Flat-Rate Research Funding: Two Views page 3

The Endless Frontier Meets Today's Realities page 6

MSEB Comes of Age page 9

JANUARY 1993, VOLUME 40, NUMBER 1

Providence, Rhode Island, USA ISSN 0002-9920 Calendar of AMS Meetings and Conferences

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

Abstract Program Meeting# Date Place Deadline Issue 879 • March 26-27, 1993 Knoxville, Tennessee Expired March 880 • April9-10, 1993 Salt Lake City, Utah January 29 April 881 • April17-18, 1993 Washington, D.C. January 29 April 882 • May 20-23, 1993 DeKalb, Illinois February 26 May-June 883 • August15-19, 1993 Vancouver, British Columbia May 18 July-August (96th Summer Meeting) (Joint Meeting with the Canadian Mathematical Society) 884 • September 18-19, 1993 Syracuse, New York May 18 September 885 • October 1-3, 1993 Heidelberg, Germany May 18 September (Joint Meeting with the Deutsche Mathematiker-Vereinigung e.V.) 886 • October 22-23, 1993 College Station, Texas August4 October 887 • November 6-7,1993 Claremont, California August 4 October 888 • January 12-15, 1994 Cincinnati, Ohio October 1 December (100th Annual Meeting) 889 • March 18-19, 1994 Lexington, Kentucky 890 • March 25-26, 1994 Manhattan, Kansas 891 * April9-10, 1994 Brooklyn, New York 892 • June 16-18, 1994 Eugene, Oregon October 28-29, 1994 Stillwater, OklahOma January 25-28, 1995 Denver, Colorado (1 01 st Annual Meeting) March 24-25, 1995 Chicago, Illinois November3-4, 1995 Kent, Ohio January 10-13, 1996 Orlando, Florida (102nd Annual Meeting) March 22-23, 1996 Iowa City, Iowa • Please refer to page 43 for listing of Special Sessions. Conferences

June 7-18, 1993: AMS-SIAM Summer Seminar in Applied Mathematics July 11-30, 1993: AMS Summer Institute on Stochastic Analysis, on Tomography, Impedance Imaging, and Integral Geometry, Mount Cornell University, Ithaca, New York. Holyoke College, South Hadley, Massachusetts. August 9-13, 1993: AMS Symposium on Mathematics of Computation July 10-August 6, 1993: Joint Summer Research Conferences in the 1943-1993: A Half-Century of Computational Mathematics, Mathematical Sciences, University of Washington, Seattle, University of British Columbia, Vancouver, Canada. Washington. Other Events Cosponsored by the Society ~.--~·· ... ···········~··~················ ·············~···· ··~··········································································· .....

February 11-16, 1993: Section A (Mathematics) Sessions at the AAAS Annual Meeting, Boston, Massachusetts. May 30-June 13,1993: First Caribbean Spring School of Theoretical Physics and Mathematics on Infinite Dimensional Geometry, Noncommutative Geometry, Operator Algebras, and Particle Physics, Pointe a Pitre, Guadeloupe. Cosponsored by the Societe Mathematique de France. Deadlines

March Issue April Issue May-June Issue July-August Issue Classified Ads* February 4, 1993 February 24, 1993 April1, 1993 June 24, 1993 News Items January 22, 1993 February 19, 1993 March 19, 1993 June 8, 1993 Meeting Announcements•• January 26, 1993 February 22, 1993 March 23, 1993 June 14, 1993 • Please contact AMS Advertising Department for an Advertising Rate Card for display advertising deadlines. •• For material to appear in the Mathematical Sciences Meetings and Conferences section. ···············································~·····~··········-··············------OTICES OF THE

AMERICAN MATHEMATICAL SOCIETY

DEPARTMENTS ARTICLES 12 Forum 31 News and Announcements 3 Flat-Rate Research Funding: Two Views 36 Funding Information for the What are the advantages and problems associated with instituting a flat-rate Mathematical Sciences grant scheme at the NSF? This article presents two opposing viewpoints 37 1993 AMS Elections on this controversial issue, one written by former Division of Mathematical Sciences (OMS) program officer Robert Molzon and one written by former 41 Meetings and Conferences of OMS director John Polking. the AMS Knoxville, TN March 26-27, 41 6 The Endless Frontier Meets Today's Realities Richard H. Herman Invited Speakers, 43 The federal government and the general public are asking tough questions Joint Summer Research about how well higher education and scientific research are serving the Conferences in the Mathematical needs of the nation. This scrutiny comes at a time of dwindling resources Sciences, 47 for mathematics departments and for academia in general. This speech, 1993 Summer Seminar in Applied delivered at the annual Chairs' Colloquium last October, explores how Mathematics, 49 departments can respond to the changing climate. 1993 Summer Research Institute, 50 9 MSEB Comes of Age 1993 Symposium on Some . Mathematical Questions in Biology, The Mathematical Sciences Education Board (MSEB) has been a major 51 player in the mathematics education reform movement. With a new 1993 Symposium, Mathematics of executive director, Lynn Steen, and a number of other new senior staff Computation, 52 members, the MSEB is moving beyond just writing reports to taking a more active role in the implementation of reforms. Allyn Jackson reports on some 53 Mathematical Sciences Meetings of the current activities of the MSEB. and Conferences 65 New Publications Offered by the FEATURE COLUMNS AMS 68 AMS Reports and Communications 15 Computers and Mathematics Keith Devlin Reports of Past Meetings, 68 In this month's feature article, Larry Wos of the Argonne National Laboratory 70 Miscellaneous describes his experiences in developing and using the automated reasoning Personal Items, 70 system OTTER. Following the article, William Ruckle reviews Mathcad, Deaths, 70 Suzanne Molnar takes a look at Matrix Algebra, and Roger Pinkham road Visiting Mathematicians tests the Tl-85 calculator. Supplementary List, 70 71 New Members of the AMS 74 AMS Policy on Recruitment Advertising 75 Classified Advertising 91 Forms

JANUARY 1993, VOLUME 40, NUMBER 1 1

Flat-Rate Research Funding: Two Views

such as the Scientific Computing Research Equipment in the Mathematical Sciences program, have been set up to provide In the early fall of 1992, the Division of Mathematical Sciences (DMS) of the National Science Foundation (NSF) announced that it support independent of salary. These programs have oper­ would institute a "ftat-rate" funding demonstration project. This ex­ ated to a large extent outside of the traditional disciplinary periment would have moved the DMS to a two-tiered grant system, programs in the DMS. The tradition within the disciplinary in which grantees would receive either $20,000 or $30,000, depend­ programs in the DMS was to make awards very closely ing on seniority, with additional fixed-rate supplements for graduate linked to a PI institution salary for the academic year, and the students and postdoctoral researchers (see ''NSF Proposes Changes Advisory Committee, in making a recommendation that the in Funding Mode for Mathematics", Notices, November 1992, page 1091, for more details on the project). Under pressure from the math­ DMS reconsider this close link between award size and salary, ematics community, the DMS decided to put the project on hold was certainly departing from tradition, but was not charting Another strong move against the project came when the NSF's Ad­ completely unknown territory. visory Committee for the Mathematical Sciences passed a resolution At its Spring 1992 meeting, the Advisory Committee saying they did not support implementation of the project at this time moved more firmly in this direction with a recommendation (see "Flat-Rate Funding Project at NSF', Notices, December 1992, system. The article "Flat­ page 1171). that the DMS set up a tiered award Although it appears that the flat-rate project will not be instituted Rate Funding Project at NSF' (Notices, December 1992, in the near future, there has been a great deal of discussion within the page 1171) discussed the history of the DMS response to community about the advantages and disadvantages of such a grant that recommendation and the subsequent response from the system. The following two articles present arguments on both sides mathematics community. The discussion which led to the of the flat-rate funding issue. The first article is by Robert Molzon, recommendation by the Advisory Committee that the NSF currently on leave at the University of Nevada at Las Vegas from the focused on the best possible uses of University of Kentucky. In August 1992, Molzon finished a two-year establish the tiered system tour of duty as program director for Geometric Analysis in the DMS. funds currently available to the NSF. Proposals to unlink award The second article is by John C. Polking of Rice University. Polking size from PI institution salary have generally been driven by a served as director of the DMS from 1984 to 1987. perceived need to provide research support for a broader base of individuals and for the need for research support outside the area of salary. The Committee seemed to feel that changes could be made which would enable excellent mathematicians For Flat-Rate Funding: to continue strong research and make it possible for other Best Use of Budget to Support Mathematics excellent mathematicians not currently supported to carry out Robert Molzon research. Of course, whenever there is a shift of support, there Approximately two years ago, the Advisory Committee to will be a negative impact on someone. The Committee seemed DMS made a preliminary recommendation that DMS consider to be trying to balance the negative impact of decreasing some unlinking to some extent the size of the NSF awards from salary support with the positive impact of enabling excellent Principal Investigator (PI) institution salary. Although this people to carry out research. Any reasonable attempt to make idea may have been presented in a somewhat new guise, the the best use of currently available funds must involve such concept had been previously discussed within the mathemati­ a balance. Marginal costs and benefits must be considered cal community and the NSF. In fact, the NSF has been using a in allocating resources under ~e present circumstances, in funding mechariism along these lines for postdoctoral support which strong and important research is not receiving even for years. The Presidential Young Investigator (now called minimal support. the National Science Foundation Young Investigator award) The Divisions within the NSF that have received substan­ and the Research Opportunities for Women planning grants tial increases in funding used an approach that did not focus are also fixed awards of $25,000 and $18,000 respectively. on the bottom line of PI salary, but on the importance of These awards support a wide range of research activities science or science education in the context of the total scien­ and do not follow a two-ninths formula. Some programs, tific and economic development of the country. The Division

--'""'"''""""""'""___ """""""""""""""""""'"' ______,___ ,,_, ...... ,, .. _...... __,, ...... _,...... ,,__ , ...... -...... _, ___,_,_, ...... _...... JANUARY 1993, VOLUME 40, NUMBER 1 3 ·----~---~------··---·--········~·····-····--~························~········· Flat-Rate Funding at NSF of Materials Research won large increases in funding not by mathematics community to return to funding proposals at showing that Pis in Materials Research need to be well paid, two-ninths the academic year salary regardless of the number but by showing that the research could have a strong economic of awards that would have to be cut to do so. This would impact. Education did not win big increases because educators send a discouraging message to young mathematicians that are well paid, but because someone convinced the Adminis­ the chances for funding will be remote. If Geometric Analysis tration and the Congress that a strong education program was had not limited salary the past two years, approximately ten vital to the national interest. If we wish to increase funding to fifteen percent fewer proposals that reviewed in the "Very support for mathematics, then we might do well to focus on Good" to "Excellent" range would have been funded. There convincing the public, the Administration, the Congress, and is not a scintilla of evidence that indicates that an increase colleagues in other sciences that support for mathematical in salary support to a limited number of individuals would research is in their best interests. result in increased funding for mathematics. Although there The rationale for continuing to tie the award size to has been substantial discussion of the question of funding institution salary even under today's dire funding situation mode, relatively few mathematicians seem willing to play seems to be based primarily on two arguments, the "you get a more active role in the issue. If people are concerned what you pay for" argument and the "cheap science" argument. about the direction the NSF funding is to take, they must The "you get what you pay for" argument maintains that if the begin to become more politically active. They must write as NSF wants research done well then it must be willing to pay for individuals and as groups to the NSF and to officers of the it. Supporters of the traditional ''two-ninths summer salary" AMS. mode of support apparently feel that this implies that the In order to win increased support for mathematics the price the federal government should pay for work well done community must become more politically active in another is to be set independently by the researcher and university. way. Individual mathematicians must make their work more The argument fails to make even the most basic marginal accessible to other scientific communities, to the business cost-benefit analysis. It is highly unlikely that the NSF would community, and the public. There have been numerous get the most research for the dollar by paying salary at an articles written on how this might be accomplished, and it is not arbitrarily high level on one proposal and turning down other necessary to repeat that advice here. The budget figures coming proposals that reviewed in the "Very Good" to "Excellent" out of Washington indicate that other sciences and education range. That this strategy would not be optimal becomes even are successfully stating their case in terms that Congress and clearer when one realizes that it is essentially impossible to the educated public understand. If mathematicians do not linearly rank proposals in terms of mathematical quality. Few wish to write about problems outside their immediate field of seriously believe that there was a great surge forward in the interest, they probably cannot expect the outside support they research accomplished by mathematicians when the salary would receive if they took an active interest in a broader range cap was lifted a few years ago, but this is exactly what the of activities. This does not mean mathematicians should stop "you get what you pay for" advocates would have us swallow. doing the work on which they thrive; it simply recognizes The "cheap science" argument as used to bolster the that funding is going to be tied to a perception of benefit traditional two-ninths salary rule claims that if the DMS does for the party providing the funds. Redistribution of currently not pay the traditional two-ninths salary then mathematics available resources to pay higher salary support for fewer will be viewed as a cheap science. This of course completely individuals provides a perception of benefit only to those who ignores the possibility that mathematics may be viewed as receive the salaries. The mathematical community is more a cheap science if the DMS sends a message that only a likely to convince the economic interests in the country that few people are needed to carry out research. It also focuses research in mathematics is important if there is a strong and very heavily on salary (salary supplements) to relatively few diverse group of mathematicians active in research. Shrinking individuals. It ignores the adjustments other Divisions at the the size of that group is a step in the wrong direction for the NSF are making with respect to salary in an attempt to long-term health of the field. deal with a need that cannot be completely met with the present NSF budget. When other sciences can so effectively argue that there are many needs beside salary in effective research programs, the message that the primary need of the Against Flat-Rate Funding: mathematics community is salary supplement for relatively Deleterious Long-Term Effects few individuals does not seem to be a strong one for support of John C. Polking mathematics. One will not convince the higher administration The recent announcement by the Division of Mathematical at the NSF or the Congress that mathematics should receive Sciences (DMS) at the National Science Foundation (NSF) of more support by sending a message to the DMS that a great an experimental, fiat-rate funding system for the mathematical deal of excellent mathematics is worthless. sciences has taken most of the community by surprise. The proposed "fiat rate" plan is, at the time of this Suggestions to move in this direction have been made by writing, on hold. Various modifications to the plan have been mathematical scientists from time to time, but the community suggested, and the NSF is apparently willing to consider as a whole has not discussed it seriously. I am writing this alternatives. There has been a strong push by some in the article to start that serious discussion.

4 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Flat-Rate Funding at NSF

As I write these paragraphs, the proposed NSF program of investigators supported will be negligible. In examining is on hold. At its latest meeting in October, the Advisory this point, we have to look to the motivations of the people Committee to the DMS failed to endorse the experiment. who will be making the decisions-in particular, to the The issue is probably not dead, but the program is far from upper administration of the NSF. Administrators at this level being well defined at the moment. For that reason I will have many goals, including maintaining the general health keep my discussion fairly general. What I will discuss is any of the various scientific communities. The goal that has program that would have the effect of untying the level of received the most attention lately has been improving the compensation for research time from the academic salary of contribution of basic research to the economic well-being of the researcher. The basic assumption that I am making about the nation. The mathematician's goal to increase the number the program is that it will reduce the salary compensation of mathematicians supported is not a direct goal of research of many researchers, and, just as importantly, reduce the administrators. When mathematicians tell administrators that compensation of mathematical scientists without affecting individual mathematicians need less .support per individual that of other scientists and engineers. than do other researchers, the administrators are as likely The primary reason that many mathematical scientists to decrease the number of mathematicians supported as to favor such a program is that seemingly these schemes will increase that number. allow more researchers to be funded. Since so few of our To me, the situation is similar to what occurred in the early colleagues are currently funded in comparison to other fields, 1970s. At that time, many graduate students, in mathematics such proposals have wide appeal. I will argue that such a as well as in other fields, were supported through special program undervalues research in the mathematical sciences, programs that made grants directly to departments for this and as a result will have serious deleterious long-term effects purpose. It was decided to end these programs, and, to on the mathematical sciences community. continue support for graduate students, some of the funds One of the principal findings of the David Report, pub­ previously allocated to these special programs were assigned lished in 1984, was that it was necessary for the health of our to the research divisions at the NSF, except in mathematics. community that support for mathematics be comparable to that Mathematicans advised the NSF that because mathematics in other fields. The report made it clear that parity was needed students could be supported as teaching assistants, the DMS in the support for individuals as well as for the community as would need no new money to support graduate students. It a whole. In fact it pointed to support for research time as one was later realized that this was a mistake, but it was too late. of the most important needs of mathematicians, as it is for all The DMS has never recovered from that loss, and to this day scientists. there is too little money provided by the DMS to support In comparison to other fields, individual mathematics mathematics graduate students. researchers are already underfunded. If we examine the The program proposed by the NSF is called an exper­ support level of our colleagues in other fields, we discover iment, but I think that if it is ever officially a policy that that many of them receive as much as three months salary mathematicians do not need salary compensation at the same in support of their efforts. Many of them get academic year level as others, it will be very difficult to recover the loss. support as well. Of course these researchers are not limited It is distressing that this experiment is proposed at this to the NSF as a source for their funding. Very few of our particular moment in time. The entire science and engineering mathematical colleagues receive support like this. In fact, community is faced with major challenges and decisions the NSF's Division of Mathematical Sciences has slowly arising from the changing mission of the NSF and of federal been reducing the number of months of salary support that it funding for academic research in general. There seems to provides to its average awardee. be a consensus developing among the leadership of the The long-range effect of reduced levels of support is that NSF, the National Science Board [the policy-making body fewer people are attracted into the mathematical sciences. of the NSF], and Congress, as well as the administration, We already have difficulty c<;>mpeting with our scientific and that the NSF and other funding agencies should take a engineering colleagues, especially for the best students. The much larger role in fostering connections between research fact that the number of American citizen Ph.D.s produced and technology. I strongly support efforts to develop links each year is at the same level as it was in the early 1960s between the academic research community and industry. That is, in large part, a reflection of the lack of parity in federal said, I do worry that this change at the NSF will undercut support for research in the mathematical sciences. In my the funding for mathematics and the funding for undirected opinion, reducing the individual level of support further will scientific research in general. only make this situation worse. The possible redirection of the mission of federal funding It is the hope that more investigators will be supported for academic research is the issue that should have the full that motivates program officers in the DMS and many of attention of the mathematics community. As important as the our colleagues to support this- program. However, it is not new funding experiment by the DMS is, it should not be clear to me that this will actually happen. In fact, I predict allowed to distract the community from the more important that, after a brief transition period, the effect on the number issue of federal funding for academic research.

JANUARY 1993, VOLUME 40, NUMBER 1 5 The Endless Frontier Meets Today's Realities Richard H. Herman

shrink. Some should go out of business." Samuelson's voice is bellicose, but when he lists his The following text is based on a speech presented by complaints-low admission standards, high dropout rates, Richard H. Herman, Dean of the College of Computer, decreasing teaching loads for faculty, and an explosion of Mathematical, and Physical Sciences, and Chair of the graduate degrees-we all know that this is part of the reason Joint Policy Board for Mathematics, on October 16, 1992, we are in the dock accused of a lack of social responsibility. His at the Department Chairs Colloquium sponsored by the comments are skewed to the extreme, yet the less polemical Board on Mathematical Sciences of the National Research comments of former New Jersey Governor Thomas Kean do Council. not provide a source of comfort: "Here is the reality, plain and simple. Our ivory tower is under siege. People are questioning What I tell you three times is true. our mission and questioning who we are. They claim we cost -"Hunting the Snark," Lewis Carroll Today, I shall speak to you both as a concerned member of the too much, spend carelessly, teach poorly, plan myopically, mathematical sciences community and as a dean. It is my view and when we are questioned, act defensively." To the last that the community needs to bring about substantive changes point we might examine the present "overhead wars" and Don in itself before we are brought to an untenable position. Kennedy's response, and the allegations of price-fixing in the We have missed opportunities which have been presented in Ivy League. the past. You, the department chairs, have always been in a In summary, we have lost the public trust. Now couple position to play a pivotal role not just in the future of your own this with the recession and remember that in most states the department but, as I will argue, in the.future of the community. funding of universities appears as a healthy portion of the I served as one of you for five years-as a department chair discretionary funds. The result is that we are suffering severe at Penn State-and, contrary to popular wisdom, I am willing cuts while being subject to calls from the state for greater to admit that I enjoyed it. accountability and visible signs that we are delivering on I want to delineate the choices facing the mathemati­ promises implicit to our existence. cal sciences community, especially at universities. Broadly Continuing with pressures on the university, let me turn speaking, I will break my comments into three categories: to the government-university partnership. Most of us hearken 1) problems at universities-pressures from constituencies, back to the beginning of it all, Vannevar Bush's report 2) the mathematics department as part of the university, and Science-The Endless Frontier. This report, delivered to 3) opportunities for the future. President Truman in 1945, and its progenitors are ultimately The following quotation captures the essence of some responsible for today's science policy. We need to turn to substantial recent criticism of universities: "The discipline of some recent policy statements to understand how things have colleges and universities is, in general, contrived, not for the changed. benefit of the students, but for the interest, or more properly Congressman George Brown, in an article for the Los speaking, for the ease of the masters." Angeles Times, points out that "Science, Inexplicably, has Of course the last word gives away the time of this remark. come to occupy a place in American culture alongside Indeed, the quotation is from the early 1700s and is due to Plymouth Rock, Johnny Appleseed, and the Bill of Rights." Adam Smith. For a more up-to-date version of this comment Brown says that society needs to negotiate a new contract just pick up your local newspaper. Here is one from mine, with the scientific community. He suggests that we need to The Washington Post. Robert Samuelson, in an article entitled require the application of science to the critical problems in ''The Low State of Higher Ed", writes the following: "Higher the civilian sector. In any event he points out in a carefully Education is a bloated enterprise. Too many professors reasoned way that while science has arrived at a position do too little teaching to too many ill-prepared students. of world leadership by many standards, other countries have Costs can be cut and quality improved without reducing the radically different science policies which have afforded them number of graduates. Many colleges and universities should greater success in linking research with national goals. The call

6 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY The Endless Frontier for change comes from one of science's biggest supporters. role in the university. These arguments need to be made Additional evidence for change can be found in Walter continually, but ask yourself if this differs from the physics Massey's remarks to the National Science Board. Hopefully, chair who goes to the same dean and says virtually the same as George Brown proposes, there will first be "carefully thing, points to ~e importance of superconductivity, and defined and modular experiments to avoid throwing out the perhaps speaks to the exciting nature of the Superconducting good with the bad." So, as a new contract is being drawn, SuperCollider and the hopes of the field to make discoveries of and surely it will be, it is necessary for us to help guide the a fundamental nature (and then argues for another condensed process. This will entail making some changes at universities, matter theorist). On the assumption that both departments are accepting further responsibilities in a way consistent with equally regarded, it is more than likely that the long-term preserving "the taproot", the research effort that has brought distribution of resources will be split and equal attention (or us a justifiably high world reputation. Peter Likins, speaking lack thereof) will be given to both arguments. on these issues, closed with a challenge to his audience ''to Suppose we try a different approach. Try to imagine what draft their own rules and try to establish a new social contract." the pressures are on this administrator. As Phil Griffiths has For a reaction to some budget reversions, I will recount pointed out, "Universities will either emerge from this decade some of my own experiences as a dean at the University of leaner, more focused on teaching, more socially relevant, and Maryland. Over the past several years Maryland has suffered able to do fewer things better, or they will further erode their considerable cuts in its state budget. In an effort to improve sources of support and end up weaker." communication, I went around to departments in the college, Instead of taking the view that your job as chair is to made a presentation on the finances, and then allowed for a "protect the department", why not ask yourself how the discussion period. In one department I was greeted with a department can help the university meet the pressures on it. question by one of the best researchers-more of a complaint Think then of the department as the "minimal corporate unit". actually. So, if the mission of the university is teaching, research, and "A few years ago things were very different," he said, and service, the department as a whole must address all of these asked, "When do you see a return to those times?" Actually issues. he was pointing out that in the budget reversions a good deal Let us turn to one of these pressure points. Many students of the traditional ability of the department to follow its own do poorly in early mathematics courses in college-with nose had been lost. Several responses came to mind. I tried to the overall withdrawal and failure rate being quite large imagine what he was thinking; for example: a) in a couple of at some institutions. And this says nothing of repeats. The years things will get better (so let's ignore the situation), b) as causes are many and certainly include admission standards. soon as we get rid of this dean, c) never. In a very real sense Nevertheless, we can certainly do better with a very likely "never" is the right answer, and perhaps that is optimistic. long-term effect. First, I would suggest that success in these Let us recall some major changes that have taken place over courses translates into success elsewhere and ultimately could the years and how they have affected mathematics. In the late change the graduation and retention rates at your university. 1960s the Department of Defense, in response to the Mansfield This has a long-term effect on funding for your (state) amendment, increased emphaSis on goal-oriented programs university and certainly on recruiting-think of the headlines and decreased support of the mathematical sciences. At the when your graduation and retention rates go from 55% to same time, as pointed out in David 1, there were reductions in 65%. Yes, it is labor intensive in the freshman and sophomore federal fellowships for graduate students and postdoctorals. years, and perhaps it means shifting departmental resources a Shortly thereafter, financial problems hit universities causing bit to accomplish this. However, your administration would a tightening in the job market. At the same time mathematics dearly love to have this done (as should you), since efforts enrollments doubled. We reacted by stemming the flow lavished in the first two years will reward the department with of Ph.D.s, and many university mathematics departments strong enrollments and strong students in the upper division succumbed to the view of themselves as service departments and graduate courses. But what is the approach to this dean? by offering calculus in large, larger, and largest sections. (The view of deans is sometimes intriguing. Frank Warner Simultaneously, folks in English made a convincing case that tells the story of a phone call from an irate mother who called composition should be taught in small sections. Perhaps we to complain about a grade for her son in a math course. On missed an opportunity. We certainly did not turn ''the close picking up the phone he was asked who he was. On informing identification of mathematics departments with teaching" to the parent that he was chair of the Math Department, he our own advantage. Likewise, we paid little attention to was told that the mother expected that she would speak creating new opportunities for Ph.D.s. to no one lower than a dean. Frank, being quick of mind, What can you as a department chair do to ensure resources offered that there was no one lower than a dean!) Let me tell for the department wQ.en your entire university is under you how I have been approached on occasion (not [on] this extreme pressure? Well, you can go to your dean and argue that issue and not [about] the math department). "Well if it is so the mathematical sciences are important in and of themselves, important, why doesn't the university provide the resources?" that applications of pure mathematics, applied mathematics, Wrong! The department is part of the university. Run a pilot statistics, operations research, etc., are no surprise considering program on your own, get it to succeed, and then appeal to the founding of the discipline, and that you play an important the administration to share the long-term costs.

JANUARY 1993, VOLUME 40, NUMBER 1 7 ··--·--···---~----·-··-~--~----··-·-·-·--·-·~·······-······-···-···------·····························•···················································-~·-······················· The Endless Frontier

But you say resources are decreasing. You are right, but ations research. The difficulty is that we have, on the whole, that is unimportant. There is always a certain amount of only grudgingly accepted activities in this area. We have money for important things. (And the issue of graduation certainly not encouraged or rewarded them generally. But and retention is central to the university existence.) Recently, now, perhaps motivated by need, we will change. Perhaps tilt at a major state university, a decision was made by the the axes and offer new types of degrees, such as professional administration to provide [Teaching Assistants] TAs based on masters degrees or something entirely new. Universities, overall enrollment-with a lag time built in. Math enrollments themselves, are now viewing departmental structures and are decreasing, and the department is thus concerned. Why college structures as more than occasional impediments to not offer to run a "Treisman-like program" with its success­ "getting the job done". Mathematics (all of it), by virtue of its using TAs. If that department only improved success rates in fundamental nature, is singularly positioned to address some calculus, the argument for the extra TAs would be made. of these issues. Continuing on the education front, I would observe that Finally, and here I would risk calumny, suppose we leading mathematics departments have not often exercised ef­ decided that it was okay not to look like some of the fective leadership in the preparation of mathematics teachers. "better known" universities. This might be called "diversity This is probably one of the hottest issues of the day, and of mission". Some departments produce many masters degree history does not position us well. Moreover, the answer is not students directly for local industry. If we judged them by their as simple as ''just let them take the usual math major courses excellence in algebraic geometry or any one of a set of "hot" and everything will work out fine." If the teachers teach their fields, the departments would not emerge high. Yet, they are students mathematics the way we teach them ("sit and git"), doing something quite important. I would suggest that there they will not succeed. There should be some changes. Again, is a community responsibility to address a certain number of here is an opportunity to make a real difference. Keep in mind issues, and maybe one does this by a division of labor with that the half-life of school teachers is seven years, so that appropriate credit going to all from all. if colleges and universities produce strong teachers ready to Now history has it that we have been here before. In involve students as recommended in the [National Council 1971 Gail Young wrote an article for the Notices bemoaning of Teachers of Mathematics] NCTM "Standards", we could the employment situation and how all the predictions had tum around the entire school mathematics program in one been wrong. He spoke of the importance of "a steady supply generation. of brilliant young scholars" and that 1971 had ''the most Now, what type of graduates are we producing? By this I talented, best trained young mathematicians in history," and mean masters or Ph.D.s. We still produce for academe. There went on to say that "if we are not careful the supply will be are some isolated instances of the contrary. Are we doing cut off." This is no less true today with all of mathematical those who study mathematics a service by continuing to clone research, pure and applied, flourishing as well as having the ourselves? Are we paying attention to areas of national need? community significantly involved in education. But Young Now do not, please, confuse my comments with the idea went on to say that only 15% of the Ph.D.s went into industry, of discipline bashing. But over the years we have permitted and questioned whether we really know what industry needs. the mathematical sciences community to become fragmented, (We know a lot more now as the programs at the Institute for with each of our parts attacking common problems separately. Mathematics and its Applications have shown us.) Here are Why not make common cause again? There is one certainty. Young's closing remarks: "What I do believe is that we must Many of the problems facing the country (environmental make fundamental changes in the nature of graduate work studies, for example) are interdisciplinary by nature. A good in mathematics which will prepare most of our students for model for weather prediction requires physical modeling of at­ something other than academic life." mospheric flows on various spatial scales, functional-analytic Compare this to a comment from the 1992 AMS Task understanding of the equations of fluid dynamics on those Force on Employment, chaired by Don Lewis. It says that scales, numerical analysis to create algorithms, and ability the American Mathematical Society should "advocate for the to match the algorithms with various sequential, vector, and broadening of doctoral programs in mathematics to recognize parallel computer architectures. Adding the effects of the land the value of nonacademic employment and the matching of into such models requires additional disciplines such as biol­ talent with the teaching needs of the community, to produce ogy. Advanced materials, manufacturing processes, molecular doctorates with wider employment options." manufacturing, biomanufacturing, statistical quality improve­ Sound familiar? Arguably, the situation now is more ment, and design of flexible manufacturing systems are areas serious than it was in 1971, and hopefully we will not have to that need pure and applied mathematics, statistics, and oper- wait as long as a generation to take some definitive action.

8 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY MSEB Comes of Age

This brochure was a collaborative effort of the Mathe­ matical Sciences Education Board of the National Research The Mathematical Sciences Education Board (MSEB) of Council and the Children's Television Workshop, based on an the National Research Council (NRC) was established in earlier kit, "Math Matters," which was developed jointly with 1985 to advocate for and stimulate reform in mathematics the national PTA. The scale of the distribution illustrates the education. Currently, Alvin W. Trivelpiece, director of reach of the MSEB as it comes of age at a time of increasing Oak Ridge National Laboratory, is chair of the Board. interest-and increasing political heat-in education. In addi­ Lynn A. Steen of St. Olaf College became executive tion, the brochure exemplifies the MSEB's large-scale efforts director of the MSEB in September 1992. He succeeds to get the general public to view mathematics differently. Ray C. Shiflett, who has returned to California State With connections to a dizzying array of constituencies having Polytechnic University at Pomona. Other new MSEB an interest in mathematics education, the MSEB has become staff include Susan Forman of Bronx Community College an increasingly sophisticated organization that's charting a of the City University of New York, who is directing new course for itself in the mathematics education reform college and university programs; and J. Arthur Jones of movement. Futura Technologies, who serves as director of minority programs. Other senior staff members are: Linda Rosen, director of policy studies; Robert Kansky, project director From Reports to Implementation of educational networks; Joan Donahue, director of state The reports MSEB has produced over the last several years, coalitions; Ann Kahn, director of organizational relations; starting with "Everybody Counts" in 1989, have gone a long Kathleen Holmay, consultant for public information; and way toward building consensus on the need for change in Claudia Dissel, director of the Corporate Council for mathematics education. Together with the "Curric:ulum and Mathematics and Science. Evaluation Standards for School Mathematics", issued in MSEB is located at 2001 Wisconsin Avenue, NW, 1989 by the National Council of Teachers of Mathematics Washington, DC 20007. MSEB can be reached by telephone (NCTM), the MSEB reports have spurred a great deal of at 202-334-3294; by email at [email protected]; by fax at national discussion about mathematics education. They have 202-334-1453; and by mail at 2101 Constitution Avenue also outlined the basic shape of the reforms: appropriate use Ave., NW, HA 476, Washington, DC 20418. Individual of computers and calculators, more student-centered learning, staff email addresses are of the form [email protected], less rote memorization, an emphasis on problem solving, a where "i" is the initial of the first name and "name" is the wider and richer menu of mathematical topics, and so on. full last name. Now that the first wave of reports is out and there is general agreement on the broad outlines for change, the MSEB has In the past year, 1,000,000 copies of a brochure about been rethinking its role. ''The MSEB has moved beyond just mathematics were distributed to parents, teachers, school writing reports to an activist, political stance to bring about administrators, guidance counselors-anyone interested in implementation of the recommendations in the reports," notes encouraging youngsters in mathematics. This is no high-tech Steen. But this doesn't mean that the MSEB staff will start publication, just a simple 8 112" by 11" piece of paper, writing worksheets for fourth-grade classes and software to folded into three sections, that presents a number of simple help teach geometry; the MSEB has never been involved at mathematical games and experiments kids can have fun with. that nitty-gritty level. That's the bailiwick of agencies like The brochure, entitled "Yes You Can!", presents a view of the National Science Foundation, whose education budget has mathematics different from that held by most of the general risen dramatically over the last several years. So there is no public; it shows how mathematics permeates the activities of shortage of ideas for reform, but the schools have to start everyday life, from traveling in a car, to cutting up a pizza using them. "Some communities have been content to keep for friends, to daydreaming about the patterns in kitchen floor operating the way they have been," Steen says. ''They haven't tiles. yet bought into the national agenda." One role for the MSEB

JANUARY 1993, VOLUME 40, NUMBER 1 9 to play is as a kind of national coordinator to make sure program, they can make important intellectual contributions that the relevant organizations have the knowledge, means, to the reform effort. She says she has heard "lots of compli­ support, and encouragement to bring about change. This kind ments but not much substantive discussion" about such MSEB of outreach is at the heart of MSEB's "implementation" projects as "On the Shoulders of Giants", which explored new activities. intellectual bases for school mathematics curricula. As former Part of this effort is to get schools to start thinking in terms MSEB chair Shirley Hill put it, if you take the "spine"­ of national standards. "We want to get the expectations of a namely, arithmetic-out of school mathematics, what should standards-based curriculum embedded in the decision-making take its place? "We would like to engage mathematicians processes of schools," says Steen, so that change does not in rethinking what mathematics is in order to provide rich always require an outside impetus. "The strategy of the MSEB frameworks for curriculum development, teacher training, and with regard to standards is that the standards represent goals, so on," says Rosen, "so we insure that the beauty and breadth but there are many different curricula that might get you of mathematics is well represented." there ... We don't say one is right, and one is wrong." For example, what works in one community might not work, for MSEB Projects historical, cultural, social, or economic reasons, in another The various projects under the MSEB umbrella have very community. It's tricky to judge a curriculum in isolation, different flavors and very different sets of activities. Rosen's he says, but it is possible to develop standards by which a program on policy studies tries to develop a message about variety of curricula can be measured-this is what the NCTM mathematics education reform that's based on research­ "Standards" have tried to do. either traditional educational research or "research in prac­ The MSEB will also strengthen ties to science education. tice", that is, the accumulated wisdom of experts. One area A group at the NRC is developing standards for science Rosen has been looking at is the international arena. Every education analogous to the NCTM "Standards". Although so often yet another dire report comes out showing how coordinating mathematics and science education has some American youngsters are trailing in mathematics achievement clear advantages, Steen notes that "mathematicians hesitate when compared to their counterparts in other countries. Rosen to lose their discipline's identity to science." However, he points out that, while such comparisons are useful, many notes that the science standards are picking up on some of believe that the tests do not reflect the consensus in this the same intellectual themes in the NCTM "Standards", so country about what is valued in reform. Rather than preparing philosophically the two are unlikely to be far apart. "The students for "international horse races", she says, educators fact that the science standards are coming out compels us to should be taking a close look at what other countries are doing coordinate with what they're doing," says Steen. "And the in education and what could be useful here. "Everyone has the political reality dictates that we need a 'big tent'." same questions about mathematics education worldwide, but Another area of focus for the MSEB is teacher preparation. different countries have different answers," she says. "Some Steen points out that it is only through change in the answers will translate, some will not." undergraduate preparation of teachers that reform will be In fact, there has been a great deal of contention over the sustained. "If you don't get at this problem, everything else issue of testing just within this country. Currently, standardized you do, like in-service programs, is in effect patching up tests are given to students in virtually every grade; national things that weren't done right to begin with." Steen calls for samples are gathered in grades four, eight, and twelve. a "thorough change" in undergraduate mathematics courses, Considering the influence these tests have on curricula, teacher so that the teachers of the future are themselves taught with accountability, funding for schools, and so on, it is important the methods they will be expected to use in the classroom: that the tests reflect current thinking about what students more student interaction, less lecturing and memorization, should be learning. One project under Rosen's program is a open-ended problem solving, and so on. This means that set of prototype assessment tasks at the fourth grade level. college and university professors, those who train future These tasks were pilot-tested last spring and fall, and a report school teachers, need to change their own teaching methods. about them, called "Measuring Up", was issued in December The MSEB office of college and university programs is 1992. The assessment tasks do not themselves constitute a beginning to explore the kinds of source materials that would standardized test, nor do they cover the whole fourth grade be useful to faculty interested in changing their teaching curriculum, Rosen notes, but they do provide some exemplars methods. Effective materials would document examples of of good assessment materials and indicate directions to move teaching that model alternative methods that faculty may wish in. This project is part of a larger MSEB effort in assessment, to incorporate into their repertoire of classroom strategies. which includes a major report, scheduled for fall of 1993, Although the MSEB has always had research mathe­ called "Measuring What Counts", a guide to state and local maticians among its members, the voice of the mathematics school districts that want to change their use of assessment. research community is generally a minority among the broader In addition to these projects, others having policy impli­ educational interests represented on the Board. The commu­ cations are just getting off the ground. Susan Forman's office nity has little experience with the MSEB's efforts with school of college and university programs will be working with a boards, PTAs, and state education departments. However, task force charged with starting to formulate a study of the notes Linda Rosen, director of the MSEB 's policy studies impact of calculus in high schools to examine, for example,

