­ address by Edwin E. Catmull, Director of Computer search Symposium, US Army Logistics Management Cen­ Research and Development at Lucasfilm Ltd., who ter, Ft. Lee, Virginia. (June 1983, p. 437) will speak on the future of computer graphics in film 5-10. Fifth GAMM Conference on Numerical Methods in entertainment. Fluid Mechanics, Rome, Italy. (August 1983, p. 541) 24-27. Seventh Symposium on Computer Applications in 5-12. Week of Algebraic Geometry, Barcelona, Spain. Medical Care, Baltimore, Maryland. (June 1983, p. 438) (August 1983, p. 541) 24-28. Conference on Algebraic Topology and K-Theory, 6-10. Twentieth Anniversary Meeting of the American Princeton University, Princeton, New Jersey. Society for Cybernetics, Foothill College, Los Altos Hills, Purpose: The purpose of the conference is to honor the California. (August 1983, p. 541) sixtieth birthday of John Moore.

670 Speakers: J. F. Adams (University of Cambridge); D. 7-9. Twenty-fourth Annual IEEE Symposium on Founda­ Anick (Massachusetts Institute of Technology); E. tions of Computer Science, Tucson Marriott Hotel, Tucson, Brown (Brandeis University); G. Carlsson (University Arizona. (February 1983, p. 210) of California at San Diego); F. Cohen (University 7-11. Society for Industrial and Applied Mathematies 1983 of Kentucky); R. Cohen (Stanford University); W. Fall Meeting, Norfolk, Virginia. (April1983, p. 364) Dwyer (University of Notre Dame); E. Friedlander (Northwestern University); D. Kan (Massachusetts 8-11. Fifth International Seminar on Boundary Elements, Institute of Technology); J. Lin (University of California Hiroshima, Japan. (August 1983, p. 542) at San Diego); M. Mahowald (Northwestern University); 10-13. Ameriean Mathematical Association of Two-Year H. Miller (University of Washington); J. Neisendorfer Colleges Annual Convention, Court of Flags Hotel, (Ohio State University); F. P. Peterson (Massachusetts Orlando, Florida. (February 1983, p. 210) Institute of Technology); D. Ravenel (University of Washington); P. Selick (University of Western Ontario); 13-18. Symposium on Measurements in Fluid Transients, W. Singer (Fordham University); C. Soule (University Boston, Massachusetts. (August 1983, p. 542) of Paris); J. Stashefl' (University of North Carolina); 16-18. Eighth Conference on Probability & Statistics in R. Swan (University of Chicago); R. Thomason the Atmospheric Sciences, Hot Springs, Arkansas. (June (Johns Hopkins University); F. Waldhausen (Universitiit 1983, p. 438) Bielefeld); A. Zabrodsky (Hebrew University). Organizing Committee: W. Browder (Princeton University); **24-27. International Congress on Computational and F. P. Peterson (Massachusetts Institute of Technology); Applied Mathematics, University of Leuven, Belgium. J. Stashefl' (University of North Carolina); R. Swan (February 1983, p. 210) **These dates as previously listed (University of Chicago). are incorrect. See July 24-27, 1984.** Information: Topology Conference, Fine Hall-Box 37, 24-28. First Asian-Pacific Conference on Science Educa­ Princeton, New Jersey 08544. tion, Taipei, Republic of China. 24-28. Conception des Systemes de Synthese d'lmages, Program: The theme of the conference will be "Science Rocquencourt, France. Education for Changing Times." There will be discussions on science curricula for changing times, the Information: Institut National de Recherche en Infor­ matique et en Automatique, Service des Relations frontiers of educational technology in science education, and science teacher preparation, including pre- and Exterieures, "Cours et Seminaires", B.P. 105, 78153 Le Chesnay, Cedex, France. in-service training for the future. Information: Conference Secretariat, The First Asian­ 24-29. International Conference on Mathematical Methods Pacific Conference on Science Education, National in Operations Research, Sofia, Bulgaria. (June 1983, p. 438) Taiwan Normal University, 162 East Hoping Road, SEC 27-29. Conference on K-Homology, Index Theory and 1, Taipei, Taiwan, Republic of China. Dift'erential Operators, Indianapolis, Indiana. 28-December 2. Eighth Australasian Fluid Mechanics Program: The principal lecturer is Ronald G. Douglas Conference, Newcastle, Australia. (State University of New York, Stony Brook), who will Information: R. A. Antonia, Department of Mechanical give the first of five lectures describing the relation Engineering, University of Newcastle, New South Wales between analytic and topological definitions of K­ 2308, Australia. homology, and applications to differential operators on manifolds. Additional lectures will be given by Edward Efl'ros (University of California at Los Angeles), DECEMBER 1983 Paul Muhly (University of Iowa), and Claude Schochet (Wayne State University). 1-2. International Conference on Collective Phenomena, (A Information: Jerry Kaminker, Bernie Morrel, or Neal Roth­ Moscow Refusenik Seminar-in-Exile), Stockholm, Sweden. man, Department of Mathematical Sciences, Indiana Program: The program will include sessions on mathe- University-Purdue University at Indianapolis, 1125 East matical physics; mathematical models in biology; and 38th Street, P. 0. Box 647, Indianapolis, Indiana 46223, statistical theory and pattern recognition. 317-923-1321, ext. 218 or 210. Information: Committee of Concerned Scientists, 330 Seventh Avenue, New York, New York, 10001, 212-695- 28-November 1. The Rey Pastor Symposium, Logroiio, 2560. Rioja, Spain. Program: The purpose of the symposium is to discuss the 5-7. Everett Pitcher Lecture Series, Lehigh University, work and life of Spanish mathematician Don Julio Rey Bethlehem, Pennsylvania. (August 1983, p. 542) Pastor (1888-1962). M. Hormig6n (Zaragoza) and E. 5-7. Second Latin American Conference on Applied L. Ortiz (Imperial College, London), will give the main Mathematics, Laboratorio de Computa<;ao Cientifica lectures. Other speakers include R. Taton (Paris), L. LCC/CNPq, Rio de Janeiro, Brazil. (April 1983, p. 364) Pyenson (Montreal), A. P. Calderon (Chicago), J. Babini (Buenos Aires), R. Gomes (Porto), G. Israel (Florence), 5-16. Workshop on Pattern Recognition and Analysis of and A. Mehrtens (Berlin). Seismicity, Miramare-Trieste, Haly. (June 1983, p. 438) Information: Simposio sobre Julio Rey Pastor, Obispo 6-9. Congres du Centenaire de Ia S.F..E., "Electricite, Bustamante 3, Colegio Universitario de Ia Rioja, electronique et civilisation", Paris, France. (August 1983, Logroiio, Spain. p. 542) 31-November 10. Ninth International Conference on Very Large Data Bases, Firenze, Italy. (August 1983, p. 542) JANUARY 1984

NOVEMBER 1983 1-December 14. Symposium on Hyperbolic Geometry, Kleinian Groups and Three-Dimensional Manifolds, 1-9. Sixth International Summer School on Problems University of Warwick, Coventry, England. of Model Choice & Parameter Estimation in Regression Information: D. B. A. Epstein, Mathematics Institute, Analysis, Sellin, German Democratic Republic. (June 1983, University of Warwick, Coventry, England. p. 438) 6-10. NSF-CBMS Regional Conference on Some Global 4-5. Third Southeastern-Atlantic Regional Conference on Problems Concerning Curvature of Riemannian Manifolds, Dift'erential Equations, University of Tennessee, Knoxville, Polytechnic Institute of New York, Brooklyn, New York. Tennessee. (August 1983, p. 542) (August 1983, p. 542)

671 9-13. NSF-CBMS Regional Conference on Minimax 11-13. Symposium on Theoretical Aspects of Computer Methods in Critical Point Theory and Applications to Science, Paris, France. Differential Equations, University of Miami, Coral Gables, Topics: Theoretical studies of computer systems; theory Florida. of: databases and networks, VLSI, parallel and Program: Paul H. Rabinowitz (University of Wisconsin) asynchronous computation, data structures, program­ is the principal speaker, and will deliver ten lectures. ming; analysis of algorithms; application of mathemati­ There will also be lectures given by Antonio Ambrosetti, cal logic to computer science; formal languages; mathe­ A. Bahri, Vieri Benci, H. Berestycki and Alan Weinstein. matical aspects of programming languages; mathematics Support: Some support for travel is provided by the NSF of computation. under the CBMS Regional Conference Program. Some Information: Symposium Office, STACS/AFCET, 156 additional support will be provided by the University of Boulevard Pereire, 75017 Paris, France. Miami. Information: Shair Ahmad, Department of Mathematics 12-14. Annual Lecture Series in the Mathematieal and Computer Science, University of Miami, Coral Sciences: Estimation and Control of Distributed Systems, Gables, Florida 33124. Fayetteville, Arkansas. 16-20. Symposium International "Signatures Miero-ondes Program: The principal lecturer will be H. T. Banks en Teledeteetion", Toulouse, France. (Brown University). Other speakers will be invited and Information: Centre Nat. Et. Spat., Dep. AJT. Univ., 18 av. contributed talks are welcome. Edouard Belin, 31055 Toulouse, Cedex, France. Deadline for Abstracts: February 15, 1984. 27-29. Mathematical Association of America Annual Information: D. W. Brewer, Department of Mathematical Meeting, Louisville, Kentucky. Sciences, University of Arkansas, Fayetteville, Arkansas Information: Mathematical Association of America, 1529 72701, 501-575-6317. Eighteenth Street, N.W., Washington, D.C. 20036. 17-19. Sixth Colloque International sur Ia Programmation, Toulouse, France. FEBRUARY 1984 Information: B. Robinet, Inst. Programm., 4 place Jussieu, 6-9. Second International Modal Analysis Conference, 75230 Paris, Cedex 05, France. Orlando, Florida. 19-20. Fifteenth Annual Pittsburgh Conference on Model­ Information: Union College, Graduate and Continuing ing and Simulation, University of Pittsburgh, Pittsburgh, Studies, Wells House, 1 Union Avenue, Schenectady, Pennsylvania. New York 12308. Topics: Microprocessors, robotics, and social, economic MARCH 1984 and global modeling and simulation and papers on all traditional areas of modeling and simulation. 12-16. Seventeenth Annual Simulation Symposium, Bay Call for Papers: Two copies of titles, authors, all authors' Harbor Inn, Old Tampa Bay, Florida. addresses, abstracts and summaries should be submitted Information: Alexander Kran, IBM Corporation, B/300- to the address below by January 31, 1984. 40E, Hopewell Junction, New York 12533, 914-894- Information and Abstracts: William G. Vogt or Marlin 7142. For research grant information, write the Grants H. Mickle, Modeling and Simulation Conference, 348 Committee Chairman, Dr. W. Marvin Bunker, General Benedum Engineering Hall, University of Pittsburgh, Electric Company, P. 0. Box 2500, Room 4337, Daytona Pittsburgh, Pennsylvania 15261. Beach, Florida 32015 no later than November 15, 1983. 19-21. International Conference on Numerical Analysis, Technische Universitat Munich, Munich, Federal Republic MA¥1984 of Germany. Program: The program will include 30 invited contributions 4-6. Midwest Algebraic Geometry Conference, Purdue covering a broad spectrum of numerical analysis. The University, West Lafayette, Indiana. invited speakers who have accepted to date include Information: Joseph Lipman, Department of Mathematics, I. Babuska (College Park), R. Bulirsch (Munich), Purdue University, West Lafayette, Indiana 47906. P. G. Ciarlet (Paris), M. Fiedler (Prague), W. Gautschi (Lafayette), G. H. Golub (Stanford), J. 7-11. ACM-IEEE Computer Society Tutorial& for Profell­ Stoer (Wiirzburg), R. S. Varga (Cleveland), and J. H. sional Development, Chicago, lllinois. Wilkinson (Teddington). Program: There will be a two-track series of in­ Deadline for Registration: December 15, 1983. depth tutorials on topics of current concern to Information: C. Zenger, Technische Universitat Miinchen, computer professionals. Seminars will be presented Institut fiir Informatik, Arcisstr. 21, D-8000 Miinchen 2, on such subjects as software engineering, reliability Federal Republic of Germany. and maintenance, distributed processing, computer networks, computer communications protocols, local APRIL 1984 area networks, computer performance and reliability, the UNIX Operating System and the C Programming 2-4. Third ACM SIGACT-SIGMOD Symposium on Language. Principles of Database Systems, Waterloo, Ontario, Canada. Information: IEEE Computer Society, P. 0. Box 639, Silver Topics: Suggested topics include artificial intelligence Spring, Maryland-20901, 301-589-8142. for databases, concurrency control, database design, 13-17. Computer Graphies '84, Anaheim Convention database security, data models, data structures for· Center, Anaheim, California. databases, dependency theory, distributed databases, Information: National Computer Graphics Association, file organization, logic for databases, performance 8401 Arlington Boulevard, Fairfax, Vrrginia 22031, 703- evaluation of database systems, query languages, and 698-9600. schema design. Call for Papers: Eight copies of a detailed abstract should 17-18. IMACS International Symposium on Modelling and be submitted by October 17, 1983, to the program Simulation of Electrical Maehinea and Convertera, Liege, chairman, Ronald Fagin, IBM Research K55/281, 5600 Belgium. Cottle Road, San Jose, California 95193. Information: H. Buysse, Unite Courant Fort et Electrotech­ Information: Daniel Rosenkrantz, Department of Computer nique, Universite Catholique de Louvain, Batiment Science, State University of New York at Albany, Maxwell, Place du Levant 3, B-1348 Louvain-la-Neuve, Albany, New York 12222. Belgium.

672 JUNE 1984 11-14. Conference on Universal Algebra and Lattice Theory, The Citadel, Charleston, South Carolina. 4-8. Fifth International Conference on the Theory Program: The conference is devoted to recent developments and. Applications of Graphs, With Special Emphasis in universal algebra, lattice theory and related areas. on Computer Science Applications, Western Michigan There will be eight one-hour lectures by invited speakers University, Kalamazoo, Michigan. (June 1983, p. 438) and sessions for short contributed papers. 6--8. 1984 American Control Conference, San Diego, Invited Speakers: G. Bruns (McMaster), R. Freese California. (Hawaii), A. M. W. Glass (Bowling Green), J. Jezek Topics: Linear and nonlinear systems, estimation, (Czechoslovakia), E. Kiss (Hungary), R. McKenzie identification, robotics, computer-aided design, signal (California}, G. McNulty (South Carolina), and I. processing, computers and communication in control Nemeti (Hungary). and automation and real time control of processes. Call for Papers: Send title and abstract to the address Information: AACC Secretariat, 1051 Camino Velasquez, below no later than April15, 1984. Green Valley, Arizona 85614, 602-625-0401. Information: S. D. Comer, Department of Mathematics and Computer Science, The Citadel, Charleston, South 12-14. Tenth International Symposium on Machine Carolina 29409. Processing of Remotely Sensed. Data, Purdue University, West Lafayette, Indiana. **24-27. International Congress on Computational and Program: The emphasis of the symposium will be on Applied Mathematics, University of Leuven, Belgium. thematic mapper data and geographic information (February 1983, p. 210)** (The dates previously systems. There will be a short course on "Numerical announced were incorrect.) Analysis of Remote Sensing" held the week immediately Invited Speakers: (Additional) Wang Ren-Hong (China), T. preceding the symposium. Yamamoto (Japan). Topics: Scene simulation and modeling; geometric and 25-August 4. Edinburgh Mathematical Colloquium, radiometric preprocessing; stratification and sampling; University of St. Andrews, Scotland. feature extraction and classifier training; classification Sponsor: Edinburgh Mathematical Society. algorithms; merging of radiometric and ancillary data; Invited Speakers: J. M. Ball, F. Hirzebruch, D. Passmann, remote sensing technology transfer; digital geographic W. K. Hayman. information systems; inventorying and monitoring of Information: Dorothy M. E. Foster, Colloquium Secretary, resources; resource databases and database management. Department of Pure Mathematics, University of St. Deadline for AbstTacts: Abstracts should be sent by Andrews, The Mathematical Institute, The North December 1, 1983, to D. B. Morrison, Symposium Haugh, St. Andrews, Scotland KY16 9SS. Coordinator, at the address below. Information: Paul E. Anuta, Purdue University/LARS, AUGUST 1984 1291 Cumberland Avenue, West Lafayette, Indiana 47906-1399, 317-494-6305. August 1984. Fifth International Congress on Mathematics 19-21. Fifth IMACS International Symposium on Com­ Education, University of Adelaide, Australia. (June 1982, puter Methods for Partial Dift'erential Equations, Lehigh pp. 331, 376) University, Bethlehem, Pennsylvania. 19-25. Sixteenth International Congress of Theoretical Program: Papers are invited on all aspects of recent and Applied Mechanics, Lyngby, Denmark. developments in the computer solution of partial Topics: The following topics will receive particular differential equations, including methods, applications, attention: micro-level studies of properties of programming and hardware. The symposium will also multi­ component media; marine-structure wave interaction; include a Mini-Symposium on the Numerical Solution of and development of chaotic behavior Singular Integral Equations of Cauchy- in dynamical Type, for which systems. papers are invited. Call for Papers: Six copies of an abstract (100-150 Call for Papers: Papers are sought for half-hour or fifteen­ words) and six copies of an extended summary (500 minute presentations. Preliminary manuscripts or words) should be sent by February comprehensive abstracts should be sent by December 6, 1984, to the Congress office: ICTAM, Technical University of 15, 1983, to Dr. R. S. Stepleman, Exxon Research Denmark, Building 404, DK-2800 Lyngby, and Engineering Company, P. 0. Box 51, Denmark. Linden, New United States Jersey 07036. authors should also send two copies of each to Richard T. Shield, 212 Talbot Laboratory, Information: William E. Schiesser, Department of Chemical Department of Theoretical and Applied Mechanics, Engineering, Whitaker Laboratory #5, Lehigh Univer­ University of Illinois, Urbana, lllinois 61801. sity, Bethlehem, Pennsylvania 18015. Information: ICTAM Office or Richard Y. Dow, Staff 20-22. Third. International Conference on Boundary and Officer, USNC/TAM, National Research Council, 2101 Interior Layers (BAIL III), Dublin, Ireland. Constitution Avenue, N.W., Washington, D.C. 20418. Information: BAIL III Conference, 39 Trinity College, University of Dublin, Dublin 2, Ireland. OCTOBER 1984

JULY 1984 15-18. International Symposium on Orthogonal Polyno­ mials and their Applications, Bar-le-Duc, France. 2-11. Canadian Mathematical Society Summer Seminar Purpose: The purpose of the symposium is to honor the on Algebraic Geometry, University of British Columbia, 150th anniversary of E. N. Laguerre. Vancouver, Canada. Organizing Committee: C. Brezinski, A. Draux (Lille, Program: There will be a series of invited talks on recent France); AI. Magnus (Louvain-la-Neuve, Belgium); P. developments in some area of algebraic geometry. There Maroni (Paris, France); A. Ronveaux (Namur, Belgium). will also be seminars. Deadline for Abstracts: April 15, 1984. Invited Speakers: William Fulton, Joe Harris, Phillip Information: C. Brezinski or A. Draux, UER IEEA-M3, Griffiths, Mark Goresky, Steven Kleiman, Eduard Universite de Lille 1, 59655 - Villeneuve d'Ascq Cedex, Looijenga, Robert McPherson, Tonny Springer. France. Information: J. B. Carrell, Department of Mathematics, #121-1984, Mathematics Road, Vancouver, Canada, V6T 1Y4.

673 New AMS Publications

AMS Book Orders-Toll Free Number For Users of VISA, MasterCard. Individuals in the continental United States may order books published by the Society by calling 80()..556-7774 and using a charge card. The number will be attended from 8:00 a.m. to 4:15 p.m. Eastern Time, Monday through Friday except on holidays. When using a charge card for mail orders, please be sure to specify whether VISA or MasterCard and include the account number, expiration date, and signature. Order from AMS, P. 0. Box 1571, Annex Station, Providence, Rl 02901. A reminder: the individual member rate applies to the purchase of one copy of any book for personal use, and is not an alternative means of lowering costs for libraries.