10 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY MSEB Comes of Age how successful completion of AP calculus affects students' teachers, and so on, than can the MSEB, which sits at the later choices about what mathematics to take in college or more rarefied level of the National Academy of Sciences. Your how having a calculus program affects a high school's overall typical parent, for example, is unlikely to read "Everybody mathematics curriculum. "We may find that there are 'un­ Counts". ''The coalitions know they're dealing with Mr. and expected outcomes' of offering calculus in high school and, Mrs. Average American and their kids," says Donahue. "How as a result, may want to think about alternative courses," do you convince them of the importance of mathematics?" notes Forman. In addition, the office of college and university Having the state coalitions establishes a local link that brings programs hosted a meeting of presidents-elect and executive in many groups who otherwise might not be convinced that directors of the AMS, the American Mathematical Associ­ change is needed. ''There needs to be a huge effort to educate ation of Two-Year Colleges (AMATYC), the Mathematical the public on what needs to be done, what kind of mathematics Association of America (MAA), the NCTM, and the Society we're talking about," says Donahue. for Industrial and Applied Mathematics (SIAM) to discuss The MSEB also helps to bring together groups whose issues of common concern contained in their long-range plans primary interest is not necessarily mathematics education, and explore ways in which the societies might cooperate to but which have some stake in seeing improvements in advance their agenda. this area. For example, Jones coordinates the Alliance to J. Arthur Jones' program on equity and diversity is starting Involve Minorities in Mathematics (AIMM), which comprises work on a systematic study of existing programs for minorities fifty-six organizations, from federal agencies, to community­ in mathematics, to guide policy leaders in understanding what based organizations, to professional societies. Jones says kinds of programs are effective and what issues they should AIMM seeks to address cross-cutting issues that depend address. Jones is particularly interested in improving minority on many different groups working in a coordinated way. achievement in the early grades because he believes that ''These issues are the responsibility of many who don't work without a solid early training, ''we won't have anything to do directly in education but who have indirect influence on it," in college [mathematics] because there won't be any minority Jones notes. For example, there are media representatives on students." AIMM, because the media can exert an influence on attitudes about mathematics. Jones says that he is also working on Outreach a Major Focus a clearinghouse of information on successful programs for Outreach is a centerpiece of the MSEB's efforts-in fact, minorities in mathematics. four MSEB programs are primarily concerned with outreach. One of these is the state coalitions project, directed by Joan Predicting the Future Donahue. Begun in 1989, this program has now established Steen says that, as work on reform proceeds, the MSEB will coalitions in all fifty states and the District of Columbia. have to focus on the transition to new ways of teaching and The purpose is to develop a national network of independent learning mathematics. ''The number of variables is so huge, organizations to work toward reform in mathematics education and the pressures are so great, that we will go through a at the state level. The coalitions include classroom educators transition period in which the old ways of doing things get and mathematicians as well as representatives from business thrown out or modified, but no one knows what will take and industry and government. The coalitions are at various their place," he notes. Part of the difficulty is that the issues stages of development, and their activities, says Donahue, unique to mathematics education are only a small part of the are "all over the place". They vary from organizing teacher whole education scene. Organizations like the MSEB have in-service programs to working with politicians to change to work for change amid battles over school management, educational policies at the state level. In addition, some of control of curricula, pressures to assess teachers' competence, the coalitions work to establish strong links to business and school choice, and so on. Just what's next leaves everyone industry, and some are combining their efforts with work in guessing, including Steen. "In that context," he says, "it would science education reform. be foolhardy to predict the future." The advantage of having coalitions ·at the state level is that Allyn Jackson they can more directly influence school boards, parent groups, Staff Writer

JANUARY 1993, VOLUME 40, NUMBER 1 11 Forum

of certain publicists and writers, mostly of Jewish origin and mostly emigrants. Those writings present Russian history The Forum section publishes short articles on issues that and the Russian national character itself in a distorted and are of interest to the mathematical community. Articles humiliating way. should be between 1000 and 2500 words long. Readers are Although these writers and their literary output are mostly invited to submit articles for possible inclusion in Forum known in quite restricted circles of intellectuals, they still can to: somehow have a fatal effect on the Russian People. They are Notices Forum Editor "deadly dangerous for the Russian People, since they deprive American Mathematical Society it of self-confidence". · P.O. Box 6248 I would like to say at once that I respect all peoples, Providence, RI 02940 including the great Russian People. So it goes without saying or electronically to [email protected] that I respect the national feelings of Shafarevich, his devotion to his people, his sorrow about the tragic events in its past, and his concern with its future. I disapprove of the statements of some Jewish authors about the Russian People that Professor Some Remarks about Shafarevich has cited. Even if these citations are possibly Shafarevich's Book Russophobia taken out of context, they are regrettable. Boris A. Kushner It is rather difficult for me to discuss the part of Russo­ University of Pittsburgh at Johnstown phobia related especially to Russian national problems. Being I was asked by Professor Carolyn Gordon, the Editor of the Jewish and feeling myself Jewish, I abstain from such dis­ Forum, to present my personal opinions concerning the well­ cussions. Problems that touch sensitive points of the Russian known controversy surrounding Professor I. R. Shafarevich national self-consciousness are not for outsiders. So, I would and his book Russophobia. rather dwell on the part of Shafarevich's writings that in some I read this book (in a samizdat copy) in Moscow in the way is addressed to me. spring of 1987. There is no room here to present at length It is astonishing to observe how a man, who just a few the contents of the book and its central concept of the "lesser pages before defended the national dignity of his people, can people" (malyi narod). The author discovered this concept launch a violent attack against another people. After arriving in works of the French historian A. Cochin and found it at the conclusion that persons of Jewish origin form the kernel an indispensable tool for explaining fundamental historical of the Russian "lesser people", Shafarevich undertakes an events, especially events of a revolutionary nature. Applying all-out search to find reasons for it. This search involves a sort this concept to the modem and recent history of Russia, of essay about Jewish history, national traditions, and national Professor Shafarevich discovers a "lesser people" behind character, beginning from Biblical times and finishing in our the scenes. A "lesser people" organized the catastrophic century. I presented my criticism of and my feelings about Revolution of 1917; a "lesser people" is trying right now to this essay at length in my open letter to Professor Shafarevich. alter the natural course of historical development in Russia. This letter was distributed in samizdat in 1987 when I was As in previous historical manifestations of the phenomenon, still a resident of Moscow. Later, it was widely published the spiritual values and aspirations of the "Russian lesser and broadcast by the Russian-language media in the West. people" are completely alien, even hostile, to those of the Now this document is available in English in an excellent "greater people". Inevitably, the "lesser people" despises, translation by Professor David Webb. even hates, the "greater people" and regards them as material It is general knowledge that the Bible is a document of for social experiments. The presence of and the dangerous unparalleled significance and complexity. It is as rich and activities of this "lesser people" in contemporary Russia can as complicated as life itself. It leaves freedom of choice be recognized, according to Professor Shafarevich, in writings to everyone who reads it. Professor Shafarevich uses this

12 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Forum freedom of choice to assemble a list of citations of a something about the person who is doing the citing. There is pejorative character taken completely out of their theological, an ocean of possibilities, and everyone finds what he or she is historical, and poetic contexts. For example, in Isaiah he did looking for. For example, it is not difficult to imagine a crank not notice, say, 2.4: creating a russophobic manifesto from the corpus of Russian "And He shall judge among the nations, and shall rebuke classic literature. many people: and they shall beat their swords into plowshares, What is most regrettable, however, is the hatred that I and their spears into pruninghooks: nation shall not lift up felt in every word of Shafarevich's essay. (I am aware that sword against nation, neither shall they learn war any more." Professor Shafarevich would strictly deny that any hatred ... but he did find 61.5: was intended. Moreover, I admit that he really means it. "And strangers shall stand and feed your flocks, and Alas, does it matter much to a person reading his writings the sons of the alien shall be your plowmen and your vine with pain in the heart, or for another person who faultlessly dressers." perceives the message hidden between the lines?) Perhaps It is supposed that for centuries and centuries Jewish this overwhelming hatred is responsible for some of the educators somehow used something similar to Shafarevich's elementary factual mistakes, otherwise inconceivable in the list to educate new generations of the Jewish People. Negative case of a scientist of such caliber. Well, hatred is a bad adviser. sides of the Jewish national character which manifest them­ And hatred always lacks originality: many of the anti-Jewish selves in the "Russian lesser people" are ostensibly results of allegations of Shafarevich can be found, e. g., in the notorious such an education. book of V. Shul'gin (a self-proclaimed anti-Semite and a I find it amazing that a person who professes to be a remarkable personage in recent Russian history), Chto nam v Christian can treat the Old Testament, a sacred book of both nikh ne nravitsya ("What We do not like in Them"), written the Jewish and Christian Religions, in such a blasphemous in the late 1920s. (However, I would give more credit to Mr. way. The manner in \Yhich Professor Shafarevich performs Shul' gin for his straightforwardness, his artistic style, and his his surgery on the Old Testament reminds me of the worst ex­ capacity for national self-criticism.) It is curious to note that cesses of Soviet atheist agitators (like the notorious Emel'yan Shul' gin's book finishes with a remark about the usefulness Yaroslavskil). of an Antirussizm (cf. Russophobia) in Gogol's style. The Talmud, not being a sacred book for Christians, is Professor Shafarevich, being widely recognized as an still widely recognized as a very important and complex excellent mathematician, probably wants to be considered as historical and theological document. It is a shame to see an a distinguished historian as well. He has resources for it: excellent scientist-mathematician launching a cavalier attack erudition, phenomenal memory, and a strong critical mind. on this tremendous work of many generations. One can But one crucial thing is missing: the heart. He treats awful imagine my feelings when I read that Jews were permitted human tragedies exactly like polynomials in his mathematical to desecrate non-Jewish graves. As I was reading it, I could works. In the entire text of Russophobia anti-Semitism, a see directly from the windows of my Moscow apartment tragedy that began long before, say, the conscious life of the a Jewish cemetery (Vostryakovo Cemetery) with desecrated Russian People and that still goes on, is denounced in exactly Jewish graves. Incidentally, Professor Shafarevich is rather one passing sentence-and this in a book where Jews are at vague about the sources of his talmudic erudition. I found the center of the investigation! On the other hand, one can references neither in the samizdat version of Russophobia, read that anti-Semitism is "a concept" ("an empty political nor in the recent Munich edition, nor in Shafarevich's recent slogan" in Shafarevich's latest writings), the main essence of work "Russophobia: 10 years later". It is true that "a recent which is the presumption of national (Jewish) innocence, and book of J. Katz, Professor at Tel-Aviv University" [sic!] is that this concept is designed to silence non-conformists and mentioned in connection with the Talmud in Shafarevich's to manipulate public opinion (the favorite trick of all "lesser latest work, but this reference generates more questions than peoples" in history) by distracting it from more important answers. To what period does "recent". belong, and what book problems. As examples of such manipulations, Professor does Professor Shafarevich have in n1ind? A distinguished Shafarevich mentions the well-known cases of Dreyfus (in historian, Professor Jacob Katz of the Hebrew University at France) and Beilis (a blood libel case in Russia). A reader Jerusalem has published quite a few excellent books. Certainly is left to guess whether the Jews themselves manufactured none of them lends any support to the biased and superficial these incidents in order to attain some national goal or to interpretations of the Talmud that Professor Shafarevich has influence political developments in the relevant countries. adduced. I think that we have here a clear case of misuse of Need I comment on this? sources. And after all, did Professor Shafarevich really study After reading this summer the above-mentioned work the Talmud? of Shafarevich, Russophobia: 10 years later, I felt myself Answering his opponents, Professor Shafarevich has re­ obliged to defend the national dignity of my people again. cently argued that he cited in his book authors of Jewish My second open letter to Professor Shafarevich is available ancestry who also criticize the trends denounced in Russopho­ to the interested individual (it is in Russian). In his new bia. I need hardly say that this proves absolutely nothing. Jews work Shafarevich speaks of Russophobia in an elevated, even are not a rigid body: there are plenty of individuals, moods, poetic way, envisioning future generations reading it, and so and trends among them. Moreover, a citation quite often says forth. It is amazing: the world is collapsing all around, already

JANUARY 1993, VOLUME 40, NUMBER 1 13 Forum

the "greater people" is becoming (literally) a "lesser one" group of colleagues, Professor Shafarevich deplores dwindling here and there in the former Soviet empire, but Professor American freedom of speech and opinion, supp?sed~y ~o Shafarevich continues in the midst of this tragedy his holy fatally undermined by the above open letter. !he s1tuat10n 1s war against a small handful of (mostly) second-rate literati. hardly so tragic: after all, Professor Shafarev1ch was able to Through private correspondence with my friends in Russia publish his answer in these very Notices, where the open letter and via the Russian-language media, I am aware that unfortu­ appeared. Moreover, the open letter, signed by a few hundr~d nately Professor Shafarevich has recently lent his name more mathematicians, was published as "an advertisement", while and more to certain circles of an extremist, nationalistic char­ Shafarevich's reply found a much more prominent place in acter. For example, he is listed as a member of the Editorial the magazine. I would like to add that all~sio~s t~ former Board of the magazine Nash Sovremennik (Our Contempo­ Soviet practices made by Professor Shafarev1ch m h~s. ans~er rary); the direction and the level of this monthly are only too rely upon the naivete of a reader completely unfam1har w1th well-known. It is worth mentioning that one can enjoy yet Soviet reality. Those who lived in the (former) USS~ c_an another literary fulmination on the subject of the "universal only laugh when reading these passages. When_was a ~~~tlm Jewish-Masonic conspiracy" in the very issue of the magazine of communist persecution allowed to defend hls conv1cuons in which Russophobia : 10 years later is published. and his dignity in public? The fate of those victims is only too To conclude these necessarily short notes, I would like well known. to say a few words about recent developments concerning I have to admit that reading Russophobia was a really Professor Shafarevich that have to some extent polarized painful experience for me. I was once among Sha~are~ich's the mathematical community. I am not in a position to students at Moscow University; I used to see him ~~ the discuss questions of membership in the National Academy corridors and halls of that University, in libraries, and m the of Sciences, but I am not sure that ousting members is Great Hall of the Moscow Conservatory. I deeply respected the best way of solving moral problems. At the same time him as an outstanding mathematician and teacher. A ~atred I can not believe that any self-respecting scientific body loves a hatred. There is a strong temptation to pay back m the can accept the principle proclaimed by some scientists that same currency. I will not do it. I am simply infinitely sad. "only scientific work counts". Answering the open letter of a

Nonlinear and Global Analysis Felix E. Browder, Editor Volume 1

This volume contains a number of research-expository articles that appeared in the Bulletin of the AMS between 1979 and 1984 and that address the general area of nonlinear functional analysis and global analysis and their applications. The central theme concerns qualitative methods in the study of nonlinear problems arising in applied mathematics, mathematical physics, and g_eo~etry. Since these articles first appeared, the methods and ideas they describe have been applied in an ever-widening array of apphc~tJ.ons. Readers will find this collection useful, as it brings together a range of influential papers by some of the leading researchers m the field.

1991 Mathematics Subject Classification: 35, 47, 49, 58 ISBN 0-8218-8500-6, 625 pages (softcover), December 1992 Individual member $44, List price $73, Institutional member $58 To order, please specify BULLRFJINA

14 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics

Edited by Keith Devlin

This month's column Smullyan, and John Kalman. In addition to proving significant In November's "Computers and Mathematics" column, Donald Macken­ theorems, a single automated reasoning program is used to zie discussed the nature of mathematical proof, the role of computers in construct a needed specific object or structure, to find an the proof-process, and the growing likeli?ood that the use of co.mputer­ appropriate model or counterexample, to supply a new axiom software systems wtll result produced or computer-aided proofs to venfy more elegant in some mathematicians finding themselves in the law courts any day system, to check a given proof, to discover a now. In this month's feature article, Larry Wos of the Argonne National proof, and to settle conjectures-positively or negatively. Laboratory describes his own experiences in developing and using the Noting that such powerful and versatile automated rea­ automated reasoning system OTTER. soning programs exist, one naturally wonders about the ease Following the Wos article, William Ruckle reviews Mathead, Suzanne of using such a program and which program is recommended. Molnar takes a look at Matrix Algebra 2.2, and Roger Pinkham road tests The program I recommend is the one that continues to play the TI-85 calculator. a vital role in my research: Its name is OTTER [3]. OTTER Editor's address: is rather easy to use, requiring one to prepare an input file that contains no more than a statement of the problem under Professor Keith Devlin attack and an instruction concerning the type of reasoning to Department of Mathematics and Computer Science Colby College employ-when the choice is simply to rely on the program's Waterville, Maine 04901 defaults. (Because the presentation of a question or problem is ordinarily the most burdensome aspect of using a program to: Correspondence by electronic mail is preferred, reasons logically, I postpone its discussion until after [email protected]. that introducing the five elements of automated reasoning.) Of course-as one expects with an increase in the challenge of research, games, or puzzles-to complete assignments of in­ creased complexity demands an increase in the sophistication Automated Reasoning of program use. Fortunately, however, increased complexity Answers Open Questions and required sophistication are not commensurate: An in­ crease of a factor of 1000 in complexity is frequently reflected LarryWos* in an increase in sophistication of only a factor of 10. For overcoming the obstacle of ever-growing complexity, the program OTTER offers the use of strategy of various types. Researchers, poker players, chess players, each can attest An Automated Research Assistant to the appeal and intrigue of using strategy. To further aid When a computer program applies logical reasoning so the user of OTTER, the program offers (through use of the effectively that the program yields proofs that are published chosen output file) some assistance in verifying that all is in in mathematics and in logic journals, an important landmark order regarding one's attempt to solve a problem or answer has been reached. That landmark has been reached by various a question. In addition to echoing in the output the various automated reasoning programs. Their use has led to answers options from which one can choose, for each deduced con­ to open questions from fields that include group theory, clusion the program presents the precise history of its origin. combinatory logic, finite semigroup theory, Robbins algebra, An examination of such histories enables one to determine propositional calculus, and equivalential calculus. Among the accuracy of the chosen representation and to evaluate the answered the successes, automated reasoning programs have wisdom of the choices regarding strategy, type of reasoning, Dana Scott, Raymond questions posed by Irving Kaplansky, and parameter settings. To facilitate and encourage both the use of the recom­ *Larry Wos is a research scientist in the Mathematics and Computer Sci~nce Division at the Argonne National Laboratory. He can be reached by emml at: mended program and the reliance on automated reasoning to [email protected]. assist in research, written material is available: a taste offered

JANUARY 1993, VOLUME 40, NUMBER 1 15 ~~------~~~~~~~~~~a··-~····-··················································-···············-···~··································~······ Computers and Mathematics by this article, a meal offered by a problem database accessi­ For this area of logic, condensed detachment considers ble electronically, and a veritable banquet offered by the new two formulas, (A --+ B) and C, and, if C unifies with A, yields McGraw-Hill book Automated Reasoning: Introduction and the formula D, where D is obtained by applying to B the most Applications, by Wos and coauthors [13]. With the tutorial general unifier of C and A. Unification is a procedure that given in Chapter 16 and with the program OTTER provided considers two expressions and seeks to find the most general on diskette in that book, one can soon experience ·the use of substitution that makes the two identical; unification will be an automated reasoning program as a valuable research as­ discussed further in the section on the elements of automated sistant. OTTER runs well on workstations, (IBM-compatible) reasoning. personal computers, and Macintoshes. One might now wish some insight into the difficulty of Coming Attractions the questions answerable with the assistance of OTTER. To For the curious and for those who have been tempted to fulfill such a wish, I prefer and enjoy offering conjectures that consider the three given conjectures, in this article I settle were settled by using the program, and, for added interest, I each, touching briefly on the role the program OTTER played suggest (as a possibly intriguing contest) that the researcher and drawing on earlier research. Because the brevity of that attempt to settle the conjectures unaided. I have selected three discussion may leave various questions unanswered, I focus conjectures for consideration: one conjecture from group in greater detail later in this article on the basic elements of theory, one from combinatory logic, and one from two-valued automated reasoning, enabling the researcher to gain a fuller sentential calculus (also known as propositional calculus). In appreciation for how OTTER attacks a question or problem; the following, lower-case u through z are variables. the use of strategy may be of particular interest. One learns that, in contrast to the programs that are symbolic calculators Conjectures to Settle, a Friendly Contest between Re­ for integration and the like, the type of program in focus searcher and OTTER in this article applies logical reasoning, rather reminiscent Conjecture 1. The following equation fails to provide a of that found in mathematics-and sometimes with totally complete axiomatization for the variety of groups of exponent unexpected and intriguing results that are publishable. 5, all of those groups in which, for all x, the fifth power of x To complete the picture, I discuss the general type of is the identity e: problem for which OTTER provides valuable assistance and feature specific open questions that were answered. The focus (1) (x(x((x(x((xy)z)))(e(z(z(zz))))))) = y. is mainly on the research at Argonne National Laboratory, for, more than any other effort concerned with the automation of The preceding conjecture can be viewed as asserting that reasoning, my colleagues and I at Argonne have emphasized equation ( 1) fails to imply at least one of the following: the study of open questions. As one learns in this article, product is associative, ex = x = xe, the fifth power of x (for our approach to the automation of reasoning differs sharply all x) is the identity. One need not be concerned with inverse, from approaches one often finds in artificial intelligence; for the inverse of x is simply equal to the fourth power of x indeed, our paradigm relies on types of reasoning and other for groups of the type under consideration. procedures that are not easily or naturally applied by a person. Conjecture 2. Using the following two equations for the To complement the successes reported here, I pose ad­ combinators B and N, one can show that there exists a fixed ditional open questions and offer challenges, each focusing point combinator F expressed solely in terms of B and N, on some area of mathematics or logic. As may already be where a fixed point combinator F is a combinator such that obvious, I conjecture that the use of the program OTTER Fx =x(Fx): provides substantial potential for an attack on the posed questions and the offered challenges, as well as an attack (2) ((Bx)y)z = x(yz), on other questions of which I have no knowledge. If one is (3) ((Nx)y)z = ((xz)y)z. interested in research and challenges concerned directly with automated reasoning, the cited program will also serve well in Conjecture 3. Where"--+" can be interpreted as implica­ that regard; a good source for appropriate research problems is tion and "-," as negation in the following six formulas, one the book Automated Reasoning: 33 Basic Research Problems can show that there exists a model that satisfies condensed [11]. Therefore, for those who may be interested in using detachment (to be defined almost immediately) and formulas this new research assistant, this article provides the details (4), (5), and (6) and that fails to satisfy at least one of (7), (8), for obtaining a copy of the program. Should researchers use and (9): OTTER profitably, I would enjoy hearing of the results; the appropriate electronic mail address is [email protected]. I (4) (((x--+ y)--+ z)--+ (y--+ z)), also encourage researchers to send additional open questions (5) (((x --+ y) --+ z) --+ ( -,(x) --+ z)), to consider. (6) ((u--+ (-,(x)--+ z))--+ (u--+ ((y--+ z)--+ ((x--+ y)--+ z)))), · (7) ((x--+ y)--+ ((y--+ z)--+ (x--+ z))), Open Questions Answered and Challenges Offered (8) ((-,(x)--+ x)--+ x), To add to the temptation of using an automated reasoning (9) (x--+ (-,(x)--+ y)). program and of suggesting other areas to explore, I now tum

16 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics to various open questions that were answered with heavy is dependent on the remaining four, no proofs were obtained. assistance from OITER and its predecessors. As for areas of Fortunately, Steve Winker (a member of the Argonne group) mathematics and logic totally unrelated to those of concern in then devised a method enabling one of our reasoning programs this article, they are also amenable to study with an automated to generate models [9]. By using a program (whose design reasoning program-for example, set theory [6, 11], number preceded that of OITER) to apply Winker's method, we theory [8], and Tarskian geometry [7]. Although this article quickly established the independence of each of the first three focuses mainly on recent studies of group theory, combinatory axioms. Although the models that suffice are disappointingly logic, and various logic calculi, it also touches on questions small-each consisting of four or fewer elements-we had, answered little more than a decade ago, for they serve nicely nevertheless, succeeded for the first time in our research in to illustrate types of problems that can be attacked with a using an automated reasoning program to answer an open reasoning program. At least from the historical perspective, question. (For those interested in history, I note that, prior to the successful use of an automated reasoning program to our attempt at Argonne National Laboratory to answer open answer open questions is simply astounding. questions, the only successful use of a reasoning program in Indeed, to see how pessimistic was the view concerning that context is the one concerning SAM's lemma in the theory the possibility of automating logical reasoning so success­ of modular lattices [1]. I also note that our programs are still fully as to permit proving interesting theorems-'-Or, for that not very effective for model generation.) matter, proving even simple theorems--one need only glance at the following quote taken from a 1948 paper by the em­ Finite Semigroups inent logician J. Lukasiewicz [2]: "A formalized proof can To obtain a question from a field of far greater interest be checked mechanically but cannot be mechanically dis­ than offered by ternary Boolean algebra, we turned for an covered." Obviously-and most fortunately-as this article appropriate challenge to Irving Kaplansky. He suggested repeatedly demonstrates, Lukasiewicz was mistaken. That seeking an answer to the following. such a famous logician held this position is completely under­ standable; indeed, to have believed otherwise in 1948 might Does there exist a finite semigroup that admits a nontrivial have required clairvoyance. Even further, but four decades antiautomorphism but that does not admit any nontrivial ago, how could any mathematician or logician have conjec­ involutions? tured with conviction that the late 1980s and early 1990s A nontrivial antiautomorphism is a one-to-one onto map­ would find that computer programs not only "discover" sig­ ping h such that h(xy) = h(y)h(x) and such that h is not nificant proofs, but often discover such proofs in astonishingly the identity mapping. A nontrivial involution is a nontrivial little computer time? antiautomorphism j such that j(j(x)) = x. I begin with questions taken from pre-OITER history, The nature of the Kaplansky question suggested the questions answered with a predecessor of this newest auto­ avoidance of an exhaustive search. After all, there exist more mated reasoning program. than 800,000 semigroups of order 7 alone, no two of which are isomorphic. Recognizing the difficulty of telling a reasoning Ternary Boolean Algebra program that the sought-after structure must be finite, we The first example focuses on the esoteric field of ternary chose to have the program explore candidate semigroups, Boolean algebra and the question that marked Argonne's keying on various sets of generators and relations. The study entrance into the use of an automated reasoning program to succeeded: An appropriate semigroup was found, one of order attempt to answer open questions. The question asks which, 83 [10]. To attempt to find a smaller semigroup of the desired if any, of the first three of the following five axioms is type, we had the program proceed more or less as one would independent of the remaining four axioms: in the study of quotient groups. Again success: One of order 7 was found, and, later, it was proved that there exist four (TBA1) f(f(v,w,x),y,j(v,w,z)) = f(v,w,f(x,y,z)), nonisomorphic semigroups of that order and none of smaller (TBA2) f(y, x, x) = x, order. (TBA3) f(x, y, g(y)) = x, (TBA4) f(x, x, y) = x, Equivalential Calculus (TBA5) f(g(y), y, x) = x. The third success focuses on a field of logic known as equivalential calculus and on questions that proved to be A nonempty set satisfying these five axioms is a ternary far more difficult to answer. The formulas of equivalential Boolean algebra. It was known that the fourth and fifth axioms calculus are the set of expressions in the two-place function are dependent on the first three axioms. e (for equivalent) and the variables x, y, z, and so on. My colleagues and I were faced with two possible uses Fortuitously, from the viewpoint of automated reasoning, the of an automated reasoning program, that of proving theorems unification procedure can be relied upon, that procedure (as and that of finding models. Although not in the context of defined earlier) that considers two expressions and seeks attacking open questions, we had had many successes in the to find the most general substitution that makes the two former; in the latter, we had had none. When we attempted identical; unification is illustrated later, in the discussion of to have our program prove that each of the first three axioms the elements of automated reasoning. The inference rule that is

JANUARY 1993, VOLUME 40, NUMBER 1 17 Computers and Mathematics often employed to prove theorems is condensed detachment. that this formula held no interest for logicians, for it was For this area of logic-similarly to the use in two-valued already known to be too weak to be a single axiom. sentential calculus-condensed detachment considers two But luck was with us: we had already answered some of formulas, e(A, B) and C, and, if C unifies with A, yields the the seven open questions of concern before we learned of the formula D, where D is obtained by applying to_ B the most lack of interest in XBB. Even better, the approach gleaned general unifier of C and A. from our use of our program proved to play the key role Encouraged by John Kalman (the University of Auckland), in completing the study, the approach of identifying some who had heard of our prowess in proving theorems, we began number of patterns to describe all deducible formulas from the study of seven open questions: Which, if any, of the a given formula [15,14]. Each of the first five of the seven following seven formulas provides a complete axiomatization formulas is too weak to serve as a single axiom; but, contrary of equivalential calculus (a formula is a single axiom if and to conjecture, the last two, XHK and XHN, were proved only if one can use it with condensed detachment to deduce strong enough. all formulas in which variables occur twice): Group Theory and the Era of OTTER (XJL) e(x, e(y, e(e(e(z, y), x), z))), Having covered the pre-OTTER history of our attempts to (XKE) e(x, e(y, e(e(x, e(z, y)), z))), answer open questions, I now tum to the era of OTTER. My (XAK) e(x, e(e(e(e(y, z), x), z), y)), colleagues and I used this automated reasoning program to (BXO) e(e(e(e(x, e(y, z)), z), y), x), settle the three conjectures posed earlier and to answer various (XCB) e(x, e(e(e(x, y), e(z, y)), z)), related open questions, some of which I discuss in this article. (XHK) e(x, e(e(y, z), e(e(x, z), y))), Although the questions taken from group theory were studied (XHN) e(x, e(e(y, z), e(e(z,·x), y)))? most recently, I nevertheless begin with them [5]. One often studies group theory as a whole structure, To attack each of the seven questions, as is obvious, closed under an associative operation, in which a (two-sided) one could seek an appropriate proof or one could seek an identity exists, and in which, for every x, a (two-sided) inverse appropriate model. Since the conjecture was that none of the exists. Instead, one often studies a class or variety of groups in seven was strong enough to be a single axiom for the calculus, which an additional equation is assumed to hold. For example, the path that appeared best to pursue was to seek appropriate when xy = yx, one has the variety of commutative groups, models. Unfortunately, from what we were told, to seek a and when xx = e (the identity), one has Boolean groups. model might entail the examination of too many candidates. Here I shall confine my attention to varieties of groups of Since our programs have never demonstrated marked power odd exponent-all groups in which the cube of x equals the for model generation, the path concerned with establishing a identity, the fifth power equals the identity, the seventh power formula too weak to be a single axiom would almost certainly equals the identity, and the like. For a given variety, I focus require the formulation of a new approach. Our discovery on the search for a single equation that axiomatizes all groups of the needed approach nicely illustrates the symbiosis that in the variety; in particular, I show how my colleagues and I sometimes exists between a researcher and an automated settled the first conjecture. reasoning program, and it also illustrates that luck often plays When the focus is on all of group theory, Alfred Tarski a key role in science. proved that, if constrained to rely explicitly on product, Our foray into equivalential calculus began with the study inverse, and identity, one cannot find a single equation to of the formula XBB: serve as a complete axiom system. If the focus is switched from all of group theory to some variety obtained by adding (XBB) e(x, e(e(e(x, e(y, z)), y), z)). one equation, Ken Kunen (University of Wisconsin) has outlined a proof that again one cannot find an axiom system We chose that formula more or less arbitrarily, motivated by of the type discussed by Tarski. (Historical note: Kunen the belief that it corresponded to an open question. Using supplied us with his proof after we had completed the research condensed detachment as an inference rule and using various reported here and after we had answered various other related known single axioms as targets to establish assignment questions.) If one drops the requirement of the explicit use of completion, we instructed OTTER to study the formula XBB. the identity e, then B. H. Neumann has provided a schema for If the program was to succeed in deducing any of the target obtaining a single axiomatizing equation. However, because formulas, then we would have a proof that XBB is· a single our interest concerns the axiomatic question when the identity axiom-but such did not occur. Instead, an examination of the is explicitly present, the Neumann schema is of no assistance. program's output revealed that the deduced formulas steadily I begin with groups of exponent 3, those in which the third grew in symbol count. power of x (for all x) is the identity e, then settle the first Closer inspection showed that the handful of deduced conjecture, and close with a result that focuses on all varieties formulas could be described with a single iterative pattern, of odd exponent. William McCune (also an Argonne scientist) which led us to conjecture that all theorems deducible from had used OTTER to successfully study other varieties. His XBB would satisfy the pattern. On the one hand, we quickly research focused on single equations in which e is absent. proved our conjecture; on the other hand, we shortly learned Nevertheless, his work was clearly the impetus for asking the

""'""""""""""'""'"""'"""""""""" """''""""""'"""""""""'""""" ·--~-~--·-· .. -·~"~"''"""'"'''"""-""'"""""""""""""""'""'""""'~""' ...... _.... _.. ~_ .. __ .... ~ ...... _..•.••. ~.~--...... _.~---""'_'_"""~·-·--·----·~---·---- 18 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics following question. Does there exist a single equation in which F, a combinator expressed solely in terms of Band N with only the product and the constant e occur such that it serves as Fx = x(Fx). From what we know, no systematic approach a complete axiomatization for groups of exponent 3? Given with or without the aid of a computer exists for attacking this a candidate equation of the desired syntactic form, one must type of question-other than those we formulated when we use it to prove that product is associative, that the constant e studied combinatory logic with OTTER. is in fact an identity, and that the third power of x (for all x) is Barendregt defines combinatory logic as an equational equal to e. By using the inference rule paramodulation and the system satisfying the combinators Sand K with ((Sx)y)z = procedure demodulation (for canonicalization), in the style (xz)(yz) and (Kx)y = x; the set consisting of S and K of Knuth-Bendix, OTTER succeeded in finding the following provides a basis for all of combinatory logic. Rather than desired equation: studying all of the logic, logicians often focus on fragments of the logic, subsets whose basis is obtained by replacing (x)((x((xy)z))(e(zz)))) = y. S or K or both by other combinators. Where A is a given (Paramodulation and demodulation are discussed in the section fragment with basis B, the strong fixed point property holds on the elements of automated reasoning.) When we turned our for A if and only if there exists a combinator y such that, for attention to groups of exponent 5-and hence to the the first all combinators x, yx = x(yx), where y is expressed purely conjecture-OTTER again succeeded, finding the following: in terms of elements of B. The weak fixed point property holds for A if and only if for all combinators x there exists a (x(x((x(x((xy)z)))(e(z(z(zz))))))) = y. combinatory such that y = xy, where y is expressed purely in terms of the elements of B and the combinator x. Therefore, In other words, the first conjecture was refuted. the focus of attention for the second conjecture is the possible To be precise, we had actually conjectured that the presence of the strong fixed point property for the fragment preceding equation does provide an axiomatization for groups with basis consisting of B and N alone. of exponent 5 and, further, that it is a member of a family of As for the second conjecture, use of OTTER settles it in closely coupled equations for groups of odd exponent. To test the affirmative by constructing the following combinator: our more general conjecture, we had OTTER study groups of exponent 7, 9, 11, 13, 15, and 17, each with the appropriate B(B(N(BB(N(BBN)N))N)B)B. member of the family we had in mind. We were thus using Of far greater interest is the manner our program as a research assistant; without such an assistant, in which the combinator is constructed. Indeed, a researcher might find this study more than cumbersome. this combinator, as well as various others that answered open questions Although we were forced to experiment to find the of the type on which the second conjecture appropriate parameter settings for the different cases under focuses, was constructed by applying a new strategy, the kernel strategy study, OTTER succeeded eventually in all six. To provide [4, 12]. This strategy is what I had in mind when some insight into the magnitude of OTTER's achievement, I remarked about the lack, prior to our research, of a systematic approach I note that the case focusing on exponent 17 required more to answering the type of question under discussion. than 23 CPU hours on a SPARCstation 2, producing a proof For a given fragment, the application by OTTER of the kernel (for associativity alone) consisting of 181 applications of strategy often settles the question concerning the presence paramodulation. For those who may wish to use some other of either fixed point property in less than 3 CPU seconds reasoning program to consider the same precise question, I on a SPARCstation 2-by constructing an appropriate object-or note that excluded from the cited proof length count are the suggests what is needed for an argument to show that hundreds of canonicalization steps. I also note that, were the the desired property is absent. proof written out in its fullest, it would contain equations with more than 4,000 symbols. Immediately, two queries demand attention: (1) from where does the kernel One of the charming properties of the family of single strategy derive its power, and (2) how might one explain its formulation axioms for the various varieties of groups of odd exponent by researchers in automated reasoning rather than by researchers is that no need exists for recursion; instead, given an odd in combinatory logic? The power of the strategy rests mainly on three exponent, one can immediately provide the desired single aspects. First, the strategy relies on the use axiom-or so it appears. Since an appropriate proof has not of the inference rule paramodulation (to be discussed later), a rule that yet been completed, I offer for research the conjecture that, generalizes equality substitution and in a manner for all odd exponents, the type of equation we have exhibited not reminiscent of some researcher's reasoning. Second, various for exponents 3 and 5 generalizes. In that regard, I now give strategies are used to control the application the corresponding equation for exponent 17: of paramodulation to deter the program from deducing unneeded information. Third, when (x(x(x(x(x(x(x(x((x(x(x(x(x(x(x(x((xy)z))))))))) the question under study concerns the strong fixed point ( e(z(z(z(z(z(z(z(z(z(z(z(z(z(z(zz))))))))))))))))))))))))) = y. property, the kernel strategy attacks it in two stages, in the first stage attacking the easier-to-answer question concerning Combinatory Logic the weak fixed point property and, if the answer is in the The second conjecture focuses on the adequacy of the com­ affirmative, in the second stage using only the relevant results binators B and N for constructing a fixed point combinator to attack the harder question. In particular, the second stage of

JANUARY 1993, VOLUME 40, NUMBER 1 19 Computers and Mathematics the strategy relies heavily and directly on the results (obtained sentential (or propositional) calculus, I thank Dana Scott, for it in the first stage) that establish the presence of the weak fixed was his interest in our research and in OITER that eventually point property, gaining marked effectiveness by ignoring all (though indirectly) led to our study of the conjecture. The path other information produced by the first stage. Regarding the to that study began with a challenge from Scott: See whether researchers who formulated the kernel strategy, we had the OITER can prove all of the 68 theorems he selected from distinct advantages of access to a powerful reasoning program two-valued sentential calculus. Although our first attempt to and detailed knowledge concerning its elements, such as prove all 68 yielded proofs of only 33 of the theorems-a paramodulation, unification, and demodulation (a procedure result that many researchers might indeed consider rather for automatically canonicalizing deduced conclusions). impressive-the story has a beautiful ending. Our entrance into combinatory logic was indirectly Indeed, prompted in part by greed-manifested in the prompted by Raymond Smullyan, with whom we later com­ objective of proving all 68 theorems in one run-and in municated moderately often. That communication led to his part by curiosity concerning a possible new approach, we posing various open questions, questions we answered before formulated a new strategy, called the resonance strategy, our study of B and N, but during our formulation of the kernel which sharply differs from any other with which we were strategy. In response to his question, we proved that the frag­ acquainted at the time. In the context of the Scott challenge, ment with basis consisting of B and L alone does not satisfy the strategy in effect says to OITER: if the theorem T is the strong fixed point property, where (Lx)y = x(yy). Again proved and if T matches at the function occurrence level any prompted by Smullyan, we then proved that the fragment with of the 68 theorems to be proved, then focus heavily on T to basis consisting of L and Q alone fails to satisfy the strong direct the attack. When the new strategy was put to the test, fixed point property, where ((Qx)y)z = y(xz). Each of the OITER proved all68 theorems in a single run in less than 16 cited fragments does satisfy the weak fixed point property, CPU minutes on a SPARCstation 1+. proved by considering the expression (Lx)(Lx). (For the One significant criterion for measuring the power of a curious, I note that the preceding expression is a kernel.) As strategy is its effectiveness when used to study problems part of our research, we also showed that, from B and W other than those that prompted its formulation. The resonance alone, one can construct an infinite class of infinite sets of strategy meets that criterion. The new context is that of fixed point combinators. As it turns out, the same is true forB finding more elegant proofs, especially where elegance is and N. The reported successes provide yet more evidence of reflected in proof length. One of our more satisfying successes the value of relying on an automated reasoning program as a focuses on two-valued sentential calculus and on the following research assistant, for the program played a key role in all of axiomatization supplied by Lukasiewicz: the results cited here and in many not cited. Of course, many fascinating research questions concern­ (Ll) ((x ~ y) ~ ((y ~ z) ~ (x ~ z))), ing the strong fixed point property remain open, providing (L2) ((-.(x) ~ x) ~ x), challenges for the team of a researcher and an automated (L3) (x ~ (-.(x) ~ y)). reasoning program. Of the more interesting is one posed by Smullyan: Does the fragment with basis consisting of B The three formulas are, respectively, (7), (8), and (9) of and M alone satisfy the strong fixed point property, where the third conjecture. M x = xx? By considering the expression M(BxM)-another The Lukasiewicz proof that (Ll) through (L3) axiomatizes kernel-one quickly sees that this fragment satisfies the weak the calculus consists of 33 steps, each an application of fixed point property. Especially if one is interested in an condensed detachment. With the goal of finding a shorter and open question focusing on the weak fixed point property, I more elegant proof of the Lukasiewicz result, we decided to offer the following two questions. Does the fragment with base our attack on the use of the resonance strategy and on basis consisting of B and S alone satisfy the weak fixed the use of a feature in OITER that, for each conclusion that is point property? Does the fragment with basis consisting of reached more than once, compares the proof lengths and gives B and N 1 alone satisfy the weak fixed point property, where preference to the shorter. Therefore, at the beginning of the ((N1x)y)z = ((xy)y)z? One can immediately prove that the attack, we instructed OITER to focus heavily on any formula presence of the strong fixed point property implies the pres­ that is similar to one of the 33 steps in the Lukasiewicz proof. ence of the weak. For a different type of open question to We iterated, on the whole finding shorter and still shorter consider, I suggest that one attempt to find a finite model that proofs. For each step of the iteration-some of which yielded satisfies the equations for B and L but fails to satisfy the nothing of added interest-we changed various parameters strong fixed point property. That some model exists follows and, more important, keyed OITER's attack on using the from our earlier cited result; but it is not known whether a resonance strategy to focus heavily on any formula that is finite model exists. For additional open questions and for a similar to one of the steps of the shortest proof available. detailed treatment of the kernel strategy and numerous results We were rewarded: OITER eventually found a 22-step proof of its use, see [12]. establishing that (L1) through (L3) axiomatizes two-valued sentential calculus. Two·Valued Sentential Calculus During our study of this area of logic,. we used OITER Regarding the third conjecture, which focuses on two-valued to focus profitably on other axiom systems, including that

20 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics of Frege, Hilbert, and Church. One of the benefits resulting from the corresponding research was the accrual of additional 39 [hyper,l,l0,9] P(i(i(i(x,y),z),i(i(u,z),i(i(x,u),z)))). evidence (to be cited shortly) of the value of using an 51 [hyper,l,39,8] P(i(i(x,i(y,z)),i(i(i(u,y),x),i(y,z)))). automated reasoning program as a research colleague. Indeed, 212 [hyper,l,51,8] P{i(i(i{x,y),i(i(z,y),u)),i(y,u))). as a result of an odd concatenation of circumstances, we were 8405 [hyper,l,212,10] P(i(i(n(x),y),i{i(z,y),i(i(x,z),y)))). driven to seek a new axiom system-the motivating force for the third conjecture. The conjecture asserts that failure Clause (8405) contradicts results from an attempt to use condensed detachment to show clause (25), and the proof is complete, requiring approximately that the formulas I numbered (4), (5), and (6) provide an 108 CPU seconds on a SPARCstation 2. axiomatization for two-valued sentential calculus, where the In the context of elegant proofs, specific objective is to deduce (7), (8), and (9), which are, one might find intriguing the challenge of seeking, respectively, (Ll), (L2), and (L3). As one may have correctly if possible, proofs shorter than the three cited here of respective lengths 22, 23, and 4, surmised from the current discussion, our goal was actually to where length is measured strictly in terms of the number refute the conjecture and, instead, show that we had an axiom of applications of condensed system-a new axiom system. detachment. Rather than considering the conjecture as stated and seeking to deduce (7), (8), and (9) from (4), (5), and (6), we chose what we suspected to be an easier question to attempt The Five Elements of Automated Reasoning, to answer. In particular, we had learned (from browsing a Short Course in various papers of Lukasiewicz) of yet another axiom At this point, I will briefly review the five basic elements of system, one that shares (with the system under study) the automated reasoning: representation of information, inference formulas numbered (4) and (5). In place of (6), the system rules for drawing conclusions, strategy for controlling the has (( -,(x) --+ y) --+ ((z --+ y) --+ ((x --+ z) --+ y))) as its third reasoning, a means for canonicalization, and a means for member; Lukasiewicz calls this formula thesis 59. In fact, purging trivial information. I will concentrate on the features our choice of (4), (5), and (6) was an intuitive one, based on found in what might be called the Argonne paradigm [11, knowledge of the cited closely related system. 13]. Among those features are the retention of deduced Here is the "additional evidence" alluded to earlier: From conclusions, the emphasis on strategy, the use of various (4), (5), and (6), OTTER deduced thesis 59, and we had found inference rules, the control of redundancy, and the detection a new axiom system. Therefore, as a bonus, we refuted the of assignment completion almost always by completing a third conjecture. Then, from curiosity, we had OTTER seek proof by contradiction. At the most general level, since my to prove (7), (8), and (9) directly. Success: The shortest proof entrance into the field in 1963, these features have played a obtained consists of 23 applications of condensed detachment. key role in Argonne's research and in Argonne's design of Returning to thesis 59 with the objective of adding to reasoning programs. the intrigue of using an automated reasoning program, I now present an elegant proof found by OTTER, a proof that Scott commented is the type that a person might never have discovered. (Since the following proof relies on unification Progress In in a nontrivial way, one might wish to delay its detailed Automated Reasoning examination until briefly studying the examples given in 1960-1991 the review of the elements of automated reasoning.) In the following proof, the steps are numbered based on the OTTER run, where"-" means not, "I" means or, and the predicate P can be interpreted as "is deducible". Also, [hyper,lj,k] means I that the inference rule hyperresolution (exemplified later) is I used with clause (1) to capture condensed detachment, that the clause numbered j is the major premise used with the first literal of (1), and that the clause numbered k is the minor I premise used with the second literal of (1). In the proof, a, b, and care constants, the function i is used for--+, and the function n is used for ...,. UU-66 1978-85 1U6-91

An Elegant Proof Figure 1: Progress in Automated Reasoning l [] -P(i(x,y)) I -P(x) I P(y). 8 [] P(i(i(i(x,y),z),i(y,z))). Compared to the paradigm now reviewed, I have never 9 [] P(i(i(i(x,y),z),i(n(x),z))). believed there existed as much potential in seeking to emulate 10 [] P(i(i(u,i(n(x),z)),i(u,i(i(y,z),i(i(x,y),z))))). person-oriented reasoning, a common theme found in artificial 25 [] -P(i(i(n(a),b),i(i(c,b),i(i(a,c),b)))). intelligence. That belief perhaps explains my introduction of

JANUARY 1993, VOLUME 40, NUMBER 1 21 Computers and Mathematics the explicit use of strategy (in the early 1960s ), my formulation attempts to find a substitution for variables to simultaneously of the inference rule paramodulation, and my endorsement apply to the first three clauses to yield the fourth. The variables of the use of the clause language to present questions and are renamed for convenience. problems to a reasoning program. For a small taste of my position, I note that people find instantiation to be a powerful 1 [] -P(i(x3,y3)) I -P(x3) I P(y3). and useful inferenc.e rule; however, I recommend against its 9 [] P(i(i(i(x1,y1),z1),i(n(x1),z1))). use by a computer program. Indeed, where the researcher can 10 [] P(i(i(u2,i(n(x2),z2)),i(u2,i(i(y2,z2),i(i(x2,y2),z2))))). and typically does choose well which instance of a fact to use-for example, profitably choosing the instance {yz)(yz) = e of the equation xx = e when seeking to prove commutativity 39 [hyper,1,10,9] P(i(i(i(x,y),z),i(i(u,z),i(i(x,u),z)))). for Boolean groups-! conjecture that countless years will pass before a means will exist for a program to apply The desired substitution that will (ignoring sign) unify instantiation wisely. clause (10) with the first literal of clause (1) and at the Nor am I in favor of the currently popular approach (to same time unify clause (9) with the second literal of clause the automation of reasoning) based on logic programming, (1) is x for x1, y for y1, z for z1, i(i(x, y),z) for u2, especially when the question or problem under study is even x for x2, u for y2, z for z2, i(i(i(x, y),z),i(n(x),z)) for moderately deep. Indeed, for the type of question of greatest x3, and i(i(i(x, y),z),i(i(u, z),i(i(x, u),z))) for y3. After the interest to me-questions from mathematics and logic are my substitution is applied simultaneously to clauses (1), (9), and favorites-! consider it essential to retain deduced conclu­ (10), the cited literal pairs (ignoring sign) become identical sions, of course, filtered greatly to control redundancy and to and, because of being opposite in sign, are canceled to yield emphasize significance. I maintain this view-or bias?-in clause (39). part because of making various comparisons among reason­ Although logicians with diverse interests have for years ing programs. As those who are familiar with my research applied condensed detachment by hand, we have a good illus­ can attest, my conviction continues to grow concerning the tration of why a program such as OITER finds its application potential of the paradigm I now discuss. far less of a burden. For a more powerful illustration­ showing why the cited 4-step proof might indeed not have Representation and Unification been discovered by a person-one need only complete a Regarding the clause language for communicating with detailed analysis of the last three steps of that proof with the OITER, the following example serves well for introducing it objective of obtaining the appropriate sets of substitutions for and for providing a minute taste of unification, the procedure the various variables. The fourth step is particularly interest­ so crucial to so many procedures used by the program. ing, for it rests on the use of nontrivial variable replacement Were OITER to deduce the following two clauses, it would in all three of its ancestors. immediately "know" that a proof by contradiction had been Let me now illustrate the use of paramodulation in the completed. . case where one is permitted to make nontrivial replacement of terms for variables in both the from statement and the GT(a,x). into statement. For an example of the latitude permitted -GT(y,b). in the use of paramodulation-an example showing how this inference rule generalizes the usual notion of equality Of course, strictly speaking, neither clause has any se­ substitution-consider the following three clauses and apply mantic content. But one can interpret them, respectively, in paramodulationfrom the first into the second to yield the third; the following way. "For all x, the constant a is greater than from the viewpoint of mathematics, paramodulation applied to x." "For all y, y is not greater than the constant b." OITER boththeequationx+(-x) = Oandtheequation y+(-y+z) = z detects a contradiction by using unification, substituting b for yields in a single step the conclusion y + 0 = -(-y). x in the first clause and a for y in the second. Unification is that procedure that finds, if one exists, a most general substi­ EQUAL(sum(x,minus(x)),O). tution for two given expressions such that, when applied, the EQUAL(sum(y,sum(minus(y),z)),z). resulting expressions become identical. In the given example, EQUAL(sum(y,O),minus(minus(y))). the two expressions are the clauses with the not sign ignored. To see that this last clause is in fact a logical consequence Inference Rules and Unification In Greater Detail of its two parents, one unifies the argument sum(x, minus(x)) In contrast to considering just two clauses at a time, OITER with the term sum(minus(y), z), applies the corresponding also uses inference rules that consider three (or more) clauses substitution to both the from and into clauses, and then makes at a time-as suggested by the 4-step proof given earlier. For the appropriate term replacement justified by the typical use an example of this type of reasoning-actually, an example of of equality.·The substitution found by the attempt to unify the hyperresolution-1 select the first deduced conclusion in the 4- given argument and given term requires substituting minus(y) step proof cited earlier as evidence of elegance; let us examine for x and minus(minus(y)) for z. To prepare for the (standard) how it is obtained. Of the following four clauses, OITER use of equality in this example-and here one encounters a

22 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics key feature of paramodulation-a nontrivial substitution for the program from proving a known theorem by restricting variables in both the from and the into clauses is required, the search too severely. I can address that justifiable concern which illustrates how paramodulation generalizes the usual with an informal and then a formal observation, suspecting notion of equality substitution. I also note that, most likely, a that neither is intuitively obvious. Informally, one is safe if researcher would not find delight in applying paramodulation S - T consists of the general background information-for by hand: This inference rule is not particularly reminiscent of example, the axioms and lemmas to be used-and T consists person-oriented reasoning. of the assumption that the purported theorem under study is false, together with the information specific to the purported Strategy theorem. As an illustration, if the objective is to prove that Having touched on the language and some of the inference groups in which the square of every x is the identity e are rules used by OTTER, I tum next to strategy. In view of some commutative, then T might consist of the given exponent of the current efforts in automated reasoning, apparently many 2 property (the special hypothesis) and the assumption that still feel that strategy is unneeded or believe that the simplest commutativity is absent. Formally and from the viewpoint of of strategies suffices. Obviously, I do not share this view, at logic, one is guaranteed refutation completeness when using least when the domain of study concerns even moderately deep the set of support strategy whenever S - T is satisfiable and, questions from mathematics or logic. Certainly, excellence therefore, has a model. in program design and implementation is required-as one Of a totally different nature is the restriction strategy finds in McCune's program OTTER-and also required is a known as weighting. One use of this strategy enables the language possessing representation adequacy, as is offered by researcher to assign a maximum on the complexity of in­ the clause language. Also, one must have access to inference formation to be retained. One can, for example, instruct the rules whose use, in addition to drawing conclusions only program to immediately discard any conclusion if it contains if they follow logically, contributes significantly to program a term of the form f(f(f(q, r), s), t) for terms q, r, s, and t, effectiveness. However, far more is required, for the heavy where, for example, the function f might be used for product. sword of potential combinatoric explosion always hangs over Of course, as one would suspect, weighting permits the use the head of the program attempting to answer a deep question. of far more complex templates, giving the researcher the Indeed, as observed by Woody Bledsoe (University of Texas), opportunity of providing little or much advice concerning for hard problems from mathematics even access to 10,000 the undesirability of expressions. Undesirable expressions as times more computing power will not suffice. One thus sees defined by the researcher-those whose weight, based on the why I and others are so interested in some means to address given templates, exceeds the user-assigned maximum-are the potential combinatoric explosion-and strategy to control immediately purged by the program; where templates are the program's reasoning seems to offer by far the best attack not applicable, the program simply uses symbol count to against this obstacle. determine the weight of a deduced conclusion. At the most general level, strategy can be classified into Weighting can also be used to direct a program's search. two types: one type to restrict the search for information Indeed, if one wishes the program to choose (as the focus and one type to direct the search. If history is a good of attention) information by substituting for symbol count teacher, powerful restriction strategies are of far greater value a different measure of complexity, one includes (in the than are powerful direction strategies-because the former input) templates with assigned values to enable the program offer a greater reward by directly addressing the potential of to place priorities on each item of retained information. combinatoric explosion and the latter address this obstacle The smaller the weight of an item (a clause), the higher only indirectly. Especially for the following discussion, recall the priority it has. For example, for questions focusing on that, almost always, seeking a proof by contradiction is group theory, the researcher can cause the program to prefer the goal when attacking a .question or a problem with the statements concerned with inverse over those concerned with assistance of an automated reasoning program. the identity. For questions taken from propositional calculus, The most powerful restriction strategy of which I am a researcher can cause the program to emphasize the role aware is called set of support. Informally, the user selects a of formulas containing a term of the form n(i(x, y)) while subset of the input statements, and the strategy requires that placing far less emphasis on those containing a term of the all lines of reasoning must begin with some statement in the form i(n(x), y). Thus, by judicious choice of the weight chosen subset. Formally, to use the set of support strategy, the templates, if desired, the researcher can have an automated researcher partitions the set S of statements (or clauses) that reasoning program direct its search based on the researcher's present the question or problem under study into two sets, T intuition and expertise. and S-T. The strategy also dictates that all newly retained Of a different flavor, one can instruct a reasoning pro­ statements (or clauses) are adjoined to T. The set of support gram to make a breadth-first search, considering each item of strategy restricts the search by prohibiting an inference rule information in the order it is retained. I note that for many from being applied to a set of statements all of which are years I considered this strategy, called level saturation, to members of S - T. be naive and of little value for answering interesting ques­ Of immediate concern is the possibility of using the strat­ tions. However, despite numerous experiments supporting egy and getting into serious trouble; for example, preventing that original position, I have recently modified my stand, for

JANUARY 1993, VOLUME 40, NUMBER 1 23 Computers and Mathematics

my colleagues and I have put this simple strategy to good checking. Indeed, experiments with OTTER suggest that an use, obtaining some shockingly short proofs. Were it not for intriguing challenge exists: Find, if possible, a small set of the ease of having OTTER apply level saturation, I almost clauses-perhaps 14 or fewer-that the program can use to certainly would have missed this opportunity of revising and easily prove numerous simple theorems and, in the main, updating my views and, therefore, missed the corresponding without guidance from the researcher. Clearly, I am implying amusement-a glance in the mirror of history does sometimes that finding proofs rather than checking proofs is more useful, produce laughter. For the curious, I note that the implied more satisfying, and more demanding. conclusion is correct: In the vast majority of cases, weight­ Regarding the use of OTTER for the study of areas of ing is a far more effective direction strategy than is level mathematics and logic for which no template exists, the saturation. But there exists a strategy, the ratio strategy, that researcher finds a substantial challenge-but a challenge that, combines some of the advantages of the two strategies just almost certainly, can be met. Even in the context of proof compared. Its use permits a program to occasionally use very checking, which is less taxing than is proof finding, one may complex formulas-however complexity is defined by the be required (for a new area of study) to make a substantial researcher-while mainly concentrating on the less complex. effort to produce clauses that the program can use effectively. The ratio strategy is of particular value when a proof requires Although not at all obvious, regarding proof checking, the vast getting over a hump whose form is a long, long clause. majority of theorems is within range of automated reasoning, at least in principle. In particular, although exceedingly far from delectable, one can always fall back on the use of clauses Redundancy Control for GOdel's finite axiomatization of set theory [11]. Even though a program such as OTTER offers various other Instead, for each new venture, I conjecture that-risky useful strategies-some of which powerfully restrict the though it clearly is-the possible reward merits an attempt at application of paramodulation-the obstacle of redundancy finding suitable clauses that avoid the use of GOdel's axioms, nevertheless exists. The same conclusion can be reached and, further, of finding clauses that OTTER can use effectively repeatedly, and no reason exists for retaining more than one in the context of finding proofs. The important point to keep in copy. Further, a more general conclusion can be reached, mind is that neither the use of the clause language nor the use either before or after instances of it are deduced. Ordinarily, of OTTER limits the researcher to those areas of mathematics no need exists for retaining the less general conclusions. A and logic contained within the convex hull of what has been somewhat subtler form of redundancy is that found in a set of studied (to this point in 1992) with the assistance of an expressions all of whose members can be canonicalized to a automated reasoning program. common expression. The subtler obstacle is addressed in the If one wishes to use OTTER as a research assistant, but Argonne paradigm by using demodulation to canonicalize and prefers to avoid the task of producing appropriate clauses, simplify conclusions through the use of demodulators (rewrite the program does offer an alternative-at least, for those who rules). The researcher can supply the demodulators or OTTER know first-order predicate calculus. In particular, one can can find them by applying user chosen criteria. Regarding present to OTTER a question or problem in the form of a the more blatant form of redundancy, the program relies on fully quantified formula relying on the various connectives of subsumption to identify and purge statements (clauses) that the calculus, and the program will translate the formula into are captured as corollaries of other statements. acceptable clauses. Regardless of how clauses are produced, an important distinction exists between an accurate representation of the question or problem under study and an effective The Challenge of Problem Presentation representation. Indeed, because the representation admits At this point, I fulfill my earlier promise concerning the various choices-as in mathematics and in logic, uniqueness discussion of the sometimes burdensome aspect of presenting a of representation is absent-to be effective, one best take into question or a problem to an automated reasoning program and, account the inference rule and strategy that the program is more specifically, answer the natural question concerning the instructed to use. difficulty of producing the clauses needed to convey to OTTER For an illustration, I focus on group theory; choosing as the the nature of the intended study. When the area of interest inference rule paramodulation, a rule that treats equality as a is one that has been the subject of numerous experiments in built-in concept. Once paramodulation is chosen from among automated reasoning, little difficulty is encountered, at least at the inference rules offered by OTTER, the representational the start. For example, if the area is group theory, ring theory, choice is virtually dictated, if effectiveness is of paramount lattice theory, Tarskian geometry, or equivalential calculus, consideration. For the respective clauses for the existence of the book Automated Reasoning: 33 Basic Research Problems a two-sided identity, a two-sided inverse, and associativity­ [11] provides the researcher with a decent start. For clauses and the often overlooked reflexive property of equality-! to study combinatory logic-especially in the context of the recommend the following, given in OTTER notation. kernel strategy-! suggest [12]. As for set theory, although a nice start is provided by [6] and by [11], experimentation (1) EQUAL(prod(e,x),x). quickly leads to the conclusion that far more is desired-in (2) EQUAL(prod(x,e),x). particular, when the context is more proof finding than proof (3) EQUAL(prod(inv(x),x),e).

24 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics

(4) EQUAL(prod(x,inv(x)),e). Whether the tum of the century will find many open (5) EQUAL(prod(prod(x,y),z),prod(x,prod(y,z))). questions under attack by a team consisting of a researcher (6) EQUAL(x,x). and an automated reasoning program is left to time to settle. Clearly, the preceding decade has witnessed a sharp increase in If one then assumes that the theorem to be proved asserts that regard, sometimes culminating in the answer to a question that Boolean groups (those in which, for all x, the square of x that had remained open for decades. Thus we have evidence is the identity e) are commutative, one would add to the input that an automated reasoning program can and occasionally the following clauses. does contribute to mathematics and logic. The field of automated reasoning is relatively young (dated (7) EQUAL(prod(x,x),e). by some as beginning in the early 1960s) and, fortunately, still (8) -EQUAL(prod(a,b),prod(b,a)). most challenging. Approximately 40 years ago, one might indeed have wondered how research could possibly address Motivated by the intention of seeking a proof by contra­ the three main obstacles to the automation oflogical reasoning: diction, I include clause (8), asserting that commutativity is a language to present to a computer the specific question of absent-absent for at least two elements. As for strategy, I interest, a means for the computer to draw sound conclusions, recommend the set of support strategy, instructing OTTER to and a strategy for sufficiently controlling the reasoning to follow only those lines of reasoning that begin with clause (7) permit the computer to complete the underlying research. or clause (8), using the other six clauses to complete appli­ In this article, I show how these obstacles and others that cations of paramodulation. To gain some familiarity with the were eventually identified were overcome, focusing mainly use of the chosen inference rule and the chosen strategy--or on the approach taken within the Mathematics and Computer simply for entertainment--one might attempt to use the eight Science Division of Argonne National Laboratory. Because clauses in the prescribed fashion to find a proof by hand; in open questions have played such a key role in the development other words, the use of instantiation is not permitted. of our approach, I eagerly seek additional open questions to attack with our newest program OTTER. Although at the simplest level an automated reasoning program (of the type featured in this article) just accrues conclusions with no understanding of their meaning, I show Summary and Conclusions in this article how the program's use of strategy can totally Rather than releasing a torrent of information and evidence, I change the game. Indeed, strategy plays a key role in have instead presented little more than a trickle to suggest how our paradigm. The paradigm also relies on the use of a an automated reasoning program serves well as a research number of inference rules, some of which are clearly oriented assistant. In that regard, my colleagues and I have used such to application by a computer rather than by a person­ a program to prove theorems, test and suggest conjectures, for example, paramodulation, which effectively generalizes construct objects, produce more elegant proofs than previously equality substitution. Thus a program such as OTTER is far known, and-clearly of greatest satisfaction-answer open more than a symbolic calculator offering impressive speed questions from various unrelated fields of mathematics and and accuracy: Such a program reasons logically, sometimes logic. Through the use of automated reasoning-and mainly so effectively that the results are published in mathematics through the use of the automated reasoning program OTTER­ and in logic journals. we have answered questions from group theory, combinatory Rather than ever being a replacement for the mathe­ logic, finite semigroup theory, and various logic calculi. Some matician or logician, automated reasoning programs nicely of the questions were posed by Irving Kaplansky, some by complement the researcher. Indeed, their value as research as­ Dana Scott, some by Raymond Smullyan, and some by John sistants should continue to grow-and perhaps at an increasing Kalman. rate. Our successes motivate my . recommendation that re­ searchers be at least skeptical when reading articles such as "Computers Still Can't Do Beautiful Mathematics" (New Source Material York Times, July 14, 1991, Week in Review). Indeed, to see More than any other reasoning program of which I have knowl­ that beautiful mathematics sometimes results from the use edge, we recommend McCune's program OTTER, which runs of an automated reasoning program, one need only consider effectively on workstations, (IBM-compatible) personal com­ the three conjectures offered at the beginning of this article, puters, and Macintoshes. Among its excellent features, its use review OTTER's approach to settling each, and study the produces proofs that include all steps and the corresponding additional open questions whose answers I cite. Were one to justification, permitting one to follow the typical practice in apply a Turing-like test to the results produced by OTTER-a mathematics and logic of a thorough reading, occasionally test that asks if an observer can know wh~ther a computer or a gleaning from one of the proofs unexpected insight into the researcher produced them, emphasizing quality, significance, field under study. and elegance-! suspect that rather high marks would be Consistent with my objective of encouraging researchers given. to use an automated reasoning program and my objective

JANUARY 1993, VOLUME 40, NUMBER 1 25 Computers and Mathematics of accruing additional open questions to attack-awkward though it may be-l recommend consideration of my newest book Automated Reasoning: Introduction and Applications, Reviews of Mathematical Software second edition [13]. This McGraw-Hill volume contains a copy of OTTER on diskette, the source for workstations, and load modules for personal computers. The sixteenth chapter is devoted solely to a tutorial on the use of OTTER, and useful input files are found throughout the book. Also, information Mathcad 3.1: for obtaining a copy of OTTER is available by sending Calculations for the Rest of Us email to [email protected], and information for accessing a database of problems and proofs is available electronically, Reviewed by William H. Ruckle* by accessing info. mcs. anl. gov via anonymous FTP. Contributors to this column sometimes give me the impression that computational power is the only legitimate goal of mathematical software. If you believe this, then you need only References know that Mathcad is not in the same league as Mathematica [1] J. Guard, F. Oglesby, J. Bennett, and L. Settle, "Semi-Automated or Maple and let the matter rest. Maybe you also open cans of the ACM 16,49-62 (1969). Mathematics", Journal instead of a can opener, because the chain saw [2] J. Lukasiewicz, "The Shortest Axiom of the lmplicational Propo­ with a chain saw sitional Calculus," Proc. of the Royal Irish Academy 52A, no. 3, 25-33 is a more powerful tool-1 don't know. Obviously you want (1948). a program that can do all the computing that your research [3] W. McCune, OTTER 2.0 Users Guide, Technical Report ANL- requires, but you don't want to spend extra time programming 909, Argonne National Laboratory, Argonne, Dlinois (1990). the tool and organizing the output. Mathcad emphasizes [4] W. McCune and L. Wos, "The Absence and the Presence of Fixed convenience and attractive output. The screen display looks Point Combinators," Theoretical CoTri{Juter Science 87, 221-228 (1991 ). like standard mathematics: two story fractions, derivatives [5] W. McCune and L. Wos, "Application of Automated Deduc­ tion to the Search for Single Axioms for Exponent Groups," Proc. *·integral signs J: sin(x) dx, matrices with brackets around LPAR'92, Springer-Verlag Lecture Notes in Artificial Intelligence (to them, summation symbols, etc. You can add commentary appear), Preprint MCS-P291-0292 (1992). with a rudimentary word processor. You can create attractive [6] A. Quaife, "Automated Deduction in von Neumann-Bemays­ graphics. You can organize your calculations and comments Goedel Set Theory," Journal of Automated Reasoning 8, no. 1, 91-147 and create a nice-looking printed output. The figures on the (1992). [7] A. Quaife, "Automated Development of Tarski's Geometry," next page match the screen except they lack color and the Journal ofAutomated Reasoning 5, no. 1, 97-118 (1989). printing is better. [8] A. Quaife, "Unsolved Problems in Elementary Number Theory," Mathcad 3.1 runs as a Windows application. In addition to Journal ofAutomated Reasoning 1, no. 2, 287-300 (1991). a Windows configuration, it requires an 80286 or better CPU, [9] S. Winker, "Generation and Verification of Finite Models and at least 2 megabytes of memory (you need this for Windows Counterexamples Using an Automated Theorem Prover Answering 1\vo 3.0 anyway), and at least 7 megabytes on your hard disk. A Open Questions," Journal of the ACM 29,273-284 (1982). mathematics coprocessor is recommended. I ran the review [10] S. Winker, L. Wos, and E. Lusk, "Semigroups, Antiautomor­ phisms, and Involutions: A Computer Solution to an Open Problem, I," copy on a generic (V-Com) 80486 with 4 megabytes of ram Mathematics of Computation 37, 533-545 (1981). running at 33 megahertz. The printer was an Epson Action [11] L. Wos, Automated Reasoning: 33 Basic Research Problems, Laser II configured as a Hewlett Packard liP. Prentice-Hall, Englewood Cliffs, N.J. (1987). The most significant addition in the present edition of [12] L. Wos, ''The Kernel Strategy and Its Use for the Study of Mathcad is a symbolic calculator utilizing the Maple engine. Combinatory Logic," Journal ofAutomated Reasoning (to appear). A nice test of the power of Maple is to take the determinant of Boyle, Rea­ [13] L. Wos, R. Overbeek, E. Lusk, and J. Automated see that soning: Introduction and Applications, 2nd ed., McGraw-Hill, New York an 8 x 8 skew symmetric matrix and then factor it to (1992). it is a perfect square. Mathcad did this for a 4x4, but for a [14] L. Wos, S. Winker, R. Veroff, B. Smith, and L. Henschen, 6x6 gave me the message "discarding huge symbolic result' "A New Use of an Automated Reasoning Assistant: Open Questions when I tried to take the determinant. I would have liked to in Equivalential Calculus and the Study of Infinite Domains," Artificial factor this "huge symbolic result", for then it wouldn't have Intelligence 22, 303-356 (1984). been so huge. Mathcad did give the correct result 0 for the [15] L. Wos, S. Winker, R. Veroff, B. Smith, and L. Henschen, determinant of a 5 x 5 general skew symmetric matrix. "Questions Concerning Possible Shortest Single Axioms in Equivalential Calculus: An Application of Automated Theorem Proving to Infinite Another notable Mathcad feature is a set of electronic Domains," Notre Dame Journal of Formal Logic 24, 205-223 (1983). handbooks which you can open within Mathcad. You can paste material including diagrams and formulas from a handbook into your worksheet and manipulate it. This seems useful for an engineer writing a report or a student doing an assignment. There are two ways to summarize Mathcad's capabilities.

*William Ruckle is a Professor of Mathematics at Clemson University. His email address is: [email protected].

26 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics

Examples of Mathcad

l, A simple equation. X := l.} root (ex + x - 2 , x) = 0.443

2. The determinant of a general four by four skew synunetric matrix using Maple. It failed on a 6 by 6, but did show that a five by five has determinant 0.

You first enter the matrix. 0 -a - b - C a 0 -d -r b d 0 - f c r f 0

Then you ask for the determinant. 2 Then you factor the determinant to see it is a ( f.a + d ·c - b · r) perfect square.