AMS Catalogue of Publications The most profound result in the volume is the The 1983-1984 AMS Catalogue of Publications, side approximation theorem. However, as a reference a catalogue of AMS books and journals, is ready for tool some of the preliminary results and some of the distribution. In addition to a complete listing of the applications may be used more frequently. Society's publications and an author/title index to Contents them, this catalogue has a subject index of the books Preface included in the catalogue, as well as descriptive para­ 1. Planar complexes graphs about publications new in the past year. 2. PL planar maps Copies have been sent to members, libraries and 3. The Schoenflies theorem book agents throughout the world and will be sent 4. Wild 2-spheres to new members throughout the coming year. Others 5. The generalized Schoenflies theorem interested in receiving a copy may obtain one by 6. The fundamental group requesting it from the Providence office of the 7. Mapping onto spheres Society, P. 0. Box 6248, Providence, Rl 02940, 8. Linking Attn. Donna Porter. 9. Separation

COLLOQUIUM PUBLICATIONS (ISSN 0065·9258) The Geometric Topology of 3-Manifolds R. H. Bing The book starts with a treatment of some of the geometric and topological properties of the plane. This treatment is expanded to study such funda­ mental properties of 3-space as the PL Schoenflies theorem, Dehn's lemma, the loop theorem, and the side approximation theorem. Applications of these fundamental results are made to develop further properties of 3-manifolds. The Table of Contents provides a general summary of the book's major points. This book is most meaningful to a mathematician interested in geometry who has had at least a begin­ ning graduate course in topology. While a student About the author: can start the book with less preparation, the chances Although R. H. Bing attended a small high school, are that those with weaker backgrounds will bog through the influence of his mother and other teachers he down if they work without the benefit of discussion. learned to enjoy the challenge of solving puzzles, working The book belongs in both graduate and under­ hard problems, and proving interesting theorems. After re· graduate libraries. It can serve as a usefu I reference ceiving a bachelors degree from Southwest Texas State for a graduate student in topology or a researcher Teachers College, he taught in various high schools for six years before obtaining a Ph.D. from the University of Texas. in topology. A study of the book should provide Both as a student and as a teacher at various levels he has the reader with a better understanding of the phys­ enjoyed doing and pushing mathematics. ical properties of Euclidean 3-space-the space in Bing spent twenty-five years at Wisconsin and has been which we presume we live. The reader should learn at the University of Texas at Austin for the last ten years. Thirty-six students have taken their Ph.D.'s under his direc· of some unsolved problems that continue to baffle tion. Bing combines the techniques of geometry and topol· researchers. ogy to study the physical properties of 3·manifolds. He and

674 his students have been responsible for making many of the Christian Coatmelec, Prolongement explicite des ele­ recent discoveries about 3-manifolds. ments de LP (n) et majoration du module de regu. Bing has national and international interests in mathe­ larite du prolongement-applications a Ia convergence matics. He has lectured in forty-nine states. He was president of AMS, President of MAA, Counciler of NAS, Vice President des suites d'operateurs lineaires positifs of AAAS, member of the National Science Board, and a Frank Deutsch, When does the metric projection member of the American Academy of Arts and Sciences. He admit a linear selection? has lectured in seventeen foreign countries, is a foreign asso­ Ronald A. Devore, Maximal functions and their appli­ ciate of the Polish Academy of Sciences and has twice been a delegate to the General Assembly of the International cation to rational approximation Mathematical Union. However, Bing regards his main forte john j. F. Fournier, Some remarks on the recent as working with mathematical research and students. proofs of the Littlewood conjecture 1980 Mathematics Subject Classification: 57-XX W. H. j. Fuchs and A. A. Gon~ar, Approximation of Colloquium Publications entire functions on unbounded continua Volume 40, viii + 240 pages (hard cover) T. N. E. Greville, I. j. Schoenberg and A. Sharma, List price $54, institutional member $41, The behavior of the exponential Euler spline individual member $27 Sn(x; t) as n---+ 00 for negative values of the ISBN 0-8218-1040-5; LC 83-14962 Publication date: October 1983 base t To order, please specify COLL/40N j. Korevaar, Muntz-type theorems for arcs and for Rn M. A. Lachance and E. B. Saff, Bounds for algebraic polynomials with zeros in an interval CONFERENCE PROCEEDINGS OF THE D. Leviatan, The degree of comonotone approxi­ CANADIAN MATHEMATICAL SOCIETY mation of differentiable functions (ISSN 0731-1036) G. G. Lorentz, Some problems in Birkhoff inter­ Second Edmonton Conference polation on Approximation Theory M. J. Marsden and S. D. Riemenschneider, Asymp­ totic formulae for variation-diminishing splines Zeev Ditzian, Amram Meir, Paul Nevai, Orthogonal polynomials associated with Sherman D. Riemenschneider, exp(-x4 ) and Ambikeshwar Sharma, Editors J aak Peetre, Hankel operators, rational approxima­ The Second Edmonton Conference on Approxi­ tion and allied questions of analysis mation Theory was held in Edmonton, Alberta, Q. I. Rahman and St. Ruscheweyh, On the zeros of June 7-11, 1982. The Conference was devoted to rational functions arising from certain determi­ Approximation Theory and related topics, including nants spline approximation, computational problems, com­ Robert C. Sharpley, Cone conditions and the modu­ plex and rational approximation, and techniques from lus of continuity harmonic analysis and the theory of interpolation of P. C. Sikkema, Approximation with convolution operators. In conformity with the requirements of operators this series, this volume consists of refereed papers by P. W. Smith and j. D. Ward, Compression and fac- some of the invited speakers. torization of diagonally dominant matrices Sponsored by the Canadian Mathematical Society, Hans Wallin, Markov's inequality on subsets of R11 the Conference was supported by grants from the 1980 Mathematics Subject Classifications: 41 -06; 41 A 10, Natural Sciences and Engineering Research Council 41A15, 41A20, 42A10 of Canada and the University of Alberta. Conference Proceedings of the Contents Canadian Mathematical Society Volume 3, xii + 400 pages (soft cover) Dan Amir and jaroslav Mach, Best n-nets in normed List price $29, institutional member $22, spaces individual member $15 R. Bojanic and F. H. Cheng, Estimates for the rate ISBN 0-8218-6004-6; LC 83-12271 of approximation of functions of bounded varia­ Publication date: September 1983 To order, please specify CMSAMSI3N tion by Hermite-Fejer polynomials P. L. Butzer and R. L. Stens, The Poisson summa­ CONTEMPORARY MATH EM A TICS tion Formula, Whittaker's cardinal series and (ISSN 0271-4132) approximate integration A. S. Cavaretta, jr., T. N. T. Goodman, C. A. Micch­ low Dimensional Topology elli and A. Sharma, Multivariate interpolation and Samuel J. Lomonaco, Jr., Editor the Radon transform part Ill: Lagrange represen­ This volume arose from a special session on Low tation Dimensional Topology organized and conducted by C. K. Chui, L. L. Schumaker and R. H. Wang, On Dr. Lomanco at the American Mathematical Society spaces of piecewise polynomials with boundary meeting held in San Francisco, California, january conditions II: Type- 1 triangulations C. K. Chui, L. L. Schumaker and R. H. Wang, On 7-11,1981. spaces of piecewise polynomials with boundary Contents conditions Ill: Type-2 triangulations joan S. Birman and R. F. Williams, Knotted periodic Z. Ciesielski, Spline bases in spaces of analytic func­ orbits in dynamical system II: Knot holders for tions fibered knots

675 Steven A. Bleiler, Doubly prime knots of Krasnosel' sk1i's Compression of a Cone Theorem, Joe Brandenburg, Michcal Dyer, and Ralph Strebel, are given. Also, fixed points, antipodal points, coin­ On /. H. C. Whitehead's aspherical question II cidences of multifunctions are discussed. Several re­ Roger Fcnn and Denis Sjerve, Geometric cohomology sults with applications in the field of partial differen­ theory tial equations arc given. Application of fixed point Ronald Fintushel and Ronald j. Stern, Seifert fibered theory in the area of Approximation Theory is also 3-manifolds and nonorientable 4-manifolds illustrated. Michael H. Freedman, A conservative Dehn's lemma Papers by the following are included: David Gabai, The Murasugi sum is a natural geometric M. Altman S. A. Naimpally, operation F. E. Browder K. L. Singh David Gillman and Dale Rolfsen, Manifolds and R. F. Brown and/. H. W. Whitfield their special spines E. R. Fadel/ P. L. Papini Sushi! jajodia and Bruce Magurn, Realizing units as and S. Husseini W. II. Petryshyn Whitehead torsions in low dimension G. Fournier S. Reich Dennis johnson, A survey of the Torelli group K. Goebel B. E. Rhoades Louis H. Kauffman, Combinatorics and knot theory and W. A. Kirk H. Schirmer R. Kramer, Dehn twists and handlebodies of genus M. von Golitschek V. M. Sehgal, S. P. Singh two and E. W. Cheney and B. Watson J. P. Levine, Localization of link modules R. Guzzardi V. M. Sehgal A. Libgobcr, Alexander modules of plane algebraic D. S. jaggi and C. Waters curves M. Martelli S. J. Lomonaco, Jr., Five dimensional knot theory 1980 Mathematics Subject Classifications: 54H25, 47Hxx. Toru Maeda and Kunio Murasugi, Covering linkage Contemporary Mathematics invariants and Fox's problem 13 Volume 21, vi + 218 pages (soft cover) Richard Mandelbaum and Boris Moishezon, Numeric List price $20, institutional member $15, invariants in 3-manifolds individual member $10 William W. Menasco, Polyhedra representation of link ISBN 0-8218-5023-7; LC 83-11824 Publication date: September 1983 complements To order, please specify CONMI21 N john G. Ratcliffe, A fibered knot in a homology 3-sphere whose group is nonclassical Martin Scharlemann and Craig Squier, Automorph­ isms of the free group of rank two without finite orbits Factorizations of 1980 Mathematics Subject Classifications: 57-06, 57Mxx, 55-06 b"= 1, b = 2, 3, 5, 6, 7, 10, 11,12 Contemporary Mathematics up to High Powers Volume 20, x + 350 pages (soft cover) List price $27, institutional member $20, John Brillhart, D. H. Lehmer, J. L. Selfridge, individual member $14 Bryant Tuckerman, and S. S. Wagstaff, Jr. ISBN 0-8218-5016-4; LC 83-10022 Publication date: August 1983 This book is the collection of hundreds of results To order, please specify CONMI20N of workers dating from the seventeenth century. It is an extension of a rare work by Cunningham (1925) with the same title. It gives an historical account of Topological Methods the various methods and machines that have been in Nonlinear Functional Analysis used to factor, and prove prime, the numbers bn ± 1. S. P. Singh, S. Thomeier, and B. Watson, Editors It is intended that the empty spaces in the tables be filled in by future workers. The back of the book This volume contains the proceedings of the special session on Fixed Point Theory and Applica­ contains an envelope for holding up-dating material. tions held during the Summer Meeting of the Ameri­ The factorizations and the very large primes are can Mathematical Society, at the University of of usc in applications to Group Theory, Number Toronto on August 21-26, 1982. The theory of con­ Theory, Random Number Generators and Cryptog­ tractors and contractor directions is developed and raphy. used to obtain existence theory under rather weak As the title suggests, the book contains tables of conditions. Theorems on the existence of fixed factorizations of bn - 1 and bn + 1 for b = 2 3 5 points of nonexpansive mappings and the convergence 6, 7, 10, 11, and 12 for n up to some large li~it: ' of the sequence of iterates of nonexpansivc and quasi­ This limit is 1200 forb = 2. For other b the limit noncxpansive mappings are given. Degree of mapping is chosen so that b goes up to about 1015 0 • Certain and its generalizations are given in detail. A class of polynomial identities permit larger n in some cases. eventually condensing mappings is studied and multi­ Primes and probable primes larger than 1025 are valued condensing mappings with multiple fixed collected in an appendix to avoid cluttering the main points arc also given. Topological fixed points includ­ tables. Another appendix lists summaries of primality ing the study of the Nielsen number of a selfmap on proofs for the large primes. A third appendix gives a compact surface, extensions of a well-known result composite cofactors up to 106 4.

676 The factorizations are presented in condensed form in the main tables. For the benefit of amateur mathe­ maticians (and professional mathematicians in a hurry) the complete factorizations of 2n - 1, 2n + 1, 1 ffl-1, and 1 on + 1 are collected in four tables. The limits on n in these tables are smaller than those in the main tables. The book has an extensive and valuable introduc­ tion to the tables. It describes the developments in computing technology and in methods of factoring and primality testing which have occurred since 1925. It discusses the multiplicative structure of bn ± 1 and explains the relation between the two kinds of alge­ braic factorizations of these numbers. Libraries will need a reference copy. Many pro­ fessional and amateur mathematicians, especially in number theory and algebra, will want a copy. Some computer scientists and cryptographers will also want a copy because the book has some connection to cryptography and data security. 1980 Mathematics Subject Classifications: 1 OA25; 1 0-04 Contemporary Mathematics Volume 22, lxiii + 180 pages {soft cover) List price $22, institutional member $17, individual member $11 ISBN 0·8218-5021-0; LC 83-12316 Publication date: September 1 983 To order, please specify CONM/22N

Chapter 9 of thoroughly develops the theory of a certain analogue Ramanujen's Second Notebook: of the gamma function. This book is a continuation of work done by Infinite Series Identities, Berndt and Joshi over the past few years which has Transformations, and Evaluations been published in various journals. It will be of special Bruce C. Berndt and Padmini T. Joshi interest to number theorists, including those interested in related analysis and transcendence, and to classical When Ramanujan died in 1920, he left behind analysts, including those interested in special functions. three notebooks containing the statements of approx­ This chapter is characteristic of Ramanujan's great­ imately 3000-4000 theorems and formulas. The est talent and love- dazzlingly beautiful formulas for second notebook is a revised, enlarged edition of the infinite series. The reader will appreciate the creative first, while the third is very short. Thus, our atten­ genius of Ramanujan. tion is focused upon the second. Immediately after About the authors: Ramanujan died, G. H. Hardy strongly urged that the Bruce Berndt received his Ph.D. in 1966 from the Uni­ notebooks be published and edited. In 1929, G. N. versity of Wisconsin, Madison, with a thesis written under Watson began this task with the help of B. M. Wilson. the direction of j. R. Smart. After one year at the University In 1957, the Tata Institute of Fundamental Research of Glasgow, he came to the University of Illinois in Urbana­ but Champaign where he is now Professor of Mathematics. For published a photostat edition of the notebooks, the past six years he has devoted almost all of his research no editing whatsoever was undertaken. As with time to the editing of Ramanujan's notebooks. Hardy, Watson, and Wilson, editing here includes Padmini T. Joshi received her Ph.D. in 1969 from the systematically proving all theorems and formulas. University of Illinois at Urbana-Champaign with a thesis Chapter 9 in Ramanujan's second notebook con­ written under ·the direction of Paul T. Bateman. Since 1969, she has been at Ball State University where she is now tains 139 theorems, formulas, and examples. Some Professor of Mathematics. Ball State University gave her the of the results found therein are classical, but many Outstanding Teacher Award for 1978-1979. are new. In the former category are several formulas 1980 Mathematics Subject Classifications: 33A 15, 33A30, in the theory of the dilogarithm. However, many 10A40, 40-00. related power series are examined, and most of these Contemporary Mathematics series transformations and identities appear to be new. Volume 23, viii + 84 pages {soft cover) List price $17, institutional member $13, This chapter also contains numerous formulas in the individual member $9 same spirit as Apery's famous formula for n3). Al­ ISBN 0-8218-5024-5; LC 83-11803 though some of these formulas are classical, many Publication date: September 1983 have not been heretofore noticed. Ramanujan also To order, please specify CONM/23N

677 CBMS REGIONAL CONFERENCE SERIES About the author: (Supported by the National Science Foundation) Lam received a Steele prize for mathematical exposition (ISSN 0160-7642) in 1982 for his book Algebraic theory of quadratic forms and four of his papers. (Reported in the October 1982 Orderings, Valuations Notices.) He was born on February 6, 1942, in Hong Kong, re­ and Quadratic Forms ceived a B.A. from the University of Hong Kong in 1963 Tsit-Yuen Lam and a Ph.D. from Columbia University in 1967. He joined the faculty of the University of California, Berkeley, in These notes were developed from the ten lectures 1968 and since 1975 he has twice been vice chairman of the the author gave at the CBMS Regional Conference department of mathematics. He was an Alfred P. Sloan held at Carleton College, Northfield, Minnesota in Foundation Fellow from 1972 to 1974, and was a Miller August, 1981. Much new material not covered in the Research Professor at Berkeley in 1978-1979. He was a lectures has been added to make this into a full­ john Simon Guggenheim Foundation Fellow in 1981 -1982. length book. 1980 Mathematics Subject Classifications: 1 OC04, 12] 10, 12]15; 10C01, 12015, 12]25. The main topics treated in this book are orderings, CBMS Regional Conference Series . valuations and quadratic forms. Orderings and valua­ Volume 52, viii+ 144 pages (soft cover) tions are related through the notion of compatibility; List price $17, individuals $9 valuations and quadratic forms are related through ISBN 0-8218-0702-1; LC 83-11729 the notion of residue forms, while quadratic forms Publication date: August 1983 To order, please specify CBMS/52N and orderings are related through the notion of sig­ natures. In the recent literature, this triumvirate of topics and their remarkable relationships and inter­ play has been the object of an intensive and fruitful Closed Geodesics study. This book provides an authoritative account of these recent developments, covering, in particular, on Riemannian Manifolds many results from original research papers published Wilhelm Klingenberg in the last fifteen years. This book contains expository lectures After a beginning chapter on the reduced theory from the CBMS Regional Conference of quadratic forms, the author lays the foundation held at the University for the study of the compatibility notion between of Florida, August 2-6, 1982. orderings (resp. preorderings) and valuations. This is Contents followed by an introduction to the techniques of 1. The Hilbert manifold of H 1-curve5 residue forms and the relevant Springer theory. The 2. The loop space and the space of closed curves author then presents the solution of the Representa­ 3. The second order neighborhood of a critical point tion Problem due to Becker and Brocker, with sim­ Appendix. The S 1- and the Z 2 -action on AM plifications due to Marshall. The notice of fans plays 4. Closed geodesics on spheres an all-important role in this approach. The text goes 5. On the existence of infinitely .many closed on to treat the theory of real places and the real geodesics holomorphy ring, and proves Brocker's theorem on 1980 Mathematics Subject Classifications: 58B20, 58015, the trivialization of fans. (The material on the holo­ 58E1 0, 53C22. morphy ring should be of interest and reference value CBMS Regional Conference Series in Mathematics for workers in commutative algebra.) Two important Number 53, iv + 79 pages (soft cover) List price $13, individuals $7 invariants of a preordering, the chain length and the ISBN 0-8218-0703-X; LC 83-5979 stability index, are studied in detail. Other topics Publication date: August 1983 treated include the notion of semiorderings, its appli­ To order, please specify CBMS/53N cations to SAP fields and SAP preorderings, and the valuation-theoretic Local-Global Principle for reduced quadratic forms. The presentation in these notes is largely self-con­ MEMOIRS OF THE AMS tained, and does not presuppose any advanced knowl­ (ISSN 0065-9206) edge of orderings or quadratic forms. The only pre­ The Selberg Trace Formula Ill: Inner requisite is perhaps a good working knowledge of Product Formulae (Initial Considerations) general valuation theory, and some familiarity with the basic notions and terminology of quadratic form M. Scott Osborne and Garth Warner theory as contained, for instance, in the first two In this Memoir, the authors lay the foundations chapters of the author's previous book published by for the study of inner product formulae, one of the W. A. Benjamin. The present notes may therefore be key technical preliminaries in the derivation of the read either as a sequel to the author's Benjamin book, Selberg trace formula. This is the third in a projected or as an independent introduction to ordered fields series of papers in which they plan to come to grips and reduced quadratic forms using valuation-theoretic with the formula, the ultimate objective being a techniques. reasonably explicit expression.

678 Contents Convergence of Solutions 1 . Introduction of the Kolmogorov Equation 2. Calculus of Hom-® to Travelling Waves 3. Eisenstein systems Maury Bramson 4. On the singularities of cuspidal Eisenstein series 5. Inner products and truncation: Level one Eisen- The classic Kolmogorov equation ut = Yzuxx + stein series f(u) is investigated under general initial data. A nec­ 6. Passage to the imaginary axis essary and sufficient condition on the initial data is 7. Extension of an earlier resu It given for convergence to a travelling wave as t ~ 00• 8. Concluding remarks In the case of convergence, a formula is given for 1980 Mathematics Subject Classifications: 10040, 32N10; computing the position of the wave. The methodol­ 22E40, 22 E46. ogy involves use of the Feynman-Kac integral and Memoirs of the AMS sample path estimates for Brownian motion. Number 283, iv + 209 pages (soft cover) Contents List price $18, institutional member $14, 1. Introduction individual member $9 ISBN 0-8218-2283-7; LC 83-3918 2. Some properties of Brownian motion and Publication date: July 1983 Brownian bridge To order, please specify MEM0/283N 3. Basic properties of the Kolmogorov equation 4. Asymptotic behavior of the Kolmogorov equation under full heating 5. Convergence of the Kolmogorov equation in the case A> 2Yz Hopf Bifurcation in the 6. Hitting probabilities for Brownian bridge Two locus Genetic Model 7. Estimates for the Kolmogorov equation in the Ethan Akin case A= 2Yz 8. Convergence of the Kolmogorov equation in the Hopf bifurcations occur in the class of simple case A = 2Yz for finite initial mass genetic models for the combined effect of selection 9. Convergence of the Kolmogorov equation in the and recombination. The demonstration of cycling in case A = 2Yz for infinite initial mass such models is biologically unexpected. To study this phenomenon we describe the locus of positions 1980 Mathematics Subject Classifications: 60)60, 35K55 at which Hopf bifurcation occurs in the two-locus­ Memoirs of the AMS Number 285, iv + 196 pages (soft cover) two-allele model. The description is given by an ex­ List price $16, institutional member $12, plicit, computable parametrization which can be individual member $8 used to generate all possible examples. Asymptotic ISBN 0-8218-2285-3; LC 83-6437 estimates show that limit cycles can occur. Publication date: July 1983 I. Cycles in simple genetic systems To order, please specify MEMOI285N 1. The space of selection matrices, 2. Eigenvalues, eigenvectors and linear differential equations, 3. Non­ linear equilibria and Hopf bifurcations, 4. The Hopf bifurcation locus, 5. Parametrization of "f;H, 6. Sym­ Geometrical Methods metries, 7. Concluding remarks. II. Parametric description of the Hopf locus in Congruence Modular Algebras 1. Linear maps, bilinear forms and matrices, H. Peter Gumm 2. Coordinates and the cylindrical frame, 3. Lineariz­ Abstract ations and Hessians, 4. The parametrization, 5. Sym­ The author develops a geometric approach to metric cases, 6. MARMC, 7. Asymptotic estimates. algebras in congruence modular varieties. The idea Ill. Programs and examples of coordinatization of lines in affine geometry finds 1. The general program, 2. The symmetric program, an almost perfect analog in the coordinatization of 3. Sample computations algebras. The geometry is the congruence class Bibliography geometry, i. e. the subspaces are the blocks of con­ 1980 Mathematics Subject Classifications: 34C25, 92A 1 0 gruence relations. Memoirs of the AMS It is shown that congruence modularity guarantees Volume 284, viii + 192 pages (soft cover) that the congruence class geometry behaves nicely, List price $16, institutional member $12, individual member $8 because the Desarguesian and the Pappian theorems ISBN 0-8218-2284-5; LC 83-6438 are true, if interpreted correctly. The innocuous Publication date: July 1983 looking "Shifting Lemma" is the basic and powerful To order, please specify MEM0/284N tool we need.