3. A rose of many petals N := 300 1t e := o ,2·- .. I0·1t 0.5 N r( e) := cos( 3.2 . e) y( 6) 0 x(6) := r(6) ·cos(6) y(6) := r(6) ·sin{6)

-o.5 0 0.5 x( 6)

4. A Surface Plot- Sombrero Function

N : = 40 i := 0 .. N j := 0 .. N x . . - -4 + ~ y. := -4 + _! I 5 J 5

cos (x2 + y2) f ( X , y ) : = _ ____:______:___:_ 2 2 } + X + y

M( . . ) .- f(x., y.) I ,j I J,

M

JANUARY 1993, VOLUME 40, NUMBER 1 27 Computers and Mathematics

• It's like an undergraduate engineering student who can draw beautiful graphs and can make A's in all her math courses except differential equations. Matrix Algebra Version 2.2 • It does everything a symbolic calculator can do; can do it faster, easier and better; and can also give you .an attractive Reviewed by Suzanne M. Molnar* annotated printout. Matrix Algebra is a program for aiding students to solve certain The User's Guide is clearly written, but you can't always linear algebra problems. Developed by Bernard Kolman find what you want in the index. It is easy to start using and Todd Rimmer of Drexel University, it is available Mathcad for routine things, and you can often discover how to from Intellimation Library™ for the Macintosh, P.O. Box do more complicated things by trial and error. There are a few 1922, Santa Barbara, CA 93116-1922, phone: 805-968-2291. quirks. For example, you can obtain subscripts by entering a The program comes with a 36-page manual which clearly period after a letter or by clicking on a subscript with a mouse; documents the operation of the program. The small system but the first kind of subscript is not the same as the second requirements for the program are one of its main features, kind and behaves differently. The mouse operation borders namely, minimum memory of 128K and System 3.2 or later. on the erratic; a performance which drove me away from the The program is designed to be used in a course in which early Macintoshes. When you click outside a formula you can basic matrix manipulation is a topic. It emphasizes the tech­ obtain at least four different actions depending on the position nique of Gauss-Jordan reduction, and as the manual admits, of the cursor. There is no way to keep this from slowing you the "program is not as thorough" in matrix multiplication. down. Combining graphic interface and wysiwyg makes it Specifically, Matrix Algebra transforms a matrix to reduced difficult for the user to align regions of text and mathematics row echelon form, solves a linear system, multiplies two as he or she really wants them. The manufacturers might add matrices, finds the inverse of a matrix, and offers explanations guidelines in a future edition. A real "math scratch pad" has if requested. The maximum size of a matrix is 6 x 12, which lines or even a grid. The symbolic tool seems not to like has the effect of being able to solve a linear system of up to subscripts; sometimes it gave me the wrong symbolic solution 6 equations in 11 unknowns. Improvements over a previous to equations containing subscripted variables. version include the ability to save matrices and equations From my comments you can rightly conclude thatMathcad on a disk, improved accuracy and range of values, expanded will appeal to engineers, scientists, technicians, and all sorts documentation and, for numerical analysis, partial pivoting of students in technology. It is also good for the everyday and control over format of numbers. calculational and educational needs of mathematicians. In Input to the program is easily accomplished by well­ my opinion, it is more appropriate than Mathematica as an designed dialog boxes that allow the user to input a matrix, instructional tool in calculus since it requires less hardware, system of equations, or two matrices to multiply. A wel­ provides an intuitive interface, and gives a readable output. It come feature is that subscripting is accomplished easily for is easier to use than a symbolic calculator, even though you WYSIWYG-looking linear systems. A not-so-welcome fea­ can't put it in your pocket. ture is that all input must be in the form of rational numbers. A good problem for a computationally oriented student is This gets a bit tedious when one enters 21.38 as, say, 2138/100, to find the value of the integral which the program happily reduces. Things get more dicey when using the program to enter 0.00609 in its rational equivalent. An unexpected plus is that students may learn how to convert from a decimal to its rational equivalent! When entering data into a dialog box, the program is very good at alerting the user to unacceptable input. A student with insight may see the value is 0 because Figures 1 and 2 are two snapshots of the screen as one the graph of the second function is just the graph of the first proceeds to solve a system of equations by row reduction. rotated through 90 degrees, and so they have the same area Figure 2 clearly shows all seven movable/resizable windows; under them. I have never received this answer from one of their functions are self-evident from their titles. Three win­ my students. Mathcad and a programmable calculator will dows (Prior Matrix, Prior System, and Floating Point) may give an answer of the order w-s. I have often received this be hidden via the Controls menu. Although matrix input answer with no indication that the tiny answer has given the must be in rational format, the floating point format can be student a clue about the truth. Mathematica gives the correct seen in the output. Matrix Algebra allows the user to step answer 0, possibly by finding an antiderivative in terms of through a row reduction. The Row Reduce menu allows one gamma functions; but, strangely, students (usually graduate to choose an elementary row operation to perform on the students) who report this call it an "approximate" answer. given matrix/system. Figure 1 shows the dialog box for such Another popular way of doing this problem is simply to find an operation; here, the user selects the row and scalar. Figure the wrong antiderivative. 2 shows the results of that operation in Prior Matrix/System

*Suzanne Molnar teaches mathematics and computer science at the College of St. Catherine, St. Paul, MN. Email: [email protected].

28 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics windows. One can also choose an explanation of the next step screen once it has been opened. One must toggle the About from the Explain menu; that step is then performed without Matrix Algebra . . . from the Apple menu to see the name user intervention. This is illustrated in Figure 2 with results of your current file. A greater problem is that a previously shown in Current Matrix/System windows. There is also an saved matrix/system cannot be edited when it is opened at a option to automatically row reduce. The Extras menu includes later time. A newly created matrix/system can be edited via Inverse and Multiply options. an appropriate selection from the File menu. There is no Edit menu as one would expect in a Macintosh application. Matrix Algebra provides increased accuracy over the previous version. All rational numbers are stored as 32 bit numerators and 32 bit denominators. Should a calculation exceed the corresponding range of values that can be stored MUltiply Row by a constant as exact rational numbers, a conversion to extended precision Row to MUltiply by a Constant floating point is made. Once terms are stored as floating point they are not converted back to rational form; a message is given that a formerly all rational matrix has at least one floating point entry. Internally, all floating point numbers are stored with precision as specified by the Standard Apple Numeric Environment. All calculations in floating point are performed to full precision. It is possible to change the format of displayed numbers. Namely, by selecting Floating Point Format from the Controls menu, the display of floating point numbers can be rounded and the display of rational numbers as floating point numbers can be specified. Another new feature is the Partial Pivoting option under the Controls menu. When this option is selected, partial Figure 1 pivoting is used to determine the inverse of a matrix and to perform automatic row reduction. Normal pivoting will continue to be used for explanations, so as not to confuse ''the 8:04:25 ., r tl File Row Reduce £atrea beginner". With suitably chosen ill-conditioned matrices, this feature allows one to get an introduction to numeric issues Using entry 1,1 as tbe pivot, we add 2/5 times row I to row 2. involving finding inverses and solutions to linear systems. In conclusion, this program has very low overhead both in terms of ease of use (no syntax to learn) and hardware requirements (minimal). Although limited in the scope of problems it can solve, it can serve as a useful aid to student understanding of elementary matrix operations and give them a glimmer of some of the problems faced when one must implement real-world problems on real-world machines. Perhaps the program could serve as a stepping stone to more general purpose packages such as MATLAB or Mathematica.

The TI-85 Figure 2 Reviewed by Roger Pinkham* Other features include the following. The Revert to Prior As chips grow smaller and some are designed for special option in the File menu allows one to go back to the previous purposes, the distinction between software and hardware matrix; it does not stack up operations, so only the immediately becomes increasingly blurred. "One man's ceiling is" indeed preceding step may be retrieved. An improvement over a "another man's floor". previous version is the ability to save a matrix or system. For purposes of this review I treat the TI-85 as a piece of This is especially useful given that you must enter data in very clever software. The case is the same size and weight rational form. The state of the calculations and any options the user has activated will be saved and restored when the file *Roger Pinkham is a professor of mathematics at the Stevens Institute is opened. A minor annoyance is that, unlike many Macintosh of Technology, Hoboken, New Jersey 07030. His email address is rpinkham@ applications, the name of the file is nowhere evident on the vaxc.stevens-tech.edu.

JANUARY 1993, VOLUME 40, NUMBER 1 29 Computers and Mathematics as the TI-81, but black in color. By means of a small cable Like the TI-81, the 85 provides the opportunity to write you can send and receive programs, data, variables, etc., your own programs, but now the language has been enlarged between one TI-85 and another. By means of special software to include For loops, While and Repeat statements, as well as (LINK-85) and another little cable you can send and receive If-Then-Else constructions. between a PC andthe TI-85, thereby storing, recovering, and I am told the handheld will list for around $120 and the printing pictures, programs, data, etc. · LINK-85 software and cable for around $65. (The latter is Although the same size as a TI-81, this handheld has 32K not yet commercially available, but the prototype I exercised bytes of memory of which some 28,226 bytes are available worked well). Yesterday I ordered my own TI-85 from a to the user. Everything is menu driven, and the user machine dealer for $109.95. This is an enormous functionality for $110 interface is a very convenient design. (much of which I have not described). Teachers can even You can effortlessly graph just abut anything, zoom in, get a $20 rebate from TI! This machine will certainly give zoom out, trace along a curve, store, and recall. You can turn Hewlett-Packard's HP48S and HP48SX a run for the money. pixels on and off, draw circles and lines, and shade figures A very good calculus course, numerical linear algebra class, at will. The menus allow the user to find slopes and local or numerical methods course could be built around the use of extrema without effort. There is also a numerical integration this machine. routine which works easily and well. My only complaint in testing the software was that once In contrast to the TI-81 there is a proper polar graphing a variable was created by assigning a value to it in the midst mode as well as parametric graphs. Variables can be real or of a program, I could find no way to purge the variable from complex. Strings, lists, vectors, and matrices are all supported within the program when it was no longer needed. data types. There is a matrix editor to make entry and In summary I find this a remarkable piece of software for modification easy, and the only restriction is that one may the money and an ideal tool for the college crowd. not have more than 255 rows or 255 columns(!). The TI-85 will give the determinant, exponential, sine, or cosine of a square matrix. It will also give the integer part or fractional part element by element of any matrix. You may also have, at Announcement the punch of a button, the LU decomposition, eigenvectors, eigenvalues, the condition number, and a variety of norms. You may also swap rows, multiply a row by a constant and add GP/PARI System to yet another row, or concatenate two matrices together. Just as the software admits adding , multiplying, etc., matrices, so Fernando Gouv@a does it give dot products, addition, conjugates, absolute value, Fernando Gouv~a reports that, since his article on the GP/PARI etc., of vectors. system was published here some time ago, he has received The SOLVER menu automatically finds zeroes of equa­ several queries about a version that would run on 386- tions of the form f(x) = 0 or f(x) = g(x). A special feature class mM-compatible machines. Two such versions are now finds roots of polynomials up to degree 30 (real or com­ available from ftp at math.ucla.edu. The first is simply a plex). The SIMULT menu effortlessly handles the solution of gp executable that will run under DOS on 386 machines. systems of simultaneous linear equations up to 30 by 30. It is offered anonymously with no promise of support. The There is a full complement of tools for entering and second is a port of the whole GP/PARI package that includes analyzing statistical data. You may have linear, exponential, an executable that will run under both DOS and OS/2 on or logarithmic regressions with all the attendant means, 386 machines. The latter was prepared by Fernando himself variances, and correlations. There is a built-in sort routine, using the "emx" port to OS/2 of the Gnu C compiler. Both scatter plots, and histograms. When I get a machine of my versions require an arithmetic coprocessor when running on own I· shall certainly add a boxplot routine, some smoothers, 386 machines (the 486 chip includes a coprocessor); under and something to give tail areas of the normal. OS/2, such a coprocessor is automatically emulated if it An unexpected and very useful feature is the ability to is absent, but the emulation will likely render the program solve up to 9 simultaneous differential equations numerically unusably slow. While Fernando can offer only limited support and view the output graphically. for the program, he would like to know of any serious glitches.

30 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements

Derrick Henry Lehmer engineering, but who, after two years, and researcher, publishing some forty­ 1905-1991 changed to mathematics and began to six papers during that period. He had Derrick Henry Lehmer was born in assist the two Lehmers in their math­ nineteen Ph.D. students. Berkeley, California on February 23, ematical work. Emma graduated from Lehmer was a transitional figure in 1905. One of five children of Der­ Berkeley in mathematics in 1928. computational mathematics whose early rick Norman Lehmer and [Clara] Eunice From 1927 to 1930 Lehmer was a prominence was gained by his work Mitchell, he grew up and was educated graduate student, for one year at the with sieves and his impressive comput­ in the public school system of Berke­ University of Chicago where he met ing with hand calculators combined with ley. At that time Berkeley was already (but did not like working with) L. E. theoretical developments. In his later becoming an intellectual center, with Dickson, and for two years at Brown mathematical research, he did his com­ the new University of California hav­ University where he received his Ph.D. puting on the ENIAC and the SWAC, ing relocated there from Oakland some in 1930 under J.D. Tamarkin. and after that the IBM 701, 704, 709, twenty-five years earlier. Also, his fa­ From 1930 to 1933 he was a fel­ 7090, 7094, 360, and the CDC 6400. He ther had been professor of mathematics lowship student at CalTech (where he also used the Illiac 4, well utilizing the at U.C. Berkeley since 1900 when he studied with E.T. Bell) and at Stanford paralellism in that machine, a kind of had obtained his Ph.D. in mathematics University (where he became acquainted computing he had espoused even from under E. H. Moore at the University of with J. V. Uspensky). In 1933 his the time of the ENIAC. Chicago. (See The National Cyclopedia ingenious and powerful photo-electric The Lehmers, as a life-long research of American Biography, vol. 28, pp. 78- number sieve became operational in team (they were married for some sixty­ 79, for an excellent biography and photo Pasadena. With this sieve he did factor­ two years and were joint authors of of this remarkable man.) izations and carried out primality tests twenty-one papers), were always direct When Lehmer was a boy, and later, that were amazing in that era. The sieve and very independent. He was a mas­ his father was a major influence in was also displayed (nonoperationally) ter of computing and was aggravated his mathematical education, introducing at the Chicago World's Fair during that in recent years when algorithm theo­ him to and involving him in the use summer. He spent the year 1933-1934 rists, who were ignorant and had not of the basic algorithms of arithmetic on a fellowship at the Institute for Ad­ bothered to read the literature or talk and number theory and the process of vanced Studies at Princeton. to computing experts, would rediscover sieving to solve various mathematical From 1934 to 1940 Lehmer was on and publish (often with a new name at­ problems. (For a discussion of a lifetime the staff at Lehigh University, with a tached) what he and other computational involvement with the sieving machines year's leave in 1938-1939 on a Guggen­ number theorists had known and used D. H. Lehmer designed and used, see heim Fellowship to Cambridge, Eng­ for years. paper #155 in Selected Works of D.H. land. In 1940 he accepted a proffered Lehmer was a wonderful teacher Lehmer, The Charles Babbage Research position in the mathematics department and lecturer. Witty and urbane, he al­ Centre, P. 0. Box 272, St. Norbert Postal at U.C., Berkeley, a position he held ways put his audience at ease through Station, Winnipeg, Manitoba, Canada until his retirement in 1972, except for his amiability, knowledgableness, and R3V 1L6.) leaves and a two year hiatus (1950- clear presentations. He savored the ba­ As an undergraduate at U.C. Berke­ 1952) when he left Berkeley in a huff sic arithmetic and combinatorial nature ley, Lehmer studied mathematics and over the loyalty oath and went to UCLA of his mathematics, leaving it to others physics, graduating in physics in 1927. to head the Bureau of Standards' Insti­ to recast his results or to fit them into In 1928 he married Emma Markovna tute for Numerical Analysis. From the more general settings. Troskaia (born in 1906 in Samara, Rus­ time of his retirement until he passed From 1953-1957 he was Chairman sia), a young student who had come to away in Berkeley on May 22, 1991, he of the Mathematics Department at U.C. Berkeley from Harbin in 1924 to study remained active as a traveler, lecturer, Berkeley. He was also Vice President

JANUARY 1993, VOLUME 40, NUMBER 1 31 ------·································································News and Announcements of the American Mathematical Society at Stony Brook is working on geo­ Report on the Mathematical from 1953-1954 and Vice President of metric and statistical methods in the Preparation of Teachers the American Association for the Ad­ computation of topological invariants of The Consortium for Mathematics and vancement of Science from 1955-1956. lattice-gauge fields. its Applications (COMAP) has released In 1965 he delivered the Gibbs Lecture Information on how to apply for a report entitled, "In the Beginning: in Denver. thes-e fellowships and grants may be Mathematical Preparation for Elemen­ Lehmer was an editor of MTAC (later found in the Stipends for Study and tary School Teachers". Written by Mathematics ofComputation) from 1943 Travel section in the October 1992 issue Solomon Garfunkel, executive director to 1954 and a member of the Advisory of the Notices. of COMAP, and Gail S. Young, an ed­ Board of Acta Arithmetica from 1958 ucational consultant, the report provides until his death. In 1975 Mathematics of a great deal of insight on how much Computation dedicated an issue to him Mathematics Awareness Week mathematics background is supplied in in honor of his 70th birthday. (There is a 1993 the training of elementary school teach­ fine color photo of him in this issue.) In Mathematics Awareness Week (MAW), ers. Improvements in. teacher training 1993 Mathematics of Computation will an annual nationwide event, will be held are clearly needed if mathematics edu­ publish an issue in his memory. He was a April25 to May 1, 1993. The theme for cation reform efforts are to succeed. But, reviewer for Mathematical Reviews for MAW 1993 is Mathematics and Manu­ considering the findings of this report, over 50 years. facturing, a timely and appropriate topic the barriers to such improvements are The complete bibliography of for communicating the beauty and utility deep, wide, and firmly planted. Lehmer's 181 major publications, as of mathematics to a wide audience. The report is based on the results well as a review of his Selected Works A number of recent reports have of a questionnaire sent to mathematics and a list of his nineteen Ph.D. stu­ touched on the uses of mathematics in departments and education departments dents, will be published in 1993 by Acta manufacturing: two examples are ''The or schools of 400 colleges; there was Arithmetica. His twenty-three mathe­ Mathematical and Computational Sci­ at least one answer from 199 schools. matical notebooks and other personal ences in Emerging Manufacturing Tech­ Because the questionnaire resulted in papers are now permanently housed at nologies and Management Practices", a tremendous variety of responses, the the Bancroft Library at U.C. Berkeley. published by the Society for Industrial writers decided not to simply tabulate Dr. Robin Rider of the Bancroft Library and Applied Mathematics; and "Mathe­ the results, but to also provide quotes has stated that the library is interested in matical Sciences, Technology, and Eco­ from many of the responses. Some of obtaining any Lehmer correspondence nomic Competitiveness", published by these quotes indicate just how severe the that anyone may wish to donate to the the National Research Council. These problems are. permanent collection at the library. reports describe some of the contribu­ For example, in one section of the John Brillhart tions mathematics has made to manufac­ report, respondents were asked about University of Arizona turing. In addition, the Notices carried the quality of the students in elemen­ the article, "Scientific Issues in Manu­ tary education majors, and the perspec­ facturing" (May/June 1992, page 404), tives varied widely. One respondent said AAUW Awards Grants which described a recent meeting ex­ that "many of our elementary preser­ to Women amining how mathematics can be used vice teachers are the worst of their high The American Association of University to solve problems in manufacturing and school classes. . . [T]hese people have Women (AAUW) Educational Founda­ industry. math anxiety in addition to their al­ tion has awarded fellowships and grants In November 1992, the Joint Policy ready low achievement level." Another from under $1000 to $25,000 to 101 Board for Mathematics sent informa­ pointed to a "lack of intellectual cu­ women. The awardees will do postdoc­ tion packets containing ideas for MAW riosity" and an undeveloped sense of toral research, complete doctoral dis­ 1993 to a wide segment of the math­ personal standards exemplified by the sertations, or· work on graduate degrees ematical sciences community, includ­ students' desire for "detailed directions in professional fields in which female ing all department chairs. Last year, for each task in terms of what is accept­ participation has traditionally been low. there were numerous radio and televi­ able or required." Among the awardees are three in sion spots about MAW, as well as news Other responses faulted not the stu­ the mathematical sciences who received articles and editorials in local newspa­ dents but the mathematics department. dissertation fellowships. ELSA NEWMAN pers. The mathematical sciences com­ One noted that a course taught by the of Emory University is working on some munity is urged to participate in this mathematics department was dropped direct and inverse problems in geometric important and exciting event. For more from the elementary education curricu­ optics; REBEKAH VALDIVIA of Washing­ information on MAW, contact the Joint lum because "it was doing great harm ton State University is working on a Policy Board for Mathematics, Office of to the students' attitude toward math­ reaction-diffusion model of transdermal Governmental and Public Affairs, 1529 and nothing to increase their knowledge drug delivery; and JANET WooDLAND Eighteenth Street, NW, Washington, DC (at least in appropriate ways)." Another of the State University of New York 20036; telephone 202-234-9570. said that such courses are "generally a

32 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements failure when taught by Ph.D.s in math ICMI Study on Gender puter activities and problems in classical with no school background ... [They] do and Mathematics Education geometry and elementary algebraic ge­ not realize that the students will learn The International Commission on Math­ ometry will be explored by the various more if the instructor does not start at ematical Instruction (ICMI) will hold a participants. the abstract, formal level." Study Conference on Gender and Math­ Also pending funding, a highlight of The report also notes that state certi­ ematics Education in Sweden in October the 1993 Summer Institute will be a spe­ fication requirements act as a ceiling, not 1993.' Gila Hanna of the Ontario Insti­ cial joint program with the Mathematical a floor, on the amount of mathematics in tute for Studies in Education at the Uni­ Sciences Research Institute (MSRI) in teacher education programs. Responses versity of Toronto chairs the Program Berkeley, California, for undergraduate and graduate student women. The pro­ indicated that education schools worry Committee. A discussion document, entitled gram is specifically designed to invite that raising requirements would prevent "Gender and Mathematics Education: talented young women to consider a too many students from enrolling. As Key Issues and Questions", outlines the career in pure mathematics in general the report points out, programs for ele­ main issues the conference will deal and in the area of algebraic geometry mentary teacher programs already have with. Individuals and groups are invited in particular. Women students admitted enough requirements to elicit calls for to submit contributions to the study to the Summer Geometry Institute in the programs to be lengthened to five for consideration by the Committee no Park City will also be invited to attend years, "but the fear of students not com­ later than February 1, 1993. Contribu­ a special two-week program at MSRI in ing is strong and not unjustified, consid­ tions should be related to the problems May 1993. There they will be offered a ering salaries for beginning teachers." and issues identified in the discussion program of introduction to algebraic ge­ Despite the problems the report document but need not be limited to ometry and participation in small work­ points out, there is some hope for the addressing only these. Participation in ing groups with individual mentoring, future. "Our impression. . . is that five the conference is by invitation only. organized especially for them by partic­ years ago our survey would have pro­ For more information, contact: Gila ipants of the Special Year in Algebraic duced a worse picture. There are places Hanna, MECA, Ontario Institute for Geometry at MSRI. Mentors from this where changes are being discussed or Studies in Education, 252 Bloor Street program will then accompany the group where there are individuals concerned West, Toronto, Ontario MSS 1V6, Can­ to the Summer Institute in Park City in about the present state." However, the ada; tel: 416-923-6641; fax 416-926- June and July to continue their support report goes on to note that there is no 4725; email [email protected]. activities. sign of coordinated actions in states or For more information about the regions, except in isolated cases. Summer Geometry Institute women's joint program with MSRI, The report concludes that, after read­ Pending funding, a Summer Geome­ please write to either Professor Karen ing the responses to the survey, it will try Institute sponsored by the National Uhlenbeck, Department of Mathemat­ ics, University of Texas, Austin, TX be difficult to reach the goals outlined Science Foundation will be held in 78712, or [email protected]; or in such recent reports as "A Call for Park City, Utah, from Sunday, June 20, Professor Robert Bryant, Department of Change" from the Mathematical As­ through Saturday, July 17, 1993. The Institute incorporates learning, teaching Mathematics, Duke University, Durham, sociation of America or "Professional NC 27706, or [email protected]. Standards for Teaching Mathematics" and research activities, and interactions in geometry for high school geometry Please include your email address, mail­ from the National Council of Teach­ ing address, and daytime phone number. ers of Mathematics. The report lists a teachers, undergraduate math majors, . graduate students, and university teach­ For general information about the number of immediate actions that could Summer Geometry Institute and applica­ help, such as increasing the amount of ers and researchers. High school teach­ ers, in partnership with university math­ tion forms, please contact the Regional mathematics required, changing teach-: ematicians and students, will explore the Geometry Institute, 18C de Trobriand ing methods and content of the required evolution of classical geometry to mod­ Street, Fort Douglas, Salt Lake City, UT courses, and considering using more ern geometry on curved spaces, and will 84113. Phone: 801-585-3488. Fax: 801- specialists in mathematics in grades discuss issues of geometry education at 585-5793. Email: [email protected]. K-8. all levels. Undergraduates and gradu­ The Summer Geometry Institute This report would be of interest to ate students will be offered an intense, specifically invites applications from any mathematics department member yet accessible introduction to areas of women and members of minority groups. concerned about issues of teacher train­ geometry research and application by ing. In addition, it points to problems nationally and internationally respected that the entire community should seri­ leaders in algebraic geometry and related News from the Centre de ously address. Copies of the report are fields. The Research and Graduate Sum­ Recherches Mathematiques available from COMAP, Suite 210, 57 mer School topic for the 1993 Summer During 1993-1994 the Centre de Re­ Bedford Street, Lexington, MA 02173; Institute is "Higher Dimensional Com­ cherches Mathematiques (CRM) ofl 'Uni­ telephone 617-862-7878. plex Geometry". A full range of com- versite de Montreal will host a theme

JANUARY 1993, VOLUME 40, NUMBER 1 33 News and Announcements year in Dynamical Systems consisting de Montreal, C.P. 6128, Succursale A, envisaged by the designers for the fuzzy of the following activities: Montreal, Quebec, H3C 3J7, Canada, or control methodology, a clear and step­ Mathematical biology: CRM Sum­ email to pellet1 @ere.umontreal.ca. by-step description of the fuzzy control mer School at the University of British approach to control system design, and Columbia, July 19-August 13, 1993. Or­ News from the a description of some of the successful ganizer: R. Miura (UBC). Lecturers: C. Institute for Mathematics fuzzy control designs for trains, wash­ Clark, A. Dobson, L. Keshet, S. Levin, and Its Applications ing machines, cameras, automobiles, etc. D. Ludwig, M. Mangel, J. Milton, R. University of Minnesota Finally, there will be a roundtable dis­ Miura, S. Pimm, J. Rinzel, L. Segel, and The Institute for Mathematics and its cussion featuring both experts in fuzzy J.1)rson. Applications (IMA) 1992-1993 aca­ control system design and other ap­ Spatial and temporal dynamics: demic year program Control Theory proaches, for the purpose of assessing a semester at CRM, August-December and its AppUcations continues, under the utility of the fuzzy approach to con­ 1993. Organizers: J. Guckenheimer and the guidance of Coordinators H.J. Suss­ trol system design and comparing it to P. Holmes (Cornell). Visitors include: mann (Chairman), W.H. Fleming, P.P. other alternative control system design L. Abbott, N. Aubry, W. Bialek, A. Khargonekar, P.R. Kumar, D.L. Russell, methodologies. Cohen, J.P. Eckmann, M. Golubitsky, and S.E. Shreve. Details concerning the P.R. Kumar and P. Varaiya are orga­ M.W. Hirsch, D. Koditschek, N. Kopell, winter segment of the program Nonlin­ nizing a 'futorial, May 3-7, 1993 which A. Libchaber, R. Mackay, A. Mielke, J. ear systems and optimal control, January will cover verification issues in discrete Rinzel, T. Sejnowski, and Y. Pesin. 2-March 30, 1993 can be found in the event systems, as well as performance Bifurcations and the geometry of November Notices. The spring segment and control. They are also the organizers vector fields: a semester at CRM, January­ of the program is Stochastic and adap­ of the workshop immediately following: June 1994. Organizers: C. Rousseau and tive systems, April1-June 30, 1993. Discrete Event Systems, Manufactur­ D. Schlomiuk (CRM). Visitors include: The spring program will begin with ing Systems, and Communication Net­ D. Cerveau, C. Christopher, F. Du­ a 'futorial, April 5-9, 1993 which will works, May 10-14, 1993. Mathematical mortier, Y. ll'yashenko, A. Lins Neto, R. cover the design and analysis of adap­ systems theory traditionally has been Roussarie, M. Singer, and H. Zoladek. tive systems. The tutorial speakers will concerned with systems of continuous Alsenstadt Chair: Prof. David Ru­ be K.J. Astrom, G.C. Goodwin, and P.R. variables modeled by difference or dif­ elle of IHES will be in residence during Kumar. This program will be followed ferential equations. However, there is the fall semester as Andre Aisenstadt immediately by the workshop Adaptive a growing need for dynamical models Professor. Control, FUtering, and Signal Pro­ of systems whose states have logical or Large Eddy simulation in aero­ cessing, April 12-16, 1993, organized symbolic, rather than numerical, values. dynamics and the environment: a by the tutorial speakers. The area of We call these systems discrete event workshop organized jointly by CERCA, adaptive systems has been one of the dynamical systems (DEDS). The study CERFACS, and CRM, September 27- most active of the past decade. Since of DEDS has become rapidly popu­ 28, 1993. adaptive controllers are fundamentally lar among researchers in systems and Dynamical disease: a workshop in nonlinear controllers which are applied control, in communication networks, in the Laurentian mountains north of Mon­ to nominally linear, possibly stochastic, manufacturing, and in distributed com­ treal, February 1994. Organizers: J. and time-varying systems, their theoret­ puting. This development has created Belair (CRM), L. Glass (McGill), U. ical analysis is usually very difficult. problems due to the veritable Babel of an der Heiden (Witten/Herdecke) and J. The workshop will concentrate on re­ languages and approaches among the Milton (Chicago). Cosponsored by the cent progress concerning the stability, competing groups and due to the dif­ Fields Institute. convergence, performance, and robust­ ferent traditions and experiences that Courses offered by the ISM, In­ ness of adaptive controllers, as well scholars bring to their study of DEDS, stitut des Sciences Mathematiques, a as practical applications. Also attention depending on whether they come from consortium of the mathematics depart­ will be paid to reexamining the fun­ control, communication, computer sci­ ments of Montreal's universities. A va­ damental principles of adaptive system ence, or mathematical logic. The pur­ riety of credit/noncredit graduate and design, especially from the viewpoint of pose of the Workshop is to promote postgraduate courses will be offered, robustness. exchange among scholars representing including: Introduction to Dynamical The minisymposium Fuzzy Control some of the major "schools" of thought Systems, Equations differentielles non­ will be held April19-20, 1993. In recent in DEDS. It is hoped that (1) greater lineaires, and a Seminar in theoretical years many successful designs based on clarity will be achieved and (2) cross­ biology. fuzzy control have been reported; our fertilization will lead to more fruitful Junior and Senior Visiting Fellow­ aim here is to obtain first-hand accounts questions. ships are available. of some of these control systems from D. Duffie and I. Karatzas are or­ Those wishing to participate in the their designers: S. Kawaji, K. Tanaka, ganizing a 'futorial, June 7-11, 1993 above activities are invited to write to T. Yamakawa, and S. Yasunobu. The that will outline the mathematical theory M. Louis Pelletier, CRM, Universite topics to be covered include the role which has become an integral part of

34 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements modern financial economics. This the­ and quasi-linear parabolic equations, op­ mathematics department of Palm Beach ory will be complemented by a series timal stopping and free boundary prob­ Atlantic College, with support from the of lectures on the important issues in lems, martingale representations, fixed University of Florida. The first two is­ finance and demonstrations of how the point theory, singular stochastic con­ sues include a significant and unpub­ mathematical theory can be brought to trol, stochastic differential games, and lished work ofN. Jacobson and an inter­ bear on them. Following this will be held approximation theory for stochastic inte­ pretation of Alexandre Grothendieck's the workshop Mathematical Finance, grals. The workshop will bring together prenotes for EGA V on Bertini type June 14 - June 18, 1993, organized mathematicians and people working in theorems. by M.H.A. Davis, D. Duffie, and S. finance to discuss these developments The Ulam Quarterly is available us­ Shreve. As the world has become more and their implications. ing anonymous FTP from math.ufi.edu interdependent and the pace of finan­ For more information about IMA or goliath.pbac.edu in the directory cial decision-making has quickened, it activities, see the Meetings and Con­ pub/ulam/volumel. For more informa­ has become apparent that our inability ferences section of this issue or con­ tion, contact Piotr Blass, Department to understand many of the underlying tact the IMA: [email protected]. of Mathematics, Palm Beach Atlantic principles of finance can have a substan­ Also, weekly IMA seminar schedules College, telephone 407-835-4353, email tial negative impact on the economy. In with titles and abstracts are available blass@ goliath. pbac.edu. recent years, the mathematical content on U senet: umn.math.dept and by fin­ of the analysis used to price financial gering [email protected], and 1EX New Bank Address for AMS instruments and determine their riski­ files for the Newsletter and the Up­ Please note that, effective January 1, ness has risen precipitously. The single date are available via anonymous ftp at 1993, the AMS has new bank ad­ most notable event in this development ima.umn.edu. dresses for payments and wire transfers. was the invention of the Black-Scholes Checks and money orders should now be option pricing formula, which allowed Ulam Quarterly Available Online sent to: American Mathematical Society, traders to discover "incorrect" option The Ulam Quarterly is now available P. 0 . Box 5904, Boston, MA 02206- prices and subsequently move to take electronically. This refereed journal, es­ 5904. For foreign bank wire transfers, advantage of this "incorrectness". These tablished in January 1992 as a memorial the address is: State Street Bank & advances have involved a high level to Stanislaw Ulam, is available online in Trust Company, 225 Franklin Street, of mathematical sophistication, includ­ either ~-'lEX or Postscript form. It ABA #011000028, Account #0128-262- ing stochastic optimal control, nonlinear is offered without charge, courtesy of the 3, Boston, MA 02110.

Free Random Variables D. V. Voiculescu, K. J. Dykema, and A. Nica

This book presents the first comprehensive introduction to free probability theory, a highly noncommutative probability theory with independence based on free products instead of tensor produCts. Basic examples of this kind of theory are provided by convolution operators on f ree groups and by the asymptotic behavior of large Gaussian random matrices. The book is ideally suited as a textbook for an advanced graduate course and could also provide material for a seminar. In addition to researchers and graduate students in mathematics, this book will be of interest to physicists and others who use random matrices.

1991 Mathematics Subject Classification: 46; 47, 60 ISBN 0-8218-6999-X, 70 pages (hardcover), December 1992 Individual member $23, List price $39, Institutional member $31 To order, please specify CRMM/1NA

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

JANUARY 1993, VOLUME 40, NUMBER 1 35 Funding Information for the Mathematical Sciences

NSF Young Investigators Program total annual support of up to $100,000. sion of Mathematical Sciences, National The National Science Foundation (NSF) For a list of last year's NYI awardees in Science Foundation, Room 339, 1800 has announced the opening of the com­ the mathematical sciences, see "Faculty G Street, NW, Washington, DC 20550. petition for the NSF Young Investigator Fellows Announced", Notices, October Copies of the program announcement (NYI) Awards. The NYI program rec­ 1992, page 849. may be obtained by requesting the pub­ ognizes outstanding young faculty in Nominations for the awards must lication "NSF 92-116-NSF Young In­ science and engineering by providing be made by academic departments. The vestigator Awards Program Guidelines" support for research and educational ac­ deadline for receipt of nominations is from the Forms and ·Publication Unit tivities. The NYI program replaces the January 29, 1993. More information of NSF, telephone 202-357-7861. Email Presidential Young Investigators pro­ on the NYI program may be obtained requests can be sent to pubs@nsf (Bit­ gram, which operated from 1984 to from the Division of Mathematical Sci­ net) or [email protected] (Internet). In the 1991. ences (OMS) at the NSF. Two program request, be sure to include your name, Approximately 150 NYI awards will officers have been assigned to handle your complete mailing address, and the be made in this competition. Awards are the NYI program in OMS: Alan !zen­ number of copies you need. Information for up to five years. Each consists of man, telephone 202-357-3693, email is also available on STIS, NSF's online an annual base grant of $25,000 from [email protected] (Internet) and aizen­ information system. For an electronic the NSF plus up to $37,500 in addi­ man@nsf (Bitnet); and Joe Jenkins, copy of information about STIS, send tional funds per year on a dollar-for­ telephone 202-357-3697, email ijenk­ email to [email protected] (Internet) or dollar matching basis from industrial [email protected] (Internet) andijenkins@nsf stisflyer@nsf (Bitnet). and not-for-profit sources, resulting in (Bitnet). The mailing address is Divi-

DIMACS: Series in Discrete Mathematics and Theoretical Computer Science Mathematical Methods of Analysis of Biopolymer Sequences S. G. Gindikin, Editor Volume8 This collection contains papers by participants in the seminar on mathematical methods in molecular biology who worked for several years at Moscow State University. The seminar united mathematicians and biologists around the problems of biological sequences. The collection includes original results as well as expository material and spans a range of perspectives, from purely mathematical problems to algorithms and their computer realizations. For this reason, the book is of interest to mathematicians, statisticians, biologists, and computational scientists who work with biopolymer sequences.

1991 Mathematics Subject Classification: 62, 90, 92; 05, 94 ISBN 0-8218-6601-X, 150 pages (hardcover), December 1992 Individual member $29, List price $48, Institutional member $38 To order, please specify DIMACS/8NA /t.ti).?~ Anpd= mbjoaw-...... ,_.,..... , fir moon...,.,,_ old$6.50"'""" .....,....._..,, \~ • ; 1; Order from: American Mathematical Society, P.O. Box 5904, Boston, MA 02206-5904, or call toU free 800-321-4AMS • ... (321-4267) in the U.S. and Canada to charge with VISA or MasterCard. Residents of Canada, please include 7% GST. ~\~

36 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY 1993 AMS Elections Nominations by Petition

Vice-President or Member-at-Large The President will name at least six candidates for these One position of vice-president and member of the Council three places, among whom may be candidates nominated by ex officio for a term of three years is to be filled in the petition in the manner described in the rules and procedures. election of 1993. The Council intends to nominate at least The candidate's assent and petitions bearing at least 100 two candidates, among whom may be candidates nominated valid signatures are required for a name to be placed on by petition as described in the rules and procedures. the ballot. In addition, several other rules and operational Five positions of member-at-large of the Council for a considerations, described below, should be followed. term of three years are to be filled in the same election. The Council intends to nominate at least ten candidates, among whom may be candidates nominated by petition in the manner Rules and Procedures described in the rules and procedures. Use separate copies of the form for each candidate for vice­ Petitions are presented to the Council, which, according to president, member-at-large, or member of the Nominating and Section 2 of Article VII of the bylaws, makes the nominations. Editorial Boards Committees. be addressed to Robert 23 January 1979 stated the intent of the 1. To be considered, petitions must The Council of M. Fossum, Secretary, P. 0. Box 6248, Providence, Rhode Island Council of nominating all persons on whose behalf there were 02940, and must arrive by 28 February 1993. valid petitions. 2. The name of the candidate must be given as it appears Prior to presentation to the Council, petitions in support of in the Combined Membership List ( CML) . If the name does not a candidate for the position of vice-president or of member-at­ appear in the list, as in the case of a new member or by error, large of the Council must have at least 50 valid signatures and it must be as it appears in the mailing lists, for example on the must conform to several rules and operational considerations, mailing label of the Notices. If the name does not identify the candidate uniquely, append the member code, which may be which are described below. obtained from the candidate's mailing label or the Providence office. 3. The petition for a single candidate may consist of several Editorial Boards Committee sheets each bearing the statement of the petition, including the of the candidate Committee will be filled name of the position, and signatures. The name Two places on the Editorial Boards must be exactly the same on all sheets. by election. There will be four continuing members of the 4. On the next page is a sample form for petitions. Copies Editorial Boards Committee. may be obtained from the Secretary; however, petitioners may The President will name at least four candidates for these make and use photocopies or reasonable facsimiles. two places, among whom may be candidates nominated by 5. A signature is valid when it is clearly that of the member petition in the manner described in the rules and procedures. whose name and address is given in the left-hand column. The candidate's assent and petitions bearing at least 100 6. The signature may be in the style chosen by the signer. name and address will be checked against to be placed on However, the printed valid signatures are required for a name the Combined Membership List and the mailing lists. No attempt the ballot. In addition, several other rules and operational will be made to match variants of names with the form of name in considerations, described below, should be followed. the CML. A name neither in the CML nor on the mailing lists is not that of a member. (Example: The name Robert M. Fossum is that of a member. The name R. Fossum appears not to be.) 7. When a petition meeting these various requirements ap­ Nominating Committee pears, the Secretary will ask the candidate whether he is willing Three places on the Nominating Committee will be filled to have his name on the ballot. Petitioners can facilitate the by election. There will be six continuing members of the procedure by accompanying the petitions with a signed statement Nominating Committee. from the candidate giving his consent.