679 The obstacle to a perfect coordinatization is a Part II. Generalized solutions of quasilincar systems congruence relation called the "commutator." The of equations in the mechanics of continuous commutator is zero iff nonparallel lines have pre­ media cisely one point of intersection. This approach leads V. Quasiconformal mappings and generalized solu­ to a simple geometric development of commutator tions of elliptic systems of equations on the plane theory for arbitrary congruences. Results about VI. Boundary-value problems affine algebras on the one hand and about distribu­ VII. Boundary-value problems in hydrodynamics and tive varieties on the other hand arc tied together subsonic gas dynamics where only the commutator appears as a parameter. VIII. Problems in filtration theory for a fluid with For the extreme values of this parameter we find free boundaries theorems about affine, nilpotent and solvable con­ IX. Some planar problems with an unknown bound­ gruences and varieties at one end and theorems gen­ ary in elasticity theory eralizing Jonsson's lemma at the other end. A radical, 1980 Mathematics Subject Classifications: 30C60, 35 j 65, .J:4, is defined and we show that j onsson's lemma 35015, 35R35, 76-02, and others is true for every algebra '"!/VI. Translations of Mathematical Monographs Volume 57, xiv + 522 pages (hard cover) 1980 Mathematics Subject Classifications: 08B1 0, 08B05, List price $110, institutional member $83, 081130, 08A05. individual member $55 Memoirs of the AMS ISBN 0-8218-4510-1; LC 83-2754 Number 286, viii + 80 pages (soft cover) Publication date: September 1983 List price $8, institutional member $6, To order, please specify MMON0/57N individual member $4 ISBN 0·8218·2286·1; LC 83-11810 AMS TRANSLATIONS, SERIES 2 Publication date: September 1983 (ISSN 0065-9290) To order, please specify MEM0/286N The Kourovka Notebook: Unsolved Problems in Group Theory TRANSLATIONS OF translated by D. L. johnson and others MATHEMATICAL MONOGRAPHS Lev j. Leifman and D. L. johnson, Editors (ISSN 0065-9282) From the Preface: To form an up-to-date picture of what is going Boundary-Value Problems on in a given area of mathematics, we usually consult with Free Boundaries a shelf of current periodicals or, to save time, the for Elliptic Systems of Equations appropriate section of a reviewing journal. Thus we V. N. Monakhov learn of new advances in the area, which problems have been solved, what progress has been made with translated by H. H. Mcfaden others, while rarely, and then only in the context of Abstract the author's own results, we learn which problems This book is concerned with certain classes of the author failed to solve but considers interesting. nonlinear problems for elliptic systems of partial In all this, a summary of current problems has no differential equations: boundar·y-valuc problems with less a place in the development of a subject than a free boundaries. The first part has to do with the list of achievements, though the apparent connection general theory of boundary-value problems for ana­ between the two is often deceptive. Thus, it is de­ lytic functions and applications of it to hydrody­ sirable to publish from time to time a summary of namics. The second presents the theory of quasi­ important problems with the participation of a large conformal mappings, along with the theory of circle of authors. The Kourovka notebook is such a boundary-value problems for elliptic systems of equa­ collection of unsolved problems in group theory. tions and applications of it to problems in the The current edition is the seventh, the first having mechanics of continuous media with free boundaries: appeared in 1965. Experience has shown that the problems in subsonic gas dynamics, filtration theory, idea of collecting problems of interest in a given area and problems in elastico-plasticity. at a given time is fully justified. Of the 422 prob­ Part I. Boundary-value problems in the theory of lems in the sixth edition, 151 have now been solved. analytic functions and their application to hydro­ This edition is augmented by Chapter 7. The dynamics first six chapters have been reproduced from the I. The boundary-value problems of Riemann and sixth edition with slight editorial changes. The com­ Hilbert ments on the problems have been reviewed and II. Singular operators in spaces of summable functions. augmented. Application to boundary-value problems and to 1980 Mathematics Subject Classification: 20-06 the study of boundary properties of analytic func­ AMS Translations, Series 2 tions Volume 121, vi + 112 pages (hard cover) Ill. The mixed boundary-value problem with free List price $33, institutional member $25, boundary individual member $17 ISBN 0-8218-3079-1; LC 83-9965 IV. Flows of an incompressible fluid with free Publication date: August 1983 boundaries To order, please specify TRANS2/121 N

680 PROCEEDINGS OF THE S. A. Vinogradov, A strengthening of Kolmogorov's theorem on the conjugate function and interpola­ STEKLOV INSTITUTE tion properties of convergent power series (ISSN 0081-5438) E. M. Dyn'kin, A constructive characterization of the classes of S. L. Sobolev and 0. V. Besov S. V. Kislyakov, The Fourier coefficients of the Spectral Theory boundary values of functions analytic in the disk of Functions and Operators. II and in the bidisk V. G. Kulakova, Positive projections in symmetric N. K. Nikol' skii, Editor KB-spaces Abstract V. V. Peller, An analogue of an inequality of The papers comprising this collection are devoted }. von Neumann, isometric dilation of contractions to the connections of spectral theory with the theory and approximation by isometries in spaces of of functions of a complex variable. The classical measurable functions problem of interpolation by uniformly convergent S. V. Khrushchev, Men'shov's correction theorem and Fourier or Taylor series is illuminated, and imbedding Gaussian processes theorems dual to interpolation problems are proved; 1980 Mathematics Subject Classifications: 42, 46, 47, 60, a constructive characterization of Besov and Sobolev 30, and others classes, well-known and widely used in analysis, is Proceedings of the Steklov Institute given; an analogue of von Neumann's inequality is Volume 155, viii+ 176 pages (soft cover) obtained by a combination of spectral theory meth­ List price $52, institutional member $39, ods, combinatorial constructions and complex analy­ individual member $26 ISBN 0-8218-3072-4; LC 80-11102 sis; positive projections in Banach lattices are de­ Publication date: August 1983 scribed. To order, please specify STEKL0/155N

Prepayment is required for all AMS publications. Order from AMS, P. 0. Box 1571, Annex Station, Providence, Rl 02901, or call toll free 800-556-7774 to charge with Visa or MasterCard.

PROCEEDINGS OF SYMPOSIA IN PURE MATHEMATICS

THE SANTA CRUZ CONFERENCE ON FINITE GROUPS edited by Bruce Cooperstein and Geoffrey Mason

In the last year or so there have been widespread just come of age. This conference was partially sup­ rumors that group theory is finished, that there is ported by a grant from the National Science Founda- nothing more to be done. It is not so. tion. -from the Preface by G. Mason While it is true that we are tantalizingly close to that pinnacle representing the classification of finite There are 90 papers in this book by almost as simple groups, one should remember that only by many authors. The major divisions ot the book are: reaching the top can one properly look back and 1. Classification theory of finite simple groups, survey the neighboring territory. It was the task of 2. General theory of groups, the Santa Cruz conference not only to describe the 3. Properties of the known groups, tortuous route which brings us so close to the sum­ 4. Representation theory of groups of Lie-type, mit of classification, but also to chart out more 5. Character theory of finite groups, accessible paths-ones which might someday be open 6. Combinatorics, to the general mathematical public. 7. Computer applications, A third concern was the elucidation of topics in 8. Connections with number theory and other fields. related fields, and it is to one of these three areas The table of contents includes so many mathe­ that the papers in this volume are devoted. maticians well known and active in the field that it Just a quick glance at the table of contents [too would be unfair to list a sample. lengthy to be included here] will reveal a wide variety of topics with which the modern group theorist must Volume 37, xviii + 634 pages (hard cover) contend. Some of these, for example the connections List price $44, institutional member $33, individual member $22 with the theory of modular functions, have very re- ISBN 0-8218-1440-0; LC 80-26879 cent origins, but they leave us with the clear impres- Publication date: january 1981 sian that, far from being dead, group theory has only To order, please specify PSPUM/37N Prepayment is required for all American Mathematical Society publications. Send for the book(s) above to: AMS, P. 0. Box 1571, Annex Station, Providence, Rl 02901

681 PROCEEDINGS OF SYMPOSIA IN PURE MATHEMATICS

Operator Algebras and Applications }. Bellissard Calvin C. Moore Richard V. Kadison, Editor Ola Bratteli Paul S. Muhly Detlev Buchholz john Phillips These volumes present a state-of-the-art account Man Duen Choi Robert T. Powers of the theory of operator algebras and its applica­ Erik Christensen lain Raeburn tions. They stem from a conference that represented Ph. Combe Arion Ramsay the first meeting dealing with the full range of the F. Combes jean N. Renault subject in over thirteen years. The major part of the Alain Connes j. R. Ringrose volumes is expository in nature-the conference was Raul E. Curto john E. Roberts arranged to survey advances and developments in Alfons van Daele R. Rodriguez recent years. Many articles have been written to give Kenneth R. Davidson B. Russo expository descriptions of these advances. There are George A. Elliott Kazuyuki Saitli groups of related articles (for example, in the theory G. G. Emch SMichirli Sakai of C*-dynamical systems, the theory of unbounded David E. Evans Norberta Salinas derivations, applications to quantum physics, and the Klaus Fredenhagen Geoffrey L. Sewell cohomology theory of operator algebras). There are Y. Friedman M. Sirugue major articles by many of the leading contributors P. Ghez M. Sirugue-Collin to the field. F. Goodman Christian F. Skau The Symposium was held at Queen's University, Rudolf Haag Erling St(Jrmer Kingston, Ontario, july 14-August 2, 1980. It was Harald Hanche-Oisen Dennis Sullivan partially supported by a grant from the National Richard H. Herman Colin E. Sutherland Science Foundation. R. Hoegh-Krohn Hiroshi Taka/ M. Hugenholtz Authors included in Part one are: N. Hideo Takemoto B. lochum Masamichi Takesaki }. Archbold Richard V. Kadison R. B. E. johnson William Arveson A. Kishimoto D. Testard Paul Baum E. Christopher Lance V. F. R. jones Harald Upmeier Ola Bratteli Henri Moscovici Palle E. T. Nrgensen A. Verbeure Lawrence G. Brown Dorte Olesen Daniel Kastler Martin E. Walter john W. Bunce William L. Paschke W. P. C. King Simon Wasserman Hisashi Choda Gert K. Pedersen Burkhard Kummerer E.}. Woods Alain Connes Niels Vigand Pedersen Magnus B. Landstad j. D. Maitland Wright Joachim Cuntz L. Pukanszky R. Lima Lrisz/0 Zsido Ronald G. Douglas jean N. Renault Roberto Longo Edward G. Effros Norbert Riedel George A. Elliott Marc A. Rieffel Thierry Fack jonathan Rosenberg Claude Schochet Masatoshi Fujii 1980 Mathematics Subject Classifications: 46L05, 46L10; Elliot C. Gootman Frederic W. Schultz 43A80, 81 E05, 82A 15. Philip Green Georges Skandalis David Handelman ~erban Strlitllli Proceedings of Symposia in Pure Mathematics Pierre de Ia Harpe Hiroshi Taka/ Volume 38: Parts 1 and 2 {hard cover) xix 513 pages {Part 1); xv + 625 pages {Part 2) Herman Yasuo Watatani + Richard H. Set: List price $80, institutional member $60, Authors included in Part two are: individual member $40 Charles A. Akemann C.}. K. Batty Each port: List price $46, institutional member $35, individual member $23 Huzihiro Araki Horst Behncke Port 1: ISBN 0-8218-1441-9; LC 82-11561 Port 2: ISBN 0-8218-1444-3; LC 82-11561 Set: ISBN 0-8218-1445-1; LC 82-11561 Publication date: September 1982 To order, please specify (Set) PSPUM/38N (Part 1) PSPUM/38.1M; (Part 2) PSPUM/38.2N

Prepayment is required for all AMS publications. Order from AMS, P.O. Box 1571, Annex Station, Providence, Rl 02901, or call toll free 800-556-7774 to charge with Visa or MasterCard_

682 Miscellaneous

Personal Items Bruce L. Rothschild of the University of Califor­ nia, Los Angeles, has been appointed to a visiting Y"mg Cheng of the University of Chicago has been professorship at the University of Western Ontario appointed to an assistant professorship at Louisiana for the fall semester of 1983. State University. John J. Saccoman of Setan Hall University has Peter R. Christopher of Worcester Polytechnic been appointed Chairman of the Department of Institute has been appointed to an associate profes­ Mathematics at that university sorship at that institution. Cora S. Sadosky of Howard University will be Allan H. Clark, dean of the School of Science, a member of the Institute for Advanced Study at Purdue University, has been elected a Fellow of Princeton during the academic year 1983-1984. the American Association for the Advancement of Eberhard L. Stark of RWTH, Aachen, has been Science. appointed to an apl. professorship at that institution. Lokenath Debnath of East Carolina University Nicole Tomczak-Jaegermann of Texas A&M has been appointed to a professorship and appointed University, College Station, has been appointed Chairman of the Department of Mathematics at the to an associate professorship University of Central Florida. at the University of Alberta. This is a correction of an announcement Gary L. Ebert of the University of Delaware that appeared in the Notices of August 1983, page has been appointed to a visiting professorship at 549. the University of Western Ontario for the 1983-1984 academic year. Eugene Wachspress of the Knolls Atomic Power Laboratory has been appointed to a professorship at Peng Fan of Marshall University has been the University of Tennessee, Knoxville. appointed to an assistant professorship at Texas Christian University. Samuel S. Wagstaff of the University of Georgia has been appointed to an associate professorship at Guillermo Ferreyra of Rutgers University has Purdue University. been appointed to an assistant professorship at Louisiana State University. Sherwood Washburn of Seton Hall University has been appointed to an associate professorship at that Ryoh Fuji-Hara of the University of Waterloo has university. been appointed to an assistant professorship at the University of Tsukuba, Japan. Marianne L. Gardner of Worcester Polytechnic Deaths Institute has been appointed to an associate profes­ sorship at that institution. Ella E. Bemstorf of Mosquero, New Mexico, died in February 1981. She was a member of the Society Helmut Jurgensen of the Technische Hochschule, for 53 years. Darmstadt, Federal Republic of Germany, has been appointed to a professorship at the University of Jeanne E. Brocavich of Saint Mary's College of Western Ontario. Maryland, died on December 10, 1982 at the age of 53. She was a member of the Society for 2 years. J. J. Malone of Worcester Polytechnic Institute has been appointed to a five-year term as John L. Earle Bush, Professor Emeritus of Kent State Sinclair Professor of Mathematics at that institution. University, died on May 27, 1983 at the age of 83. He was a member of the Society for 53 years. R. K. Oliver of the University of Pittsburgh has been appointed to an assistant professorship at Gustave Efroysom of the University of New Indiana State University. Mexico died on August 13, 1983 at the age of 46. He was a member of the Society for 23 years. Margot S. Pallman of Harris-Stowe College has been appointed to an associate professorship at Harry S. Everett of West Chester, Pennsylvania, Maryville College, Saint Louis. died at the age of 92. He was a member of the Society for Donald Plank of Stockton State College has been 63 years. appointed to a professorship and appointed Chairman Edmund H. Feller of the University of Wisconsin, of the Department of Mathematics at the University Milwaukee, died on June 17, 1983 at the age of 59. of Bridgeport. He was a member of the Society for 31 years. Henry Crawford Rhaly, Jr., of the University Nicholas Glyptis of Oak Brook, Illinois, died on of Mississippi has been appointed to an assistant July 30, 1982 at the age of 60. He was a member of professorship at Millsaps College. the Society for 23 years. Caroll V. Riecke of Cameron University has been Eberhard Hopf, Professor Emeritus of Indiana appointed to an associate professorship at Franklin University, Bloomington, died on July 24, 1983 at and Marshall College. the age of 81. He was a member of the Society

683 for 50 years. Professor Hopf, who gave the Gibbs Reciprocity Agreements Lecture at the Society's annual meeting in Atlantic City (January 1971), was awarded the Steele Prize for works of fundamental importance at the summer meeting in Pittsburgh, August 1981 (see the October The listings below update the reports published in 1981 Notices, page 508). the Notices, June 1983 (pages 439-444) and August 1983 (page 543). Donald 0. Koehler of Miami University, Oxford, died on February 3, 1983 at the age of 46. He was a Asia member of the Society for 15 years. • Indian Mathematical Society Joseph P. LaSalle, Professor Emeritus of Brown University, died on July 7, 1983 at the age of 67. He Apply to: T. Ramesan, Hon. Secretary, Indian was a member of the Society for 43 years. Professor Mathematical Society, Principal, Central College, LaSalle was a winner of the Chauvenet Prize of Bangalore, India. the MAA, a past president of SIAM, and had served Dues: $7 (Rupees 25/-); payable to K. M. Saxena, the Society on its Joint Committee on Employment Hon. Treasurer, IMS, 79 Burdwan Compound, Ranchi Opportunities (1963). (Bihar), India. Viktors Linis, Professor Emeritus of the University Privileges: Journal of Indian Mathematical Society of Ottawa, died on July 2, 1983 at the age of 66. He or Mathematics Student. was a member of the Society for 29 years. Officers: R. S. Mishra (President), T. Ramesan (Secretary), K. M. Saxena (Treasurer), S. R. Forrest H. Murray of Urbana, Illinois, died at the Sinha (Academic Secretary), K. G. Ramanathan age of 91. He was a member of the Society for 65 (Editor of Journal of Indian Mathematical Society), years. N. Sankaran (Editor of Mathematics Student). Oscar J. Peterson, Professor Emeritus of Emporia State University, died on July 13, 1982 at the age of 89. He was a member of the Society for 55 years. Europe Samuel S. Smith, Professor Emeritus of the • Societe Mathematique de France University of Utah, died on May 10, 1983 at the age Address for mail: Societe Mathematique de France, of 90. He was a member of the Society for 45 years. B.P. 126-05, 75226 Paris, Cedex 05, France. Hugh E. Stelson of East Lansing, Michigan, died Apply to: American Mathematical Society, P.O. Box on June 19, 1983 at the age of 80. He was a member 6248, Providence, Rhode Island 02940. of the Society for 52 years. Dues: $18 or $24; payable to American Mathematical Ernst Gabor Straus of the University of California, Society. Los Angeles, died on July 12, 1983 at the age of 61. Privileges: Individuals who pay dues of $18 are en­ He was a member of the Society for 41 years. titled to receive Circulaire and Gazette. Individuals of are entitled to Circulaire, JosephS. Vigder of Ottawa, Canada, died on July who pay dues $24 per year of 19, 1982 at the age of 72. He was a member of the Gazette, and Bulletin. Four issues at a discount price. Society for 40 years. Asterisque may be purchased (Members in the U.S., Canada, or Mexico should Yue Kei Wong of Drayton, South Carolina, died order their copies from the AMS. See the AMS on April 21, 1983 at the age of 78. He was a member Catalogue of Publications.) of the Society for 55 years. Officers: C. Houze! (President), J. P. Aubin, G. Joanne B. Wuneh of Pacific Palisades, California, Lachaud, B. Malgrange (Vice Presidents), .P. Mazet died on October 15, 1982 at the age of 51. She was a (Treasurer), M. David (Secretary). member of the Society for 3 years.

MEMOIRS OF THE AMS Contents (ISSN 0065·9266) Part I. Preliminaries II. Reliefs and continuous functions Constructive Continuity Ill. Monotone functions Mark Mandel kern IV. Relief functions and the limited continuity principle There arc two long-outstanding constructivity References problems concerning real-valued functions on the closed unit interval: Is every function continuous? Memoirs of the American Mathematical Society Is every continuous function uniformly continuous? Number 277, vi+ 122 pages (soft cover) List price $9, institutional member $7, This paper determines the numerical content in the individual member $5 method of Urysohn's Lemma, applies this to the ISBN 0-8218-2277-2; LC 82-24358 continuity problems, obtains a few partial results, and Publication date: March 1983 provides a basis for further work. To order, please specify MEM0/277N

Prepayment is required for all AMS publications. Order from AMS, P. 0. Box 1571, Annex Station, Providence, Rl 02901, or call toll free 800-556-7774 to charge with Visa or MasterCard.

684 Visiting Mathematicians (Supplementary List}

The following lists of visiting mathematicians include both foreign mathematicians coming to the United States and Canada, and Americans going abroad. The original lists appeared on pages 450-452 of the june 1983 Notices;a supplement­ ary list appeared on pages 550-552 of the August 1983 issue. American Mathematicians Visiting Abroad Name and Home Country Host Institution Field of Special Interest Period of Visit Fein, Burton (U.S.A.) Universitat Stuttgart, Algebra 9/83 - 7/84 West Germany Gundersen, Gary G. (U.S.A.) Imperial College, England Differential Equations 11/83 Hartshorne, Robert (U.S.A.) Kyoto University, japan Algebraic Space Curves, Vector 7/82 - 6/84 Bundles on Projective Spaces Hochberg, Kenneth ). (U.S.A.) Hebrew University Probability, Stochastic Processes 8/83 - 7/84 Kim, Paik K. (U.S.A.) Seoul National University Topology 1 /84 - 6/84 Kirkman, Ellen E. (U.S.A.) University of Leeds, England Ring Theory 1/84 - 6/84 Lanford, Oscar (U.S.A.) I. H. E. S., France Mathematical Physics, Statistical 7/82 . 6/84 Mechanics Lieberman, Gary M. (U.S.A.) Australian National University Partial Differential Equations 1/84 . 6/84 Meyerson, Mark D. (U.S.A.) Brittannia Royal Naval College, Algebraic Topology 9/83 - 6/84 England Ribes, Luis (Canada) Universidad Autonoma de Madrid Algebra 9/83 . 6/84 Summers, William H. (U.S.A.) University of Essen, West Germany Functional Analysis 10/83 - 4/84 University of Paderborn, West Germany Visiting Foreign Mathematicians Agmon, Shmuel (Israel) California Institute of Technology Partial Differential Equations 9/83 . 3/84 Alencar, R. (Brazil) Kent State University Analysis 8/83 - 8/84 Attele, Rohan (Sri Lanka) University of Arkansas Functional Analysis 8/83 . 12/83 Bandler, Wyllis (England) Florida State University Mathematics, Computer Science 8/83 . 5/84 Benyamini, Yoav (israel) University of Texas at Austin Banach Spaces 9/83 - 5/84 Bernstein, David (U.S.S.R.) University of California, Berkeley Algebraic Geometry, Newton Polyhedra 7/82 - 6/84 Bertsch, Michie! Brown University Differential Equations 9/83 - 2/84 (The Netherlands) Birch, Bryan ). (England) Institute for Advanced Study Automorphic Forms 9/83 - 12/83 Dahlberg, Bj¢rn E.). (Sweden) University of Texas at Austin Harmonic Analysis 9/83 . 5/84 Dalenius, Tore (Sweden) Brown University Probability and Statistics 9/83 . 6/84 Delyon, Franc;ois (France) California Institute of Technology Mathematical Physics 9/83 - 4/84 Denker, Manfred Indiana University Statistics 8/83 . 12/83 (West Germany) Dupont, johan L. SUNY at Stony Brook Algebra, Geometry 9/83 - 7/84 (West Germany) Edelstein, Leah (Israel) Brown University P. D. E., Biomathematics 9/83 - 5/84 Elaydi, Saber (Kuwait) Case Western Reserve University Dynamical Systems 8/83 - 5/84 Engler, Hans P. University of Texas at Austin Functional Differential Equations 9/83 - 5/84 (West Germany) Fraenkel, Aviezri S. (Israel) University of Calgary Combinatorics, Complexity 9/83 - 4/84 of Algorithms Gillespie, Alastair Indiana University Functional Analysis 8/83- 5/84 (United Kingdom) Gonzalez, Francisco (Mexico) University of Iowa Knot Groups 8/83 - 5/84 Govil, Narendra Kumar (India) Auburn University Approximation Theory 9/83 - 6/84 Gurarii, D. (Israel) Case Western Reserve University Harmonic Analysis 8/83 - 5/84 Hagen, Hans (West Germany) Arizona State University Computer Aided Design 8/83 - 5/84 Heffernan, Peter M. University of Texas at Austin Statistics 9/83 - 5/84 (New Zealand) Hitchin, Nigel ). (England) SUNY at Stony Brook Algebraic and Differential Geometry 9/83 - 4/84 Hua, L. K. (People's Republic California Institute of Technology Number Theory 10/83- 7/84 of China) Huang, Hai (Taiwan) Brown University Stochastic Control 9/83 - 5/84 Jankovic, Dragan S. (Yugoslavia) University of Arkansas General Topology 10/83- 5/84 )ourne, jean-Lin (France) Yale University Harmonic Analysis 9/83- 12/83 Kalman, john (New Zealand) Indiana University Algebra-Lattice Theory 8/83 - 12/83 Kamishima, Yoshinobu (japan) Institute for Advanced Study Topology 9/83 - 12/83 Kaniewski, Janusz (Poland) Auburn University Topology 9/83 - 6/84 Kawohl, Bernhard Brown University Partial Differential Equations 4/83 - 9/84 (West Germany) Kleimann, Wolfgang Iowa State University Stochastic Differential Equations 8/83 - 6/84 (West Germany) Kocak, Huseyin (Turkey) Brown University Differential Equations 9/83 - 5/84 Kwapisz, Marian (Poland) University of Missouri, Rolla Numerical Analysis, Differential 3/84- 4/84 Equations 685 Name and Home Country Host Institution Field of S11ecial Interest Period of Visit Lal, Bansi (India) University of Iowa Applied Mathematics Lin, Long-wei (People's Brown University Hyperbolic Conservation Laws 3/83- 3/84 Republic of China) Lizana-Pena, Marcos Brown University Functional Differential Equations 9/83 - 8/84 (Venezuela) Luus, Hermanus G. (Republic University of Texas at Austin Statistics 1/84- 5/84 of South Africa) Markanda, Raj (Venezuela) University of Iowa, Iowa City Algebra 8/83 - 5/84 Meyer, Yves F. (France) Yale University Harmonic Analysis 9/83 - 12/83 Mi, Zhong-Chun (People's Brown University Applied Fluid Mecahnics 6/83 - 6/84 Republic of China) Moricz, Ferenc (Hungary) Indiana University Functional Analysis 8/83- 5/84 Nakki, Raimo (Finland) University of Texas at Austin Complex Analysis 9/83 - 5/84 Nevanlinna, Olavi (Finland) Stanford University Numerical Analysis 10/83- 11/83 Niederhausen, Henrich Arizona State University Statistics, Combinatorics 8/83 - 5/84 (West Germany) Piotrowski, Zbigniew (Poland) Auburn University Real Analysis 9/83- 6/84 Ramasubramanian, S. (India) Indiana University Probability 8/83- 6/84 Ricci, Fulvio (Italy) Institute for Advanced Study Harmonic Analysis 9/83- 4/84 Rosinski, jan (Poland) Case Western Reserve University Probability 8/83 - 5/84 Santanilla, jairo (Colombia) University of Iowa Differential Equations 8/83- 5/84 Schlichtkrull, Henrik Institute for Advanced Study Representations of Lie Groups 9/83 - 4/84 (Denmark) Siedentop, H. (West Germany) California Institute of Technology Mathematical Physics 9/83 - 6/84 Sitaramachandrarao, R. (India) University of Toledo Number Theory 9/83- 6/84 Sitaraman, Y. (India) University of Toledo Analysis 9/83- 6/84 Soares de Souza, Ger.aldo Auburn University Harmonic Analysis 9/83- 6/84 . (Brazil) Stavroulakis, Joannis (Greece) Brown University Functional Differential Equations 7/83 - 1/84 Trudinger, Neil (Australia) Indiana University Partial Differential Equations 8/83 - 12/83 Van Der Woude, jaap Case Western Reserve University Topological Dynamics 8/83 - 5/84 (The Netherlands) Weron, Aleksander (Poland) Louisiana State University Probability Theory and Stochastic 9/83 - 6/84 Processes Wojtkowski, Maciej (Poland) University of California, Berkeley Ergodic Theory, Bifurcation Theory, 8/82 - 9/84 Dynamical Systems Zajaczkowski, W. (Poland) University of Victoria Partial Differential Equations 1/84- 6/84 Zhou (China) Rutgers University Statistics 2/83 - 12/83

CONTEMPORARY MATHEMATICS PROCEEDINGS OF THE CONFERENCE ON state-of-the art flavor, the book contains several re­ INTEGRATION, TOPOLOGY, AND GEOMETRY search articles devoted to topics as diverse as spectral IN LINEAR SPACES theory (by N. Dunford) and weak and strong com­ pactness in spaces of Pettis integrable functions (by edited by William H. Graves j. Brooks and N. Dinculeanu). This book contains survey articles contributed The book gives an overview of the current state by speakers at a conference held at the University of of affairs in the study of measure and integration in North Carolina in Chapel Hill in the spring of 1979 linear spaces and applications thereof. Those who and organized around contributions of the late B. j. will enjoy these papers arc workers in functional Pettis to the development of measure and integration analysis with an interest in measure and integration in linear spaces and the role of general linear spaces in linear spaces, especially the many delighted readers in measure-theoretic considerations. Topics covered of Diestel and Uhl's Vector Measures (Amer. Math. include strict topologies in topological measure theory Soc. Mathematical Surveys, Volume 15). (by H. Collins), the Dunford-Pettis property (by j. Diestel), the Radon-Nikodym property (by R. Huff), the Orlicz-Pettis phenomenon (by N. Kalton), appli- Volume 2, x + 269 pages (soft cover) cations of measure and integration in linear spaces List price $18, institutional member $14, individual member $9 (by I. Kluvanek), and the role of the Pettis mcasur- ISBN o-8218-5002-4; LC 80-25417 ability theory (by J. j. Uhl, Jr.). In addition to these Publication date: November 1980 survey articles which impart both a historical and a To order, please specify CONM/2·N Prepayment is required for all AMS publications. Order from AMS, P. 0. Box 1571, Annex Station, Providence, Rl 02901, or call toll free 800-556-7774 to charge with Visa or.MasterCard.

686 Application Deadlines for Grants and Assistantships

Many fellowship programs have deadlines for Lady Davis Fellowship Trust [TSA] receipt of applications. These deadlines are noted Lady Davis Visiting Professorships [TSA] in news items and in the Stipends Section of the * Royal Norwegian Council for Scientific and In­ December Notices. They are listed below for dustrial Research (Postdoctorate Fellowships) your convenience, and as a reminder since many of [TSA] these deadlines occur before the publication date of * Sigma Delta Epsilon, Graduate Women in Science the special December issue on Assistantships and (Eloise Gerry Fellowship) [GS] Fellowships. Dates taken from the 1982 special issue have been updated with information received December 15 in preparation for the December 1983 issue. For * Los Alamos National Laboratory (J. Robert information about the various programs, the reader Oppenheimer Research Fellowship) [PS] is referred to the appropriate part of the Stipends * State University of New York, Buffalo (George Section of the December 1982 Notices as follows: [GS] William Hill and Emmy Noether Research = Graduate Support Section; [PS] = Postdoctoral Instructorships) [PS] Support Section; [TSA] = Travel and Study Abroad December 31 Section; [SFN] = Study in the U.S. for Foreign Nationals. Institute for Advanced Study Memberships [PS] * Information from the December 1982 issue not yet Massachussetts Institute of Technology (C. L. E. confirmed for this year. Moore Instructorships in Mathematics) [PS] • Refers to a news item in this issue of the Notices. University of Wisconsin, Madison (Van Vleck Assistant Professorships in Mathematics) [PS] October 1 January 1 American Philosophical Society [PS] * Bunting Institute of Radcliffe College (Science Brown University (Jacob David Tamarkin Assistant Scholar Fellowships) [PS] Professorships) [PS] John Simon Guggenheim Memorial Foundation * California Institute of Technology (Harry Bateman Fellowships [PS] Research Instructorships) [PS] * Courant Institute (Instructorships in Mathematics) October 15 [PS] • Fulbright Scholar in Residence Program [TSA] * Courant Institute (Postdoctoral Visiting Member­ October 31 ships [PS] Kennedy Scholarships [SFN] Indiana University, Bloomington (Vaclav Hlavaty Research Assistant Professorships) [PS] November Mathematical Sciences Research Institute [PS] NSF Graduate Fellowships [GS] * University of California, San Diego (S. E. NSF Minority Graduate Fellowships [GS] Warschawski Assistant Professorship) [PS] November 1 January 2 American-Scandinavian Foundation [TSA] Harvard University (Benjamin Peirce Lectureships) * Fannie and John Hertz Foundation Fellowships [PS] [GS] January 3 November 7 * University of Michigan, Ann Arbor (Theophil • National Academy of Sciences (Exchange Programs Henry Hildebrandt Research Assistant Profes­ with China) [TSA] sorships) [PS] November 15 January 15 NSF Mathematical Sciences Postdoctoral Research * Committee on Institutional Cooperation [PS] (Minorities Fellowships in the Sciences, Mathe­ Weizmann Institute of Sciences (Feinberg Graduate matics and Engineering) [GS] School Postdoctoral Fellowships) [TSA] Dartmouth College (John Wesley Young Research * Woodrow Wilson Women's Studies Research Instructorships) [PS] Grants [GS] Institute for Mathematics and its Applications [PS] November 30 * Kosciuszko Foundation [GS] [SFN] Foundation (Graduate and * North Atlantic Treaty Organization [TSA] * Kosciuszko Postgraduate Exchange with Poland) [TSA] December 1 National Research Council (Research Associateship American Philosophical Society [PS] Program) [PS)

687 * Natural Sciences and Engineering Research Council February 15 of Canada (Visiting Fellowships) [TSA] American Society for Engineering Education (ONR Rice University (Griffith Conrad Evans Instructor­ Graduate Fellowship Program) [GS] ships) [PS] • AMS-MAA-SIAM Congressional Science Fellowship Smithsonian Institution (Predoctoral Fellowships) [PS] [GS] * University of California, Irvine (Visiting Irvine Smithsonian Institution (Postdoctoral Fellowships) Lectureship) [PS] [PS] February 18 University of California, Los Angeles (Earle Raymond Hedrick Assistant Professorships in * AAAS Science, Engineering and Diplomacy Fellow­ Mathematics) [PS] ships [PS] University of Chicago (Leonard Eugene Dickson February 22 Instructorships in Mathematics) [PS] * Hubert H. Humphrey Doctoral Fellowships [GS] * University of Pittsburgh (Andrew Mellon Postdoc­ toral Fellowships) [PS] February 28 January 16 Australian Institute of Nuclear Science and En­ gineering (Research Fellowships) [PS] National Research Council (Postdoctoral Fellow­ ships for Minorities) [PS] March 1 of January 27 Kenneth 0. May Fellowship in the History Mathematics [GS] * National Center for Atmospheric Research American Philosophical Society [PS] (Advanced Study Program) [PS] March 14 January 30 NSF United States-India Exchange [TSA] * Centro de Investigacion del IPN (Solomon Lefschetz Research Instructorships) [TSA] March 31 IBM Thomas J. Watson Research Center Hubert H. Humphrey Doctoral Fellowships [GS] (Mathematical Sciences Department Postdoc­ * North Atlantic Treaty Organization [TSA] toral and Junior Faculty Research Fellowships) April1 [PS] American Philosophical Society [PS] January 31 April30 * Yale University (Josiah Willard Gibbs Instructor­ * Organization of American States [SFN] ships) [PS] May1 February 1 Air Force Office of Scientific Research (Research * AAAS Summer Fellowship [GS] Contracts and Grants) [PS] American Philosophical Society [PS] American Society for Engineering Education July 1 (NASA-ASEE Summer Faculty Fellowships) [PS] Indo-American Fellowship Program [TSA] American Society for Engineering Education August 1 (Navy- and DOE-ASEE Summer Faculty Re­ American Philosophical Society [PS] search Programs) [PS] Carnegie-Mellon University (Zeev Nehari Instruc­ August 15 torship in Mathematics) [PS] * North Atlantic Treaty Organization [TSA] * Minna-James-Heinemann-Stiftung (Research Abroad) August 31 [TSA] Institute of Nuclear Science and En­ * Sigma Delta Epsilon, Graduate Women in Science Australian (Grants-in-Aid) [GS] gineering (Research Fellowships) [PS] * University of Cincinnati (Charles Phelps Taft * Organization of American States [SFN] Postdoctoral Fellowships) [PS] September 14 February 9 NSF United States-India Exchange [TSA] * California State Graduate Fellowships [GS]

688 AMS Reports and Communications

Recent Appointments Gregory Mine (1984). Terms on expire on September 30. Committee members' terms of office on standing Angus J. Macintyre (1987), and Evelyn Nelson committees expire on December 31 of the year (1987), have been appointed by President Julia given in parentheses following their names, unless B. Robinson to the AMS-IMS-SIAM Committee otherwise specified. on Joint Summer Research Conferences in the Mathematical Sciences. Continuing members of the Chandler Davis (1983) has been appointed chair­ committee are Benedict H. Gross (1986), Malcolm R. man of the Committee on Human Rights of Math­ Leadbetter (1986), Jerrold E. Marsden (1985), James ematicians by President Julia B. Robinson. He McKenna (1986), Katsumi Nomizu (1986), Julius replaces Eduardo Sontag (1984) who will remain on Shaneson (1984), R. 0. Wells, Jr., chairman (1985), the committee. Other members of the committee are and Shmuel Winograd (1984). Terms expire on June Ed Dubinsky (1983), Leon A. Henkin (1985), Peter 30. J. Hilton (1984), John A. Nohel (1985), and Gail S. A new AMS-MAA-SIAM Joint Coordinating Com­ Young, Jr. (1983). mittee on Public Understanding of Mathematics President Julia B. Robinson has appointed Susan has been appointed by Presidents Julia B. Robinson Montgomery (1984) to be chairman of the Committee (AMS), Ivan Niven (MAA) and Hirsh G. Cohen on Postdoctoral Fellowships. Continuing members (SIAM). The members of the committee are Ronald of the committee are George E. Andrews (1985), L. Graham (AMS), Lynn A. Steen (MAA) and Joseph H. Jerome Keisler (1985), Stewart 8. Priddy (1984), B. Keller (SIAM). Irving Reiner (1984), and Alan D. Weinstein (1985). Terms expire on June 30. Reports of Past Meetings Melvin Hochster, Franklin P. Peterson, and Paul J. Sally, Jr., have been appointed by President Julia The Summer Meeting in Albany 8. Robinson to a new ad hoc Committee on Abuse The report of the mathematical portion of this of Subscriptions. Professor Sally will serve as meeting will appear in a later issue of the Notices. chairman. Council Meeting. The Council met in the Squire Charles W. Curtis (1986), Harold M. Edwards Room of the Ramada Inn adjoining the campus of (1986), Lawrence E. Payne (1986), George B. Seligman the State University of New York at Albany at 5:00 (1986), and Patricia Lilaine Sipe (1986) have been p.m. on 7 August 1983. President Robinson was in appointed by President Julia B. Robinson to the the chair. Committee to Select the Winner of the Steele The President announced the designation of two Prize. Continuing members of the committee are additional candidates for the Nominating Committee H. Jerome Keisler (1985), Yiannis N. Moschovakis of 1984 and 1985, namely John H. Ewing and Barry (1985), and Edwin H. Spanier (1984). Professor Simon. Moschovakis has been appointed chairman. Terms The Council authorized for the Society the creation expire on June 30. of an office tentatively named Coordinator of Federal President Julia B. Robinson has appointed Boris Relations for the Mathematical Sciences. The M. Schein (1985) to the AMS-IMS-ASL Committee on Trustees had previously provided the Society's share Translations from Russian and Other Foreign of initial funding for the position. Languages. Chairman of the Committee is The Coordinator will be responsible to the Joint Lawrence Zalcman. Continuing members of the Concerns Committee in Mathematics, which is a AMS Subcommittee are Israel Berstein (1983), Frank joint committee with the Mathematical Association B. Cannonito (1985), David G. Ebin (1983), Jack of America and the Society for Industrial and Applied K. Hale (1983), Raymond L. Johnson (1984), Neal Mathematics, which are also contributing funds. See I. Koblitz (1984), Boris Mityagin (1983), Melvin a position description and call for applications in the B. Nathanson (1983), Andrew M. Odlyzko (1984), back of this issue. Marian B. Pour-EI (1985), Marina Ratner (1985), The Council made three additional nominations Donald E. Sarason (1985), and Lawrence Zalcman, for the position of Member-at-Large of the Council chairman (1984). The IMS Subcommittee members in the election of 1983, namely, Carl R. Riehm, are A. T. Bharucha-Reid, Miklos Csorgo, Eugene Jonathan M. Wahl, and William K. Allard. M. Klimko, Eugene Lukacs, chairman, and Lajos The Council established a Committee on Profes­ F. Takacs. The ASL Subcommittee members are sional Ethics. It is to be available for consultation, Solomon Feferman (1984), James P. Jones (1984), advice, and informal professional investigation as Gregory Cherlin (1985), Vladimir Lifschitz (1984), called for. The scope of putative violations of

689 professional ethics to be considered will be defined by at the Leningrad Polytechnic Institute following his practice and precedent and will surely include those application for permission to emigrate. connected with refereeing or plagiarism. The Council authorized the application for The Council was concerned over some recent affiliation of the Society with Section U, Statistics, instances of attempts to secure scientific grants of the American Association for the Advancement of through a political approach, that is, directly through Science. the legislative process without the usual scientific The Council had recessed for dinner from 6:30 p.m. review. The Council passed the following resolution. to 8:15 p.m. and adjourned at 11:25 p.m. The Council of the American Mathematical Business Meeting. The Business Meeting was Society deplores the intervention of political held in Room 18 of the Lecture Center on the processes in scientific decisions that should be State University of New York, Albany, campus on made on the basis of scientific judgments through Wednesday, 10 August 1983, immediately following the peer review process. In particular, we view the award of the Steele Prizes. President Robinson with dismay that funding for certain scientific was in the chair. projects has been incorporated in legislation that The Secretary reported on actions of the Council was passed by the House of Representatives of interest to the members. See the account of the although these projects have not been subjected April Council Meeting in the June Notices, page to the review processes that have in the past 463, as well as the report above from the Summer guided federal funding. Such action opens the Meeting. prospect that in the future federal support of There was neither old nor new business. science may be determined more by political considerations than by scientific merit. We A motion by Professor Mary Ellen Rudin thanking believe that this prospect constitutes a grave the Committee on Arrangements was passed by ac­ threat to the 'health of science in the United claim and was followed immediately by adjournment States. at 5:30p.m. The Council authorized a letter of inquiry into Everett Pitcher the reasoning by which E. P. Gil'bo, a Soviet Bethlehem, Pennsylvania Secretary mathematician, was stripped of his degrees and pressured to resign from his long-standing position

CONTEMPORARY MATHEMATICS ized explicit formulas of number theory" associated Advanced Analytic Number Theory to the L-functions of automorphic representations and algebraic varieties over number fields. Part 1: Ramification Theoretic Methods An introductory chapter outlines some of the Carlos J. Moreno most significant discoveries in algebraic number the­ ory dealing with the phenomenon of ramification, ABSTRACT notably the introduction by Hilbert of the higher The book presents in a coherent way all the ram· ramification groups and the generalization to infinite ification results from local fields which are necessary extensions by Herbrand. The same chapter also gives for an understanding of the new developments in an introduction to the powerful technique of the advanced analytic number theory. "explicit formulas" which leads to some far reaching Chapter Ill gives an elementary introduction to generalizations of the known prime number theorems. /-adic Haar measures, a topic which has gained much importance in recent years due to the work of Mazur Contents and others. 0. Introduction Chapters I, II, IV, V and VI are basic and could I. Galois theory for infinite extensions very well serve as an introduction to local class field II. Projective lif11its theory. Ill. Elementary theory of /-adic integration Chapter VII gives a detailed discussion of the rela- IV. Ramification theory tive Weil group; it includes a proof of Grothendieck's V. Multiplicative versus additive reduction local monodromy theorem which is the essential in- VI. Ramification of abelian extensions gredient in the construction of the Weii-Deligne VII. The Weil groups of a local field group. The chapter ends with the precise statement VIII. Shafarevitch's theorem of the conjectural non-abelian local reciprocity law. IX. The Herbrand distribution After some preparations in chapter VIII, chapter 1980 Mathematics Subject Classifications: 10D15, 12A65, IX presents a detailed study of the Herbrand distri- 12810, 12825, 12827, 14G1 0, 10H99 bution which serves as a suitable substitute for the Contemporary Mathematics Artin and Swan representations when dealing with Volume 15, viii + 192 pages (soft cover) · h f List ~rice $18, institutional member $14, conductor questions. The point of view IS t at 0 individual member $9 harmonic analysis and /-adic valued distributions. The ISBN 0-8218-5015-6; LC 82-22620 main goal of the chapter has been to prepare the Publication date: January 1983 way for the development of the so-called "general· To order, please specify CONM/15N Prepayment is required for all AMS publications. Order from AMS, P.O. Box 1571, Annex Station, Providence, Rl 02901, or call toll free 800-556-7774 to charge with Visa or MasterCard.