JANUARY 1993, VOLUME 40, NUMBER 1 37 NOMINATION PE11'110N FOR 1993 ELECTION

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

as a candidate for the position of (check one): 0 Vice-President 0 Member-at-Large of the Council 0 Member of the Nominating Committee 0 Member of the Editorial Boards Committee of the American Mathematical Society for a term beginning 1 February, 1994.

Name and Address (printed or typed)

Signature

Signature

Signature

Signature

Signature

Signature

38 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY CALL FOR SUGGESTIONS

There will be a number of contested seats in the 1993 AMS elections. Your suggestions are wanted by

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

THE PRESIDENT for three Nominating Committee members and two Editorial Boards Committee members.

In Addition

THE EDITORIAL BOARDS COMMITTEE requests suggestions for appointments to various editorial boards of Society publications.

Send your suggestions for any of the above to:

Robert M. Fossum, Secretary American Mathematical Society Department of Mathematics University of Illinois 1409 West Green Street Urbana, Illinois 61801 Jour~als American Mathematical Society

Journal of the American Mathematical Society

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

1993 Subscription Prices List $144*, Institutional member $115*, Individual member $86* (ISSN 0894-0347). Back volumes are also available. Call AMS Customer Services for prices. Your ordering code is 93JAMS/NA

Transactions of the American Mathematical Society

American Mathematical Society journals are respected worldwide for publishing high-quality research. Transac­ tions of the American Mathematical Society features well­ written papers devoted to pure and applied mathematics. This important monthly journal was first published in 1900.

1993 Subscription Prices List $893**, Institutional member $714** (ISSN 0002-9947). Back volumes are also available. Call AMS Customer Services for prices. Your ordering code is 93TRAN/NA

*Postage surcharge: India $18; other foreign $8 Optional delivery: First class $13; airmail $36, **Postage surcharge: India $50; other foreign $27 Optional delivery: First class $38; airmail $127. All prices subject to change. Prepayment required. Order from: American Mathematical Society, P.O. Box 5904, Boston, MA 02206-5904, or call toll free 800-321- 4AMS in the U.S. and Canada to charge with VISA or MasterCard. Residents of Canada, please include 7% GST. Knoxville, Tennessee University of Tennessee March 26-27, 1993

First Announcement

The eight-hundred-and-seventy-ninth meeting of the Amer­ Stochastic processes, Balram S. Rajput and Jan Rosin­ ican Mathematical Society will be held on the campus of ski, University of Tennessee, Knoxville. the University of Tennessee, Knoxville, Tennessee on Friday, Algebraic combinatorics, Michelle L. Wachs. March 26 and Saturday, March 27, 1993. All sessions and in­ Abstracts for consideration for these sessions should have vited addresses will be in the Humanities and Social Sciences been submitted by the June 26, 1992 deadline. This deadline Building. was previously published in the Calendar of AMS Meetings and Conferences and in the Invited Speakers and Special Sessions section of the Notices. Invited Addresses

By invitation of the Southeastern Section Program Committee, Contributed Papers there will be four invited one-hour addresses. The speakers, their affiliations, and the titles of their talks where available There will also be sessions for contributed ten-minute pa­ are: pers. Abstracts should have been submitted by the January Paul R. Blanchard, Boston University, title to be an­ 5, 1993 deadline previously published in the Calendar of nounced. AMS Meetings and Conferences. Late papers will not be Olav Kallenberg, Auburn University, On basic symme­ accommodated. tries in probability theory. Richard Tapia, Rice University, The historical develop­ Registration ment of computational optimization. Michelle L. Wachs, University of Miami, Homology of The meeting registration desk will be located in the second partially ordered sets ofpartitions. floor lobby of the Humanities and Social Sciences Building and will be open from 8:00 a.m. to 5:00 p.m. on Friday, March 26, and 8:00 a.m. to noon on Saturday, March 27. Special Sessions The registration fees are $30 for members of the AMS, $45 By invitation of the same committee, there will be nine special for nonmembers, and $10 for emeritus members, students, or sessions of selected twenty-minute papers. The topics of these unemployed mathematicians. sessions, and the names and affiliations of the organizers, are as follows: Social Event Commutative ring theory, David F. Anderson and David E. Dobbs, University of Tennessee, Knoxville. A cash-bar reception is planned for 8:00p.m. to 10:00 p.m. Interventions to assure success: calculus through junior on Friday, March 26 at the Campus Inn. faculty, Bettye Anne Case, Florida State University. Optimal control and applications, Ben G. Fitzpatrick and Accommodations Suzanne M. Lenhart, University of Tennessee, Knoxville. Variational problems in geometry, Alexandre S. Freire Rooms have been blocked for participants at the Campus and Conrad P. Plaut, University of Tennessee, Knoxville. Inn, Knoxville Hilton, and Radisson Hotel Knoxville. The Sturm-Liouville operators, applications, and extensions, Campus Inn is adjacent to the university campus and is a Don B. Hinton and Kenneth Shaw, University ofTennessee, short walk from the Humanities and Social Sciences Building Knoxville. (HSS). The Knoxville Hilton and Radisson Hotel Knoxville Numerical methods in optimization, Tim Kelley, North are located downtown and are approximately three-quarters Carolina State University. of a mile from the HSS Building; morning and evening Continua theory and dynamical systems, John C. Mayer, van transportation will be provided between these hotels University of Alabama-Birmingham. and the HSS Building. Participants should make their own

JANUARY 1993, VOLUME 40, NUMBER 1 41 Meetings arrangements with the hotel of their choice and ask for the Parking AMS conference rate. All rates are subject to a 13.25% tax. The AMS is not responsible for rate changes or the quality Parking will be available in the University Center Parking Garage at a reduced rate of $3.00 per day (no in-and-out of the accommodations offered by these hotels/motels. privileges) if the parking ticket is validated at the registration Campus Inn table. The garage is accessed from Stadium Drive. 1706 Cumberland Avenue, Knoxville, TN 37916 Telephone: 615-521-5000 The deadline for reservations is March 11, 1993. Travel and Local Information The University of Tennessee, Knoxville campus is located Single $39 Double $42 approximately twelve miles from the Knoxville McGhee­ Tyson Airport, which is served by most major airlines KnoxviUe Hilton (including American, Delta, Northwest, United, and USAir). 501 Church Avenue, S.W., Knoxville, TN 37902-2591 Participants also can arrive by Greyhound-Trail ways Bus Telephone: 615-523-2300 Lines. The deadline for reservations is March 3, 1993. Participants traveling by car from the north on 1-75 first should take 1-275 and then follow, in order, the signs for Single $59 Double $69 1-40 West/1-75 South, 17th Street, and the university. Those traveling by car from the west or east on 1-40 or from the Radisson Hotel Knoxville south on 1-75 may use the 17th Street exit and follow 17th 401 Summit Hill Drive, Knoxville, TN 37902 Street south to the campus. Telephone: 615-522-2600 The deadline for reservations is March 11, 1993. Weather and Local Attractions Single $69 Double $65 The weather in Knoxville in late March is variable. The normal daily low in March is 39.3°F, the normal daily high is Food Service 60.1 °F, and the normal rainfall for the month is 5.49 inches. Knoxville and the surrounding area offer many interesting Numerous eating establishments from diners and national fast attractions, including historical sites, museums, galleries, food chains to finer restaurants are located along Cumberland an outstanding zoo, the. vacation towns of Pigeon Forge Avenue within walking distance of the HSS Building. Addi­ and Gatlingburg, the "Atomic City" of Oak Ridge , the tional restaurants are located approximately one mile away Great Smoky Mountains National Park, and Big South Fork in the downtown area and from three to fifteen miles west National River and Recreation Area. Nightlife offerings along Kingston Pike, an extension of Cumberland Avenue. include lounges, sports bars, comedy clubs, and the "Old The University Center will offer only limited food service City", a restored historic neighborhood featuring restaurants because UTK will be on spring break during the meeting. and saloons with live music, antiques stores, and other shops.

Amedoan ...... - TRANSlATIONS American Mathematical Society Translations, Series 2 ae....:a •Y*-154 Selected Papers in K-Theocy Volume 154 Selected Papers inK-Theory This book contains papers ranging over a number of topics relating to K -theory, including algebraic number theory, Grothendieck and Whitehead groups, group representation theory, linear algebraic groups, selfadjoint operator algebras, linear operators, homology and cohomology, and the use of K -theory in geometry. 1991 Mathematics Subject Classification: 11, 13, 16, 18, 19, 20, 46, 47, 55; 12 ISBN 0-8218-7504-3, 195 pages (hardcover), December 1992 Individual member $50, List price $83, Institutional member $66 ·--- To order, please .specify TRANS2/154NA

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

42 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Invited Addresses and Special Sessions

Invited Addresses Syracuse, NY, September 1993 at AMS Meetings Tadeusz Iwaniec James M. Renegar The individuals listed below have accepted invitations to Charles A. McGibbon Alvany Rocha address the Society at the times and places indicated. For some meetings, the list of speakers is incomplete. Invited addresses Heidelberg, Germany, October 1993 at Sectional Meetings are selected by the Section Program Gerd Faltings Committee, usually twelve to eighteen months in advance of a meeting. Members wishing to nominate candidates for invited addresses should send the relevant information to the College Station, TX, October 1993 Associate Secretary for the Section who will forward it to the Steven P. Lalley Theodore A. Slaman Section Program Committee. Gilles Pisier Stephan A. Stolz

Knoxville, TN, March 1993 Organizers and Topics Please see the first announcement of this meeting elsewhere of Special Sessions in this issue. The list below contains all the information about Special Sessions at meetings of the Society available at the time this issue of the Notices went to the printer. The section below Salt Lake City, UT, April1993 entitled Information for Organizers describes the timetable Michael Christ Robert M. Guralnick for announcing the existence of Special Sessions. Kenneth M. Golden Michael S. Waterman March 1993 Meeting in Knoxville, Tennessee Southeastern Section Washington, DC, April1993 Associate Secretary: Fan R. K. Chung Joel Sprock Joseph A. Cima (until 1131193) Leopold Flatto A. Zamolodchikov Robert J. Daverman (after 1131193) Deadline for organizers: Expired Deadline for consideration: Expired DeKalb, IL, May 1993 Please see the first announcement of this meeting elsewhere in this issue. Susan J. Friedlander Clark Robinson Russell D. Lyons April1993 Meeting in Salt Lake City, Utah Western Section Vancouver, British Columbia, Canada Associate Secretary: Lance W. Small Deadline for organizers: Expired August 1993 Deadline for consideration: Expired Armand Borel Yuri Manin M. Salah Baouendi and Linda P. Rothschild, Partial differen­ (Progress in Mathematics (Colloquium Lectures) tial equations and several complex variables Lecture) Curt McMullen Andrej Cherkaev and Kenneth M. Golden, Effective properties Avner Friedman (AMS-CMS) of inhomogeneous materials (Progress in Mathematics Louis Nirenberg Davida Fischman, Hopf algebras and Hopf algebra actions Lecture) (AMS-CMS) Naomi Fisher and Hugo Rossi, Mathematics and education Robert E. Gompf (AMS-CMS) Jill Pipher (AMS-CMS) reform H. Blaine Lawson Libin Mou and Nat Smale, Singularities of geometric partial (AMS-CMS) differential equations

JANUARY 1993, VOLUME 40, NUMBER 1 43 Invited Addresses and Special Sessions

Paul C. Roberts, Roger A. Wiegand, and Sylvia M. Wiegand, Nassif Ghoussoub, Variational methods in partial differential Commutative algebra and modules equations (AMS-CMS) Simon Tavare, Stochastic processes in population genetics Linda Keen, Dynamical systems (AMS-CMS) James L. Lewis and Barry Mazur, Algebraic cycles (AMS­ CMS) April1993 Meeting in Washington, DC Eastern Section Ram M. Murty and Rajiv Gupta, Number theory (AMS-CMS) Associate Secretary: Gregory Verchota, Harmonic analysis techniques in partial W. Wistar Comfort (until 1131/93) differential equations (AMS-CMS) Lesley M. Sibner (after 1131193) Deadline for organizers: Expired Deadline for consideration: Expired Roy L. Adler and Leopold Flatto, Geodesic flows, hyperbolic September 1993 Meeting in Syracuse, New York geometry, and symbolic dynamics Eastern Section Associate Secretary: Lesley M. Sibner Joseph A. Ball and Cora S. Sadosky, Dilation and interpola­ Deadline for organizers: Expired tion: operator theoretic methods Deadline for consideration: April 27, 1993 John J. Benedetto and Rodney B. Kerby, Wavelets in sampling Douglas R. Anderson, Geometric topology theory and signal processing Steven P. Diaz and Anthony V. Geramita, Commutative Joseph E. Bonin, Geometric methods in combinatorics algebra and algebraic geometry Nathaniel Dean, Graph theory Wu-Teh Hsiang, Differential geometry and global analysis Edward Frenkel, Mathematics of two-dimensional quantum Mark Kleiner and Dan Zacharia, Representations of finite field theory dimensional algebras Anant P. Godbole and Gary J. Sherman, Undergraduate Juan J. Manfredi, Nonlinear potential theory research in applied mathematics Terry R. McConnell, Topics in probability Anant P. Godbole and Gary J. Sherman, Undergraduate RobertS. Strichartz, Harmonic analysis research in pure mathematics Valentina S. Harizanov and James C. Owings, Pure and applied recursion theory October 1993 Meeting in Heidelberg, Germany Kevin G. Hockett and E. Arthur Robinson, Ergodic theory, (Joint Meeting with the Deutsche dynamical systems, and applications Mathematiker-Vereinigung e. V.) Victor J. Katz, History ofmathematics Associate Secretary: Robert M. Fossum Yongwu Rong, Low dimensional topology Deadline for organizers: Expired Joel Sprock, Nonlinear elliptic problems in geometry and Deadline for consideration: April 27, 1993 physics

May 1993 Meeting in DeKalb, Illinois October 1993 Meeting in CoUege Station, Texas Central Section Central Section Associate Secretary: Andy R. Magid Associate Secretary: Andy R. Magid Deadline for organizers: January 22, 1993 Deadline for organizers: Expired Deadline for consideration: July 14, 1993 Deadline for consideration: February 3, 1993 Harold P. Boas, AI Boggess, and Emil J. Straube, Several Gregory S. Ammar, Advances in linear algebra: theory, computation, application complex variables Randall K. Campbell-Wright, Carl C. Cowen, and Barbara D. Michael A. Filaseta and Carl Pomerance, Number theory MacCluer, Susan J. Friedlander, Mathematical topics in fluid dynamics Composition operators on spaces of analytic Zoltan Furedi, Combinatorics functions David R. Larson, Andrew J. Granville, Analytic number theory Non self adjoint operator algebras Frank Harary, Beautiful graph theory John C. Meakin, Amitai Regev, Mark V. Sapir, and Samuel M. Vovsi, Mohsen Pourahmadi, Stochastic processes Identities and varieties of algebraic structures Jeanne LaDuke, History of mathematics Efton L. Park, Noncommutative differential geometry Linda R. Sons, Function theory Gilles Pisier and Thomas Schlumprecht, The geometry of Joel H. Spencer, Probabilistic methods Banach spaces and operator spaces Peter Waterman, Discrete groups Sung Yell Song and Paul M. Terwilliger, Algebraic combina­ torics

August 1993 Meeting in Vancouver, British Columbia, Canada November 1993 Meeting in Claremont, CaUfornia Associate Secretary: Lance W. Small Western Section Deadline for organizers: Expired Associate Secretary: Lance W. Small Deadline for consideration: April 27, 1993 Deadline for organizers: February 5, 1993 David M. Austin, Four-manifolds (AMS-CMS) Deadline for consideration: July 14, 1993

44 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Invited Addresses and Special Sessions

January 1994 Meeting in Cincinnati, Ohio March 1996 Meeting in Iowa City, Iowa Associate Secretary: Central Section Joseph A. Cima (until 1131193) Associate Secretary: Andy R. Magid Robert J. Daverman (after 1131193) Deadline for organizers: June 22, 1995 To be announced Deadline for organizers: April 5, 1993 Deadline for consideration: Deadline for consideration: September 23, 1993

March 1994 Meeting in Lexington, Kentucky Information for Organizers Southeastern Section Special Sessions at Annual and Summer Meetings are held Associate Secretary: under the supervision of the Program Committee for National Joseph A. Cima (until 1131193) Meetings (PCNM). They are administered by the Associate Robert J. Daverman (after 1131193) Secretary in charge of that meeting with staff assistance from Deadline for organizers: June 18, 1993 the Meetings Department in the Society office in Providence. Deadline for consideration: To be announced According to the "Rules for Special Sessions" of the Society, Special Sessions are selected by the PCNM from March 1994 Meeting in Manhattan, Kansas a list of proposed Special Sessions in essentially the same Central Section manner as individuals are selected to give Invited Addresses. Associate Secretary: Andy R. Magid Deadline for organizers: June 25, 1993 The number of Special Sessions at a Summer or Annual Deadline for consideration: To be announced Meeting is limited. The algorithm that determines the number of Special Sessions allowed at a given meeting, while simple, is not repeated here, but can be found in "Rules for Special April1994 Meeeting in Brooklyn, New York Sessions" on page 614 in the April1988 issue of the Notices. Eastern Section Each person selected to give an Invited Address is invited Associate Secretary: Lesley M. Sibner Deadline for organizers: July 9, 1993 to generate a Special Session, either by personally organizing Deadline for consideration: To be announced one or by having a Special Session organized by others. Pro­ posals to organize a Special Session are sometimes requested either by the PCNM or by the Associate Secretary. Other June 1994 Meeting in Eugene, Oregon proposals to organize a Special Session may be submitted to Western Section the Associate Secretary in charge of that meeting (who is an Associate Secretary: Lance W. Small may Deadline for organizers: September 7, 1993 ex-officio member of the committee and whose address Deadline for consideration: To be announced be found below). These proposals must be in the hands of the PCNM at least nine months prior to the meeting at which the Special Session is to be held in order that the committee may October 1994 Meeting in Stillwater, Oklahoma Central Section consider all the proposals for Special Sessions simultaneously. Associate Secretary: Andy R. Magid Proposals that are sent to the Providence office of the Society, Deadline for organizers: January 28, 1994 to the Notices, or directed to anyone other than the Associate Deadline for consideration: To be announced Secretary will have to be forwarded and may not be received in time to be considered for acceptance. It should be noted that Special Sessions must be announced Colorado January 1995 Meeting in Denver, in the Notices in such a timely fashion that any member of Associate Secretary: Andy R. Magid Deadline for organizers: April 20, 1994 the Society who so wishes may submit an abstract for Deadline for consideration: To be announced consideration for presentation in the Special Session before the deadline for such consideration. This deadline is usually for the meeting March 1995 Meeting in Chicago, Illinois three weeks before the deadline for abstracts Central Section in question. Associate Secretary: Andy R. Magid Special Sessions are very effective at Sectional Meetings Deadline for organizers: June 24, 1994 and can usually be accommodated. The processing of pro­ Deadline for consideration: To be announced posals for Special Sessions for Sectional Meetings is handled in essentially the same manner as for Annual and Summer November 1995 Meeting in Kent, Ohio Meetings by the Section Program Committee. Again, no Spe­ Central Section cial Session at a Sectional Meeting may be approved so late Associate Secretary: Andy R. Magid that its announcement appears past the deadline after which Deadline for organizers: February 4, 1995 Deadline for consideration: To be announced members can no longer send abstracts for consideration for presentation in that Special Session. The Society reserves the right of first refusal for the January 1996 Meeting in Orlando, Florida publication of proceedings of any Special Session. These Associate Secretary: Lance W. Small Deadline for organizers: April 12, 1995 proceedings appear in the book series Contemporary Mathe­ Deadline for consideration: To be announced matics.

JANUARY 1993, VOLUME 40, NUMBER 1 45 Invited Addresses and Special Sessions

More precise details concerning proposals for and orga­ announced above and in the announcements of the meeting at nizing of Special Sessions may be found in the "Rules for which the Special Session has been scheduled. Contributors Special Sessions" or may be obtained from any Associate should know that there is a limitation in size of a single Secretary. Special Session, so that it is sometimes true that all places are filled by invitation. Papers not accepted for a Special Session Proposals for Special Sessions to the are considered as ten-minute contributed papers. Associate Secretaries Abstracts of papers submitted for consideration for presen~ The programs of Sectional Meetings are arranged by the tation at a Special Session must be received by the Providence Associate Secretary for the section in question: office (Abstracts Coordinator, Meetings Department, Amer­ Western Section ican Mathematical Society, P. 0. Box 6887, Providence, RI Lance W. Small, Associate Secretary Department of Mathematics 02940) by the special deadline for Special Sessions, which is University of California, San Diego usually three weeks earlier than the deadline for contributed La Jolla, CA 92093 papers for the same meeting. The Council has decreed that Electronic mail: [email protected] no paper, whether invited or contributed, may be listed in the (Telephone 619-534-3590) program of a meeting of the Society unless an abstract of the Central Section Andy R. Magid, Associate Secretary paper has been received in Providence prior to the deadline. Department of Mathematics Electronic submission of abstracts is available to those University of Oklahoma who use the 1&X typesetting system. Requests to receive 601 Elm PHSC 423 the electronic package of files via email should be sent to Norman, OK 73019 Electronic mail: [email protected] [email protected]. Users may also obtain the pack­ (Telephone 405-325-6711) age on IBM or Macintosh diskettes, available free of charge Eastern Section by writing to: Electronic Abstracts, American Mathematical W. Wistar Comfort, Associate Secretary (until January 31, 1993) Society, Meetings Department, P.O. Box 6887, Providence, Department of Mathematics RI 02940, USA. When requesting the abstracts package, Wesleyan University Middletown, CT 06457 users should be sure to specify whether they want the Electronic mail: [email protected] plain '!&X, .4MS'-'I&X, or the J.t\'I&X package. Requests for (Telephone 203-347 -9411) general information concerning abstracts may be sent to Lesley M. Sibner, Associate Secretary (beginning February I, 1993) [email protected]. Department of Mathematics Polytech University of New York Brooklyn, NY 11201-2990 Number of Papers Presented Electronic mail: [email protected] (Telephone 718-260-3505) Joint Authorship Southeastern Section Although an individual may present only one ten-minute Joseph A. Cima, Associate Secretary (until January 31, 1993) contributed paper at a meeting, any combination of joint Department of Mathematics authorship may be accepted, provided no individual speaks University of North Carolina, Chapel Hill more than once. An author can speak by invitation in more Chapel Hill, NC 27599-3902 Electronic mail: [email protected] than one Special Session at the same meeting. (Telephone 919-962-1050) An individual may contribute only one abstract by title Robert J. Davennan, Associate Secretary (beginning February I, 1993) in any one issue of Abstracts, but joint authors are treated as Department of Mathematics a separate category. Thus, in addition to abstracts from two University of Tennessee individual authors, one joint abstract by them may also be Knoxville, TN 37996-1300 Electronic mail: [email protected] accepted for an issue. (Telephone 615-974-6577) As a general rule, members who anticipate organizing Special Sessions at AMS meetings are advised to seek approval at least nine months prior to the Site Selection for Sectional Meetings scheduled date of the meeting. No Special Sessions can be approved too late to Sectional Meeting sites are recommended by the Associate provide adequate advance notice to members who wish to participate. Secretary for the Section and approved by the Committee of Proposals for Special Sessions at the October 1-3, 1993 meeting in Associate Secretaries and Secretary. Recommendations are Heidelberg, Germany, only, should be sent to Robert M. Fossum at the Department of Mathematics, University oflllinois, Urbana, ll 61801, Telephone: usually made eighteen to twenty-four months in advance. 217-244-1741, email: [email protected]. Host departments supply local information, ten to twelve rooms with overhead projectors for contributed paper sessions Information for Speakers and Special Sessions, an auditorium with twin overhead A great many of the papers presented in Special Sessions at projectors for invited addresses, and registration clerks. The meetings of the Society are invited papers, but any member Society partially reimburses for the rental of facilities and of the Society who wishes to do so may submit an abstract for equipment, and for staffing the registration desk. Most host consideration for presentation in a Special Session, provided departments volunteer; to do so, or for more information, it is received in Providence prior to the special early deadline contact the Associate Secretary for the Section.

46 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Joint Summer Research Conferences in the Mathematical Sciences University of Washington, Seattle, July 10 to August 6, 1993

The 1993 Joint Summer Research Conferences in the Mathe­ Please type or print the following: matical Sciences will be held at the University of Washington, 1. Title and dates of conference desired; Seattle, from July 10 to August 6. It is anticipated that the 2. Full name; series of conferences will be supported by grants from the 3. Mailing address; National Science Foundation and other agencies. 4. Telephone number and area code for office and home, There will be seven conferences in seven different areas email addresses, FAX number; of mathematics. The topics and organizers for the conferences 5. A short paragraph describing your scientific background were selected by the AMS, the Institute of Mathematical relevant to the topic of the conference; Statistics (IMS), and the Society for Industrial and Applied 6. Financial assistance requested; please estimate cost of Mathematics (SIAM) Committee on Joint Summer Research travel; Conferences in the Mathematical Sciences. The selections 7. Indicate if support is not required and if interested in were based on suggestions made by the members of the attending even if support is not offered. committee and individuals submitting proposals. The com­ The deadline for receipt of requests for information is mittee considered it important that the conferences represent March 1, 1993. Requests to attend will be forwarded to the diverse areas of mathematical activity, with emphasis on Organizing Committee for each conference for consideration areas currently especially active, and paid careful attention to after the deadline of March 1. All applicants will receive subjects in which there is important interdisciplinary activity a formal invitation, Brochure of Information, notification of at present. financial assistance, and a tentative scientific program (if The conferences emulate the scientific structure of those the Chair has prepared one in advance; otherwise, programs held throughout the year at Oberwolfach. These conferences will be distributed at on-site registration) from the AMS by are intended to complement the Society's program of annual May 1. Funds available for these conferences are limited and Summer Institutes and Summer Seminars, which have a individuals who can obtain support from other sources should larger attendance and are substantially broader in scope. The do so. The allocation of grant funds is administered by the conferences are research conferences and are not intended to AMS office, and the logistical planning for the conferences provide an entree to a field in which a participant has not is also done by the AMS. However, it is the responsibility of already worked. the Chair of the Organizing Committee of each conference to It is expected that funding will be available for a limited determine the amount of support participants will be awarded. number of participants in each conference. Others, in addition This decision is not made by the AMS. Women and minorities to those funded, will be welcome, within the limitations are encouraged to apply and participate in these conferences. of the facilities of the campus. In the spring a brochure Any questions concerning the scientific portion of the of information will be mailed to all who are requesting to conference should be directed to the Chair or any member of attend the conferences. The brochure will include information the Organizing Committee. on room and board rates, the residence and dining hall The Joint Summer Research Conferences in the Mathemat­ facilities, travel, local information, and a Residence Housing ical Sciences are under the direction of the AMS-IMS-SIAM Form to request on-campus accommodations. Information on Committee on Joint Summer Research Conferences in· the off-campus housing will also be included in the brochure. Mathematical Sciences. The following committee members Participants will be responsible for making their own housing chose the topics for the 1993 conferences: John A. Burns, Fan and travel arrangements. Each participant will be required to R. K. Chung, Leonard Evens, Martin Golubitsky, Anthony W. pay a conference fee. Knapp, Peter W. K. Li, Stewart B. Priddy, Robert J. Serfting, Michael Shub, and Gregg J. Zuckerman. Those interested in attending one of the conferences should send the following information to the Summer Research Conference Coordinator, Conferences Department, American N.B. Lectures begin on Sunday morning and run Mathematical Society, Post Office Box 6887, Providence, RI through Thursday. Check-in for housing begins on Saturday. No lectures are held on Saturday. 02940 or by email [email protected].

JANUARY 1993, VOLUME 40, NUMBER 1 47 ~--~~--J--WilMW-IlM*______Jjv '~ """ VV"•"v ••••v v• •• v ••••• vvv •••• o•••• - •••v Joint Summer Research Conferences

Please refer to the complete announcement with descriptions Saturday, July 17 to Friday, July 23 of each conference which appeared in the November Notices. Recent developments in the inverse Galois problem WALTER FElT (Yale University), Chair MIKE FRIED (University of California, Irvine), Co-Chair Saturday, July 10 to Friday, July 16 Curvature equations in conformal geometry Saturday, July 24 to Friday, July 30 SUNG-YUNG A. CHANG (University of California, Los Mathematics of superconductivity Angeles), Co-Chair M. GUNZBURGER (Virginia Tech), Co-Chair RicK SCHOEN (Stanford University), Co-Chair J. OcKENDON (University of Oxford), Co-Chair

Saturday, July 31 to Friday, August 6 Saturday, July 10 to Sunday, July 18 Distributions with fixed marginals, doubly stochastic measures, Multivariable operator theory and Markov operators RAuL E. CURTO (University of Iowa), Co-Chair HOWARD SHERWOOD (University of Central Florida), RoNALD G. DoUGLAS (SUNY at Stony Brook), Co-Chair Co-Chair JoEL D. PINCUS (SUNY at Stony Brook), Co-Chair MICHAEL D. TAYLOR (University of Central Florida), Co-Chair NoRBERTO SALINAS (University of Kansas), Co-Chair Saturday, July 31 to Friday, August 6

Saturday, July 17 to Friday, July 23 Applications of hypergroups and related measure algebras WILLIAM C. CONNETT (University of Missouri, St. Louis), Spectral geometry Co-Chair RoBERT BROOKS (University of Southern California), OLIVIER GEBUHRER (Universite Louis Pasteur, Strasbourg), Co-Chair Co-Chair CAROLYN GORDON (Dartmouth College), Co-Chair ALAN L. SCHWARTZ (University of Missouri, St. Louis), PETER PERRY (University of Kentucky), Co-Chair Co-Chair

ADVANCES IN SOVIET MATHEMATICS Idempotent Analysis V. P. Maslov and S . N. Samborski!, Editors Volume 13 Idempotent analysis is a new branch of mathematical analysis concerned with functional spaces and their mappings when the algebraic structure is generated by an idempotent operation. The articles in this collection show how idempotent analysis is playing a unifying role in many branches of mathematics related to external phenomena and structures- a role similar to that played by functional analysis in mathematical physics, or numerical methods in partial differential equations. Such a unification necessitates study of the algebraic and analytic structures appearing in spaces of functions with values in idempotent semirings. The papers collected here constitute an advance in this direction. 1991 Mathematics Subject Classification: 16, 20, 35 , 47, 49, 90; 81 ISBN 0-8218-4114-9, 210 pages (hardcover), December 1992 Individual member $65, List price $108, Institutional member $86 To order, please specify ADVSOV/13NA

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48 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY 1993 Summer Seminar in Applied Mathematics

The mathematics of tomography, impedance imaging, and integral geometry Mount Holyoke College, South Hadley, Massachusetts, June 7-18

The twenty-third AMS-SIAM Summer Seminar in Applied David Barber, Gregory Beylkin*, Allan Cormack, Leon Mathematics will be held June 7-18, 1993, at Mount Holyoke Ehrenpreis*, Simon Gindikin*, Sigurdur Helgason, David College, South Hadley, Massachusetts. The seminar will Isaacson*, Frank Natterer*, Lawrence Shepp*, and Gunther be sponsored by the American Mathematical Society and Uhlmann* (those with * have accepted as of October 21, the Society for Industrial and Applied Mathematics. It is 1992). It is anticipated they will give research talks as well. anticipated that the seminar will be supported by grants A very preliminary and partial list of other possible speakers from federal agencies. The proceedings of the seminar will includes Carlos Berenstein, Jan Boman, Adel Faridani, Josip be published by the American Mathematical Society in the Globevnik, Fulton Gonzalez, Allan Greenleaf, Eric Grinberg, Lectures in Applied Mathematics series. Alberto Gruenbaum, Gabor Herman, Michael Klibanov, Al­ One of the most exciting features of tomography is the fred Louis, Wolodymyr Madych, Ziqi Sun, John Sylvester, and Michael Vogelius. strong relationship between high level pure mathematics (such as harmonic analysis, partial differential equations, integral Those interested in attending the Seminar should send geometry, microlocal analysis,. and Lie group theory) and the follwing information before March 15, 1993, to AMS­ applications to medicine, impedance imaging, radiotherapy, SIAM Summer Seminar Conference Coordinator, American and industrial nondestructive evaluation. Mathematical Society, P.O. Box 6887, Providence, R.I. 02940, email [email protected]. Please type or print the following: The aim of the conference is to strengthen the connection between the pure and applied aspects of these areas and 1. Full name; to facilitate dialogue between researchers in the various 2. Mailing address; areas. The seminar will provide introductory talks on tomo­ 3. Telephone number and area code for office and home; graphy, impedance imaging, and integral geometry intended 4. email address if available; for younger researchers and other beginners in the field (in 5. Anticipated arrival and departure dates; the first part of the conference) and a research component 6. Your scientific background relevant to the topic of the in which researchers will have the opportunity to define and seminar; articulate the main problems of current interest and to isolate 7. Financial assistance requested (please estimate cost of common themes and approaches. A number of the anticipated travel), indicate if support is not required and if interested participants will be experts from foreign countries. in attending even if support is not offered. The organizing committee consists of Margaret Cheney, Participants who wish to apply for a grant-in-aid should Rensselaer Polytechnic Institute; Simon Gindikin, Rutgers so indicate; however, funds available for the seminar are University; Peter Kuchment, Wichita State University; Eric very limited and individuals who can obtain support from Todd Quinto (Chair), Tufts University; and Lawrence Shepp, other sources should do so. Graduate students who have Bell Laboratories. completed at least one year of graduate school are encouraged A tentative list of proposed introductory lecturers includes to participate.

JANUARY 1993, VOLUME 40, NUMBER 1 49 1993 Summer Research Institute Stochastic analysis Cornell University, Ithaca, New York, July 11-30

The forty-first Summer Research Institute sponsored by the Mueller, D. Nualart, D. Ocone, B. 0ksendal, G. Papanicolaou, American Mathematical Society will be devoted to Stochastic E. Pardoux, E. Perkins, R. Pinsky, M. Rockner, C. Rogers, B. Analysis and will be held at Cornell University from July Rozovskii, T. Shiga, I. Shigekawa, A. Sznitman, A. Truman, 11-30, 1993. The Co-Chairs of the Organizing Committee A.S. Ustunel, M. van den Berg, S. Watanabe, V. Wihstutz, R. are Mike Cranston, University of Rochester; Rick Dur­ Williams, Z. Zhao, and W. Zheng. rett, Cornell University; and Mark Pinsky, Northwestern It is anticipated that the institute will be partially funded University. The speakers were selected with the advice of a by a grant from the National Science Foundation. Proceedings committee that consists of Rodrigo Banuelos, Purdue Uni­ will be published in the AMS series titled Proceedings of versity; Peter Baxendale, University of Southern California; Symposia in Pure Mathematics. It is expected that the papers Hans Follmer, Universitiit Bonn; Nobuyuki Ikeda, Univer­ for the proceedings will closely parallel the content of the sity of Osaka; Paul Malllavin, Universi~ Pierre et Marie lectures and will be distributed to the conference participants Curie; Alain Sznitman, ETH Zurich; and Ruth Williams, at the time of the lectures. University of California, San Diego. All persons who are interested in this topic are welcome The topic was selected by the 1992 AMS Committee on to attend. The organizers anticipate being able to provide par­ Summer Institutes whose members at the time were: Craig tial support for travel and subsistence for young researchers, Evans, Nicholas Katz, Barbara Lee Keyfitz, Brian Parshall especially women and minorities. Those interested in receiv­ (chair), Francois Treves, and Edward Witten. ing an invitation to participate in the institute should send In recent years there have been exciting interactions the following information to: Summer Institute Conference between probability theory and analysis, geometry, and math­ Coordinator, American Mathematical Society, P.O. Box 6887, ematical physics, with these three fields furnishing a rich Providence R.I. 02940, prior to April 1, 1993, or through source of problems for probability theory. The conference electronic mail to [email protected]. will highlight recent achievements in the field and promising directions for future research. The meeting will be divided Please type or print the following: into six two-and-one-half day periods (Sunday morning to 1. Full name; Tuesday noon, Wednesday morning to Friday noon, etc.) that 2. Mailing address; will feature the following topics in the order indicated: 3. Telephone number and area code for office and home, FAX number, and email address; 1. Stochastic ordinary differential equations (7/11-7/13) 4. Which week or weeks you wish to attend; 2. Applications to analysis (7/14-7/16) 5. Your scientific background relevant to the institute topic; 3. Applications to geometry (7/18-7/20) 6. Financial assistance required (or indicate if no support 4. Stochastic flows (7/21-7/23) required). 5. Infinite-dimensional problems (7/25-7/27) 6. Stochastic partial differential equations (7/28-7/30) · Information on housing, dining, travel, and the local area will be sent to invited participants in the Spring. Each par­ The institute will have approximately sixty-six one-hour ticipant will be required to pay a Conference fee. Questions lectures, eleven in each period. To allow time and energy for about the scientific program can be addressed to any of informal discussions there will be no short talks or parallel the organizers, preferably by email to [email protected], sessions. The precise content of the meeting will reflect the [email protected], or [email protected]. Ques­ interests of the following list of speakers who have indicated tions about local arrangements should be sent to Rick Durrett that they will attend: L. Arnold, S. Albeverio, R. Banuelos, via email or write to him at the Department of Mathematics, P. Baxendale, G. Ben-Arous, I. Benjamini, E. Bolthausen, J. White Hall, Cornell University, Ithaca, NY 14853-7901. Brossard, K. Burdzy, E. Carlen, R. Carmona, K. L. Chung, R. Dalang, B. Davis, D. Dawson, B. Driver, E. B. Dynkin, D. Requests for invitations will be forwarded to the Orga­ Elworthy, M. Emery, H. Ftillmer, L. Gross, T. Hida, E. Hsu, nizing Committee for consideration up to the deadline of N. Ikeda, G, Kallianpur, W. Kendall, Y. Kifer, S. Kotani, P. Aprill. All applicants will receive formal invitations. Partici­ Kotelenez, N. Krylov, H. Kunita, S. Kusuoka, T. Kurtz, R. pants receiving financial support will be notified beginning in Uandre, F. Ledrappier, J.F. Le Gall, Y. Le Jan, T. Lindstrom, mid-May. M. Liao, T. Lyons, P.. Malliavin, P. March, S. Molchanov, C.