690 Call for Applications and Nominations Coordinator of Government Relations for the Mathematical Sciences A new position has been authorized by the governing bodies of AMS, MAA, and SIAM to be under the direction of the Joint Concerns Committee in Mathematics. The appointment is half-time during the academic year and full-time during the summer. The position will continue for at least one year starting 1 January 1984. The coordinator must be prepared to spend a considerable amount of time in Washington-one or two trips a week if he or she does not live in the Washington area. The following are important qualifications for the job: • stature and broad acquaintanceship in the mathematical sciences community; • good understanding of political and legislative processes in the Federal Government; • awareness of and concern about the problems facing the mathematical sciences community with regard to mathematics education, funding of research, and nurture of young mathematicians. Salary will be commensurate with background and experience. Applications and nominations should be sent to: Joint Concerns Committee in Mathematics cjo American Mathematical Society Post Office Box 6248 Providence, Rhode Island 02940 and must be received by October 31, 1983. Names of suitable references should be provided.

American Mathematical Society New Society Position: Acquisitions Editor

One of the principal functions of the Society is to publish first-rate mathematics books at reasonable prices. To further that goal, the Executive Committee and Trustees have authorized the creation of a position of a kind new to the Society, that of Acquisitions Editor. This person would be charged with actively seeking out excellent authors (potential, budding or actual) and encouraging them to submit their ideas or manuscripts to the editorial committees of either the Surveys and Monographs Series or of the Colloquium Series. While the acquisitions editor would be an associate editor ex officio of both of these editorial committees, he or she would not have the power to accept manuscripts; but with manuscripts of the level envisaged this would presumably not be a problem. The acquisitions editor will receive (a) travel and subsistence costs for attending the two national meetings each year, if interviews with authors are scheduled, (b) reimbursement for incidental expenses, and (c) an annual payment of the greater of $2,000 or a royalty on books he or she has procured. Obviously desirable qualifications include broad understanding of contemporary research mathematics, wide acquaintanceship among currently active mathematicians, and willingness to pursue the expressed goal vigorously. Interested persons should write to Dr. W. J. LeVeque, Executive Director, American Mathematical Society, Post Office Box 6248, Providence, RI 02940, outlining their backgrounds and qualifications. Applications should be received by October 31, 1983.

691 Classified Advertisements

SUGGESTED USES for classified advertising are books or lecture notes for sale, books being sought, positions available, exchange or rental of houses, and typing services. THE RATE IS $.55 per word with a minimum of $5.00. The same ad in 7 consecutive issues is $3.50 per word. Type will be set solid unless centering and spac­ ing are requested. A centered line of any length or the equivalent in white space is $5.00. A word is defined as a group of characters with space at each end. Prepayment is required of individuals but not of institutions. For an additional $10.00 charge, announcements can be placed anonymously. Correspon­ dence will be forwarded.

DEADLINES are listed on the inside front cover.

U.S. LAWS PROHIBIT discrimination in employment on the basis of color, age, sex, race, religion or national origin. "Positions Available" advertisements from institutions outside the U. S. cannot be published unless they are accompanied by a statement that the institution does not discriminate on these grounds, whether or not it is subject to U.S. laws. Details and specific wording may be found on page 98 of the january 1983 issue of the Notices. SITUATION WANTED advertisements are accepted under terms spelled out on page A-355 or the April 1979 Notices. (Deadlines are the same as for othe-r classi­ fied advertisements.)

SEND AD AND CHECK TO: Advertising Department, AMS, P. 0. Box 6248, Providence, Rhode Island 02940. Individuals are requested to pay in advance, in­ stitutions are not required to do so.

POSITIONS AVAILABLE DEPARTMENT OF MATHEMATICS UNIVERSITY OF CALIFORNIA, SANTA BARBARA UNIVERSITY OF CALIFORNIA, SANTA BARBARA DEPARTMENT OF MATHEMATICS Applications are invited for a tenure-track assistant Applications are invited for assistant professor positions professor position in statistics. Candidates must have out­ in the general areas of nonlinear differential equations and standing research potential and have demonstrated excel­ global analysis. Successful candidates must have outstanding lence in teaching. Qualified candidates from minority groups research potential and have demonstrated excellence in and qualified women are encouraged to apply. Exceptionally teaching. Exceptionally well-qualified persons, whose back­ well-qualified persons, whose background and experience ground and experience warrant a tenure-level appointment warrant a tenure-level appointment are also encouraged to are also encouraged to apply. We especially encourage apply. Resumes and three letters of recommendation should applicants in the following areas: dynamical systems, global be sent prior to December 15, 1983 to james B. Robertson, or qualitative theory of nonlinear partial differential equa­ Department of Mathematics, University of California, Santa Barbara, CA tions, or modern mathematical physics. R~sum~s and 93106. letters of recommendation should be sent no later than The University of California, Santa Barbara is an equal December 15, 1983 to: James B. Robertson, Chairperson, opportunity/affirmative action employer_ Department of Mathematics, University of California, Santa Barbara, CA 93106 Mathematics The University of California, Santa Barbara, is an equal Virginia Polytechnic Institute & State University opportunity affirmative action employer. Applications and nominations are invited for anticipated tenure-track positions at the Assistant Professor level begin­ UNIVERSITY OF CALIFORNIA ning September 1984. Candidates should have demonstrated DEPARTMENT OF MATHEMATICS, IRVINE, CA 92717 strong research potential in an area of computational mathe­ Position for an Assistant Professor in the Department of matics. These persons should have expertise in areas such as Mathematics. Duties involve undergraduate and graduate numerical analysis, numerical solutions of differential equa­ teaching. Research area: Algebra or Analysis in the broad tions, software, hardware, and applications. Applications sense (including Mathematical Physics and Probability). accepted until positions are filled. Applicants must possess a Ph.D. Send applications, curricu­ Applicants should send a r~sume and three letters of lum vitae (work in print or preparation), a brief description recommendation to Bruce E. Reed, Assistant Chairman, of research plans, and three letters of recommendation. Department of Mathematics, Virginia Polytechnic Institute Appointment begins on July 1, 1984. U. C. Irvine is an & State University, Blacksburg, Virginia 24061-4097. Affirmative Action/Equal Opportunity Employer. The University is an Equal Opportunity/Affirmative Action Employer. UNIVERSITY OF ALABAMA IN BIRMINGHAM CHAIR, DEPARTMENT OF MATHEMATICS Mathematics Applications and nominations are invited for the position Virginia Polytechnic Institute of chairperson of the department. Applicants should be & State University proven research mathematicians with a commitment to re­ Applications and nominations are invited for anticipated search and teaching and with leadership experience. The senior level position beginning September 1984. Candidates successful candidate will hold the position of professor in should have a demonstrated record of outstanding research the department, and should possess qualifications for this ability in an area of computational mathematics. This person rank. Salary commensurate with qualifications. 12-month should have expertise in areas such as numerical analysis, appointment to start September 1984. numerical solutions of differential equations, software, UAB is an urban university with a commitment to re­ hardware, and applications. The person chosen to fill this search and teaching. The department has 21 faculty mem­ position will have an unusual opportunity to aid in the bers and currently offers the B.S. and M.S. degrees. development of a program in computational sciences. Appli­ Applications will be accepted until the position is filled, cations accepted until position is filled. but to ensure proper consideration should be submitted by Applicants should send a resume and three letters of December 2 to Richard j, Crittenden or Robert M. Kauffman, recommendation to Bruce E. Reed, Assistant Chairman, Department of Mathematics, University of Alabama in Department of Mathematics, Virginia Polytechnic Institute Birmingham, University Station, Birmingham, AL 35294. & State University, Blacksburg, Virginia 24061-4097. For further information, please write to the above address The University is an Equal Opportunity/Affirmative or call either of the above at 205-934-2154. Action Employer. UAB is an affirmative action/equal opportunity employer.

692 POSITIONS AVAILABLE Faculty of Science Opening 1983/1984 THE INSTITUTE FOR ADVANCED STUDY Princeton, New Jersey 08540 An independent Arab University in the Israeli-occupied SCHOOL OF MATHEMATICS West Bank of jordan has the following faculty openings for The Institute for Advanced Study invites applications for a the academic year 1983/1984 in the field of: Mathematics, professorship in the School of Mathematics. Candidates preferred areas of specialization: Topology, Applied or pure must have distinguished records of achievement in mathe­ Mathematics, Algebra and Analysis, and Computer Science. matical research. The professors in the Institute's School of English is the basic language of instruction and candi­ Mathematics are collectively responsible for maintaining a dates should have a Ph.D. or a Master's Degree. Starting strong program of research through their own work and annual salary for Ph.D. 4414 J Ds., approximately $12,433, also by selecting a number of visiting members every year. and for Masters Degree 2680 J Ds., approximately $7,550. Applications, including curriculum vitae and list of publica­ Higher salaries are offered depending on experience. Fringe cations, should be addressed to Executive Officer, School benefits include air ticket and relocation allowance for new of Mathematics, Institute for Advanced Study, Princeton, faculty members, accident and health insurance, cost of New jersey 08540. An equal opportunity employer: women living coverage. and minority group members are encouraged to apply. All applications should include resume and be addressed to: ASSOCIATE EDITOR-MATHEMATICS-Springer-Verlag Dean of the Faculty of Science New York, Inc. is seeking an Associate Editor, Mathematics. Birzeit University Requirements include an undergraduate degree and some P.O. Box 14 graduate work in mathematics and a solid foundation in Birzeit research-oriented mathematics. Experience in publishing or West Bank teaching is desirable but nor required. Send r~sum~ to Via Israel Helen Salinger, Springer-Verlag New York, Inc., 175 Fifth Avenue, New York, N.Y. 10010. We are an affirmative action/equal opportunity employer. LOUISIANA STATE UNIVERSITY CHAIRPERSON DEPARTMENT OF MATHEMATICS SYRACUSE UNIVERSITY Department of Mathematics Applications and nominations are invited for the position of chairperson of the Department of Mathematics. The Chair­ Applications are invited for several tenure-track renewable person is the chief administrative officer of the Department positions effective 1 September 1984. Strong research poten­ and has responsibility for all aspects of the departmental work. tial is of primary importance, teaching ability is essential, Candidates should have a strong record of research, a com­ and the Ph.D. is required. Preferred research areas include mitment to excellence in teaching, and should be able to statistics, numerical analysis, and any of the specialties with­ effectively administer a large department within a state uni­ in the broad area of analysis; other areas compatible with versity. the research activity in the department will be considered. The position will commence in August 1984. Applications Candidates should send a detailed vita, and arrange to have should include a curriculum vitae and names and addresses of three letters of reference and a transcript sent to Professor at least three references. Applications will be accepted until L. ). Lardy, Chairman, Department of Mathematics, Syracuse the position is filled, but to insure consideration, applications University, Syracuse, New York 13210. Syracuse University should be submitted by December 1, 1983. Applications and is an affirmative action equal opportunity employer. nominations should be submitted to: Chairperson Search Committee, Department of Mathematics, Louisiana State UNIVERSITY OF SOUTH CAROLINA University, Baton Rouge, LA 70803. Applications are invited for faculty positions in mathe­ LSU is an Affirmative Action/Equal Opportunity Employer. matics, applied mathematics, and statistics, starting Fall 1984. Ph.D. degree with strong research potential and dedication to teaching at undergraduate and graduate level required. COMPUTER SCIENCE Candidates should send vita and arrange for four letters of UNIVERSITY OF MARYLAND BALTIMORE COUNTY recommendation to be sent to Dr. William T. Trotter, Jr., The UMBC Mathematics and Computer Science Depart­ Chairman, Department of Mathematics and Statistics, Univer­ ment anticipates having several tenure-track and tenured sity of South Carolina, Columbia, SC 29208. AA/EOE. faculty positions at the assistant, associate, or full professor level beginning September 1984. Candidates should have Ph.D. STATISTICS in computer science or in a closely related field, demon­ UNIVERSITY OF MARYLAND BALTIMORE COUNTY strable research potential, and strong ability to teach a broad The UM BC Mathematics and Computer Science Depart· range of basic computer science courses and graduate courses ment invites applications for positions at the assistant, asso· in one's field of specialty. The Department offers a B. A. ciate, and full professor levels beginning September 1984. program in mathematics, a B.S. program in computer science, Candidates should have Ph.D., strong teaching ability and M.S. and Ph.D. programs in applied mathematics. Current demonstrable research potential in either mathematical or graduate course offerings are grouped in the following areas: applied statistics. The Department offers a B. A. program in applied analysis, computer science, control systems, numerical mathematics, a B.S. program in computer science, M.S. and analysis, operations research, statistics and probability. Appli­ Ph.D. programs in applied mathematics. Graduate programs cations should be received by I anuary 15, 1984. Send a in Statistics are under deve!opment. Applications should be curriculum vitae, reprints and/or preprints, name of at least received by January 15, 1984. Send a curriculum vitae, re­ three references to: Richard C. Roberts, Chairman, Depart­ prints and/or preprints, names of at least three references to: ment of Mathematics and Computer Science, University of Richard C. Roberts, Chairman, Department of Mathematics Maryland Baltimore County, Catonsville, Maryland 21228. and Computer Science, University of Maryland Baltimore Telephone 301-455-2405. EQUAL OPPORTUNITY/ County, Catonsville, Maryland 21228. Telephone 301-455·2405. AFFIRMATIVE ACTION EMPLOYER. EQUAL OPPORTUNITY/AFFIRMATIVE ACTION EMPLOYER.

693 POSITIONS AVAILABLE Department of Mathematics THE OHIO STATE UNIVERSITY The Ohio State University The Department of Mathematics of the Ohio State Univ­ Department of Mathematics ersity hopes to fill several positions at all ranks, both visiting Research Instructorships in Mathematics and permanent, effective Autumn Quarter 1984. Candidates in areas of applied and pure mathematics are invited to apply. Applications are invited for the position of research in­ Significant research accomplishments or exceptional research structor in mathematics for the academic year 1984/1985. promise and evidence of good teaching ability will be expected Candidates should hold a Ph.D. (or equivalent) in mathe­ of successful applicants, matics and show strong research promise. The position is Please send credentials and have letters of recommendation renewable up to two additional years. sent to Professor Alan Woods, Department of Mathematics, Please send credentials and have letters of recommenda­ The Ohio State University, 231 W. 18th Avenue, Columbus, tion sent to Professor Alan Woods, Department of Mathe­ Ohio 43210. Review of resumes will begin immediately. matics, The Ohio State University, 231 W. 18th Avenue, The Ohio State University is an Equal Opportunity/ Columbus, Ohio 43210. The Ohio State University is an Affirmative Action Employer. Equal Opportunity/Affirmative Action Employer.

DEPARTMENT OF MATHEMATICS UNIVERSITY OF TORONTO KANSAS STATE UNIVERSITY Department of Mathematics Tenure-track position at the Assistant Professor level for the Toronto, Canada M5S 1A1 academic year 1984-1985. Salary commensurate with ability, The Department of Mathematics, University of Toronto, Candidates must have demonstrated research ability in global is looking for strong applicants to nominate as candidates analysis and the use of differential geometry and topology for NSERC Research Fellowships. These are five-year research for the study of problems in analysis or theoretical physics, positions (subject to a review in the third year) with a pos­ Commitment to excellence in teaching is expected. A Ph.D. sible teaching load of at most one course per year. In mathematics or equivalent required. Starting date: August The Fellowships are Intended primarily for mathematicians 13, 1984; Closing date: January 31, 1984. Contact: Depart­ of any age (with a relatively recent doctorate) who have dem­ ment Head, Department of Mathematics, Kansas State Univer­ onstrated their ability with some substantive post thesis re­ sity, Manhattan, KS 66506; (913) 532-6750. KSU is an search accomplishment, Nominees should be Canadian citizens AA/EOE. or landed immigrants at the time of application. Candidates should send an up-to-date curriculum vitae Tenure-track position at the Assistant Professor level for the and a short description of their research program to the academic year 1984-1985. Salary commensurate with ability. Department, and arrange to have sent three letters of refer­ Candidates must have demonstrated research ability in num­ ence. This material should arrive before Friday, October 7, ber theory. Some areas of particular interest arc the applica­ 1983. The Department's choice of candidates will be made tion of dynamical systems to number theory and sequences in early October, and the final decision by NSE RC is of integers. A broad background in algebraic number theory announced (by NS ERC) in the spring. is also desirable. Commitment to excellence in teaching is expected. A Ph.D. in mathematics or equivalent required. Starting date: August 13, 1984; Closing date: January 31, THE CHINESE UNIVERSITY OF HONG KONG 1 984. Contact: Department Head, Department of Mathe­ Department of Mathematics matics, Kansas State University, Manhattan, KS 66506; (913) 532-6750. KSU is an AA/EOE. Applications are invited for the following posts: Lecturer in Mathematics (2 posts) (ref. 37/509/2/83)- Ten­ APPLIED MATHEMATICS able from January 1 and August 1, 1984 respectively. Appli­ TRINITY UNIVERSITY cants should possess a Ph.D. degree in Mathematics. In ad­ Trinity University invites applications and nominations dition to participation in the activities of the Board of Studies in Mathematics, the appointees are expected to for a tenure-track position in applied mathematics at the rank of Assistant Professor, appointment beginning August, undertake research in their field of specialization and be responsible for teaching at the undergraduate and post­ 1984. Responsibilities include teaching nine credit hours per semester, continuing scholarly activity, developing and ex­ graduate level. panding applied mathematics offerings as appropriate to the Annual Salary: needs of the department and the university, interacting in a Lecturer: HK$135,780-154,140 by 2 increments BAR creative way with other departments and programs, advising HK$163,260-277,100 by 7 increments and the usual committee service. Exchange rate approximately: US$1 = HK$7.5, £1=HK$11 Minimum qualifications are the Ph.D. in mathematics, Starting salary will depend on qualifications and experience. applied mathematics or operations research, training and/or Conditions of Service: Benefits include sick leave, vacation experience in discrete mathematics, excellence in and strong leave, long leave with pay, superannuation (University 15%, commitment to teaching. Salary is $23,000 to $24,000. appointee 5%), medical benefits, education allowance for Trinity University is one of the thirty most heavily children and housing allowance for those whose annual salary financed private institutions in America. Founded in 1869, is $144,960 or above, and for appointees on overseas terms, it occupies a modern campus overlooking the San Antonio passage benefits for themselves and their dependents as well. skyline. Purposely small and selective, with about 3000 stu­ dents, Trinity stresses a high quality, largely undergraduate Application Procedure: Applications should be made out in liberal arts program. duplicate, giving full particulars, experience and the names Send vita, transcripts and three letters of reference to and addresses of three persons to whom reference may be Donald F. Bailey, Department of Mathematics, Trinity Univ­ made, and sent together with copjes of certificates/diplomas/ ersity, San Antonio, Texas 78284. Closing date for applica­ testimonials and recent publications to the Personnel Section, tions is February 25, 1984. The Chinese University of Hong Kong, Shatin, N. T. Hong Trinity University is an equal opportunity, affirmative Kong (quoting ref. 37/509/2/83) not later than October 31, action employer. 1983. Please mark' Recruitment' on cover.

694 POSITIONS AVAILABLE UNIVERSITY OF FLORIDA ANNOUNCEMENT OF VACANCY UNIVERSITY OF LOUISVILLE DEPARTMENT OF MATHEMATICS ASSOCIATE PROFESSOR OR PROFESSOR Applications are invited for a full professorship/senior DEPARTMENT OF MATHEMATICS associate professorship available August 1984. This position CHAIRPERSON. The University of Louisville, Department requires a record of substantial research accomplishment and of Mathematics is seeking an established person to be De­ teaching experience. Outstanding candidates in all areas of partment Chairperson. Candidates should have an active re­ mathematics will be given serious consideration. Departmen­ search program and other scholarly interests, interest in tal preferred research specialties include: partial differential undergraduate and graduate (Master's and Ph. D.) program equations, numerical analysis, theoretical computer science, development and evidence of the ability to administer a combinatorics, and related areas. The academic year salary growing department. A doctorate in Mathematics is required. for this position is highly competitive. Depending upon experience, the appointment will be at the Applicants should provide a resume, a list of publications, Associate Professor or Professor level. Interested candidates selected papers, and should arrange for five letters of refer­ should send a letter of application with vitae and at least ence to be sent to: three letters of recommendation to Michael S. jacobson, Chairman, Senior Search and Screen Committee Chair, Search Committee, Department of Mathematics, Uni­ Department of Mathematics versity of Louisville, Louisville, Kentucky 40292. Considera­ University of Florida tion will begin on December 1, 1983 and continue until the Gainesville, Florida 32611 position is filled. AA/EOE Application deadline is january 10, 1984. The committee urges early application. OREGON STATE UNIVERSITY Department of Mathematics UNIVERSITY OF WISCONSIN-MADISON, MATHEMAT­ Corvallis, Oregon 97331 ICS DEPARTMENT, VAN VLECK HALL, 480 Lincoln Drive, Madison, WI 53 706. The Department of Mathematics Associate Professor of Mathematics in Numerical Analysis solicits applications from Logicians of established excellence with preference for interaction with applied research groups; for a possible Assistant Professor appointment commencing extra funding may be available for interaction with a materi­ in the Fall of 1984. Applications should be sent no later als research group. Also Assistant Professor(s) of Mathemat­ than December 1, 1983 to Professor J. Marshall Osborn, Ch., ics: will consider all areas. Salary, teaching load, etc. nego­ Department of Mathematics (address above). The University tiable depending on qualifications and activities. First closing of Wisconsin is an Equal Opportunity Employer. date: january 15, 1984. Start September 16, 1984. Please write to: MATHEMATICS/COMPUTER SCIENCE Professor P.M. Anselonc, Acting Chairman ASSISTANT PROFESSOR Department of Mathematics Oregon State University CONNECTICUT COLLEGE is a very selective, coeducational, Corvallis, OR 97331 private, liberal arts institution (1600 students) located on Long Island Sound midway between New York City and Oregon State University is an Affirmative Action/Equal Boston. We invite applications for this regular position from Opportunity Employer and complies with Section 504 of Ph.D.'s committed to scholarship and teaching (3 courses the Rehabilitation Act of 1973. per semester). The teaching comprises courses in introductory and advanced computer science and mathematics. Our com­ UNIVERSITY OF NATAL, DURBAN puter resources include a PRIME 55011, a PDP11/44(UNIX), Department of Mathematics and Applied Mathematics and several micros. A starting date of either 1/84 or 9/84 Applications are invited from suitably qualified persons re­ is acceptable. Send resume and 3 letters of recommendation gardless of sex, religion, race, colour or national origin for to: S. Wertheimer, Chairman, Mathematics Department, Box appointment to the post of Lecturer/Senior Lecturer. 1614, Connecticut College, New London, CT 06320. Salary in the range: R12 657-R24 045 per annum An Equal Opportunity Employer The commencing salary notch will be dependent on the qualifications and/or experience of the successful applicant. Department of Mathematics In addition, a service bonus of 93% of one month's salary University of Kansas is payable annually. Application forms, further particulars ?f the post and information on pension, medical aid, group Applications and nominations arc invited for two or more Insurance, staff bursary, housing loan and subsidy schemes, tenure-track positions at the Assistant and Associate Pro­ long leave conditions and travelling expenses on first appoint­ fessor level beginning August 16, 1984, or as negotiated. m~mt arc obtainable from the Registrar, University of Natal, Field is unrestricted, but for one position preference will Kmg George V Avenue, Durban, 4001, South Africa, with be given to algebra. Otherwise, candidates whose interests whom applications must be lodged not later than 30 Novem­ mesh well with the department's needs are preferred. ber 1983. Requires Ph.D. or doctoral dissertation accepted with only formalities to be completed. Mathematics Computer Science: Tougaloo College, Tougaloo, Send detailed resume with description of past and present Mississippi has a tenure-track position available for a mathe­ research, and arrange for three letters of recommendation matician. Desirable to have a Ph.D. in Algebra, Applied Mathe­ to be sent to C. J. Himmel berg, Chairman, Department of matics or in Statistics. However, a master's degree in mathema­ Mathematics, University of Kansas, Lawrence, KS 66045. tics or Ph.D. in other related area will be considered. Position Deadline: December 15, 1983, for first consideration, then will be filled for the fall semester of 1983. Rank and salary will February 1, 1984, then monthly until the search is ended. be made commensurate with experience and degree. Please Complete job description will be sent on request. send application letter, Resume, college placement files, or The University of Kansas is an EO/AA employer. three letters of recommendation and an unofficial transcript to Glake Hill, Department of Mathematics and Computer Science, Tougaloo College, Tougaloo, Mississippi 39174. A member of the United Negro College Fund and Equal Oppor­ tunity/Affirmative Action Employer.

695 NEW JOURNAL American Mathematical Society QUESTIONS AND ANSWERS IN GENERAL TOPOLOGY A Newly Founded International journal Translators Wanted Devoted to rapid publication of questions and answers in general topology. Information for subscribers and contribu· tors, list. of contents of the initial issue, etc., are available by writing to Professor jun·iti Nagata (Symposium of General The fee paid by the Society for produc­ Topology), Department of Mathematics, Osaka Kyoiku Uni· ing acceptable typewritten translations of versity, Tennoji, Osaka, 543 japan. Russian mathematical papers has recently MISCELLANEOUS risen from an average of $9 per Russian page to $13 per Russian page. For qualified Inventions, ideas, technology wanted! Industry presentation/ mathematicians wishing to take advantage national exposition. 1·800-528-6050. X831. of this increase the distribution of need FOR SALE according to subject classification is as follows. MATH SCI PRESS, 53 jordan Rd., Brookline, MA 02146, The most heavily trafficked area is 617-738-0307. Announcing new series: SYSTEMS, INFOR­ differential equations, especially PDE. The MATION AND CONTROL. First volume: Geometry and identification workshop, Eds., P. Caines and R. Hermann; $23. best prepared translators will be familiar SALE: 40% reduction on titles in Lie Groups and Interdisci­ with applications of Schwartz distribu­ plinary Mathematics series. List in Oct. '82 Notices. tions, as well as recent research on pseudodifferential operators. Contributions to the global theory are also beginning to appear. Other areas in which good translators are needed are logic and computer science (much of the work involves recursion theory and algorithms), number theory (both analytic and algebraic), ring theory (including homological methods and K­ theory), algebraic geometry, nonassociative algebras (mostly Lie algebras and Jordan New Department of Statistics at algebras), group theory (discrete and the University of British Columbia topological), several complex variables, integral equations, differential geometry A new Department of Statistics ·has been (mostly global theory), optimization and established at the University of British mathematical programming, statistics, and Columbia, Vancouver, offering various numerical analysis. In applications the programs including those leading to the most prominent areas are elasticity and M.Sc. and Ph.D. degrees. fluid mechanics. The initial faculty consists of the Areas that are already well covered statisticians formerly in the Department of involve classical analysis and functional Mathematics, namely F. P. Glick, H. Joe, analysis, i.e. greater or lesser portions of A. W. Marshall (acting head), S. W. Nash the categories 26-XX, 28-XX, 30-XX, 40- (emeritus), A. J. Petkau, N. M. Reid, M. :XX:, 42-:XX:, 44-:XX:, 46-:XX:, 47-:XX: in Schulzer, and J. V. Zidek. Visitors for the subject classification scheme used by 1983-1984 include D. B. H. Cline (Texas Mathematical Reviews. A&M) and P. C. Sander (Eindhoven). Interested applicants are asked to respond to the Translations Department, Teaching and research assistantships are American Mathematical Society, Post available for graduate students. Office Box 6248, Providence, RI 02940 Inquiries should be directed to: with a specific description of their area of mathematical competence. A brief trial Head, Department of Statistics excerpt will then be sent by which the University of British Columbia applicant can demonstrate the combina­ 2075 Wesbrook Mall tion of such competence with the requisite Vancouver, British Columbia language skills. V6T 1W5 Canada

696 Employment Information in the Mathematical Sciences

Subscription Form for Institutional Subscribers

The American Mathematical Society, the Mathematical Association of America and the Society for Industrial and Applied Mathematics publish Employment Information in the Mathematical Sciences five times each academic year. The November, January, March, May, and August issues are devoted to listings of open positions. In addition, a subscription to ElMS includes an extra issue (December) prepared for the convenience of employers who participate in the Employment Register at the January meeting; it contains resumes of job applicants. On preprinted forms mailed every other month, department heads are asked to provide information (by a specified deadline) on open positions, or to state that there are none. The announcement that no positions are open may relieve the department of the obligation to answer letters from applicants, thus decreasing the burden of correspondence. Each issue contains descriptions of open positions in academic departments in the U.S. and Canada, a list of academic departments who have responded that they have no open positions, a list of academic departments not included above, descriptions of government, industrial and other nonacademic positions in the U.S. and Canada, as well as descriptions of positions available in foreign countries. The following resolution was passed on October 25, 1974, by the Council of the American Mathematical Society: "The Council of the AMS adopts the principles that all positions in the mathematical sciences shall insofar as practicable be advertised, and that the standard place for the advertisements to appear is the publication Employment Information." A similar resolution was subsequently approved by the Board of Governors of the Mathematical Association of America. Institutions may enter subscriptions at any time during the subscription year. The subscription will expire with the August issue. The chart below gives subscription prices and deadlines for orders. The first price (Type A) is the price charged to U.S. universities with the 39 departments of mathematics ranked highest in the 1982 Assessment of Research-Doctorate Programs (Group I, page 393, June 1983 Notices). The second price (Type B) is the price charged to other universities in the U.S. and Canada offering doctoral degrees in the mathematical sciences, and to nonacademic institutions in the U.S. and Canada. The third price (Type C) is the price charged to all other universities and colleges and all foreign institutional subscribers. Issues are sent by first class mail to subscribers in the United States, Canada and Mexico. Issues are sent by air mail to other countries. ($2 postal surcharge per issue.)

All subscriptions will end with the August 1984 issue.

Starting Issue Deadline for Issue Price Price Price Date Number Orders mailed Type A TypeB Type C November 1983 67 10/13/83 11/4/83 $120.00 $100.00 $90.00 January 1984 68 12/15/83 1/10/84 96.00 80.00 72.00 March 1984 69 2/15/84 3/7/84 72.00 60.00 54.00 May 1984 70 4/13/84 5/9/84 48.00 40.00 36.00 August 1984 71 7/13/84 8/1/84 24.00 20.00 18.00

Prepayment is required. No subscription will be entered until payment is received. If payment is received after the deadline, the subscription will be entered to begin with the next issue, and a refund for the overpayment will be sent. Institutions who subscribe to ElMS before November 15 will receive a copy of the extra December issue at no charge. No back issues can be supplied. Make checks payable to the American Mathematical Society and mail to Post Office Box 1571, Annex Station, Providence, Rhode Island 02901.

Ordered by: Ship to:

Institution Department Address City State/Province Postal Code/Country Order Amount Dat,.,______submitted by______enclosed $ ______

697 Employment Information in the Mathematical Sciences

Subscription Form for Individual Subscribers

The American Mathematical Society, the Mathematical Association of America and the Society for Industrial and Applied Mathematics publish Employment Information in the Mathematical Sciences five times each academic year. The November, January, March, May, and August issues are devoted to listings of open positions. In addition, a subscription to ElMS includes an extra issue (December) prepared for the Employment Register at the January meeting; it contains resumes of job applicants. On preprinted forms mailed every other month, department heads are asked to provide information (by a specified deadline) on open positions, or to state that there are none. A statement that no positions are available may relieve the department of the obligation to answer letters from applicants, thus decreasing the burden of correspondence. Each issue contains descriptions of open positions in academic departments in the U.S. and Canada, a list of academic departments who have stated they have no open positions, a list of academic departments not included above, descriptions of government, industrial and other nonacademic positions in the U.S. and Canada, as well as descriptions of positions available in foreign countries. The following resolution was passed on October 25, 1974 by the Council of the American Mathematical Society: "The Council of the AMS adopts the principles that all positions in the mathematical sciences shall insofar as practicable be advertised, and that the standard place for the advertisements to appear is the publication Employment Information." A similar resolution was subsequently approved by the Board of Governors of the Mathematical Association of America. Five issues are to be published during the 1983-1984 academic year, beginning with the November issue. Subscription rates are prorated for late orders. Single copies are not available except for the final issue, and back issues are not available. The chart below gives complete information on individual subscription rates. Issues are sent by first class mail to subscribers in the United States, Canada, and Mexico. Issues are sent by airmail to other countries.

FIRST CLASS MAIL AIRMAIL U.S., Canada, Mexico Other Countries Beginning with Employed Special* Employed Special* Deadline for orders Issue mailed November 1983 $ 35.00 $ 18.00 $ 45.00 $ 28.00 October 15, 1983 November 4, 1983 January 1984 30.00 15.00 38.00 23.00 December 15, 1983 January 10, 1984 March 1984 25.00 13.00 31.00 19.00 February 15, 1!!84 March 7, 1984 May 1984 20.00 10.00 24.00 14.00 April 13, 1984 May 9, 1984 August 1984 15.00 8.00 17.00 10.00 July 13, 1984 August 1, 1984

All individual subscriptions expire with the August issue. Individuals who subscribe to ElMS before November 15 will receive a copy of the extra December issue at no charge. Prepayment is required. Make checks payable to the American Mathematical Society and mail to Post Office Box 1571, Annex Station, Providence, Rhode Island 02901. Check one Amount Enclosed ( ) Individual rate, begin with issue: ______$______( ) Student/unemployed rate*, begin with issue: ______$______

Please Print Name: ______Address ______

City ______State/Province,______Country ______Postal Code: ______

*To qualify for this rate please complete the following form (check one): [ ] I am currently unemployed and actively seeking employment. My unemployed status is not the result of voluntary resignation or retirement from my last position. I am not enrolled in a graduate study program.

OR, [ ] I am a full-time student enrolled in a program leading to a degree or diploma at------

(signature)

698 WADSWORTH ADvANcED ]BooK )P-RoGRAM

ANNOUNCES:

COMPLEX ANALYSIS AND APPLICATIONS, Second Edition William Derrick, University of Montana The extensive revision of this undergraduate text for mathematics, engineering, and physics students features an early introduction to complex integration and a wide choice of applications, including optics, jet flows, and wakes as well as the traditional applications. Each selection contains many worked examples. Solutions to the odd-numbered problems are presented in the back of the book. Complimentary copies are available for adoption consideration. CONTENTS: 1. Analytic Functions Complex Numbers and their Algebra o Polar Representation o Sets in the Complex Plane o Continuous Functions of a Complex Variable o Necessary Conditions for Analyticity D Sufficient Conditions for Analyticity o The Complex Exponential o Complex Trigonometric and Hyperbolic Functions D Complex Logarithms and Power Functions o Applications in Optics 2. Complex Integration Line Integrals o Green's Theorem and its Consequences o The Cauchy Integral Formula o Liouville's Theorem and the Maximum Principle o The Cauchy-Goursat Theorem (Optional) 3. Infinite Series Taylor Series o Uniform Convergence of Series o Laurent Series o Isolated Singularibes o Analytic Continuation (Optional) 4. Contour Integration The Residue Theorem o Evaluation of Definite Real Integrals o Evaluation of Improper Real Integrals o Integrals with Poles on the Real Axis o Integration of Multivalued Functions (Optional) o The Argument Principle 5. Conformal Mappings Geometrical Considerations o Linear Fractional Transformations o The Symmetry Principle o Compositions of Elementary Conformal Mappings o Fluid Flow o The Schwarz-Christolfel Formula D Heat Flow and Electrostatics (Optional) D Wakes in a Fluid Flow (Optional) 6. Boundary Value and Initial Value Problems Harmonic Functions o Dirichlet's Problem D Applications o Fourier Series o Fourier Transforms D Laplace Transforms D The Inverse Laplace Transform Other texts available for adoption consideration: INTRODUCTION TO CLASSICAL REAL ANALYSIS Karl Stromberg, Kansas State University Advanced undergraduate introduction to analysis. APPLIED MATHEMATICS lames Cochran, Washington State University Beginning graduate-level text for mathematicians, engineers, and physicists. ELEMENTARY MATHEMATICAL ANALYSIS, Second Edition Colin Clark, University of British Columbia Undergraduate text for beginning analysis, analysis for secondary teachers. INTRODUCTION TO MATHEMATICAL LOGIC, Second Edition Elliott Mendelson, Queens College of CUNY Advanced introduction to logic. INTRODUCTION TO LOGIC Patrick Suppes, Stanford University Undergraduate text. Wadsworth International Group 10 Davis Drive e Belmont CA 94002

699 Springer-Verlag Your Bridge to Modern Chinese Science

To overcome the iriformation gap which has existed for more than thirty years between science in China and science in the rest ofthe world, Springer-Verlag- the first western publisher to do so - has published books in selected areas by Chinese scientists. Please take advantage ofthis unique opportunity to learn more about China's progress in the world ofscience.

Hua Loo-Keng HsuPao-Lu Hua Loo-Keng Introduction to Collected Papers Selected Papers Editor: K L. Chung Editor: H. Halberstam Number Theory With the collaboration of Translated from the Chinese by P. Shiu Cheng Ching-Shiu, Chiang Tse-Pei 1983. 14 figures. XIV, 889 pages Cloth US $ 42.00. ISBN 0-387-90744-0 1982. 14 figures. XVIII, 572 pages 1983. 11 figures. XII, 589 pages Cloth US$ 46.00. ISBN 0-387-10818-1 Cloth US$ 48.00. ISBN 0-387-90725-4 The voluminous Selected Papers reflect Hua's wide perspective and contain many " ... When Hua's book appeared, it was Hsu-Pao-Lu (1910-1970) was one of the hailed by the one or two of my acqain­ little known papers - in part original 20th century's most profound and original translations from the Chinese and tances who could read it as a riv-.U to statisticians. This volume contains several Hardy and Wright A copv has stood published in the West for the first time in papers which were published only in this edition. unreadable on my shelves for a quarter of Chinese journals and have so far been a century, but only now, with the appear­ unavailable in the West ance of this excellent translation, can I learn what it contains .... The exposition Hua Loo-Keng In preparation: is admirably clear.... " J. W.S. Cassels in Starting with the The Mathematicallntelligencer Unit Circle Hou Zheng-Ting, Kou Tzing-Fang Background to Higher Analysis Translated from the Chinese Homogeneous by Kuniko Weltin Denumerable 1981. 6 figures. XI, 179 pages Cloth US$ 32.00. ISBN 0-387-90589-8 Markov Processes " ... most readers will find something they ISBN 0-387-10817-3 do not know in this book and most of the material was new to me.... This reflects Wang Tsu-Kwen the fact that the author has dominated Chinese mathematics in a very original Birth and Death manner for the last 30 years .... The book is certainly stimulating ... " Processes and W.KHayman in Bulletin of the Markov Chains London Mathematical Society ISBN 0-387-10820-3 Hua Loo-Keng, Wang Yuan Applications of Jiang Tsa-Han Number Theory to Fixed Point Theory Springer-Verlag Numerical Analysis ISBN 0-387-10819-X 1981. IX, 241 pages Berlin Cloth US$ 39.00. ISBN 0-387-10382-1 Zhu You-Lan, Zhong Xi-chang, Distribution rights for The People's Chen Bing-Mu, Zhang Zuo-Min Heidelberg Republic of China: Science Press, Beijing "This book is doubtless the first to devote Difference Methods for New York itself exclusively to number-theoretic Initial-Boundary-Value­ methods in numerical analysis ... The Tokyo presentation is exceptionally comprehen­ Problems and Tierg;ntonstr. 17, D-6900 Heidelberg I sive ... " Flow Around Bodies 175 Fifth Ave., New York, NY 10010, USA Translation from E. Hlawko's review 37-3, Hongo 3-chome, Bunkyo-ku, Tokyo 113, Japan in Zentrtalblattfiir Mathematik ISBN 0-387-10887-4

700 JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, SERIES B.

SPECIAL ISSUE ON WAVES IN FLUIDS

The issue contains 8 current research papers on water waves, linear and nonlinear, internal waves and Rossby waves. The authors are P. J. Bryant, D. H. Peregrine, R. J. Sobey and E. J. Colman, F. Viera and V. T. Buchwald, John W. Miles, N. T. Hung and S. A. Maslowe, Roger L. Hughes, and C. B. Fandry, R. L. Hughes and L. M. Leslie. It was compiled and edited by Roger Grimshaw. Date: July, 1983 (Volume 25, Part 1) Price for separate sale: U.S. $22, 144 pages. Order from the Business Manager, Australian Mathematical Society, Department of Mathematics, University of Queensland, St. Lucia, Queensland, 4067, Australia.