50 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY 1993 Symposium on Some Mathematical Questions in Biology Theories for the evolution of haploid-diploid life cycles Snowbird, Utah

The twenty-seventh annual Symposium on Some Mathe­ generations; James Crow (University of Wisconsin), and matical Questions in Biology, focusing on Theories for the Alex Kondrashov (University of Oregon), The evolution evolution of haploid-diploid life cycles, will be held during of haploid-diploid life cycles under deleterious mutation; the annual meeting of the Society for the Study of Evolution, Cheryl Jenkins (University of Texas), Ecological selection June 19-23, 1993, in Snowbird, Utah. The symposium is and deleterious mutation in the evolution of life cycles; sponsored by the American Mathematical Society, the Society Richard Michod (University of Arizona), Genetic repair for Industrial and Applied Mathematics (SIAM), and the and life cycle evolution; Sarah Otto (Berkeley), Genetic Society for Mathematical Biology (SMB). prerequisites and consequences of life cycle evolution; and Veronique Perrot (UniversiUit Basel), Experimental tests of The AMS-SIAM-SMB Committee on Mathematics in the theories for the evolution of haploid-diploid life cycles. Life Sciences serves as the Organizing Committee for the Proceedings of the symposium will be published by the symposium. The committee members are Jack D. Cowan, AMS in the series Lectures on Mathematics in the Life James W. Curren, Marcus W. Feldman, Eric S. Lander, Marc Sciences. Mangel (Chair), and James D. Murray. Mark Kirkpatrick For further information on the symposium, contact the serves as the organizer. Symposium Conference Coordinator, AMS, P.O. Box 6887, The speakers and their topics are: Graham Bell (McGill Providence, RI 02940, or [email protected] by elec­ University), The comparative biology of the alternation of tronic mail.

Mathematical World Volume 2 Fixed Points Yu. A. Shashkin y ------

Shashkin's book contains a popular exposition of fixed point theory. Theorems on fixed points for continuous maps of a segment, a square, a circle, and a two-dimensional sphere are proved. All required notions such as continuity, compactness, and degree of a map are explained. Auxiliary propositions, such as Sperner's lemma, are proved. Applica­ tions and exercises are given. Fixed Points is accessible even to students at the high school level.

1991 Mathematics Subject Classification.: 01. 54 0 ISBN 0-8218-9000-X. 77 pages (softcover), December 1991 Individual member $19, Ust price $24 To order, please specify MAWRLD/2NA All prices subject to change. Free shipment by surface; for air delivery, please add $6.50 per title. Prepayment required. Order from: American Mathematical Society. P.O. Box 5904, Boston, MA 02206-5904, or call toll free 800-321-4AMS in the U.S. and Canada to charge with VISA or MasterCard. Canada residents, please add 7o/o GST.

JANUARY 1993, VOLUME 40, NUMBER 1 51 1993 Symposium Mathematics of Computation 1943-1993: A half-century of computational mathematics University of British Columbia, Vancouver, Canada, August 9-13, 1993

Under the auspices of the American Mathematical Society versity of Maryland; Carl Pomerance, University of Georgia; (AMS) and in celebration of the 50th anniversary of the journal Larry L. Schumaker, Vanderbilt University; Hans J. Stetter, Mathematics of Computation, an international symposium Technical University of Vienna; G. W. Stewart, University devoted to all aspects of computational mathematics will of Maryland; and Roger Temam, Indiana University. take place at the University of British Columbia, Vancouver, The deadline for submission of contributed papers is April Canada, August 9-13, 1993. The symposium will be held 1, 1993. Abstracts should be prepared on AMS abstract forms immediately prior to the joint AMS/CMS/MAA summer and should indicate whether they are being submitted for a meeting. As part of the meeting there will be a two-session poster session or for a contributed paper session. Abstract minisymposium on computational number theory dedicated forms are available at most universities or obtainable from the to the memory of D. H. Lehmer. Invited speakers will AMS upon request. Abstracts should be sent in duplicate to be presenting survey and state-of-the-art lectures in plenary Walter Gautschi, Department of Computer Sciences, Purdue sessions. There will also be poster sessions and 15-minute University, West Lafayette, IN 47907, USA. Decisions on contributed paper sessions. acceptances will be made by May 1, 1993. Proceedings will The topic was selected by the 1992 AMS Committee on be published by the AMS. Summer Institutes and Special Symposia, whose members The deadline for preregistration/housing is June 6, 1993. at the time were: Lawrence Craig Evens, Nicholas Katz, Preregistration and housing forms can be obtained after Barbara Lee Keyfitz, Brian Parshall (Chair), Francois February 1, 1993 from the Mathematics Meetings Service Treves, and Edward Witten. Bureau, P.O. Box 6887, Providence, RI 02940-6887. There The Organizing Committee for the symposium consists of will be a registration fee of $50. Inquiries with regard to James H. Bramble, Cornell University; Walter Gautschi, registration and housing should be directed to that address or Purdue University (Chair); Eugene Isaacson, New York Uni­ by email [email protected], or telephone: 401-455-4143. versity; Vldar Thorn~. Chalmers University of Technology; Other inquiries should be sent to Walter Gautschi, Chair of and Hugh C. Williams, University of Manitoba. the Orgariizing Committee at the address indicated in the The invited speakers are: James H. Bramble, Cornell previous paragraph. University; Johannes Buchmann, Universitiit des Saarlan­ It is anticipated that the symposium will be partially des; Bjftm Engquist, UCLA; Donald Goldfarb, Columbia supported by a grant from the National Science Foundation. University; James N. Lyness, Argonne National Laboratory; Additional funds for support are being sought from other J. C. Nedelec, Ecole Polytechnique Palaiseau; Andrew M. agencies. Odlyzko, AT&T Bell Laboratories; Frank W. J. Olver, Uni-

52 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Mathematical Sciences 1993 Meetings and Conferences 1993-1994. Mittag-Lerner Institute's Aca­ demic Program for 1993-1994: Topology and Algebraic K -theory, Djursholm, Swe­ den. (Dec. 1992, p. 1274) Symposium on Math­ Spring 1993. IMACS THIS SECTION contains announcements of meetings and conferences of interest to some ematical Modelling, Wiener Neustadt, Ger­ segment of the mathematical public, including ad hoc, local, or regional meetings, and many. (Jan. 1992, p. 54) meetings or symposia devoted to specialized topics, as well as announcements of regularly 1993. Second IMACS International Con­ scheduled meetings of national or international mathematical organizations. ference on Computational Physics, Univ. of AN ANNOUNCEMENT will be published in the Notices if it contains a call for papers, Colorado, Boulder, CO. (Jan. 1992, p. 55) and specifies the place, date, subject (when applicable), and the speakers; a second 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. Asterisks (*) mark those announcements containing new or revised information. IN GENERAL, announcements of meetings and conferences held in North America carry January 1993 only date, title of meeting, place of meeting, names of speakers (or sometimes a general 15-16. 1992-1993 ASL Winter Meeting, San statement on the program), deadlines for abstracts or contributed papers, and source of American area may carry more detailed Antonio, TX. (Nov. 1992, p. 1115) further information. Meetings held outside the North information. In any case, if there is any application deadline with respect to participation in 15-17. International Conference on Com­ the meeting, this fact should be noted. All communications on meetings and conferences in plex Analysis and its Applications, Hong the mathematical sciences should be sent to the Editor of the Notices, care of the American Kong University of Science and Technology, Mathematical Society in Providence, or electronically to [email protected]. Hong Kong. (Sep. 1992, p. 771) DEADLINES for entries in this section are listed on the inside front cover of each issue. In their travel plans, organizers of meetings are urged 1993 IEEE International Symposium order to allow participants to arrange 17-22. to submit information for these listings early enough to allow them to appear in more than on Information Theory, San Antonio, TX. one issue of the Notices prior to the meeting in question. To achieve this, listings should be (Feb. 1992, p. 149) received in Providence SIX MONTHS prior to the scheduled date of the meeting. 17-23. Combinatorial Optimization, Ober­ EFFECTIVE with the 1990 volume of the Notices, the complete list of Mathematical Sciences wolfach, Federal Republic of Germany. (Jan. Meetings and Conferences will be published only in the September issue. In all other issues, 1992, p. 55) only meetings and conferences for the twelve-month period following the month of that issue will appear. As new information is received for meetings and conferences that will occur later 18-21. Numerical Analysis of Partial, Differ­ than the twelve-month period, it will be announced at the end of the listing in the next possible ential Equations in Engineering and Related issue. That information will not be repeated until the date of the meeting or conference falls Topics, Research Institute for Mathematical within the twelve-month period. Sciences, Kyoto University. (Jul./Aug. 1992, p. 630) 20-22. Hyperfunctions and Differential sis and Geometric Methods in Deterministic Equations, Research Institute for Mathemat­ Optimal Control, Institute for Mathematics ical Sciences, Kyoto University. (Jul./Aug. February 1993 and its Applications, University of Minnesota, 1992,p.630) 1-3. IMA Minisymposium on Biological Minneapolis, MN. (Mar. 1992, p. 250) Partieller Dif­ 24-30. Optimale Steuerung Control of Movement, Institute for Math­ 14-20. Applicable Algebra, Oberwolfach, ferentialgleichungen, Oberwolfach, Federal ematics and its Applications, University of Federal Republic of Germany. (Jan. 1992, Republic of Germany. (Jan. 1992, p. 55) Minnesota, Minneapolis, MN. (Nov. 1991, p. 55) on 25-27. Fourth ACM-SIAM Symposium p. 1172) 15-19. 1993Mathematics-in-IndustryStudy Discrete Algorithms (SODA), Austin, Texas. 5-6. Conference on Applied Mathemat­ Group, Melbourne, Australia. (Sep. 1992, 25-29. IMA Workshop on Robotics, Institute ics (CAM), University of Central Oklahoma, p. 771) and its Applications, Univer­ for Mathematics Edmond, OK. (Dec. 1992, p. 1275) 15-19. International Conference on Math­ sity of Minnesota, Minneapolis, MN. (Nov. 5-7. Representation Theory and Analy­ ematics, Computer, Control, and Invest­ 1991, p. 1171) sis on Homogeneous Spaces in Memory of ments, Moscow, Russia. (Oct. 1992, p. 947) 26-28. The Development of Algebraic Lawrence Corwin, Rutgers University, New 21-27. Curves, Images, Massive Computa­ Toplogy, Research Institute for Mathematical Brunswick, NJ. (Dec. 1992, p. 1275) tion, Oberwolfach, Federal Republic of Ger­ Sciences, Kyoto University. (Jul./Aug. 1992, many. (Jan. 1992, p. 55) p. 630) 6-7. Second Southern California Geometric Analysis Seminar, University of California, Twenty-fourth Southeastern In­ 27-29. Modem Developments in Complex * 22-26. Irvine. (Dec. 1992, p. 1275) Conference on Combinatorics Analysis and Related Topics on the Occasion ternational Boca Raton, FL. of the 70th Birthday of J. Korevaar, Uni­ 7-11. The 29th Australian Applied Math­ Graph Theory Computing, ematics Conference (AMC '93), Hochstens, versity of Amsterdam, The Netherlands. (Nov. PROGRAM: The conference has grown to 1992, p. 771) 1992, p. 1115) Hahndorf, South Australia. (Sep. be the major annual international confer­ 31-February 6. Asymptotics and Adaptivity 7-13. Partielle Differentialgleichungen, Ober­ ence in its disciplines, bringing together in Computational Mechanics, Oberwolfach, wolfach, Federal Republic of Germany. (Jan. mathematicians and others interested in Federal Republic of Germany. (Jan. 1992, 1992,p.55) combinatorics, graph theory and comput­ p. 55) 8-17. IMA WorkshoponNonsmoothAnaly- ing, and their interactions and applications.

JANUARY 1993, VOLUME 40, NUMBER 1 53 liii&&UL&&IJ.kZUL&WIJ.Ula&£-·· Meetings and Conferences

The conference aims to promote better un­ Route Leon-Lachamp, 13288 Marseille CALL FOR PAPERS: Abstracts for contributed derstanding of the roles of modem applied Cedex 9; tel: (91) 833000. papers due by 1125/93. mathematics, combinatorics, and computer INFORMATION: R. Shivaji, Dept. of Math. science to acquaint the investigator in each 10-12. Equations d'Evolution, Theorie du & Stats., Mississippi State U., Mississippi of these areas with the various techniques Controle et Biomathematiques, CIRM, Mar­ State, MS 39762; tel: 601-325-3414; email: and algorithms which are available to assist seille, France. (Nov. 1992, p. 1115) rs 1 @ra.msstate.edu; or B.K. Soni, NSF him in his research. 10-13: The Fourth Annual Ulam Math­ Engineering Research Center, Mississippi CALL FOR PAPERS: There will be fifteen­ ematics Conference, West Palm Beach, FL. State U., Mississippi State, MS 39762; tel: minute sessions for contributed papers (Nov. 1992, p. 1115) 601-325-8278; bsoni @erc.msstate.edu. throughout the conference. Title and an 11-13. Twenty-seventh Annual Spring Topol­ Ninth Auburn Conference on Real abstract ( 10-20 lines single spaced) of each * 19-20. ogy Conference, University of South Carolina, Analysis, Auburn University, Auburn, AL. paper be received by Febraury 5, 1993. SC. (Dec. 1992, p. 1276) INFORMATION: F. Hoffman, Dept. of Math., INVITED SPEAKERS: A.S. Kechris, Caltech; 11-14. 1992-1993 Annual ASL Meeting, 407-367-3345 or 407-367-3341; email: A.M. Bruckner, UC Santa Barbara. University of Notre Dame, Notre Dame, IN. [email protected] or hoffman@ J. Brown, 228 PKH, Dept. (Nov. 1992, p. 1115) INFORMATION : acc.fau.edu. of Math., Auburn Univ., Auburn, AL * 14-18. Seventh Conference on the Scientific 36849-5310; 205-844-6565; jbbrown@ 22-28. Workshop on Pattern Formation Use of Statistical Software (SOFTSTAT '93), ducvax.auburn.edu. and Symmetry Breaking in PDE's, Fields In­ Heidelberg, Federal Republic of Germany. stitute for Research in Mathematical Sciences, 21. Thtorial on Distributed Computing INFORMATION: Softstat '93, ZUMA, Post­ Waterloo, Ontario. (Dec. 1992, p. 1275) Using PVM and HeNCE, Norfolk, VA. (Dec. fach 12 21 55, W-6800 Mannheim 1, 25-March 1. A Conference on Numerical 1992, p. 1276) Germany. Analysis with Automatic Result Verification, 21-27. Analysis auf Lokalsymmetrischen Lafayette, LA. (May/Jun. 1992, p. 495) 14-20. Gewohnliche Differentialgleichun­ Raumen, Oberwolfach, Federal Republic of 28-March 6. Medical Statistics: Statistical gen, Oberwolfach, Federal Republic of Ger­ Germany. (Jan. 1992, p. 55) Methods for Risk Assessment, Oberwolfach, many. (Jan. 1992, p. 55) 22-24. Sixth SIAM Conference on Par­ Federal Republic of Germany. (Jan. 1992, 15-18. Arithmetic Geometry with an Em­ allel Processing for Scientific Computing, p. 55) phasis on Iwasawa Theory, Arizona State Norfolk, VA. (Oct. 1992, p. 947) University, Tempe, AZ. (Sep. 1992, p. 771) * 22-26. ERCIM Advanced 5-day Course on 15-19. IMA WorkshoponSystemsandCon­ Partial Differential Equations and Group March 1993 trol Theory for Power Systems, Institute for Theory, Amsterdam, The Netherlands. Applications,. University * 1-5. Geometrie Algebrique en Liberte, Mathematics and its PROGRAM: The aim of the first part of Minnesota, Minneapolis, MN~· (Nov. 1991, CIRM, Marseille, France. of this course is to provide a self-contained p. 1172) introduction to methods in the case of (CIMPA, Nice). ORGANIZER: A. Hirschowitz * 15-April 2. Workshop on Representation linear and nonlinear systems of PDE. The International de Ren­ INFORMATION: Centre Theory of Lie Groups, Trieste, Italy. purpose of the second part of this course Case 916, 70, contres Mathematiques, will be to give a brief introduction to Leon-Lachamp, 13288 Marseille CHAIRMEN: J.H. Rawnsley and J.A. Tirao, Route differential algebra and the Galois theory Trieste. Cedex 9; tel: (91) 833000. for systems of algebraic PDE simply called The­ INFORMATION: International Centre for "Differential Galois Theory". Finally, the 2-6. The European Consortium for Mathe­ Box 586, 1-34100 oretical Physics, P.O. course will provide for the first time the matics in Industry, Montecatini Terme, Italy. Trieste. (Dec. 1992,p. 1275) long-awaited group theoretical unification of finite element approach to elasticity, 5-7. Workshop on Convexity, Monotonicity, * 16-18. International Conference on Typed heat, and electromagnetism. and Differentiability, Fields Institute, Water­ Lambda Calculi and Applications (TLCA), LECTURERS: G. Carra Ferro, P. Gragert, P. loo, Ontario. (Dec. 1992, p. 1275) Utrecht, The Netherlands. Kersten, J.F. Pommaret, F. Schwarz, and T. * 6. Midwest Group Theory Seminar, Univer- INFORMATION: TLCA Secretariat, F. Sni­ Wolf. sity of Chicago, IL. jders, CWI, P.O. Box 4079, NL-1009 AB INFORMATION: ERCIM, Domaine de Volu­ PRoGRAM: There will be a program of four Amsterdam. ceau, BP 105, F-78153 Le Chesnay lectures including talks by G. Malle and P. Cedex, France; tel: +33-1-39635378; Pure and Applied Linear Algebra: Symonds. 17-20. Fax: +33-1-39635330; email: ercim@ New Generation, University of West INFORMATION: J.L. Alperin, alperin@ The inria.inria.fr or CWI, F. Snijders, Postbus (May/Jun. 1992, p. 495) math.uchicago.edu, 312-702-7393. Florida, Pensacola, FL. 4079, 1009 AB Amsterdam, The Nether­ * 19-20. Mississippi State Annual Confer­ lands. 7-13. Mathematische Stochastik, Oberwol­ ence on Differential Equations and Compu­ fach, Federal Republic of Germany. (Jan. 1992, tational Simulations, Missi.ssippi State Uni­ 22-28. Workshop on Pattern Formation in p.55) versity, Mississippi State. Earth Sciences and Biology, Fields Theorie du Institute for Research in Mathematical * 8-12. Equations d'Evolution, INVITED SPEAKERS: R. Agarwal, McDon­ Mar­ Sciences, Waterloo, Ontario. (Apr. 1992, p. 351) Controle et Biomathematiques, CIRM, & Dev.; A. Castro, U. nell Douglas Res. * 23-28. Workshop on Applications of Pattern seille, France. Chicago; of North Texas; C. Kenig, U. of Formation, The Fields Institute, Waterloo, Miami; P. Rabinowitz, U. ORGANIZERS: W. Arendt, P. Benilan (U. de A. Lazer, U. of Ontario. Besancon). of Wisconsin; P. Roe, U. of Michigan; N. INFORMATION: Centre International de Ren­ Weatherill, U. College of Swansea, Eng­ PRoGRAM: This workshop will bring to­ contres Mathematiques, Case 916, 70, land. gether scientists and mathematicians study-

54 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences

ing pattern formation in a wide variety of Univ., Edinburgh EH14 4AS, UK. 5-9. IMA Tutorial: Design and Analysis of specific applications modeled by partial Adaptive Systems, Institute for Mathematics differential equations. Significant progress 29-April 2. Workshop on Diophantine Ge­ and its Applications, University of Minnesota, has been achieved through interdisciplinary ometry, Mathematical Sciences Research In­ Minneapolis, MN. (Nov. 1991, p. 1172) stitute, Berkeley, CA. (May/Jun. 1992, p. 495) approaches of this type in the past decade. *5-9. Theorie des Operateurs, CIRM, Mar- The emphasis in the workshop will be on * 29-April 2. Valuations, Topological Fields, seille, France. realistic physical applications and on ap­ and Geometries, Marseille, France. plying ORGANIZER: M. Mbekhta (U. de Lille). new mathematical theory in order to CHAIRMAN: S. Priess-Crampe, Miinchen. INFORMATION: Centre International de Ren­ understand the underlying mechanisms. INFORMATION: CIRM, Luminy Case 916, contres Math6matiques, Case 916, 70, INVITED SPEAKERS: S. Alama, McMaster; F-13288 Marseille Cedex 9. L. Bronsard, McMaster; S. Canic, Fields; Route Uon-Lachamp, 13288 Marseille K. Diemer, Fields; M. Golubitsky, Houston; 29-April 3. Zeta Functions in Number Cedex 9; tel: (91) 833000. J. Hale, Georgia Tech; P. Holmes, Cornell; Theory and Geometric Analysis, in honor * 6-8. NASECODE IX: The Ninth Interna­ R. Kapral, Toronto; J. Keener, Utah; B. of Jun-ichi Igusa, Johns Hopkins University, tional Conference on the Numerical Analy­ Keyfitz, Houston; W. Langford, Guelph; Baltimore, MD. (Dec. 1992, p. 1276) sis of Semiconductor Devices and Integrated A. Lawniczak, Guelph; J. Marsden, Fields; 29-April 8. Workshop on Geometric and Circuits, Copper Mountain, Colorado. B. Matkowsky, Northwestern; R. Miura, Combinatorial Methods in Group Theory, British Columbia; L. Mysak, McGill; W. International Centre for the Mathematical SESSION TOPICS: Circuit analysis, code Nagata, UBC; S. Namachchivaya, lllinois; Sciences, Edinburgh, Scotland. (Nov. 1992, validation against real devices and pro­ A. Newell, Arizona; P. Ortoleva, Indiana; p. 1116) cesses, computational techniques, device A. Peirce, McMaster; D. Peltier, Toronto; modelling, energy transport models, math­ 30-April 1. IEEE Data Compression Con­ D. Sattinger, Minnesota; J. Scheurle, Ham­ ematical analysis, Monte Carlo simulations, ference (DCC '93), Snowbird, Utah. (Nov. burg; L. Trainor, Toronto; B. Wetton, UBC; physical aspects, process simulation, quan­ 1992, p. 1116) S. Wiggins, Caltech; and J. Wu, York. tum effects. INFORMATION: Workshop Information: 1 CALL FOR PAPERS: Potential authors should Chadam, 519-725-0096, ext. 3012, email: submit a camera ready abstract (two pages, [email protected]. Registration Spring 1993 A4/297 x 210mm, 1000 words maximum) Information: J. Motts, 519-725-0096, Fax: Spring 1993. Valuations, Topological Fields, by January 31, 1993. 519-725-0704; [email protected]. and Geometries, CIRM, Marseille, France. INFORMATION: P. McKeever, Chairperson­ (Nov. 1992, p. 1116) Organizing Committee, NASECODE IX 24-28. Conference on Quantum Topology, Secretariat, 26 Temple Lane, Dublin 2, Kansas State University, Manhattan, KS. (Nov. *Spring 1993. IMACS Workshop on Inverse Problems, Berlin, Germany. Ireland; telefax: (+353-1-) 679-2469; tel: 1992, p. 1116) (+353-1) 679-7655; [email protected]. 25-27. 1993 Barrett Memorial Lectures INFORMATION: K. Doppel, Inst. fur Math I, on Infinite Dimensional Stochastic Differ­ Fachbereich Mathematik FU Berlin, Arn­ 7-10. The Ninth Conference on the Mathe­ ential Equations, University of Tennessee, imallee 3, D-1000 Berlin 33-Germany; matical Foundations of Programming Se­ Knoxville, TN. (Dec. 1992, p. 1276) email: doppe1 @math.fu-berlin.de orR. Gil­ mantics, New Orleans, LA. (Nov. 1992, p. 1116) 26-27. Southeastern Section, Knoxville, TN. bert, Dept. of Math. Sci., Univ. of Dela­ ware, Newark, DE 19716; email: gilbert@ 8-10. Clifford Algebras in Analysis, Univer­ INFORMATION: W. Drady, AMS, P.O. Box math.udel.edu. sity of Arkansas, Fayetteville, AR. (Sep. 1992, 6887, Providence, RI 02940. p. 772) 9-10. Western Section, University of Utah, ~ 27-28. Midwest Partial Differential Equa- Aprll1993 tions Seminar, University oflllinois at Chicago. Salt Lake City, Utah. 4-7. First International Conference on PuRPOSE: This is a semiannual conference INFORMATION: W. Drady, AMS, P.O. Box Mathematical Linguistics, Barcelona, Spain. 6887, Providence, RI 02940. on recent developments in partial differen­ (Sep. 1992, p. 772) tial equations. Support for graduate students 9-11. The Second Boise Extravaganza in is available. 4-9. Copper Mountain Conference on Multigrid Methods, Copper Mountain, Col­ Set Theory (BEST), Boise State Univ., Boise, INVITED SPEAKERS: E. diBenedetto, J. Es­ orado. (Nov. 1992, p. 1116) Idaho. (Dec. 1992, p. 1277) cobar, E. Fornaess, E. Fabes, N. Garofalo, 11-17. Arbeitsgemeinschaft mit Aktuellem B. Stenssones, A. Tumanov. 4-10. Topics in Pseudo-Differential Op­ Thema, Oberwolfach, Federal Republic of INFORMATION: J.E. Lewis or D. Tartakoff, erators, Oberwolfach, Federal Republic of Germany. (Jan. 1992, p. 56) Dept. of Math. (M/C 249), Univ. of lllinois Germany. (Jan. 1992, p. 56) at Chicago, P.O. Box 4348, Chicago, IL * 5-7. Predictability and Nonlinear Mod­ 12-16. IMA WorkshoponAdaptiveControl, 60680-4348; email: [email protected] elling in Natural Sciences and Economics, Filtering, and Signal Processing, Institute for or Fax: 312-996-1491. Wageningen, The Netherlands. Mathematics and its Applications, University of Minnesota, Minneapolis, MN. (Nov. 1991, 28-April 3. Combinatorial Convexity and INFORMATION: J. Grasman, Dept. of Math., p. 1172) Dreijenlaan 4, NL-6703 HA Wageningen. Algebraic Geometry, Oberwolfach, Federal 12-16. GAMM-Jahrestagung 1993, Dresden, Republic of Germany. (Jan. 1992, p. 56) * 5-8. British Applied Mathematics Collo­ Germany. (Sep. 1992, p. 772) • 28-April 8. Workshop on Geometric and quium (35th British Theoretical Mechanics * 12-17. Tenth Easter Conference on Model Combinatorial Methods in Group Theory, Colloquium), Glasgow, UK. Theory, Wendisch-Rietz (near Berlin), Ger­ Edinburgh, U.K. many. INFORMATION: I. Murdoch, Dept. of Math., INFORMATION: A. Duncan, N.D. Gilbert, Univ. of Strathclyde, Glasgow G1 1XH, INFORMATION: H. Wolter and M. Weese, and J. Howie, Dept. of Math., Heriot-Watt UK. Fachbereich Mathematik, Humboldt Univ.,

JANUARY 1993, VOLUME 40, NUMBER 1 55 Meetings and Conferences

Postfach 1297, D-0-1 086 Berlin, Germany; * 26-29. The Mathematics of Finite Elements Anal., Sokolovska 83, 18600 Praha 8, [email protected]; Fax: and Applications VIII, MAFELAP 1993, Czechoslovakia. (030)2093 22 38. Uxbridge, UK. 9-15. Reelle Algebraische Geometrie, Ober­ 14-16. Seventh SEFI European Seminar INFORMATION: MAFELAP 1993, BICOM, wolfach, Federal Republic of Germany. (Jan. on Mathematics in Engineering Educa­ Brune~ Univ., Uxbridge, UB8 3PH, UK. 1992, p. 56) tion, Eindhoven University of Technology, 27-29. NSF/DoD's National SBIR Confer­ 9-17. Jerusalem Combinatorics '93, He­ The Netherlands. (Feb. 1992, p. 149) ences, Minneapolis, MN. (Sep. 1992, p. 772) brew University of Jerusalem, Israel. (JuiJAug. 14-16. The Mathematics of Food Produc­ 1992,p.631) 30-May 2. Third Midwestern Geometry tion, Processing, and Presentation, Belfast, Conference, University of Missouri, Colum­ 10-12. IMACS Symposium on Signal Pro­ Great Britain. (Sep. 1992, p. 772) bia, MO. (Dec. 1992, p. 1277) cessing and Neural Networks-SPANN '93, * 14-17. Dynamics of Complex Systems in Universite du Quebec at Montreal, Canada. Biosciences, Marseille, France. (Jan. 1992, p. 56) CHAIRMAN: G. Weisbuch, Paris. 10-14. IMA Workshop on Discrete Event Systems, Manufacturing Systems, and Com­ INFORMATION: CIRM, Luminy Case 916, May 1993 F-13288 Marseille Cedex 9. munication Networks, Institute for Mathe­ 2-4. Workshop on Operator Algebras, In­ matics and its Applications, University of Min­ 14-23. International Conference in Abstract stitute for Advanced Studies in Mathematics, nesota, Minneapolis, MN. (Nov. 1991, p. 1172) Analysis, Kruger National Park, Republic of Technion, Haifa, Israel. (Oct. 1992, p. 948) 10-14. The Tenth International Symposium South Africa. (Oct. 1992, p. 948) 2-7. Algebraic Geometry Workshop on on Applied Algebra, Algebraic Algorithms, 15-22. Symposium on Analytic and Ge­ the Occasion of the 65th Birthday of F. and Error Correcting Codes, San Juan de ometric Aspects of Hyperbolic Geometry: Hirzebruch, Emmy Noether Institute, Bar­ Puerto Rico. (Oct. 1992, p. 948) Research Level Workshop, University of Dan Univ., Ramat Gan, Israel. (Dec. 1992, 10-14. Geometrie et Topologie des Sous­ Warwick, Coventry, UK. (Dec. 1992, p. 1277) p. 1277) Varietes, CIRM, Marseille, France. (Nov. 17-18. Eastern Section, Washington, DC. * 2-8. Design and Experiments: Optimal­ 1992, p. 1117) INFORMATION: W. Drady, AMS, P.O. Box ity, Construction and Applications, Ober­ * 10-14. International Geometric Colloquium, 6887, Providence, RI 02940. wolfach, Federal Republic of Germany. Moscow. CHAIRMEN: C.-S. Cheng, Berkeley; D. ORGANIZERS: P. Iglesias, V. Ovsienko, A. 18. Thtorial on Introduction to Paral­ Rasch, Wageningen; F. Pukelsheim, Augs­ Shoshitaishvili, V. Vasiliev, and I Yaro­ lel Computation, Houston, TX. (Dec. 1992, shevskaya. p. 1277) burg. INFORMATION: Mathematisches For­ CONFERENCE TOPICS: Symplectic and con­ 18-24. The Arithmetik of Fields, Oberwol­ schungsinstitut Oberwolfach Geschlift­ tact geometry and topology; geometry of fach, Federal Republic of Germany. (Jan. 1992, sstelle: Alberstrasse 24 D-7800 Freiburg infinite-dimensional Lie algebras; dynami­ p. 56) im Breisgau. cal systems and foliations; singularity the­ 18-24. Mathematische Grundlagen und ory and its applications to: mathematical Numerische Verfahren bei Transsonischen 3-7. IMA Thtorial: Verification Issues in physics, topology, and control; application Stromungen, Oberwolfach, Federal Republic Discrete Event Systems, as well as Perfor­ of computer algebra and symbolic calculus of Germany. (Jan. 1992, p. 56) mance and Control, Institute for Mathematics to geometry. 19-20. IMA Minisymposiumon Fuzzy Con­ and its Applications, University of Minnesota, INFORMATION: I. Yaroshevskaya, Sector trol, University of Minnesota, Minneapolis, Minneapolis, MN. (Nov. 1991, p. 1172) of Visiting Progams, SOFTAPMAT, CNI­ MN.(No~ 1992,p. 1117) 3-7. Problemes aux Limites, Equations & Iproject, Arch.Vlasova st., 51, Moscow 117393, Russia; 19-21. SIAM Conference on Mathemati­ lntegrales de Bord dans des Domaines Non Fax: (095)128 05 90, (095) 128 98 21; tel: cal and Computational Issues in the Geo­ Reguliers, CIRM, Marseille, France. (Nov. (095) 128 05 92; email: sciences, Houston, TX.(Jul./Aug.l992,p.631) 1992, p. 1117) [email protected] or [email protected]. * 19-23. Cartes Cellulaires sur les Surfaces de 3-9. Workshop on Ecological Systems, Fields Institute for Research in Mathemati­ Riemann (Th~rie des ''Dessins D'Enfants", * 12-14. Detonique, Rocquencourt, France. Marseille, France. cal Sciences, Waterloo, Ontario. (Apr. 1992, p. 352) INFORMATION: INRIA-Rocquencourt, Re­ CHAIRMAN: L. Schneps, Besancon. * 3-14. Workshop on Qualitative Aspects lations Exterieures, Bureau Cours/Colloques, INFORMATION: CIRM, Luminy Case 916, and Applications of Nonlinear Evolution F-78153 Le Chesnay Cedex. F-13288 Marseille Cedex 9. Equations, Trieste, Italy. * 13-15. The Twelfth Pacific Coast Resource 25-May 1. Low Dimensional Dynamics, CHAIRMEN: H. Beeirao da Veiga and L. Modeling Conference, Tucson, AZ. Oberwolfach, Federal Republic of Germany. Ta-tsien, Trieste. PROGRAM: The purpose of the conference (Jan. 1992, p. 56) INFORMATION: International Centre for The­ is to provide a forum for the presentation of oretical Physics, P.O. Box 586, 1-34100 * 26-28. Methodes Spectrales et Elements recent progress in the mathematical mod­ Trieste. Spectraux, Clamart, France. eling and analysis of renewable resources. INFORMATION: INRIA-Rocquencourt, Re­ 4-8. The Third International Colloquium on Particular emphasis will be given to the lations Exterieures, Bureau Cours/Colloques, Cognitive Science (ICCS-93), Donostia-San modeling of biological processes, popu­ F-78153 Le Chesnay Cedex. Sebastian, Spain. (Nov. 1992, p. 1117) lation dynamics, and bioeconomics, espe­ cially as they relate to problems in fisheries, * 6-12. Spring School on Potential Theory 26-29. NCGA '93 Computer Graphics So­ forestry, pest an!l wildlife and Analysis, Paseky, Czechoslovakia. management, as lutions: Applications for Implementation, well as water resources, environmental and Philadelphia, PA. (Nov. 1992, p. 1117) INFORMATION: J. Kottas, Dept. of Math. conservation issues.