~~aa~a~aa~aaa~~~a The Naval Surface Weapons Center has an opening for an ENGINEER OR APPLIED MATHEMATICIAN I CALL FOR PAPERS I GS-12 $29,374-$38,185 DISCRETE MATHEMATICS is pleased to an­ The Naval Surface Weapons Center is offering an nounce that it is soliciting high quality papers for opportunity for an innovative professional to work a special issue devoted to Interval Graphs and Re­ in the Applied Mathematics Branch and to perform lated Topics, It is expected that this special issue research and development on computational fluid will bring together a large number of new and in­ dynamics problems such as: teresting ideas including generalizations of interval • Explosion aerodynamics and blast wave prop­ graphs and their applications. Some sample topics agation are the following: interval graphs and higher di­ • Turbulent and separated flows mensional interval graphs, boxicity, cubicity and • Internal and external missile/aircraft aerody­ spherical dimension, interval number, algorithmic namics complexity aspects, consecutive retrieval property • Conservation laws, random choice method and other applications, circular-arc graphs, toler­ and upwind schemes ance graphs and other intersection graphs. • Numerical analysis of singular perturbation Authors are invited to submit papers (in trip­ problems licate if possible) to Martin Charles Golumbic, IBM Recently graduated Ph.D's and Ph.D candidates Guest Editor- DISCRETE MATHEMATICS, are desirable. Israel Scientific Center, Technion City, Haifa, Israel. Technical questions may be addressed to Dr. T. The deadline for submitting papers to this Zien on (202) 394-2255. special issue is January 15, 1984. All papers will Interested applicants may submit resume (or be refereed according to the usual high standard SF-171 if current or reinstateable Federal Govern­ of excellence of DISCRETE MATHEMATICS. ment employee) no later than 30 Nov. 1983 to: Authors will be notified by June 1, 1984 of the Naval Surface Weapons Center status of their papers. ATTN: E. K. Man (Code P40) White Oak, Silver Spring, MD 20910 AA/EOE - U.S. Citizenship Required ~sasssssssssssssa

701 MATHEMATICAL SCIENCES RESEARCH INSTITUTE BERKELEY, CALIFORNIA

The Institute will begin its third year of operations in August 1984, and we solicit applications for memberships in the Institute for the 1984-85 year. Memberships with partial or full fellowship sup­ port can be for any period of time ranging from a few months to the entire year; postdoctoral fellow­ ships for new or recent PhDs are generally for the entire year. and we expect to award up to 30 such postdoctoral fellowships. Postdoctoral fellowship awards for a two year period, 1984-86, are also possible. It is hoped and expected that members at the more senior level will come with partial or full support from other sources, including sabbatical leave and other fellowships. There will be two main programs during the 1984-85 year: low dimensional topology; and K theory, index theory, and operator algebras. Although these two areas will receive emphasis, we expect to make a significant number of awards outside of these areas, distributed over all fields of the mathemati­ cal sciences. There will also be a "miniprogram" in differential geometry. We emphasize that applications from candidates in all fields are welcomed. Low Dimensional Topology. The program committee consists of Robert Edwards (Chairman). Robion Kirby, and William Thurston. Topics include maps and automorphisms of surfaces, the geometry and geometries of 3 and 4-dimensional manifolds. various kinds of structures on such manifolds, group actions on low dimensional manifolds, and progress toward classification. K Theory, Index Theory, and Operator Algebras. The program committee consists of Alain Connes (Chairman), Ronald Douglas. and Masamichi Takesaki. Topics include the link of measure theor­ etic invariants of the transverse structure of a foliation with von Neumann algebras, index theorems linking analytically defined K-theoretical invariants with topological invariants, and finally noncommuta­ tive homology, algebraic K theory, and connections with mathematical physics. Miniprogram in Differential Geometry. We plan a continuing level of activity through the year under the general direction of S.S. Chern with anticipated visits for periods of two months each by Marcel Berger, Jeffrey Cheeger, Mikhael Gromov, and Blaine Lawson, together with others.

Address inquiries, suggestions, and applications to Calvin C. Moore, Deputy Director, Mathematical Sciences Research Institute. 2223 Fulton St., Room 603, Berkeley, California 94720. Applicants' files should be completed by January 1. 1984. Programs for 1985-86 are Computational Complexity (Program Committee ·- Richard Karp, Stephen Smale, Ronald Graham) and Mathematical Economics (Program Committee -- Gerard Debreu, Kenneth Arrow, Andreu Mas-Colell). The Institute welcomes suggestions from the mathematical sciences community for programs or miniprograms for future years.

The Institute is committed to the principles of Equal Opportunity and AffirmatiJ'e Action

702 INSTITUTE FOR MATHEMATICS AND ITS APPLICATIONS UNIVERSITY OF MINNESOTA

CONTINUUM PHYSICS AND PARTIAL DIFFERENTIAL EQUATIONS September 1, 1984-August 31,1985

First half: Equilibrium and Stability Questions - Incompletely posed problems, transition of phase, instability. Second half: Dynamical and Evolutionary Considerations - Dynamical behavior of materials under the influence of heat, electromagnetic fields, diffusion, or other fields. SCIENTIFIC COMMITTEE: Haim Brezis, Universite de Paris Constantine Dafermos, Brown University Jerry Ericksen*, University of Minnesota David Kinderlehrer*, University of Minnesota (*)Program Coordinators ***VISITING MEMBERSHIPS AVAILABLE*** POST-DOCTORAL MEMBERSHIPS will carry a stipend of $26,000, including $1000 for relocation expenses, for the 12-month period beginning September 1, 1984. All requirements for a doctorate should be completed by this date. SABBATICAL SUPPORT MEMBERSHIPS will provide partial support for periods from 3 to 12 months. Applicants must show evidence of mathematical excellence, but they do not need to be specialists in the field or even "applied mathematicians." Core mathematicians who are inter­ ested in studying applications are especially welcome. The following materials must be submitted: (i) Personal statement of scientific interests, research plans, and reasons for wishing to participate in the Institute program. (This is an essential part of the application.) (ii) Curriculum vitae including a list of publications (iii) Three letters of recommendation All material should be received by January 15, 1984 Some support is available for shorter visits. All correspondence should be sent to: Hans Weinberger, Director Institute for Mathematics and its Applications University of Minnesota 206 Church Street S. E. Minneapolis, Minnesota 55455 U.S.A. Telephone: (612) 373-0355 The University of Minnesota is an equal opportunity educator and employer and specifically invites and encourages applications from women and minorities.

703 PUBLICATIONS FROM L'ENSEIGNEMENT MATHEMATIQUE GENEVA EM NEW N

P. Erdos and R. L. Graham: OLD AND NEW PROBLEMS AND RESULTS IN COMBINATORIAL NUMBER THEORY 128 pages, 1980; 40 Swiss Francs. An extensive collection of open problems in elementary number theory, many of them with a com­ binatorial flavor, together with a detailed bibliography and a progress report on a previous set of prob­ lems.

THEORIE ERGODIQUE Proceedings of a Seminar Lectures by P. Arnoux, P.-L. Aubert, P. de Ia Harpe and K. Jhabvala, M. Misiurewicz, C. Series, B. Weiss. 112 pages, 1981; 38 Swiss Francs. Provides an introduction to a few chapters of ergodic theory in connection with interval exchange transformations, SL2 (Z) and Fuchsian groups, geometry of the plane, variational principle, con­ tinued fractions and orbit equivalence.

LOGIC AND ALGORITHMIC - An International Symposium held in Honour of Ernst Specker Lectures by H. Wang, W. Baur and M. Rabin, A. Borodin, R. Bott, S. Cook, G. Coray, C. Elgot and J. Shepherdson, P. Erdos, M. Fischer and M. Paterson, M. Hirer, H. Gaifman, J.-Y. Girard, J. Heintz and C.-P. Schnorr, R. Karp and R. Lipton, S. Kochen and S. Kripke, S. Koppelberg, J. Paris and C. Dimitracopoulos, W. Paul, A. Prestel, A. Schonhage, L. Valiant, M. Ziegler. 392 pages, 1982; 95 Swiss Francs. This volume contains survey papers and original contributions by leading representatives of math­ ematical logic and the theory of algorithms, illustrating the fruitful interplay between these fields.

G. de Rham:

20% discount available on prepaid orders placed to L'Enseignement Mathematique EM POB 240, CH-1211 Geneva 24, Switzerland

704 1TO INSTRUCTORS OF ANALYTIC GEOMETRY AT ALL LEVELS .... S S S Announces .... A WORK THAT PROMISES TO REVOLUTIONIZE & REVITALIZE THE TEACHING & SUBJECT MATTER OF ANALYTIC GEOMETRY STRUCTURAL EQUATION GEOMETRY THE INHERENT PROPERTIES OF CURVES & COORDINATE SYSTEMS by J. Lee Kavanau, University of California, Los Angeles Targeted at today's critical problem areas in math instruction Intriguing new approaches, basic Penetrating new insights-to concepts & problems-to stimulate sharpen comprehension & teach- student interest & imagination ing skills of instructors ----- A UNIQUE SOURCEBOOK no geometry instructor can afford to be without Nov., 1983, 512 pages, 61 pages of figs., $16.95

Recommended to innovative instructors as a college I> text. Introduces Prof.Kavanau's companion treatises

705 RESEARCH OPPORIUNITIES Competitive visiting scholar awards for one or two years' tenure in selected federal laboratories throughout the United States. Opportunities are available for specialized experimental or theoretical research experience-free of interruptions and dis­ tractions of other duties-in the general fields of:

ATMOSPHERIC AND EARTH SCIENCES ENGINEERING • LIFE AND MEDICAL SCIENCES PHYSICS • CHEMISTRY ENVIRONMENTAL SCIENCES MATHEMATICS • SPACE SCIENCES Editors: Most of the 19 programs are open to U.S. and non-U.S. nation­ als, and most are open to experienced senior investigators as M.R. Herman, A.B. Katok, well as to recent PhDs. K. Schmidt, P. Walters Application materials with details on research opportuni­ ties and laboratory locations may be requested by letter, An international quarterly journal devoted to stating the specific area of research interest. to: publishing papers on the mathematical theory of Associateship Programs {JH608-M ) dynamics. It provides a focus for this important NATIONAL RESEARCH COUNCIL 2101 Constitution Avenue and rapidly developing area of mathematics, and Washington. D.C. 20418 an opportunity to bring together many major contributions in the field which are, at the moment, scattered over a large number of non­ a1 specialist periodicals. Survey articles, conference -A proceedings and book reviews are published. ~National Academy .... of Engineering._~ •Institute of Medicine Volume 2 (1982) of Ergodic Theory and Dy­ namical Systems featured a special issue ded­ icated to the memory of distinguished Soviet mathematician and specialist in celestial mechan­ ics, Vladimir Mikhailvoich Alexeyev (1932-1980). POSTDOCTORAL RESEARCH The issue contains a biography of Alexeyev/his APPOINTMENTS IN last article (completed after his death by one of his NONLINEAR MATHEMATICS students)/contributions from colleagues, students Los Alamos National Laboratory, one of the nation's and friends. foremost scientHic research organizations, is seeking candidates for our Postdoctoral Research Program. Exciting joint appointments are available between the newly created Center for Nonlinear Studies and the Please enter my subscription to Volume 3 (1983) of Theoretical Division. Areas of particular interest in­ Ergodic Theory and Dynamical Systems. clude: nonlinear analysis, nonlinear partial differential equations, soliton theory, reaction diffusion systems, D Regular Rate $150.00 D Also send me LJ Vol. I bifurcation theory, chaos and the onset of turbulence ll Vol. 2 at $137.50 each. and numerical analysis. Applications of these studies in hydrodynamic instabHities, polymer dynamics and bio­ physics are encouraged. Operated by the University of California for the Depart· Name ment of Energy, the laboratory provides excellent work· ing conditions and opportunities for advanced research. Address Our location in the mountains of Northern New Mexico offers a pleasant lifestyle in a setting of great natural beauty. City State Zip For further information please contact: Alwyn C Scott, Chairman D Special individual members' rate $85.00 Center for Nonlinear Studies I hereby certify that I am a bona fide member of the los Alamos National laboratory DIV 83-X American Mathematical Societv. MS·B258 los Alamos, New Mexico 87545 DVISA 0 MastcrCharge(lnterbank #---- (505) 667-1444 and request application forms from: Maxine Blake Card# Expiration Date los Alamos National laboratory MS·P205 Signature Prices good through 12/31/83 los Alamos. New Mexico 87545 Umvers1ty of California ------CAMBRIDGE ~~~ 11&!1&Jm~~i'miim0 ~ UNIVERSITY ~~.~~m~ An Affirmative Action/Equal Opportunity Employer: PRESS Women, Minorities, the Handicapped, and Veterans 32 East 57 Street Are Urged to Apply. U.S. Citizenship Required. New York. NY 10022

706 Explore new theories ~!!!!!!!!!!!!!!!!!!!! vvi th Wiley books !!!!!!!!!!!!!!!!!!!!!!!!!!!!•

INTEGRAL EQUATION METHODS FIRST COURSE IN LINEAR ALGEBRA IN SCATTERING THEORY P.B. Bhattacharya, University of Delhi, S.K. Jain, David Colton, Univenity of Delaware, and Ohio University, and S.R. Nagpaul, University Rainer Kress, Unit>ersity of Gottingen, Germany of Delhi The first comprehensive work in this area, here is a (0-27442-5) 1983 190 pp. $12.95 state-of-the-art survey of integral equation methods FUZZY MATHEMATICAL APPROACH IN in acoustic and electromagnetic scattering theory, in­ cluding both the direct and inverse problems. Special PATTERN RECOGNITION PROBLEMS attention is given to the use of integral equation S.K. Pal and D. Dutta Majumder, both of the methods to reformulate the inverse scattering prob­ Indian Statistical Institute, Calcutta lem a~ a problem in constrained optimization. Presents the major results of both theoretical and (1-86420-X) 1983 271 pp. $37 . .50 experimental investigations into the effectiveness of fuzzy algorithms as classification tools in pattern FUNCTION THEORY ON recognition and image processing. Important results PLANAR DOMAINS arc systematically compared to those obtained with A Second Course in Complex Analysis statistical classification techniques. Stephen D. Fisher, Northwestern Unit>enity (0-27463-8) Dec. 1983 350 pp. $29.9.5 A high-level treatment of complex analysis concen­ OPTIMIZATION METHODS IN trating on function theory on a finitely connected OPERATIONS RESEARCH planar domain. Emphasis is given to domains AND SYSTEMS bounded by a finite number of disjoint analytic ANALYSIS, 2nd Ed. simple closed curves. K. \~ Mital, University of Roorkee, India (1-87314-4) 1983 269 pp. $34.9.5 A practical introduction to the mathematical aspects of operations research and systems analysis for re­ COMBINATORIAL ENUMERATION searchers and student~. This revised edition now Ian P. Goulden and David M. jackson, both of treats integer programming and the Dual Simplex University of Waterloo, Ontario Method, in addition to basic coverage of linear and An encyclopedic account of the mathematical theory nonlinear programming, dynamic and geometric and problem-solving techniques associated with enu­ programming, direct search and gradient methods, meration problems for a range of discrete structures. and game theory. ''Substantial introduction to op­ Combining algebraic and combinatorial ideas, it of~ timization for researchers in engineering, economics, fers new insight into large classes of problems involv­ and computer science ... excellent set of exercises." ing distinguished substrings, dominance systems, (0-27391-7) 1983 328 pp. $17.95 -Choice graphs, lattice paths, linear transformations, MacMahonian statistics, J?lanar maps, and trees. COMPUTATIONAL MATHEMATICS (1-86654-7) 1983 569 pp. $47.50 An Introduction to Numerical Approximation STATISTICS ON SPHERES Terence R.E Nonweiler, Victoria University, Geoffrey S. Watson, Princeton University Wellington, NZ Presents the theory and application of statistics on A comprehensive, readable introduction to the basic spheres, including tests of spherical uniformity, principles underlying the use of numerical analysis in inference on spherical distribution, theory of non­ the context of machine calculations and microproces­ independent directions, spherical ··normality", sors. Algorithms are developed through practical, non-parametric approaches, and probability density real-world examples, and readers are encouraged to estimation. Applications range from the analysis of explore essential aspects of computational arithmetic, data arising in paleomagnetism and sedimentary function evaluation, interpolation, and numerical geology to the navigation of birds and bees and the quadrature through a large number of problems orbits of comets. employing calculators or computers. (1-88866-4) 1983 238 pp. $21.50 (0-27472-7) 1983 470 pp. $54.9.5 q-HYPERGEOMETRIC FUNCTIONS Order through your bookstore or write L. Sullivan, AND APPLICATIONS Dept. 4-1268. Harold Exton, Preston Polytechnic FOR FASTER SERVICE CALL TOLL FREE A unique book devoted exclusively to the theoretical 1800 526-5368, Order code #4-1268. and applied aspects of basic hypergeometric func­ In New Jersey, call collect {201) 342-1\707. VISA, tions. Unifies a wide range of important results from MasterCard, American Express accepted on phone orders. fields as diverse as mechanical engineering, solid state physics, Fourier analysis, operational calculus, JOHN WILEY & SONS, Inc. quantum theory and cosmology. 605 Third Avenue, New York, N.Y. 10158 (0-27453-0) 1983 355 pp. $49.95 In Canada: 22 Worcester Road, Rexdale, Ontario M9W ILl Prices subjt'Ct to change and higher in Canada. 092 4-1268

707 MATHEMATICAL SCIENCES EMPLOYMENT REGISTER Instructions for Applicant's Fonn on facing page The fonn. Applicants' forms submitted for the Employment Register at the Joint Mathematics Meet­ ings in Louisville will be photographically reproduced in the December issue of Employment Information in Some Mathematical Questions the Mathematical Sciences to appear in December 1983. in Biology- Neurobiology They will also be posted at the Employment Register. Robert M. Miura, Editor The forms must be carefully typed using a fresh black ribbon. The best results are obtained with a The six papers presented in this book deal with carbon-coated polyethylene film ribbon, but satisfac­ three different aspects of neurobiology-the morph­ tory results may be obtained using a ribbon made of ology of nerve cells, the analysis and study of action nylon or other woven fabric if suitable care is exer­ potential phenomena, and ion movements inside and cised. It is important that the keys be clean and make outside nerve cells. The papers are addressed to a sharp, clear impression. Do not erase--it causes biologists, especially physiologists and neuroscien­ smudges which reproduce when photographed. Use tists, and mathematicians who arc interested in the a correcting typewriter or correction tape or fluid if applications of mathematics to neurobiology. They necessary. Submit the original typed version only. should also appeal to others who have general inter­ Copies will not reproduce properly and are not accept­ ests in seeing the interactions between mathematics able. Hand lettered forms will be returned. and experimental neurobiology. Applicants' forms must be received by the Society The collection of papers contains experiments by December 5, 1983 in order to appear in the spe­ and theory working together and leads to a better cial issue of ElMS, and must be accompanied by the understanding of neurobiology. Most of the earlier Preregistration and Housing Form printed in this issue books in this series have concentrated mainly on of the Notices. See pages 711 and 712 in this issue for mathematics-a few on biology. Here there is a infonnation and instructions. Fonns received past the healthy mix of the two. Four of the papers were deadline will be returned. written by experimentalists who also do mathematics. The summary strip. Information provided here will Readers should gain an appreciation of the synergy be used to prepare a printed list of applicants for dis­ between experiment and mathematics and a view of tribution to employers. Please supply all information the current state of basic research in mathematical requested, and confine your characters to the boxes neurobiology. provided. Use the codes below. Circled letters identify corresponding items on the form and the strip. These lectures were presented at the Sixteenth Annual Symposium on Some Mathematical Ques· @ Specialties tions in Biology at the AAAS meeting in Washing· AL = Algebra AN = Analysis ton, D. C. in january 1982. It was jointly organized BI = Biomathematics BS = Biostatistics and sponsored by AMS, SIAM, and Section A, CB = Combinatorics CM = Communication CN = Control Mathematics of the AAAS. CS = Computer Science CT = Circuits DE = Differential Equations EC = Economics ED = Mathematical Education CONTENTS FA = Functional Analysis FI = Financial Mathematics Speakers and session chairmen FL = Fluid Mechanics GE = Geometry Robert M. Miura, Preface HM = History of Math LO = Logic Charles F. Stevens, Quantitath•e specification of MB = Mathematical Biology ME = Mechanics neuron form MO = Modelling MP = Mathematical Physics john Rinzcl, Neuronal plasticity (learning) MS = Management Science NA = Numerical Analysis Richard E. Plant, The analysis of models for excit­ NT = Number Theory OR = Operations Research PR = Probability able membranes: An introduction SA = Systems Analysis ST = Statistics TO = Topology Alwyn C. Scott, Nerve pulse interactions john A. Connor and Georgia Nikolakopoulou, Cal­ @ Career Objectives cium diffusion and buffering in nerve cytoplasm AR = Academic Research AT = Academic Teaching Charles Nicholson and joseph M. Phillips, Diffusion NR = Nonacademic R&D NC = Nonacad. Consulting in the brain cell microenvironment NS = Nonacademic Supervision Duties 1980 Mathematics Subject Classifications: 92; 34, 35, 42, ®CD 58, 76, 94 T =Teaching U = Undergraduate Lectures on Mathematics in the Life Sciences G =Graduate R =Research Volume 15, x + 122 pages (soft cover) C = Consulting A = Administration List price $19; institutional member $14, S = Supervision IND = Industry individual member $10 GOY = Government DP = Data Processing ISBN 0·8218·1165·7; LC 82·18418 Location Publication date: November 1982 To order, please specify LLSCI/15N E =East S =South C =Central M =Mountain Prepayment is required for all AMS publications. W =West 0 = Outside U.S. I = Indifferent Order from AMS, PO Box 1571, Annex Station, U.S. Citizenship Status Providence, Rl 02901, or call 800-556-7774 C = U.S. Citizen P = Permanent Resident to charge with VISA or MasterCard. T = Temporarily in U.S. N = Non-U.S. Citizen

708 MATHEMATICAL SCIENCES EMPLOYMENT REGISTER APPLICANT FORM JANUARY 1984 LOUISVILLE, KENTUCKY

APPLICANT: Nrune'------­ Mailing address (include zip code)------

@ Specialtie"'------­ @ Career objectives and accomplishments ACADEMIC: 0 Research, 0 Teaching NON-ACADEMIC: 0 Research and Development, 0 Consulting, 0 Supervision Near-rermcare~goal~------

Significant achievements or projects, including rol.e______

Honorsandoffioo~------­ Other (e.g., paper to be presenred at THIS meeting)•------

Selected titles of papers, reports, books, patent"------

@Degree Year Institution ------@No. of abstracts, internal report.______------@No. of papers accepre'"------@No. of books and patent...______EMPLOYMENT WSTORY: Present Previous Previous @Employer ------­ Position @Duties Years ______to, ______to·------______to, ______DESIRED POSITION:._•------(!) Dutie"'------Q)Available mo. __ fyr.__ Locatiou______Salary____ _ ®References (Name and Institution)

©Citizenship ------­ @AVAILABLE FOR INTERVIEWS: (Interviews for Session 4 scheduled on the basis of employer's request only.) Session 1 0 Session 2 0 Session 3 0 Session 4 0 Fri. AM 9:30-11:45 Fri. PM 1:15-5:00 Sat. AM 9:30-11:45 Sat. PM 1:15-5:00 I do not plan to attend the Annual Meeting 0

Family Name First Name Mailing Address SUMMARY STRIP I I I I I I I Ill I I 1, I I I I I I I I 1, r-TI1....,..1-r---1 1,.1....,..1 "I 1---rl-.--1 "I lr-rl-.--1 "I 1---rl-.--1 "I I, Addren (cont'd.) Addreu (cont'd.) State & Zip Code @ Specialties I I I I I I I I I I I I I I 1, I I I I I I I I I I I I I I I I. I I I I I I I I I. OJ ITJ ITJ ITJ ITJ. @ Career objective. @M~~~=:t @Yr. @ Inatitution @ @ ® @Most recent employer ITJ ITJ ITJ ITJ CD. ITID. CD. I I I I I I I I I I I. ITJ. ITJ. OJ. I I I I I I I I I I I. @ Preaent duties (!) Desired duties 0 !.~~i~r~le @ @ Seuions I I I I I I I I I I 1, CIIIl [JJIJ, ITJ/DJ. D. D D D D

709 E~1PLOYERFORM NATHEHATICAL SCIENCES Et!PLOYMENT REGIST!o:R LOUISVILLE, KENTUCKY JANUARY 26-28, 1984

INSTRUCTIONS: Please read carefully before completinp: form l:>elow, Circled letters identify correspoodinp: items in the FORM and the SUNHARY STRIP; abbreviations to be used are provided in the notes below. Please print or type in black ink. Block capitals are suggested. The FORN itself will be placed on display at the Re!'ister exactly as submitted. The SUMIARY S~l'RIPwill be used to prepare a computer printed list of summaries for distribution at the Re!'ister sessions. Employers are encouraged to provide more than one interviewer when tbey are able to do so, in order to increase the number of interviews which may be scheduled. Please take care to indicate on the Form the number of interviewers for whom simultaneous interviews may be scheduled. (If all interviewers will he interviewing for the same position, or for the same set of positions, only one form should be submitted and only one employer code number will he assip:ned; therefore, each interviewer would then receive a separate computer schedule and separate table number.) More than one employer code will be required if some interviewers will not interview for all positions. Thus, if there are t>Jo disjoint sets of positions, two forms are required and two employer codes will be assigned. (Please refer to the section on the Employment Register following the Louisville meeting announcement.)

EI1PLOYER ~'ORN Institution Dept.

Name of lnterviewer(s)

City, State, Zip

@ Title(s) of Position(s) @Number of Positions Number of People Supervised © Starting I Salary ® Term of Appointment ® Renewal ( ) Possible Date mo. yr. yrs. ( ) Impossible Teaching hrs./week ® Specialties Sou!'ht

...... © Degree Preferred____ @ Degree Accepted ____ (D Duties Q) Experience ® Citizenship Restriction 0 @ Available for Interviews Session 1 ( ) Session 2 ( ) Session 3 ( } Session 4 ( }* Fri. AM, 9:30-11:45 Fri. PM, 1:15-5:00 Sat. AM, 9:3Q-11:45 Sat. PM, 1:15-5:00 ® Number of Interviewers : --- Interviewers --- Interviewers --- Interviewers --- Interviewers ©Start Institution City State ®Title of position @No. mo. 1 yr. I II 1111111 Ill 111111 11,1Ill I I 1111111 IIIII.DJ.IIIII,IIIII.QJ.CD/QJ. ® ID ® Specialties sought ® ®

NOTES: QP Inst, Lect, Asst Prof, Asso Prof, Prof, Dean, Open, MTS(Member Technical Staff), OPAN(Operations Analyst), PREN(Project Engineer), RESC (Research Scientist); ~ Date 01/83, e.g.; ~ Possible=P, Impossible=!; ~ Argebra=AL, Analysis=AN, Biomathematics=BI, Biostatistics=BS, Combinatorics­ =CB, Communication=CM,Control=CN, Computer Science=CS, Circuits=CT, Differential Equations=DE, Economics=EC,Mathematical Education=ED, Functional Analy­ sis=FA, Financial Mathematics=FI, Fluid Mechanics=FL, Geometry=GE,History of Mathematics=HM, Logic=LO, Mathematical Biology=MB, Mechanics=ME,Modeling­ =MO,Mathematical Physics=MP, ManagementScience=MS, Numerical Analysis=NA, NumberTheory=NT, Operations Research=OR, Probability=PR, Systems Analysis=SA, Statistics=ST, Topology=TO; ~ GDBachelor=B, Master=M, Doctor=D; CDGD Teaching=T, Undergraduates=U, Graduates=G, Research=R, Consulting=C, Adminis­ tration=A, Supervision=S, Industry=IND, Government=GOV,Data Processing=DP, No experience required=N; QD U.S. Citizen=C, u.s. Citizen or permanent resi­ dent=CP, No restriction=NR; (!;) Periods available for interviews: List 1, 2, 3, and/or 4, see the FO~above. * Interviews are scheduled in this session on the basis of employers request only. PREREGISTRATION AND HOUSING FORM, LOUISVILLE, KENTUCKY AMS Short Course Joint Mathematics Meetings MAA Minicourses january 23-24, 1984 January 25-29, 1984 January 25-29, 1984 MUST BE RECEIVED IN PROVIDENCE NO LATER THAN DECEMBER 5, 1983 Please complete this form and return it with your payment{s) to MATHEMATICS MEETINGS HOUSING BUREAU P. 0. Box 6887, Providence, Rhode Island 02940, Telephone (401) 272-9500, Ext. 239 PREREGISTRATION: Deadline for receipt of preregistration fee{s) is December 5, 1983. HOUSING BUREAU SERVICES: Participants desiring to obtain confirmed reservations for hotel accommodations must preregister by the December 5, 1983 deadline. CHANGES/CANCELLATIONS: Before January 15, 1984, make all changes to or cancellations of hotel reservations with the Mathematics Meetings Housing Bureau in Providence; after that date, changes or cancellations should be made with the Housing Office of the Louisville Convention and Visitors Bureau by telephoning 502-584-2144. REFUNDS: Please note that only 50% of preregistration fee{s) is refundable if notification is received in Providence on or before January 23, 1984. After this date, there will be no refunds. REGISTRATION FEES Preregistration {by mail prior to 12/5) At Meeting ]OINT MATHEMATICS MEETINGS Member of AMS, MAA, and NCTM $47 $61 *Student, Unemployed, or Emeritus $12 $15 Nonmember $71 $93 AMS SHORT COURSE Member/Nonmember $25 $30 *Student or Unemployed $ 5 $10 MAA MINICOURSES {payable at meeting) $20 #1 - Linear programming ..., #2 - Combinatorics r #3 - Problem solving Please affix AMS or MAA label here. Pascal #4 -· If none, complete 1-3 below. #5 - Mathematics in industry #6 - Computer graphics #7 - Conduit microcomputer software #8 - NonConduit microcomputer software L _j EMPLOYMENT REGISTER- Employer fee $50 $75 *All full-time students currently working toward a degree or diploma qualify for the student registration fees, regardless of incomt:. The unemployed status refers to any person currently unemployed, actively seeking employment, and who is not a student. It is not intended to include persons who have voluntarily resigned from their latest position. Persons who qualify for emeritus membership in either the AMS or MAA may register at the emeritus rate.

PREREGISTRATION SECTION: Please check the function{s) for which you arc preregistering: Joint Mathematics Meetings [ I Employment Register- Applicant {no charge) [ I AMS Short Course [ I NOTE: Applicants who wish to be included in the special MAA Minicourses: issue of ElMS must submit applicant forms with preregistra- #1 [ I #5 [ ] tion form and fee{s) by December 5. #2 [ ] #6 [ I Employment Register - Employer {fee $50) [ ] #3 [ ] #7 [ I Please be sure to complete and return herewith the appropri- #4 [ ] #8 [ ] ate Employment Register form {See pages and .). NOTE: I am preregistering for the joint Meetings only in order to attend the MAA Minicourse(s). I ]

1) NAME (Please print) Surname First Middle

2) ADDRESS Number and Street City State Zip Code

3) AMS Member code------orMAAmembercode ______4) ADDRESS FOR CONFIRMATION OF ROOM RESERVATION IF OTHER THAN ABOVE

5) Employing institution------Unemployed [ I Emeritus [ I

6) I am a student at------{7) Name of spouse ----..,..,---:o------::----:-.,----­ (List if a~.;~:ompanying to meeting) 8) Accompanying children {number) ___ {names, ages, sexes) ------9) Member of AMS [ I, MAA [ I, NONMEMBER [ 1. (Member discount applies only to members of AMS and MAA.) Member of other organizations: AWM [ ], NAM [ I 1O) joint Meetings fee enclosed $'------(11) Employer fee enclosed $----- {12) AMS Short Course fee enclosed $------

13) TOTAL AMOUNT ENCLOSED FOR 10 through 12 $ {Please make all checks payable to AMS. Canadian checks must be marked "In U.S. Funds". Do not include payment for MAA Minicourse{s).) 14) HOUSING DEPOSIT CHECK enclosed$ . N. B.! Please make this check payable to the Louisville Convention & Visitors Bureau and/or supply major credit card information on reverse where indicated. Please check here if you will not require a room. PLEASE BE SURE TO COMPLETE THE SECTION ON NEXT PAGE IF YOU WILL REQUIRE HOTEL ACCOMMODATIONS.

711

c c

" "

G) G)

<.ll <.ll

0 0

i5 i5

:I: :I:

0 0

;>::> ;>::>

;>::> ;>::>

0 0

rn rn

s: s:

rn rn

C: C:

"" "" 0 0

;; ;; z z

:r :r

z z

tii tii

""' ""'

;>::> ;>::>

""' ""' G) G)

> >

;>::> ;>::>

> >

.eo .eo

" "

:I: :I:

z..,., z..,.,

C"l C"l

0 0

G) G) - z

<.ll <.ll

rn rn z z

<.ll <.ll

c c

0 0

""'-

__ __

VB) VB)

an an

1984 1984

avail­

& &

at at

LC LC

longer longer

made made

January January

orB orB

orB orB

orB orB

orB orB

no no

be be

a.m./p.m. a.m./p.m.

is is

Payments* Payments*

PAYABLE PAYABLE

orB orB

orB orB

orB orB

Convention Convention

will will

B B

A A

A/CC A/CC

A/CC A/CC

A A

A A

A/CC A/CC

A/CC A/CC

Deposit Deposit

(CHECK (CHECK

requested requested

Louisville Louisville

DATE DATE

assignment assignment

rate rate

1 1

I I

I I

I I I I

I I

i i

l l

i i

! !

I I I I

i i

I I

the the

the the

to to

______

0 0

the the

If If

250 250

285 285

out out

ite---11 ite---11

hotels, hotels,

DEPARTURE DEPARTURE

100, 100,

Suites Suites

Bdrm-85 Bdrm-85

Parlor Parlor

su su

Parlor/ Parlor/

rate. rate.

180, 180,

Suites Suites

Other Other

date------

made made

I I

I I I I

! !

and and

I I

I I

I I

I I

l l

ranked ranked

at at

Phonenumber Phonenumber

the the

room room

$ $ $

Expiration Expiration

53 53

49 49

58 58

74 74

48 48

56 56

39 39

66 66

at at

applicable) applicable)

Quad Quad

filled filled

I I

requested requested

been been

the the

KENTUCKY KENTUCKY

$ $

48 48

52 52

46 46

50 50

49 49

60 60

67 67

35 35

check check (where

Triple Triple

have have

! !

I I

I I

I I

circling circling

rooms rooms

personal personal

by by

all all

my my

and and

Dbl. Dbl.

$ $

is is

43 43

49 49

54 54

44 44

59 59

43 43

31 31

46 46

LOUISVILLE, LOUISVILLE,

and and

(date) (date)

DATE DATE

Twin Twin

form, form,

Cards. Cards.

I I

I I

on on

------

ranked, ranked,

Enclosed Enclosed

depart depart

FORM, FORM,

-

Credit Credit

left left

arc arc

and and

at at

$ $

_ _

ARRIVAL ARRIVAL

54 54

46 46

59 59

N/A N/A

N/A N/A

N/A N/A

N/A N/A

N/A N/A

Major Major

Twin Twin

hotels hotels

tax. tax.

spaces spaces

I I

B B =

all all

HOUSING HOUSING

in in

a.m_fp.m., a.m_fp.m.,

hotel hotel

not not

______

etc., etc.,

If If

$ $

AND AND

38 38

54 54

59 59

49 49

44 44

43 43

N/A N/A

N/A N/A

9.2% 9.2%

3, 3,

of$ of$

Double Double

2, 2,

to to

rate. rate.

number number

1, 1,

I I

! !

I I

I I

I I

! ! i i ! !

I I

I I

identification; identification;

form. form.

amount amount

Card Card

subject subject

card card

the the

$ $

avai!J.ble avai!J.ble

writing writing

33 33

43 43

38 38

50 50

40 40

38 38

25 25

48 48

arc arc

in in

Single Single

by by

best best

credit credit

submitting submitting

! !

i i

below below

below below

next next

with with

PREREGISTRATION PREREGISTRATION

the the

listed listed

preference preference

at at

(6) (6)

at at

individual individual

(5) (5)

of of

reserved reserved

Checks Checks

rates rates

to to

parentheses parentheses

(9) (9)

hotel hotel

NOTICES.) NOTICES.)

(4) (4)

order order

room room

The The

in in

in in

only only

(8) (8)

in in

(7) (7)

INN INN

Personal Personal

each each

sent sent

= =

map map

rate. rate.

another another

(2) (2)

TRAVELODGE TRAVELODGE

for for

be be

on on

at at

choices choices

HOTEL HOTEL

(3) (3)

(Numbers (Numbers

type type

JOHNSON'S JOHNSON'S

A/CC A/CC

lowest lowest

will will

REGENCY REGENCY

five five

room room

HOUSE HOUSE

card card

WESTERN-MIDTOWN WESTERN-MIDTOWN

deposit deposit

Hotel Hotel

a a

LOUISVILLE LOUISVILLE

location location

next next

NAME NAME

least least

of of

Checks; Checks;

the the

at at

confirmation) confirmation)

HOWARD HOWARD

BEST BEST

LOUISVILLE LOUISVILLE

RODEWAY RODEWAY

occupants: occupants:

GALT GALT

THE THE

HYATT HYATT

SEELBACH SEELBACH

Credit Credit

night's night's

assigned assigned

FULL FULL

indicate indicate

Name Name

(for (for

Confirmation Confirmation

with with

one one

room room

be be

(date) (date)

is is

indicate indicate

Personal Personal

Bureau. Bureau.

I I

! !

hotel hotel

will will

Sccti9n: Sccti9n:

other other

address address

arrive arrive

NOTE: NOTE:

of of

*A= *A=

Please Please

you you

List List

Visitors Visitors

Full Full

Enclosed Enclosed

Will Will

Name Name

& &

5) 5)

unranked unranked

Housing Housing

choice choice

able, able,

Order Order

2) 2)

4) 4)

3) 3)

1) 1)

~ ~

...... -..j -..j Contributions to Lattice Theory edited by A.P. Huhn and E.T. Schmidt Colloquia Mathematics Societatis Janos Bolyai, Volume 33 This volume contains the proceedings of the Colloquium on Lattice Theory held in Szeged, August 1980. The scope of this volume covers modular lattices, distributive lattices, orthomodular lattices, Stone­ duality, Amalgation Property, free objects and products of lattice varieties. Most of the leading personalities of the North American as well as of the Eastern and Western European lattice theory schools can be found among the contributors to this work.

1983.782 pages. Price: US $.102.00/Dfl. 240.00.ISBN 0·444-86507·1 The Mathematical Theory of Knots and Braids An Introduction by Siegfried Moran, University of Kent at Canterbury, UK North-Holland Mathematics Studies, Volume 82 This book is an introduction to the theory of knots via the theory of braids, which attempts to be complete in a number of ways. Some knowledge of Topology is assumed. Necessary Group Theory and further necessary Topology are given in the book. The exposition is intended to enable an interested reader to learn the basics of the subject.

1983. xli + 296 pages. Price: US $42.50/Dfl. 100.00.ISBN 0·444·86714·7 Computational Techniques for Differential Equations edited by John Noye, The University of Adelaide, South Australia North-Holland Mathematics Studies, Volume 83 Covers the following topics: the methods of solving initial value problems in ordinary differential equations, alternative techniques which may be used to solve problems involving partial differential equations, and the basic methods of solving large sets of sparse linear algebraic equations.

1983. vi + 680 pages. Price: US $74.50/Dfl. 175.00.ISBN 0-444-86783-X Selected Papers of Kentaro Yano edited by Morlo Obata, Keio University, Yokohama, Japan North-Holland Mathematics Studies, Volume 70 Professor Kentaro Yano has made great contributions to Differential Geometry for nearly fifty years. In recognition of this, the publication of this Selecta Volume was planned by his former students, and his colleagues on the occasion of celebrating his 70th birthday. This volume consists of his own selection of papers. These papers show a breadth and depth which can only be the result of a long span of activity.

1982. liv + 366 pages. Price: US $58.25/Dfl. 125.00. ISBN 0·444-86495·4

IN AU OTHER COUNTRIES: ~~~~~~~:c~~~giANADA: ELSEVIER SCIENCE PUBLISHING CO., INC. PUBLISHERS BOOK ORDER DEPARTMENT th h II d P.O.BOX211 0 ~~A~~l-::'/RALSTATION 1000 AE AMSTERDAM nor • an . NEW YORK, NY 10183 THE NETHERLANDS

US $prices 818 valid only In tha USA and Canada. In all other countries the Dutch Guilder price is definitive. NH/MATH/BK/0869 All pnces are subject to change without prior notice. CLI-- CLI 110 Oil: "' "' J! ~ § u Ill CLI ·- fE u .~ Q 8. c "C Recipient of the 1983 CLI "C 110 P.R. Halmos: "' :s! "' .= "' > "C u"' ...Q c ·~ "C a.. P6lya Award and the 1983 Steele Prize. c Q ... "' u "' ~ ·s."C

Paul Halmos has been one of the United Volume 1: Research Contributions States' most influential mathematicians and Edited by D. Sarason and N. Friedman 1982/458 pp./5 illus./Cloth $32.00 teachers of mathematics over the last few ISBN 0-387-90755-6 decades. Writing The first of a two-volume set, Selecta: Volume II: Expository Edited by D. Sarason and L. Gillman Research Contributions documents his 1982/304 pp ./I ill us ./Cloth $19.80 influence amply and convincingly; ISBN 0-387-90756-4 D. Sarason (Berkeley) and N. Friedman (SUNY Albany), who made this selection Also by P.R. Halmos as editors of this volume, explain and served A Hilbert Space Problem Book, in a summary introduction Halmos' work 2nd Edition and its scientific-and personal-impact. 1982/369 pp./Cloth $28.00 Vol. 19 typical of Graduate Texts in Mathematics, Emphasis is placed on papers ISBN 0-387-90685-1 Halmos' work and his direct, innovative and energetic approach to problems. Particular Bounded Integral Operators on L2 Spaces (Written with V.S. Sunder) attention is devoted to those papers that are 1978/132 pp./Cloth $23.00 today and, as far as one can tell, will be for Ergebnisse der Mathematik 2, Vol. 96 the next few decades, of direct scientific ISBN 0-387-08894-6 interest. Naive Set Theory pp./Cloth $14.80 volume Selecta: Expository 1974/104 The second Undergraduate Texts in Mathematics Writings, edited by D. Sarason (Berkeley) ISBN 0-387-90092-6 and L. Gillman ( Austin) show Halmos Lectures in Boolean Algebras the teacher, the stylist and the educator. 1974/147 pp./$7 .00 Halmos' role and concepts are explained in ISBN 0-387-90094-2 introductory essay by L. Gillman. The Measure Theory reader will quickly see that Halmos' interest 1976/304 pp./Cloth $21.00 goes far beyond the narrow perspective of Graduate Texts in Mathematics, Vol. 18 ISBN 0-387-90088-8 a "professional" mathematical educator; he is concerned with imbedding mathematical Finite Dimensional Vector Spaces 1974/200 pp./Cloth $16.00 thought into everyday life and the relation of Undergraduate Texts in Mathematics ~ mathematicians and mathematics to the rest ISBN 0-387-90093-4 LU 0 0 of mankind. In addition to Halmos' papers, N u '0:1' ~ ~ 0 N this volume contains the script of an o;. VI 0 N ..J interview published in the Two-Year-College < Oil: Mathematics Journal, "Paul Halmos: A [j(l Springer-Verlag 8 u CLI~ z i= u Maverick Mathologist.'' VI c New York Berlin Heidelberg Tokyo VI < CLI li'J ~ "C LU ·;;:: -VI :I: Q ~ 1- d: To order write: Springer-Verlag New York, 175 Fifth Ave., N.Y., N.Y. 10010 < < aO CLI ~ '0:1' ..c... z N .... ID Q < X u Q "'CLI C2 CCI u LU ·~ ~ d z < a,;