56 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences

INVITED SPEAKERS: J. Brown (U. Illinois at 24-28. Ergodic Theory and Its Connections Mysak, J. Nocedal, R. Nussbaum, andY. Chicago), T. Hallam (U. of Tennessee), G. with Harmonic Analysis, Alexandria, Egypt. Wu. Leitmann (UC Berkeley), M. Mesterton­ (Dec. 1992,p. 1278) CALL FOR PAPERS: Deadline for submission Gibbons (Florida State U.), W. Schaffer (U. * 24-28. Th~rie des Nombres et Automates, of abstracts for contributed papers is April of Arizona). CIRM, Marseille, France. 2, 1993. CALL FOR PAPERS: Deadline for submission INFORMATION: J. Wu, Dept. of Math. and of abstracts and for early registration is ORGANIZERS: J.-P. Allouche (U. de Bor­ Stats., York Univ., North York, Ontario, February 1, 1993. deaux I), C. Frougny (U. de Paris 5), C. CanadaM3J IP3; [email protected]; tel: INFORMATION: J.M. Cushing, Math. Dept., Mauduit (U. de Lyon 1). 416-736-5250; Fax: 416-736-5735. B-89, Univ. of Arizona, Tucson, AZ 85721, INFORMATION: Centre International de Ren­ 602-621-6863, [email protected], contres Mathematiques, Case 916, 70, 30-June 5. Funktionalanalysis und Nicht­ Fax: 602-621-8322; or T.L. Vincent, AME Route Uon-Lachamp, 13288 Marseille lineare Partielle Dift'erentialgleichungen, Dept., Univ. of Arizona, Tucson, AZ 85721, Cedex 9; tel: (91) 833000. Oberwolfach, Federal Republic of Germany. 602-621-2325, vincentl tl @ccit.arizona.edu. (Jan. 1992, p. 56) 26-29. First International Conference on 30-June 13. First Caribbean Spring School 13-16. ASL Spring Meeting in Conjunction Dynamic Systems and Applications, More­ of Mathematics and Theoretical Physics, with a Meeting of the Society for Exact house College, Atlanta, GA. (Oct. 1992, p. 948) Guadeloupe (French West Indies). (Nov. 1992, Philosophy, York University, Toronto, Canada. * 27-28. Fifteenth Symposium on Mathemat­ p. 1118) (Nov. 1992, p. 1117) ical Programming with Data Perturbations, 31-June 4. Workshop on Nonnegative Ma· 16-22. Mathematical Problems in Viscoelas­ George Washington University, Washington, trices, Applications, and Generalizations, tic Flows, Oberwolfach, Federal Republic of DC. Technion, Haifa, Israel. (Nov. 1992, p. 1118) Germany. (Jan. 1992, p. 56) PROGRAM: This symposium is designed to 17-19. Third International Conference on bring together practitioners who use mathe­ Expert Systems for Numerical Computing, matical programming optimization models Purdue University, West Lafayette, IN. (Dec. and deal with questions of sensitivity anal­ June 1993 1992, p. 1278) ysis, with researchers who are developing techniques applicable to these problems. June 1993. Fourth IMACS International * 17-2L Algebre et Applications, Marseille, Symposium on Computational Acoustics, France. CONFERENCE TOPICS: Contributed papers in mathematical programming are solicited in Cambridge, England. (Jan. 1992, p. 56) CHAIRMAN: P.-J. Cahen, Marseille. the following areas: Sensitivity and stabil­ June 1993. GAMMIIFIP- Workshop on INFORMATION: CIRM, Luminy Case 916, ity analysis results and their applications; Stochastic Optimization: Numerical Meth­ F-13288 Marseille Cedex 9. solution methods for problems involving ods and Technical Applications, Neubibergl implicitly defined problem functions; solu­ Mtinchen, Germany. (Sep. 1992, p. 773) 18-21. Eighth Annual Conference on Struc­ tion methods for problems involving deter­ June 1993. Summer Workshop: Calcu­ ture in Complexity Theory, San Diego, CA. ministic or stochastic parameter changes; lus, Computers, Concepts, and Cooperative (Oct. 1992, p. 948) and solution approximation techniques and Learning, Purdue University, West Lafayette, 20-22. International Symposium on Ordi­ error analysis. Abstracts should be sent to IN. (Nov. 1992, p. 1118) nary Dift'erential Equations and Applica­ the address below. Abstracts should provide 1-4. Rigidite et Deformation pour les tions, Western Michigan University, Kalama­ a good technical summary of key results, Systemes HyperboHques, CIRM, Marseille, zoo, MI. (Nov. 1992, p. 1117) avoid the use of mathematical symbols France. (Nov. 1992, p. 1118) 20-22. International Conference on Ap­ and references, not exceed 500 words, and * 1-5. CBMS-NSF Conference on Appli­ proximation, Probability, and Related Fields, include a title and the name and full mail­ cations of the Representation Theory of University of California, Santa Barbara. (Dec. ing address of each author. Deadline is 15 Quantum Aftine Lie Algebras to Solvable 1992, p. 1278) March 1993. 30 minutes will be allocated Lattice Models, North Carolina State Univer­ 20-23. International Conference on Ap­ for the presentation of each paper. sity, Raleigh, NC. proximation Probability and Related Fields, INFORMATION: A.V. Fiacco, School of En­ University of California, Santa Barbara, CA. gineering and Applied Science, The George PRINCIPAL SPEAKER: T. Miwa, RIMS, Ky­ (May/Jun. 1991, p. 477) Washington University, Washington, DC oto University. 20052; tel: 202-994-7511. INFORMATION: K.C. Misra, Dept. of Math., 21-22. Central Section, Northern Illinois North Carolina State Univ., Raleigh, NC University, DeKalb, IL. 30-June L Canadian Society for the ffistory 27695-8205; 919-515-3320; Fax: 919-515- INFORMATION: W.S. Drady, AMS, P.O. Box and Philosophy of Mathematics, Carleton 3798; email: [email protected]. 6887, Providence, Rl 02940. University, Ottawa, Ontario, Canada. (Sep. 1992, p. 772) 2-4. The Lars Onsager Symposium. Cou­ 23-29. Dift'erentialgeometrie im Grossen, * 30-June 2. Fourteenth Annual Meeting of pled Transport Processes and Phase Transi­ Oberwolfach, Federal Republic of Germany. the Canadian Applied Mathematics Soci­ tions, Trondheim, Norway. (Dec. 1992, p. 1278) (Jan. 1992, p. 56) ety/Societe Canadienne de Mathematiques 2-5. Ninth Biennial Conference of the As­ 24-27. COMPEURO '93, Paris-Evry, France. Applique, York University, North York, On­ sociation of Christians in the Mathematical (Jul./Aug. 1992, p. 631) tario. Sciences, Westmont College, Santa Barbara, CA. (Sep. 1992, p. 773) 24-27. Eurocrypt '93: A Workshop on the PRoGRAM: Three symposia associated with 3-9. Fifteenth Nevanlinna Colloquium, Ann Theory and Applications of Cryptographic the meeting are fluid dynamics, functional * Arbor, MI. Techniques, Lofthus, Norway. (Nov. 1992, differential equations and mathematical bi­ p. 1118) ology, and numerical algorithms. PROGRAM: The program will consist of 24-28. Matroides et Matroides Orientes, PLENARY SPEAKERs: R. Bartels, J. Gilbert, lectures on topics of current interest in CIRM, Marseille, France. (Nov. 1992, p. 1118) J. Hale, S. Leibovich, M. Mackey, L. complex function theory and related areas.

JANUARY 1993, VOLUME 40, NUMBER 1 57 ---Meetings and Conferences

Each of the morning programs will be a spe­ ference Center, Lake Arrowhead, CA. (Dec. security. Possible topics include: access cial session of invited lectures on a single 1992,p. 1279) control, covert channels, information flow, database security, secure topic, as follows: circle packing; harmonic 13-19. DifferentiaJ.AJgebraic Equations: protocols, verifi­ cation techniques, integrity and availability measure; quasiconformal and quasiregular Theory and Applications in Technical Sim­ mappings; models, interactions of computer hyperbolic geometry; Riemann ulation, Oberwolfach, Federal Republic of security requirements with other surfaces; and discrete groups. Germany. (Jan. 1992, p. 56) system require­ INFORMATION: E.M. Rathbun, Math. Dept., ments such as dependability and timing, 14-17. The Fifth Asian Logic Conference, Univ. of Michigan, Ann Arbor, MI 48109; and the role of formal methods in computer National University of Singapore, Singapore. email: ethel.rathbun @um.cc.urnich.edu; security. Four copies of a paper (7 500 word (May/Jun. 1992, Fax: 313-763-0937. p. 496) limit) should be sent by January 31, 1993 14-18. IMA Workshop on Mathematical to the program chair at the address below. * 4-7. Sixth Meeting of European Women in Finance, Institute for Mathematics and its INFORMATION: General Chair: R. Sandhu, Mathematics, Warsaw, Poland. Applications, University of Minnesota, Min­ ISSE Dept., George Mason U., Fairfax, neapolis, MN. (Nov. 1991, p. 1172) VA 22030-4444; 703-993-1659; Program INFORMATION: A. Romanowska, B. Rosz­ 14-18. Chair: C. Meadows, Code 5543, Naval kowska, lnstytut Matematyki, Politechnika Linear Logic Workshop, Mathe­ Re­ matical search Laboratory, Washington, DC Warszawska, Plac Politechniki 1, 00 Sciences Institute, Cornell University, 20375; 661 202-767-3490; Warsaw, Poland. Ithaca, NY. (May/Jun. 1992, p. 496) Publications Chair: J. Gutt­ 14-18. Homologie des Algebres et Applica­ man, The MITRE Corp., Burlington Rd., 6-9. Annual Meeting of the Statistical tions, CIRM, Marseille, France. (Nov. 1992, Bedford, MA 01730; 617-271-2654. Society of Canada, Wolfville, Nova Scotia, p. 1119) 15-18. Third IMACS International Canada.(Feb. 1992,p. 149) Work­ * 14-19. Groups of Lie Type and Their shop on Qualitative Reasoning and Deci­ 6-12. Analysis auf Kompakten Varietaten, Geometries, Como, Italy. sion Technologies-QR&DT-3, Polytechnique Oberwolfach, Federal Republic of Germany. of Barcelona, Spain. (Jan. 1992, p. 56) (Jan. 1992, p. 56) ORGANIZING COMMITTEE: L. Di Martino (U. di Milano), W.M. Kantor (U. of Ore­ * 16-18. Fifth International Conference on 7-10. SIAM Conference on Mathematical gon), O.H. Kegel (U. ofFreiburg), L. Rosati Rewriting Techniques and Applications, Mon­ and Numerical Aspects of Wave Propagation (U. di Firenza). treal, Canada. Phenomena, University of Delaware, Newark, INVITED SPEAKERS: M. Aschbacher, A. DE. (Jul./Aug. CALL FOR PAPERS: Papers in the follow­ 1992, p. 631) Borovik, F. Buekenhout, A.M. Cohen, M. ing areas are solicited: term rewriting 7-10. The Eighth Haifa Matrix Theory Liebeck, A. Lubotzky, T. Meixner, A. systems, constrained rewriting and Conference, Technion, Haifa, Israel. (Nov. the­ Pasini, J. Saxl, G.M. Seitz, E.E. Shult, orem 1992, p. 1119) proving, graph rewriting and gram­ N. Vavilov, J. Wilson. mars, rewrite-based theory proving, lambda 7-11. IMA Thtorial: Mathematical The­ INFORMATION: L. Di Martino, Dipt. di and combinatory calculi, parallel rewriting, Matematica ory which Has become an Integral Part of "F.Enriques", Universita di solving and completion, symbolic and al­ Modern Financial Economics, Institute for Milano, via C. Saldini 50, 20133, Milano gebraic computation, equational program­ Mathematics and its Applications, University (Italy); email: [email protected] ming languages, completion procedures, of Minnesota, Minneapolis, MN. (Nov. 1991, or dimartin@ irniucca.unimi.it. unification and matching algorithms, con­ p. 1172) straint solving, 15-17. IEEE Computer Society Conference and term-based architec­ 7-11. Colloque International tures en I'Honneur on Computer Vision and Pattern Recogni­ to Program Chair, C. Kirchner, INRIA de G. Freiman. La Methode Lorraine & CRIN, Additive Inverse tion, Ornni Park Central, New York City, NY. Campus Scientifique, et ses Applications, 615, CIRM, Marseille, France. (Nov. 1992, p. 1119) rue du Jardin Botanique, BP 101, (No~ 1992,p. 1119) 54602 Villers-les-Nancy cedex, France; * 15-17. Second GAMM/IFIP Workshop on 7-11. Art and [email protected] by December 10, Mathematics Conference Stochastic Optimization, Miinchen, Federal (AM93), 1992. State University of New York, Al­ Republic of Germany. bany, NY. (Dec. 1992, p. 1279) INFORMATION: M. Okada, Dept. of Comp. INFORMATION: Sci., Concordia Univ., H3G 7-12. International Conference in Honour K. Marti, Univ. der Bun­ 1M8 Mon­ treal (Quebec), Canada; email: rta93@ of Bernard Malgrange, Grenoble, France. deswehr Miinchen Fak fur Luft-und Raum­ (Nov. 1992, p. 1119) fahrttechnik, Werner-Heisenberg-Weg 39, concour.cs.concordia.ca. W-8014 Neubiberg, Germany. *7-12. Methodes Geometriques et Topolo- 17-19. ATLAST 1993 Linear Algebra giques en Physique Theorique, Lyon, France; * 15-17. Computer Security Foundations Workshops, Michigan State University, East Workshop VI, Franconia, Lansing, MI. (Dec. 1992, p. 1279) INFORMATION: C. Roger, Lab. de Geometrie NH. 18-19. Conference et Analyse, Batiment 101, Univ. Claude PROGRAM: The purpose of this workshop is on Integration of Pre­ calculus with Calculus, Bernard, 43 Bd du 11 Novembre 1918, to bring together researchers in computer Moravian College, Bethlehem, PA. F-69622 Villeurbanne Cedex; or P. Sorba, science to examine foundational issues in (Dec. 1992, p. 1279) Lab. de Physique Theorique, Ecole Normal computer security, with emphasis on formal 20-23. Eighth Annual IEEE Symposium on Superieure de Lyon, 46 Allee d'Italic, F- models that provide a framework for theo­ Logic in Computer Science (LICS), Mon­ 69364 Lyon Cedex 07. ries of security and techniques for verifying treal, Canada. (Nov. 1992, p. 1119) security as defined by such theories. 20-26. Konvexgeometrie, Oberwolfach, Fed­ 7-13. Workshop on Pattern Formation CALL FOR PAPERS: We are interested both eral Republic of Germany. (Jan. 1992, p. 56) and Cellular Automata, Fields Institute for in papers that describe new results in the Research in Mathematical * 20-July 2. NATO Advanced Study Insti­ Sciences, Waterloo, theory of computer security and in papers, Ontario. (Apr. 1992, p. 352) tute: Real & Complex Dynamical Systems, panels, and working group exercises that Hillerod, Denmark. 13-18. The Householder Symposium XII explore open questions and raise funda­ Meeting on Numerical Algebra, UCLA Con- mental concerns about current theories of PROGRAM: The institute aims to bring to-

58 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences

gether leading researchers involved in the * 23-27. Seventeenth Summer Symposium in CALL FOR PAPERS: Papers are solicited mathematical analysis of both real and Real Analysis, Macalester College, St. Paul, on: verification and validation tools for complex dynamics, to emphasize the re­ MN. hardware and software systems, including protocols, distributed systems, real time cent exchange 'of ideas and tools between symposium will include PROGRAM: The control systems and digital circuits and sys­ the two areas. by five invited princi­ hour-long lectures tems; verification and validation methods PRINCIPAL SPEAKERS: V. Baladi (Lyon), a limited number of supple­ pal speakers, based on model checking, theorem prov­ B. Branner (Lyngby), C. Budd (Bristol), A. presentations, and mental twenty-minute ing, automata based methods; verification Douady (Orsay), J.H. Hubbard (Cornell), P. problem sessions. organized informal theories and their applicability; and com­ Jones (Yale), B. Kitchens (IBM T.J. Watson Pending Funding: C. PRINCIPAL SPEAKERS: plexity and efficiency issues in automatic Research Center), R. Perez-Marco (Orsay), M. Laczkovich (Eotvos Goffman (Purdue), verification. Submissions in the form of a J. Milnor (Stony Brook), M. Shishikura U.), A. Olevskii (Moscow and Tel Lorand J&\1EX or Postscript file to [email protected] (Tokyo Institute of Technology), S. van Aviv), D. Preiss (University College), D. Strien (Amsterdam), C.T. Sparrow (Cam­ and should be limited to 12 double-spaced Waterman (Syracuse). pages. 5 hard copies should be sent to the bridge), M. Viana (Porto/IMPA), J.-C. Yoc­ Abstracts for 20 minute CALL FOR PAPERS: program chair by January 15, 1993. coz (Orsay), L.-S. Young (Arizona/UCLA). in trip­ presentations should be received INFORMATION: Program Chair, C. Courcou­ INFORMATION: B. Branner, Math. Institute, problem licate by April 1, 1993. For the betis, Univ. of Crete, Dept. of Comp. Sci. Building 303, The Technical Univ. of Den­ statement of sessions, a background and and lnst. of Comp. Sci., FORTH, P.O. Box mark, DK-2800 Lyngby, Denmark; email: the problem should be received in triplicate [email protected]; Fax: (+45) 42 88 13 1385, GR-7111 0, Heraklion, Crete, Greece; by Aprill, 1993. email: [email protected]. 99. Requests for participation and finan­ INFORMATION: K. Saxe, Dept. of Math. and cial assistance must be received before CS, Macalester College, 1600 Grand Ave., 28-July 2. Geometrie Algebrique et Theorie February 1, 1993. St. Paul, MN 55105-1899; email: saxe@ des Codes, CIRM, Marseille, France. (Nov. 1-23. Colloquium on Elementary and An­ macalstr.edu. 1992, p. 1120) lytic Number Theory, Lillaftired, Hungary. 24-26. Twenty-fifth Anniversary of the 28-July 3. Conference in Honour of Jean­ at Orsay. Classification Society of North America, Pierre Kahane, University Paris-Sud INFORMATION: Janos Bolyai Math. Society, (Nov. 1992, p. 1120) Fo utca 68, H-1027 Budapest. Pittsburgh, PA. (Dec. 1992, p. 1280) 24-26. ATLAST 1993 Linear Algebra * 28-July 3. Sixth International Vilnius Con­ and Mathe­ 1-25. Twenty-second Conference on Sto­ Workshops, Los Angeles Peirce College, ference on Probability Theory hastic Processes and their Applications, Woodland Hills, CA. (Dec. 1992, p. 1280) matical Statistics, Vilnius, Lithuania. •msterdam, The Netherlands. (Sep. 1992, * 24-26. Ninth Summer Conference on Gen­ INFORMATION: V. Statulevicius, lnst. of '· 773) eral Topology and Applications, Slippery Math. and Informatics, Akademijos 4; 2600 .1-25. Graphs on Surfaces, Johns Hopkins Rock University, Slippery Rock, PA. Vilnius, Lithuania. Jniversity, Baltimore, MD. (Sep. 1992, p. 773) CONFERENCE TOPICS: General topology Analysis .1-25. Fifth International Conference on 28-July 9. Conference on Matrix and applications, special sessions on set­ for Applications, University of Wyoming, ~ormal Power Series and Algebraic Com­ theoretic topological semi-groups, and uni­ (Dec. 1992, p. 1280) linatorics, University of Florence, Florence, Laramie, WY. form spaces. taly. (Oct. 1992, p. 949) 29-July 2. Number Theoretic and Algebraic INVITED SPEAKERS: R.W. Heath (U. of Science, International :1-26. Homogeneisation et Methodes de Methods in Computer Pittsburgh), H. Junilla (U. of Helsinki), W. Center of Scientific and Technical Information ~onvergence en Calcul des Variations, ClRM, Just (Ohio U.), J. Kulesza (George Mason (ICSTI), Moscow. (Sep. 1992, p. 773) .farseille, France. (Nov. 1992, p. 1119) U.), J. Roitrnan (U. of Kansas), S. Warner :2-24. The Twenty-third Annual Interna­ (Duke U.). ional Symposium on Fault-Tolerant Com­ CALL FOR PAPERS: Deadlines.for abstracts: luting (FTCS 23), Toulouse, France. (Nov. May 1, 1993. July 1993 992, p. 1119) INFORMATION: Committee Chairman: E.M. 2-4. T.I.Tec!K.E.S. Conference on Non­ :2-25. Third International Conference on Grabner, [email protected]; R. Buck, reb@ linear and Convex Analysis in Economic ~lgebraic Methodology and Software Tech­ sru.bitnet; G.C. Grabner, [email protected]; Theory, Tokyo, Japan. (Dec. 1992, p. 1280) M. Ismail, [email protected]; W.F. Lind­ aology (AMAST '93), Enschede, The Nether­ 4-9. Fifth International Fuzzy Systems gren, [email protected]; A. Szymanski, aas@ ands. (Nov. 1992, p. 1119) Association World Congress, Seoul, Korea. sru.bitnet. !2-26. Cech Birthday Conference, North-· (Mar. 1992, p. 250) :astern University, Boston, MA. 27-July 3. Algebraische K-Theorie, Ober­ 4-10. Freie Randwertprobleme, Oberwol­ PROGRAM: This conference is in celebration wolfach, Federal Republic of Germany. (Jan. fach, Federal Republic of Germany. (Jan. 1992, of the centenary of Eduard Cech's birth. The 1992,p.57) p.57) focus will be on homotopy theory, stable 28-30. Second International Workshop 4-10. Fifth International Congress on Al­ and unstable, and its recent applications. on Logic Programming and Nonmonotonic gebraic Hyperstructures and Applications, ORGANIZING COMMITTEE: B. Cenkl, M.J. Reasoning, Lisbon, Portugal. (Nov. 1992, Iasi, Romania. (Sep. 1992, p. 773) Hopkins, S. Jekel, H.R. Miller. p. 1120) * 4-10. Methoden der Modul-und Ring­ INFORMATION: Cech Homotopy Confer­ * 28-July 1. Fifth Conference on Computer- theorie, Oberwolfach, Federal Republic of ence, Northeastern University, Boston, MA Aided Verification, Heraklion, Crete, Greece. Germany. 02115; [email protected]. PRoGRAM: The goal is to compare various INFORMATION: Mathematisches For­ ~3-26. Convergence in Ergodic Theory and verification methods and practical tools schungsinstitut Oberwolfach Geschiift­ t»robability, Ohio State University, Columbus, that can be used to assist the applications sstelle: Alberstrasse 24 D-7800 Freiburg )H. (May/Jun. 1992, p. 496) designer. im Breisgau.

JANUARY 1993, VOLUME 40, NUMBER 1 59 ...... ______IIBII .... ~----~------Meetings and Conferences

5-9. Communications et Reseaux d'Inter­ Federal Republic of Germany. (Jan. 1992, CONFERENCE TOPICS: Parallel or distributed connexion, CIRM, Marseille, France. (Nov. p. 57) algorithms to solve computationally in­ 1992, p. 1120) 18-24. Twelfth International Conference tensive problems across a LAN, MAN, 5-9. The Thirty-seventh Annual Meeting of on Near-rings and Near-fields, University of or WAN; architectural support for high­ the Australian Mathematical Society (AMS New Brunswick, Fredericton, N.B., Canada. speed communications or interconnection '93), University of Wollongong, Australia. (Dec. l992,p. 1281) networks; gigabit network architectures; high performance distributed shared mem­ (Nov. 1992, p. 1120) * 18-24. International Conference on Combi­ ory systems; distributed computing envi­ natorics, Keszthely, Hungary. 5-9. CTAC93 Conference and Workshops, ronments; HPDC Software Management Australian National University, Canberra, INFORMATION: Janos Bolyai Math. Society, Tools; High-speed communication trans­ A.C.T., Australia. (Dec. 1992, p. 1280) F<> utca 68, H-1027 Budapest. port protocols to achieve gigabit/sec appli­ 5-9. British Combinatorial Conference, cation-to-application transfer rates; high Keele University, Staffordshire, UK. (Dec. 19-23. Singularites, CIRM, Marseille, France. performance 110 systems; performance eval­ 1992, p. 1281) (Nov. 1992, p. 1121) uation of experimental systems to solve su­ 5-31. NSF Regional Geometry Institute: 19-23. International Congress on Com­ percomputing applications across networks Discrete Geometry, Smith College, Northamp­ puter Systems and Applied Mathematics, St. of computers. ton, MA. (Nov. 1992, p. 1120) Petersburg, Russia. (Dec. 1992, p. 1282) CALL FOR PAPERS: Authors are requested to submit by January 15, 1993 five copies of 6-9. European Multigrid Conference '93, * 19-23. Seventh ACM International Confer- their manuscript (not to exceed 25 double­ Amsterdam, The Netherlands. (May/Jun. 1992, ence on Supercomputing, Tokyo, Japan. spaced pages) to the address below. p. 496) CONFERENCE TOPICS: Parallel and high­ INFORMATION: C.S. Raghavendra, School 6-23. IMA Summer Program on Modeling, performance computer architectures; par­ of Electrical Engineering and Computer Mesh Generations, and Adaptive Numerical allelizing compilers and programming en­ Science, Washington State Univ., Pullman, Methods for Partial Differential Equations, vironments; operating systems and perfor­ WA 99164-2752; 509-335-8246; raghu@ University of Minnesota, Minneapolis, MN. mance evaluation; large-scale applications eecs. wsu.edu. (Nov. 1992, p. 1120) and algorithms; and new experimental and commercial systems. 22-24. ATLAST 1993 Linear Algebra 7-10. The Second International Confer­ INFORMATION: M. Sato, Secretary of ICS ence on Fluid Mechanics (ICFM-11), Beijing, Workshops, University of Maryland, College '93 Program Committee, Electrotechni­ Park, MD. (Dec. 1992, p. 1282) China. (Sep. 1992, p. 773) cal Laboratory, 1-1-4 Umezono, Tsukuba, 25-31. Geometric Methods in Theoreti­ 8-10. ATLAST 1993 Linear Algebra Work­ Ibaraki 305, Japan; [email protected]. cal and Computational Mechanics, Ober­ shops, University of Houston-Downtown, wolfach, Federal Republic of Germany. (Jan. Houston, TX. (Dec. 1992, p. 1281 * 19-24. The Arithmetic of Elliptic Curves, 1992,p.57) Anogeia, Crete, Greece. * 9-11. 1993 Annual Meeting of the Aus­ 26-30. NATO Advanced Research Work­ tralasian Association for Logic, University of PRoGRAM: The meeting will be addressed shop: Classical and Axiomatic Potential Adelaide, South Australia. to both graduate students and researchers, Theory, Les Arcs, Savoy, France. (Oct. 1992, 11-17. Nonlinear Evolution Equations, So­ with survey talks by experts in the field. p. 950) INFORMATION: J. Antoniadis or N. Tzanakis lutions and the Inverse Scattering Trans­ * 26-30. Groupes Ordonnes et Groupes de or T. Pheidas, Dept. of Math., Univ. of form, Oberwolfach, Federal Republic of Ger­ Permutations Infinis, Marseille, France. many. (Jan. 1992, p. 57) Crete, P.O. Box 1470, Heraklio, Crete, Greece; email: [email protected]. INFORMATION: CIRM, Luminy Case 916, 12-16. SIAM Annual Meeting, Philadelphia, F-13288 Marseille Cedex 9. PA. (Dec. 1992, p. 1281) * 19-August 13. CRM Summer School on 12-16. Chaotic Numerics (An International Mathematical Biology, University of British * 26-30. Cryptography and Computational Workshop on the Approximation and Com­ Columbia. Number Theory, North Dakota State Univer­ putation of Complicated Dynamical Behav­ sity, Fargo, ND. ORGANIZER: R. Miura (UBC). ior), Deakin University, Geelong, Australia. LECTURERS: C. Clark, A. Dobson, L. PROGRAM: This is the 1993 Summer Sem­ (Oct. 1992, p. 949) Keshet, S. Levin, D. Ludwig, M. Mangel, inar of the North Central Section of the 12-17. CoUoque Takeuti: Theorie de Ia J. Milton, R. Miura, S. Pimm, J. Rinzel, L. Mathematical Association of America. C. Demonstration et Applications en Informa­ Segel, J. Tyson. Pomerance will deliver 10 lectures cov­ tique, CIRM, Marseille, France. (Nov. 1992, INFORMATION: M. Louis Pelletier, CRM, ering such topics as primality testing and p. 1121) Univ. de Montreal, C.P. 6128, Succursale Carmichael numbers, integer factoring, dis­ 12-17. Third International Conference on A, Montreal, Quebec, H3C 3J7, Canada; or crete logarithms, and cryptographic sys­ Nonassociative Algebra and its Applica­ email: pellet! @ere.umontreal.ca. tems. tions, University of Oviedo, Spain. (Nov. 1992, INFORMATION: R. Mathsen, Dept. of Math., 20-29. 1993 ASL European Summer Meet­ p. 1121) North Dakota State University, Fargo, ND ing (Logic Colloquium '93), University of 58105-5075. 12-23. Conference on Universal Algebra Keele, United Kingdom. (Nov. 1992, p. 1121) and Category Theory, Mathematical Sciences * 21-23. Second International Symposium on 26-August 6. SMS-NATO ASI: Complex Research Institute, Berkeley, CA. (May/Jun. High Performance Distributed Computing Potential Theory, Universite de Montreal, 1992,p.496) (HPDC-2), Spokane, WA. Montreal, Canada. (Dec. 1992, p. 1282) 15-17. ATLAST 1993 Linear Algebra * 27-30. Seventh Workshop on Operator PROGRAM: This sympsoium is a forum for Workshops, Georgia State University, Atlanta, Theory and Boundary Eigenvalue Problems, presenting the latest research findings that GA. (Dec. 1992, p. 1281) Vienna Technical University, Vienna, Austria. unify parallel and distributed computing 18-24. Dynamische Systeme, Oberwolfach, fields. INFORMATION: H. Langer, lnstitut 114,

60 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences

Techn. Univ. Vienna, Wiedner Hauptstr. 8- J. Weeks, Middlebury College; S. Wein­ * 15. Tutorial on Numerical Methods in 10 A-1 040 Vienna, Austria; email: hlanger@ berger, Chicago. Control, Signal, and Image Processing, Uni­ email.tuwien.ac.at; tel: +43-(0)222-58801- versity of Washington, Seattle, WA. 5364. 4-6. SIAM Conference on Simulation and Monte Carlo Methods, San Francisco, CA. ORGANIZER: B.N. Datta, Northern Illinois * 31-August l. Conference on Logic and (Dec. 1992,p. 12822) University. Linguistics, Ohio State University. * 6-19. Stochastic Analysis and AppHcations INFORMATION: SlAM Conference Coordi­ nator, Dept. CC1192, 3600 University City CALL FOR PAPERS: Abstracts (due March in Physics, NATO Advanced Study Institute at the Universidade de Madeira. Science Center, Philadelphia, PA 19104- 1, 1993) are solicited addressing logical 2688; tel: 215-382-9800; Fax: 215-386- issues in linguistic theory or linguistic PROGRAM: The last decade saw enormous 7999; email: [email protected]. applications of logical theory and should achievements in stochastic analysis and be sent as 7 hard copies. its applications in connection with analy­ 15-21. Noncommutative Algebra and Rep­ INFORMATION: R. Oehrle, Dept. of Lin­ sis on infinite dimensional spaces. Quan­ resentation Theory, Oberwolfach, Federal Re­ guistics, Douglass 200E, University of Ari­ tum physics and dynamical systems were public of Germany. (Jan. 1992, p. 57) zona, Tucson, AZ 85721, or by email (as among the inspiring sources for these de­ 15-27. XI Latin American School of Mathe­ an ASCll or 1£\'IEX file): email: oehrle@ velopments. The school will bring experts matics (ELAM), Mexico. (Nov. 1992, p. 1121) convxl.ccit.arizona.edu. Submission via in these fields together for a comprehensive 16-19. Third SIAM Conference on Linear email is strongly encouraged. review in order to achieve coherence and to Algebra in Signals, Systems, and Control, stimulate future research. A limited num­ University of Washington, Seattle, WA. (Dec. ber of fellowships for partial support and a 1992,p. 1283) August1993 smaller one for full support are available. 16-20. First European NonHnear Oscilla­ CoNFERENCE ToPics: Markov and quan­ *August-December. A Semester at CRM: tions Conference, Hamburg, Germany. (Sep. tum fields, dirichlet forms, analysis on loop Spatial and Temporal Dynamics, Universite 1992, p. 774) groups, Monte Carlo methods, stochastic de Montreal. * 16-20. Conference on Variational Prob­ methods in quantum field theory, quantum lems in Differential Geometry and Partial ORGANIZERS: J. Guckenheimer and P. probability, stochastic (partial) differential Differential Equations, Trieste, Italy. Holmes (Cornell). equations, Feynman integration, stochas­ VISITORS: L. Abbott, N. Aubry, W. Bialek, tic dynamical systems, and white noise CHAIRMEN: P.U. Aviles and J. Escobar, A. Cohen, J.P. Eckmann, M. Golubitsky, analysis. Trieste. M.W. Hirsch, D. Koditschek, N. Kopell, LECTURERS: S. Albeverio (Bochum), P. INFORMATION: International Centre for The­ A. Libchaber, R. Mackay, A. Mielke, J. Collet (Paris), M. Fukushima (Osaka), L. oretical Physics, P.O. Box 586, 1-34100 Rinzel, T. Sejnowski, Y. Pesin. Gross (Cornell), G. Jona-Lasinio (Rome), Trieste. INFORMATION: M. Louis Pelletier, CRM, C.B. Lang* (Graz), R. Vilela Mendes (Lis­ Univ. de Montreal, C.P. 6128, Succursale bon), P.A. Meyers* (Strasbourg), P.K. Mit­ * 16-20. Twenty-second Annual Conference: A, Montreal, Quebec, H3C 3J7, Canada; or ter (Paris), B. Oksendal (Oslo), E. Pardoux* 1993 International Conference on Parallel email: pelletl @ere.umontreal.ca. (Marseille), J. Potthoff (Mannheim), R. Se­ Processing, The Pennsylvania State Univer­ neor (Paris), L. Streit (Funchal, Bielefeld). sity, University Park, PA. August 1993 ..International Conference on Speakers marked with a * are not yet fully INFORMATION: T. Feng, The Pennsylvania New Trends in Computer Science I (NET· confirmed. State University, E.E. East Bldg., Univer­ COMS 1), University oflbadan, Nigeria. (Nov. INFORMATION: L. Streit, Universidade da sity Park, PA 16802-2704. 1992, p. 1121) Madeira, Edificio do Colegio, Praca do Mu­ 1-7. Abelsche Gruppen, Oberwolfach, Fed­ nicipio, P-9000 Funchal, Madeira; email: 17-20. The Mathematical Heritage of Sir eral Republic of Germany. (Jan. 1992, p. 57) [email protected]. William Rowan Hamilton, Dublin, Ireland. 1-14. Groups 93 Galway/St. Andrews, Gal­ (May/Jun. 1992, p. 497) way, Ireland. (Nov. 1992, p. 1121) 7-21. Semlgroups and their Applications, 17-20. International Symposium on Statis­ York, England. (Sep. 1992, p. 774) 2-6. Second Gauss Symposium, Munich, tics with Non-precise Data, Innsbruck, Aus­ Germany. (Dec. 1992, p. 1282) 8-14. Konstruktive Approximationstheorie, tria.(Sep. 1992,p. 774) Oberwolfach, Federal Republic of Germany. 2-6. International Symposium on the Math• 17-21. Second International Conference (Jan. 1992, p. 57) ematical Theory of Networks and Systems, on Finite Fields: Theory, AppHcations, and Regensburg, Germany. (Sep. 1992, p~ 774) 9-12. Joint Statistical Meetings, San Fran­ Algorithms, University of Nevada, Las Vegas. cisco, CA. (Nov. 1991, p. 1172) * 2-13. Georgia International Topology Con­ (sep. 1992, p. 774) ference, University of Georgia, Athens, GA. 9-13. Sixth International Conference on 18~22. Fourth International Colloquium (Please note new information to May/Jun. Structural Safety and ReHabllity (ICOSSAR on Differential Equations, Plovdiv, Bulgaria. 1992,p.497) '93), Innsbruck, Austria. (Sep. 1992, p. 774) (Dec. 1991, p. 1341) *9-13. Analysis CoUoquium, Szeged, Hun­ * 22-26. Crypto '93, University INVITED SPEAKERS: M. Bestvina, UCLA; of California, gary. Santa Barbara. R. Bott, Harvard; A. Casson, Berkeley; Y. Eliashberg, Stanford; M. Freedman, UC INFORMATION: Janos Bolyai Math. Society, CALL FOR PAPERS: Original research papers San Diego; D. Gabai, Caltech; Z.-X. He, Fo utca 68, H-1027 Budapest. and technical expository talks are solicited Princeton; R. Kirby, Berkeley; P. Kron­ on all practical and theoretical aspects heimer, Oxford; R. MacPherson, MIT; J. 13-17. Second International Colloquium on of cryptology. Authors are requested to Morgan, Columbia; T. Mrowka, Caltech; Numerical Analysis, Plovdiv, Bulgaria. (Dec. send 12 copies of a detailed abstract (not R. Stem, UC Irvine; C. Taubes, Harvard; 1991, p. 1341) a full paper) by April 26, 1993 to the B. Thurston, MSRI; V. Turaev, Univ. Louis 14-17. First Workshop on Oscillation The­ address below. All submissions must be Pasteur; V. Vassiliev, USSR Acad. of Sci.; ory, Plovdiv, Bulgaria. (Oct. 1992, p. 950) anonymous.

JANUARY 1993, VOLUME 40, NUMBER 1 61 Meetings and Conferences

INFORMATION: D. R. Stinson (Program Technische Univ. Wien, Inst. furComputer­ to May/Jun. 1992, p. 497) Chair), Computer Science and Engineer­ sprachen E185.2, resselgasse 3/1, A-1040 INVITED SPEAKERS: K.B. Athreya, J.D. Big­ ing Dept., 115 Ferguson Hall, University Vienna, Austria; [email protected]. gins, B. Chauvin, H. Cohn, D.A. Dawson, of Nebraska, Lincoln, NE 68588-0115; S.N. Evans, K. Fleischmann, V.G. Gadag, 402-472-7791; Fax: 402-472-7767; inter­ 24-28. Equadifl' 8, Bratislava, Czecho- L.G. Gorostiza, E. Seneta, V.A. Vatutin. net [email protected]. Slovakia.. (Dec. 1992, p. 1283) 25-September 3. Forty-ninth Biennial Ses­ CALL FOR PAPERS: One abstract to be *22-27. Colloquium on Topology, Lillafiired, sion of the International Statistical Institute, submitted by May 15, 1993. Hungary. Firenze, Italy. (Nov. 1991, p. 1172) *6-10. Nombre de Points Entiers dans les INFORMATION: Janos Bolyai Math. Society, 29-30. Conference on Rings, Extensions, PolyMres et Applications, CIRM, Marseille, Fl> utca 68, H-1027 Budapest. and Cohomology on the Occasion of the France. Retirement of Daniel Zelinsky, Northwestern 22-28. Special Complex Varieties, Oberwol­ University, Evanston, IL. (Dec. 1992, p. 1283) ORGANIZERS: J.-M. Kantor and D. Zagier (Univ Paris 7). fach, Federal Republic of Germany. (Jan. 1992, 29-September 4. Random Graphs and Com­ INFORMATION: Centre International de Ren­ p. 57) binatorial Structures, Oberwolfach, Federal contres Mathematiques, Case 916, 70, 22-29. TWenty-ninth International Con­ Republic of Germany. (Jan. 1992, p. 57) gress of History of Science, Zaragoza, Spain. Route Uon•Lachamp, 13288 Marseille 30-September 3. Inverse Problems: Princi­ Cedex 9; tel: (91) 833000. (Apr. 1992, p. 352) ples and Applications in Geophysics, Tech­ * 23-27. Lattices, Ordered Sets, and Universal nology, and Medicine, Potsdam (near Berlin), * 6-11. Eleventh International Conference on Algebra (Sixteenth Algebraic Conference in Germany. (Sep. 1992, p. 774) Topology, Trieste, Italy. Szeged), Szeged, Hungary. 30-September 3. Representations des Groupes PROGRAM: The conference is part of the PRoGRAM: The program will consist of etAnalyse Complexe, CIRM, Marseille, France. celebrations for the fiftieth anniversary of 50-minute plenary lectures, delivered by (No~ 1992,p. 1121) the Faculty of Engineering of the Univer­ invited speakers, and many 20-minute talks * 30-September 3. Eleventh International sity of Trieste. A special session will be (probably in parallel sections) and a prob­ Conference on the New Quality Philoso­ dedicated to Prof. Mario Dolcher and his lem session. phy in Statistical Research and Education, work. INVITED SPEAKERS: G. McNulty (Colum­ Firenze, Italy. INFORMATION: G. Tironi, Dept. of Math. bia), I. Rival (Ottawa), R. Willard (Water­ INFORMATION: V. Shvyrkov, IS-SSE, 536 Sci., Univ. of Trieste, P.le Europa, 1-1- loo), and W. Geyer, N. Newrly, and F. Vogt Oasis Drive, Sanata Rosa, CA 95407. 34127-Trieste (Italy); tel: (39) (40) 676- (Darmstadt). 3258, -3727; Fax: (39) (40) 676-3256; DEADLINES: April30, 1993 for application * 30-September 3. Conference on the Finite email: [email protected] or dsma@ and for booking accomodations; June 25, Element Method: Fifty Years of the Courant univ.trieste.it. 1993 for abstracts; and August 1, 1993 for Element, Jyvliskylli, Finland. posters. * 9-15. IMA Tutorial, Institute for Mathematics ORGANIZING COMMITTEE: P. Neittaan­ INFORMATION: G. Czedli JATE Bolyai In­ and its Applications, University of Minnesota, mliki (Chair), M. Krizek, Yu. Kuznetsov, J. stitute, Szeged, Aradi vertanuk tere 1, Hun­ Minneapolis, MN. Periaux, R. Stenberg. gary, H-6720; email: [email protected]; CONFERENCE TOPICS: Historical develop­ INFORMATION: Institute for Mathematics Fax: (++36) 62-326246. ments; FE-grid generation, adaptive meth­ and its Applications, University of Min­ nesota, 514 Vincent Hall, 206 Church St., 23-28. International Conference on Al­ ods; A-priori and a-posteriori error esti­ S.E., Minneapolis, MN 55455. gebra Dedicated to the Memory of M.I. mates; superconvergence; irregular prob­ lems; implementation issues, paralleliza­ Kargapolov, Krasnoyarsk, Russia. (Jul./Aug. * 12-16. Third Dublin Differential Equations tion; FEM in optimal control, free bound­ 1992,p.632) Meeting, Dublin City University, Dublin, Ire­ ary problems; applications in elasticity, 23-September 4. NATO Advanced Study land. Institute on Polytopes: Abstract, Convex, fluid dynamics, electromagnetism, etc. and Computational, Scarborough, Ontario, CALL FOR PAPERS: Abstracts (10--20 lines) PROGRAM: The invited speakers will give 50 Canada. (Dec· 1992, p. 1283) of your papers should be sent to the Con­ minute lectures. There will be sessions of ference Secretariat in Jyvliskylli by January contributed 25 minute talks, which can be * 24-27. Third Kurt G&lel Colloquium, Brno, 30, 1993. on any aspect of the theory or applications Czech Republic. INFORMATION: FEM 50 Secretariat, Dept. of differential equations. PRoGRAM: This colloquium is intended for of Math., Univ. of Jyvliskylii, P.O. Box 35, INVITED SPEAKERS: P. Cooke (Delaware), logicians and computer scientists interested SF-40351 Jyvliskylii, Finland; Fax: 358 41 M.E. Gurtin (Carnegie Mellon), J. Ock­ in the proof-theoretic and algorithmic as­ 602731. endon (Oxford), F. Olver (Maryland), J. pects of logic. Serrin (Minnesota). CoNFERENCE ToPICS: Proof theory, au­ INFORMATION: D.W. Reynolds, School of tomated theorem proving, unification September 1993 Math. Sci., Dublin City Univ., Dublin 9, theory, complexity theory, logics of pro­ tel: 01 704 5290; email: [email protected]. grams, nonstandard logics for theoretical 5-11. Novikov Conjectures, Index Theorems computer science and AI, recursion theory, and Rigidity, Oberwolfach, Federal Republic 12-18. Topologie, Oberwolfach, Federal Re­ logic programming, and lambda-calculus. of Germany. (Jan. 1992, p. 57) public of Germany. (Jan. 1992, p. 57) CALL FOR PAPERS: Persons interested in 5-11. Nonlinear Numerical Methods and 13-17. Fourth European Software En­ speaking should submit 3 copies of a full Rational Approximation, University of gineering Conference, Garmisch, Germany. draft paper in English not to exceed 12 Antwerp, Belgium. (Oct. 1992, p. 950) (JulJAug. 1992, p. 632) pages by January 31, 1993. * 5-12. First World Conference on Branching 13-18. Different Aspects of Differentiability, INFORMATION: Program Chair, A. Leitsch, Processes, Varna, Bulgaria. (Please note update Warsaw, Poland. (May/Jun. 1992, p. 497)

62 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences

17-20. Technology in Mathematics Teaching * 6-8. Games, Logic, and Process, CIRM, metric Design, Seattle, WA. (Jul./Aug. 1992, (TMT '93): A Bridge between Teaching and Marseille, France. p. 632) Learning, The University of Birmingham, ORGANIZER: Y. Lafont (ENS, Paris). 27-30. Seventh International Conference on England. (Dec. 1992, p. 1283) INFORMATION: Centre International de Ren­ Domain Decomposition Methods, Penn State 18-19. Eastern Section, Syracuse, NY. contres Mathematiques, Case 916, 70, University, State College, PA. (Oct. 1992, p. 950) INFORMATION: W. Drady, AMS, P.O. Box Route Uon-Lachamp, 13288 Marseille 6887, Providence, RI 02940. Cedex 9; tel: (91) 833000. 31-November 6. Algorithmische Methoden der Diskreten Mathematik, Oberwolfach, 19-25. Mathematical Game Theory, Ober­ * 11-14. Gestion de Projets Statistiques, Federal Republic of Germany. (Mar. 1992, wo1fach, Federal. Republic of Germany. (Jan. CIRM, Marseille, France. p. 251) 1992, p. 57) ORGANIZER: R. Teekens (TES, Luxem­ 20-24. Methodes Numeriques dans Ia bourg). Theorie des Surfaces de Riemann, CIRM, INFORMATION: Centre International de Ren­ November 1993 Marseille, France. (Nov. 1992, p. 1122) contres Mathematiques, Case 916, 70, 1-5. Third SIAM Conference on Geometric 20-24. Thirteenth Congress of the Austrian Route Uon-Lachamp, 13288 Marseille Design, Tempe, AZ. (Dec. 1992, p. 1284) Mathematical Society, Linz, Austria. (Dec. Cedex 9; tel: (91) 833000. 6-7. Western Section, Claremont, CA. 1992, p. 1284) 17-23. Geometrie, Oberwolfach, Federal Re­ *20-24. IMA Workshop on Probability and INFORMATION: W. Drady, AMS, P.O. Box Algorithms, Institute for Mathematics and its public of Germany. (Jan. 1992, p. 57) 6887, Providence, RI 02940. Applications, University of Minnesota, Min­ * 18-22. IMA Workshop on Finite Markov * 15-19. IMA Workshop on Random Dis­ neapolis, MN. Chain Renaissance, Institute for Mathematics and its Applications, University of Minnesota, crete Structures, Institute for Mathematics INFORMATION: Institute for Mathematics Minneapolis, MN. and its Applications, University of Minnesota, and its Applications, University of Min­ Minneapolis, MN. nesota, 514 Vincent Hall, 206 Church St., INFORMATION: Institute for Mathematics INFORMATION: Institute for Mathematics S.E., Minneapolis, MN 55455. and its Applications, University of Min­ nesota, 514 Vincent Hall, 206 Church St., and its Applications, University of Min­ 20--26. Seventh Symposium on Classical S.E., Minneapolis, MN 55455. nesota, 514 Vincent Hall, 206 Church St., Analysis, Kazimierz Dolny, Poland. (Dec. S.E., Minneapolis, MN 55455. 1992, p. 1284) * 19-22. 1993 International Conference on Network Protocols (ICNP-93), San Francisco, * 15-19. Systemes d'Equations Algebriques, 22-23. Central Section, Texas A&M Univer­ CIRM, Marseille, France. sity, College Station, TX. CA. ORGANIZERS: J.-P. Dedieu (U. Toulouse 3), INFORMATION: W.S. Drady, AMS, P.O. Box CONFERENCE TOPICS: Network architec­ D. Duval (U. Limoges}, J.P. Merlet (INRIA, 6887, Providence, RI 02940. tures, switching protocols, routing proto­ cols, flow and congestion control, high­ Sophia Antipolis). 26--0ctober 2. Diophantische Approxima­ speed networks, real-time protocols, net­ INFORMATION: Centre International de Ren­ tionen, Oberwolfach, Federal Republic of Ger­ work security, name servers and directo­ contres Mathematiques, Case 916, 70, many. (Jan. 1992, p. 57) ries, protocol conversion, broadcast sys­ Route Uon-Lachamp, 13288 Marseille Cedex 9; tel: (91) 833000. * 27-28. Workshop on Large Eddy Simula­ tems, distributed operating systems, sys­ tion in Aerodynamics and the Environment, tem support and interfaces, protocol design 21-27. Mathematische Modelle in der Bi­ methodology, protocol verification, proto­ Universite de Montreal. ologie, Oberwolfach, Federal Republic of Ger­ col testing and debugging, protocol imple­ many. (Mar. 1992, p. 251) ORGANIZERS: Organized jointly by CERCA, mentation. CERFACS, and CRM. CALL FOR PAPERS: Authors are requested * 22-26. Geometrie Symplectique et Physique INFORMATION: M. Louis Pelletier, CRM, to send six copies of their double-spaced Mathematique, CIRM, Marseille, France. Univ. de Montreal, C.P. 6128, Succursale typed manuscript (maximum of 25 pages) ORGANIZERS: P. Dazord (U. de Lyon 1), L. A, Montreal, Quebec, H3C 3J7, Canada; or with an abstract by March 1, 1993 to: M.G. Niglio (U. d' Avignon). email: pelletl @ere.umontreal.ca. Gouda, Program Chair, Dept. of Comp. INFORMATION: Centre International de Ren­ * 27-0ctober 1. Orbites Periodiques des · Sci., Univ. of Texas, Austin, TX 78712; tel: contres Mathematiques, Case 916, 70, Systemes Dynamiques, CIRM, Marseille, 512-471-9532; [email protected]. Route Uon-Lachamp, 13288 Marseille France. INFORMATION: M.T. Liu, General Chair, Cedex 9; tel: (91) 833000. Dept. of Comp. and Info. Sci., The Ohio ORGANIZER: J.-P. Francoise (U. de Paris 6) State Univ., 2036 Neil Ave., Columbus, OH 28-December 4. Nonlinear Equations in and R. Roussarie (U. de Dijon). 43210; 614-292-6552; [email protected]. Many-Particle Systems, Oberwolfach, Fed­ INFORMATION: Centre International de Ren­ eral Republic of Germany. (Mar. 1992, p. 251) contres Mathematiques, Case 916, 70, * 20--22. Stage de Bibliothecaires de Mathe- Route Uon-Lachamp, 13288 Marseille matiques, CIRM, Marseille, France. Cedex 9; tel: (91) 833000. ORGANIZER: Mr. Barbancon (U. de Stras­ January 1994 bourg). *January-June 1994. A Semester at CRM: INFORMATION: Centre International de Ren­ Bifurcations and the Geometry of Vector October 1993 contres Mathematiques, Case 916, 70, Fields, Universite de Montreal. Route Uon-Lachamp, 13288 Marseille 3-9. Arbeitsgemeinschaft mit Aktuellem Cedex 9; tel: (91) 833000. ORGANIZERS: C. Rousseau and D. Schlo­ Thema, Oberwolfach, Federal Republic of miuk(CRM). Germany. (Jan. 1992, p. 57) 25-29. Third SIAM Conference on Geo- VISITORS: D. Cerveau, C. Christopher, F.

JANUARY 1993, VOLUME 40, NUMBER 1 63 ··········-·····-·--····-·····-···-············--···-···-······-----·-----···--·-·-·······-·------Meetings and Conferences

Dumortier, Y. Il'yashenko, A. Lins Neto, nesota, 514 Vincent Hall, 206 Church St., * 31-June 3. IMA Minsymposium on Phase R. Roussarie, M. Singer, H. Zoladek. S.E., Minneapolis, MN 55455. Transitions in Catalytic Surface Reaction INFORMATION: M. Louis Pelletier, CRM, Models, Institute for Mathematics and its Ap­ Univ. de Montr6al, C.P. 6128, Succursale plications, University of Minnesota, Minneapo­ A, Montr6al, Qu6bec, H3C 3J7, Canada; or lis, MN. @ere.umontreal.ca. February 1994 email: pelletl INFORMATION: Institute for Mathematics * February 1994. Workshop on Dynamical Dis- ll< 4-8. International Conference on Harmonic and its Applications, University of Min­ ease, Laurentian Mountains north of Montr6al. Analysis and Operator Theory, Caracas, nesota, 514 Vincent Hall, 206 Church St., Venezuela. ORGANIZERS: J. B6lair (CRM), L. Glass S.E., Minneapolis, MN 55455. (McGill), U. an der Heiden (Witten/Her­ PROGRAM: The conference offers to re­ decke), and J. Milton (Chicago). searchers and mathematicians in harmonic INFORMATION: M. Louis Pelletier, CRM, analysis and operator theory a platform to Univ. de Montr6al, C.P. 6128, Succursale June 1994 discuss recent developments, to exchange A, Montr6al, Qu6bec, H3C 3J7, Canada; or new ideas, and to analyze trends for further 1-7. 1994 Barcelona Conference on Alge­ email: pelletl @ere.umontreal.ca. * research. There will be a session dedicated braic Topology, Sant Feliu de Guixols (near to discuss the social responsibility of the * 28-March 4. IMA Workshop on Stochastic Barcelona, Spain). scientist. Networks, Institute for Mathematics and its ORGANIZING COMMITTEE: J. Aguade, UAB; PLENARY SPEAKERS: Tentative: L. Caf­ Applications, University of Minnesota, Min­ M. Castellet, CRM; G. Mislin, OSU-ETHZ. farelli, lnst. for Advanced Studies; L. neapolis, MN. INFORMATION: 1994 BCAT, CRM, Apartat Math. Royal lnst. of Tech.; C. Carleson, 50, 08193 Bellaterra; tel: 34-3-581.10.81; Fefferman, Princeton U.; L. Nirenberg, INFORMATION: Institute for Mathematics Fax: 34-3-581.22.02; email: icrmO@ Courant Inst.; E.M. Stein, Princeton U. and its Applications, University of Min­ ebccuab I. bitnet. INVITED SPEAKERS: C. Berenstein, U. of nesota, 514 Vincent Hall, 206 Church St., S.E., Minneapolis, MN 55455. Maryland; S. Chanillo, Rutgers U.; R. Coif­ * 13-17. IMA Workshop on Classical & man, Yale U.; G. Corach, Inst. Argentino Modem Branching Processes, Institute for de Math.; G. David, U. de Paris-Sud; H. Mathematics and its Applications, University Dym, Weizmann In st.; R. Fefferman, U. of of Minnesota, Minneapolis, MN. Chicago; C. Foias, Indiana U.; I. Gohberg, The following new announcements will not INFORMATION: Institute for Mathematics Tel Aviv U.; F. Grunbaum, UC Berkeley; be repeated until the criteria in the last and its Applications, University of Min­ R. Gundy, Rutgers U.; H. Helson, UC paragraph in the box at the beginning of this nesota, 514 Vincent Hall, 206 Church St., Berkeley; P. Jones, Yale U.; J.P. Kahane, section are met. U. de Paris-Sud; N. Kerzman, U. of North S.E., Minneapolis, MN 55455. Carolina; Y. Meyer, U. de Paris IX; M. * 20-24. Probabilites Quantiques, CIRM, Mar- Milman, Inst. for Adv. Studies; N. Nikol­ seille, France. sky, U. de Bordeaux I; J. Peetre, U. of May 1994 ORGANIZER: J.-L. Sauvageot (CNRS-Paris Lund; G. Ponce, UC Santa Barbara; A. de * 2-6. IMA Workshop on Image Models (and 6). Ia Torre, U. de Malaga; L. Schwartz, Ecole Their Speech Model Cousins), Institute for INFORMATION: Centre International de Ren­ Polytechnique. Mathematics and its Applications, University contres Mathematiques, Case 916, 70, CALL FOR PAPERS: Deadline for abstracts of of Minnesota, Minneapolis, MN. invited and contributed papers is September Route Uon-Lachamp, 13288 Marseille I, 1993. INFORMATION: Institute for Mathematics Cedex 9; tel: (91) 833000. INFORMATION: Comit6 Organizador Con­ and its Applications, University of Min­ ferenda Cotlar, Apartado 47.898 Caracas, nesota, 514 Vincent Hall, 206 Church St., 1041-A, Venezuela; tel: (582)-662-9734- S.E., Minneapolis, MN 55455. 662-9734, UCV or (582)-501-1412-501- July 1994 1412, IVIC; Fax: (582)-662-9734, (582)- * 16-20. IMA Workshop on Stochastic Mod­ 662-7121 or (582)-501-1416, (582)-962- els in Geosystems, Institute for Mathematics * 17-23. ConferencelnternationaledeTopolo- , France. 1695; Telex: 21657; email: wurbina@ and its Applications, University of Minnesota, gie, CIRM, Marseille dino.conicit. ve. Minneapolis, MN. ORGANIZER: Y. Mathieu (U. de Provence, INFORMATION: Institute for Mathematics Marseille). 5- 8. Joint Mathematics Meetings, Cincin­ and its Applications, University of Min­ INFORMATION: Centre International de Ren­ nati, OH. (including the annual meetings of the nesota, 514 Vincent Hall, 206 Church St., contres Math6matiques, Case 916, 70, AMS, AWM, MAA, and NAM) S.E., Minneapolis, MN 55455. Route Uon-Lachamp, 13288 Marseille INFORMATION: H. Da ly, AMS, P.O. Box Cedex 9; tel: (91) 833000. CIRM, Mar­ 6248, Providence, RI 02940. * 16-20. Geometrie Algebrique, seille, France. (This may take place from the * 24-28. IMA Workshop on Mathematical 23- 27 instead.) Population Genetics, Institute for Mathemat­ ORGANIZER: L. Szpiro (U. de Paris-Sud). August 1994 ics and its Applications, University of Min­ INFORMATION: Centre International de Ren­ nesota, Minneapolis, MN. contres Math6matiques, Case 916, 70, 3- 11 . The International Congress of Math­ INFORMATION: Institute for Mathematics Route Uon-Lachamp, 13288 Marseille ematicans 1994, ZUrich, Switzerland. (Oct. and its Applications, University of Min- Cedex 9; tel: (91) 833000. 1992,p. 951)

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

over an algebraic field; On normal simple algebras: A note on normal division COLLECTED WORKS algebras of order sixteen; (with H. Hasse), A determination of all normal [ division algebras over an algebraic number field; A note on the equivalence of algebras of degree two; On primary normal division algebras of degree eight; Non-cyclic algebras ofdegree and exponent four; Normal division algebras over algebraic number fields not offinite degree; Cyclic fields of degree eight; On A. Adrian Albert Collected the construction ofRiemann matrices I; Normal division algebras of degree 4 A. ADRIAN Mathematical Papers over F of characteristic 2; On certain imprimitive fields ofdegree rl over P of ALB~RI' characteristic p;Normal division algebras over a modular field; A solution ofthe -...-"""""""' Richard E. Block, Nathan principal problem in the theory ofRiemann matrices; Cyclic fields of degree pn Jacobson, J. Marshall over F of characteristic p; On normal Kummer fields over a non-modular field; Osborn, David J. Saltman, The principal matrices of a Riemann matrix; A note on the Poincare theorem and Daniel Zelinsky, Editors on impure Riemann matrices; On the construction of Riemann matrices IT; On cyclic fields; Involutorial simple algebras and real Riemann matrices; Normal Volume 3 division algebras of degree p• over F of characteristic p; Simple algebras of This book contains the collected degree p• over a centrum of characteristic p; p-algebras over a field generated • works of A. Adrian Albert, a leading by one indeterminate; Non-cyclic algebras with pure maximal subfields; On algebraist of the twentieth century. Albert cyclic algebras; A note on normal division algebras ofprime degree; On ordered made many important contributions to the theory of the Brauer group algebras; On p-odic fields and rational division algebras; Division algebras and central simple algebras, Riemann matrices, nonassociative algebras, over a function field; Two element generation of a separable algebra; Absolute and other topics. Part 1 focuses on associative algebras and Riemann valued real algebras; Absolute-valued algebraic algebras; Leonard Eugene matrices, and Part 2 on nonassociative algebras and miscellany. Because Dickson (1874-1954); On involutorial algebras; A property of ordered rings; much of Albert's work remains of vital interest in contemporary On involutorial associative division algebras; A normal form for Riemann research, this volume will interest mathematicians in a variety of areas. matrices; New results on associative division algebras; On associative division algebras (Retiring Presidential Address); A note on certain cyclic algebras; Contents Tensor products of quaternion algebras; Acknowledgments; .Part 2: The integers Preface; Bibliography; Professional Biography of A(braham) Adrian Albert; of normal quartic fields; A determination of the integers of all cubic flelds; The Ph.D. Students of A. Adrian Albert; A. A. Albert by Daniel Zelinsky; Abraham integers represented by sets of ternary quodrtitic forms; On universal sets of Adrian Albert, 1905-1972 by Nathan Jacobson; Abraham Adrian Albert, A positive ternary quadratic forms; A note on the Dickson theorem on universal biographical memoir by Irving Kaplansky; A. Adrian Albert by Israel N. ternaries; On a certain algebra of quantum mechanics; Integral domains of Herstein, Collection of articles dedicated to the memory of Abraham Adrian rational generalized quaternion algebras; A note on matrices defining total Albert; Part 1: A determination ofall normol division algebras in sixteen units; real fields; Normalized integral bases of algebraic number fields I; A quodratic On the rank equation of any normol division algebra; The rank function ofany form problem in the calculus of variations; Symmetric and alternate matrices simple algebra; On the structure ofnormol division algebras; Normal division in an arbitrary field, I; Quodratic null forms over a function field; A rule for algebras in 4 rl units, p an odd prime; The structure of any algebra which computing the inverse of a matrix; Quodratic forms permitting composition; is a direct product of rational generalized quaternion division algebras; The Non-associative algebras. I. Fundamental concepts and isotopy; Non-associative non-existence of pure Riemann matrices with normal multiplication algebras algebras. IT. New simple algebras; The rodical of a non-associative algebra; of order sixteen; A necessary and sufficient condition for the non-equivalence An inductive proof of Descartes' rule of signs; Quasigroups. I; Algebras of any two rational generalized quaternion division algebras; Determination derived by non-associative matrix multiplication; The matrices offactor of all normol division algebras in thirty-six units of type ~;A note on an analysis; The minimum rank of a correlation matrix; Quasigroups. IT; important theorem on normal division algebras; New results in the theory Quasiquaternion algebras; On Jordan algebras of linear transformations; of normal division algebras; A construction of all non-commutative rational The Wedderburn principal theorem for Jordan algebras; A structure theory division algebras of order eight; The structure ofpl,lre Riemann matrices with for Jordan algebras; On the power-associativity of rings; Power-associative non-commutative multiplication algebras; Dn direct products, cyclic division rings; On right alternative algebras; A theory of trace-admissible algebras; algebras, and pure Riemann matrices; On normal division algebras of type R Almost alternative algebras; A note on the exceptional Jordan algebra; A theory in thirty-six units; On the Wedderburn norm condition for cyclic algebras; A of power-associative commutative algebras; New simple power-associative note on cyclic algebras of order sixteen; On direct products; Division algebras algebras; Power-associative algebras; On nonassociative division algebras; over an algebraic field; The structure of matrices with any normal division On simple alternative rings; On commutative power-associative algebras of algebra of multiplications; On the construction of cyclic algebras with a given degree two; Rational normal matrices satisfying the incidence equation; The exponent; Algebras of degree 2• and pure Riemann matrices; A construction of structure of right alternative algebras; (with M. S. Frank), Simple Lie algebras non-cyclic normal division algebras; Normal division algebras of degree four of characteristic p; On Hermitian operators over the Cayley algebra; A property

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JANUARY 1993, VOLUME 40, NUMBER 1 65 New Publications Offered by the AMS

of special Jordan algebras; On certain trinomial equations infinite fields; (with ~ Orientation and the B. Muckenhoupt), On matrices of trace zero; On partially stable algebras; (with Ml·:'\J()I!\S Leray-Schauder Theory N. Jacobson), On reduced exceptional simple Jordan algebras; Addendum to the . ' - paper on partially stable algebras; A construction of exceptional Jordan division for Fully Nonlinear Elliptic

algebras; On the orthogonal equivalence of sets of real symmetric matrices; A Ortentation and the Boundary Value Problems Len.y-Schauder Theooy solvable exceptional Jordan algebra; (with L. J. Paige), On a homomorphism for Fully Nonlinear EDlpUc Patrick Fitzpatrick and Boundaly Value Problema property of certain Jordan algebras; (with John Thompson), 'IWo-element Jacobo Pejsachowicz generation of the projective unimodular group; Finite noncommutative division algebras; Finite division algebras and finite planes; On the collineation ----- Volume 101, Number 483 groups associated with twisted fields; On the collineation groups of certain The aim of this work is to develop non-Desarguesian planes; Generalized twisted fields; Isotopy for generalized • an additive, integer-valued degree theory twisted fields; On the nuclei of a simple Jordan algebra; On exceptional Jordan for the class of quasilinear Fredholm division algebras; On some properties of biabelian fields; On certain polynomial mappings. This class is sufficiently large that, within its framework, systems; Unpublished Articles: Some mathematical aspects of cryptography; one can study general fully nonlinear elliptic boundary value problems. (with L. J. Paige) Malcev algebras; Acknowledgments. A degree for the whole class of quasilinear Fredholm mappings 1991 Mathematics Subject Classifications: 11-xx,12-xx, 14-xx, 16-xx, 17-xx must necessarily accomodate sign-switching of the degree along ISBN (Set) 0-8218-0003-5; ISBN (Part 1) 0-8218-0005-1; ISBN (Part 2) admissible homotopies. The authors introduce "parity", a homotopy 0-8218..()()()7-8; LC 92-28744 invariant of paths of linear Fredholm operators having invertible 743 pages (Part 1); 938 pages (Part 2); 1840 pages (Set) (hardcover), endpoints. The parity provides a complete description of the possible January 1993 Set: Individual member $124, List price $206, Institutional member $165 changes in sign of the degree and thereby permits use of the degree to Part 1: Individual member $60, List price $100, Institutional member $80 prove multiplicity and bifurcation theorems for quasilinear Fredholm Part 2: Individual member $70, List price $117, Institutional member $94 mappings. Applications are given to the study of fully nonlinear elliptic To order, please specify CWORKS/3N (Set), CWORKS/3.1N (Part 1), boundary value problems. CWORKS/3.2N (Part 2) Contents Quasilinear Fredholm mappings; Orientation and the degree; General properties of the degree; Mapping theorems; The parity of a path of linear Fredholm operators; The regular value formula and homotopy dependence; Bifurcation MEMOIRS OF THE AMS and continuation; Strong orientability; Fully nonlinear elliptic boundary value problems. 1991 Mathematics Subject Classification: 35J65, 47H15, 58010 ~ ISBN 0-8218-2544-5, LC 92-33383, ISSN 0065-9266 ML\]()JJ\S G-Categories 131 pages (softcover), January 1993 Robert Gordon Individual member $16, List price $27, Institutional member $22 To order, please specify MEM0/101/483N -,,-,-,-----,------Volume 101, Number 482 A G-category is a category on G -Categories which a group G acts. This work studies ~ Duality for Actions and the 2-category G-Cat of G-categories, MI:\1()11\S G-functors (functors which commute Coactions of Measured -- ~ with the action of G) and G-natural Groupoids on von transfonnations (natural transfonnations Duall1;y for- Neumann Algebras which commute with the G-action). and Coactlona ofMeaawecl • Groupolds on wn Neumann There is particular emphasis on the Algebras Takehiko Yamanouchi relationship between a G-category and its stable subcategory, the largest Volume 101, Number 484 sub-G-category on which G operates trivially. Also contained here -- A Through classification of compact are some very general applications of the theory to various additive ._. abelian group actions on semifinite G-categories and to G-topoi. injective factors, Jones and Takesaki Contents introduced the notion of an action of a measured groupoid on a von Neumann algebra, which has proven to be G-Categories: The stable subcategory, G-limits and stable limits; Systems of an important tool for this kind of analysis. Elaborating on this notion, isomorphisms and stably closed G-categories; Partial G-sets: G-adjoints and this work introduces a new concept of a measured groupoid action G-equivalence; Par(G-set) and G-representability; Transversals; Transverse that may fit more perfectly into the groupoid setting. Yarnanouchi limits and representations of transversaled functors; Reflections and stable also shows the existence of a canonical coproduct on every groupoid reflections; G-Cotripleability; The standard factorization of insertion; von Neumann algebra, which leads to a concept of a coaction of a Cotripleability of stable reflectors; The case of 9°; Induced stable reflections measured groupoid. Yarnanouchi then proves duality between these and their signatures; The 9 G -targeted case. objects, extending Nakagami-Takesaki duality for (co)actions oflocally 1991 Mathematics Subject Classification: 18A35, 18A40, 18B25, 18C15, compact groups on von Neumann algebras. 181>05, 18E05 ISBN 0-8218-2543-7, LC 92-33390, ISSN 0065-9266 Contents 129 pages (softcover), January 1993 Relative tensor products ofHilbert spaces over abelian von Neumann algebras; Individual member $17, List price $28, Institutional member $22 Coproducts of groupoid von Neumann algebras; Actions and coactions of To order, please specify MEM0/101/482N measured groupoids on von Neumann algebras; Crossed products by groupoid actions and their dual coactions; Crossed praducts by groupoid coactions and their dual actions; Duality for actions on von Neumann algebras; Duality

66 NOTICES OF THE AMERICAN MATHEMATICAl SOCIETY New Publications Offered by the AMS

for integrable coactions on von Neumann algebras; Examples of actions and 1991 Mathematics Subject Classification: 57, 55, 05 coactions of measured groupoids on von Neumann algebras. ISBN 0-8218-8078-0 NTSC format on 112" VHS videotape; approx. 60 minutes, January 1993 1991 Mathematics Subject Classification: 46LIO, 46L55; 22025, 22035 Individual member $29.95, List price $49.95, Institutional member $39.95 ISBN 0-8218-2545-3, LC 92-33857, ISSN 0065-9266 To order, please specify VIDE0/83N 109 pages (softcover), January 1993 Individual member $16, List price $26, Institutional member $21 To order, please specify MEMO/IOI/484N SOCIETE MATHEMATIQUE DE FRANCE, ~ ASTERISQUE MEMOIJ\S Axiomization of Passage \ ,, ~ from 'Local' Structure to 'Global' Object Ax:l.omtzatton of Passage from 'Local' Structure Paul Feit An Extension of a to "Global" Object Volume 101, Number 485 Paul Felt Theorem by Cheeger Requiring only familiarity with the and Muller terminology of categories, this book will Jean-Michel Bismut ® interest algebraic geometers and students studying schemes for the first time. Feit and Weiping Zhang translates the geometric intuition of local Number205 structure into a purely categorical format, filling a gap at the foundations This work grew out of the theorem of algebraic geometry. The main result is that, given an initial category of Cheeger and MUller on the equality C of "local" objects and morphisms, there is a canonical enlargement of the Reidermeister metric and the of 1 C to a category C9 which contains all "global" objects whose local Ray-Singer metric on the determinant structure derives from C and which is functorially equivalent to the of the cohomology of a flat vector bundle equipped with a flat or traditional notion of "global objects". Using this approach, Feit unifies unimodular metric. The authors extend this theorem to the case of definitions for numerous technical objects of algebraic geometry, flat vector bundles equipped with arbitrary metrics. The ratio of these including schemes, Tate's rigid analytic spaces, and algebraic spaces. two metrics is expressed in terms of the integral of a Chem-Simons Contents current on M. In addition, the authors establish anomaly formulas for Ray-Singer metrics. The book closes Terminology; Canopies; Canopies and colimits; Smoothing; with an appendix on the Local and global Thom-Smale complex structures. by F. Laudenbach. Titles in this series are published by the Societe Mathematique de 1991 Mathematics Subject Classification: 14A, 14K, 18A, 18B, 180, 18F France and distributed by the AMS in the United States, Canada, and ISBN 0-8218-2546-1, LC 92-33858, ISSN 0065-9266 Mexico. Orders from other countries should be sent to the SMF, Maison 107 pages (softcover), January 1993 de la SMF, Case 916-Luminy, F-13 288 Marseille Cedex 9, France, or Individual member $16, List price $26, Institutional member $21 to OF.FILffi, 48 rue Gay-Lussac, 75240 Paris Cedex 05, France. To order, please specify MEM0/1011485N Contents Reidemeister metrics and Milnor metrics; Ray-Singer metrics and the de Rham VIDEOTAPES map; Berezin integrals and Morse functions; Anomaly formulas for Ray-Singer metrics; A closed !form on IR: x IR+; Some properties of the integral - JM fJ(F,gF)C'ilf)*'I/J(TM, 'il™); An extension of a theorem ofCheeger and Muller; The asymptotic structure of the matrix of the dF operator on the Helffer-Sjostrand orthogonal base; Proof of Theorem 1.6; The asymptotics as A New Look at Knot T -+ +oo of certain traces associated to the operator D}; The asymptotics of 2 Polynomials Tr8 [N exp( -tD )] as t -+ 0; An asymptotic expansion for Tr 8 [f exp( -tD})] as Joan Birman T-+ +oo; An estimateforTr,[f exp(-(tD+Tc('il/)) 2)) in the range 0 < t :$; I, 0 :$; T :$; djt; The asymptotics as t -+ 0 ofTr8 [f exp( -(tD + (T jt)C('il /))2)]; This videotape. combines a lecture The asymptotics ofTr,[f exp(-(tD + (Tjt)c('il /))2)]for 0 < t :$; I, T 2: I; A with an informal interview to bring out direct proof of a formula comparing two Milnor metries. the fascination of the subject of knot polynomials as well as a personal view 1991 Mathematics Subject Classification: 580 of the field from one of its leaders. In ISSN 0303-1179 the interview portion of the tape, Birman 235 (softcover), 1992 Individual AMS discusses her role in the discovery or SMF member $27, List price $39, of the To order, please specify AST/205N celebrated Jones polynomial, how she got started in knot theory, and some of the changes she has seen in the field. Birman's lecture, widely praised at the 1992 Joint Mathematics Meetings in Baltimore as one of the best introductions to the subject, balances the intuition of pictures with the rigor of technical details. Because she starts with the basic definition of a knot and moves up to the latest developments involving Vassiliev invariants, this lecture will interest undergraduates and researchers alike.

JANUARY 1993, VOLUME 40, NUMBER 1 67 AMS Reports and Communications

Election Results of 1992 Dame, Algorithms based on guessing: Approximation Theory, XINGPING In the Election of 1992, 4579 valid infinitely nested priority arguments; PE­ SuN and XIANG MIN Yu, Southwest ballots were returned. TER J. OLVER, University of Minnesota, Missouri State University. Anil Nerode was elected to a three­ Quantization ofLie algebra cohomology Geometry of Affine Space, DAVID year term as Vice-President and Roy L. and quasi-exactly solvable Schrodinger WRIGHT, Washington University. Adler to a five-year term as Trustee. operators; and ERNST A. RuH, Ohio Classical Complex Analysis andRe­ There are five newly-elected Mem­ State University, Nilpotent structures on lated Areas, JANG-MEI Wu, University bers-at-Large of the Council: Susan principal bundles. The speakers were of illinois, Urbana, and DAVID DRASIN, Gayle Williams, Steven G. Krantz, James introduced by David Drasin, Clayton Purdue University. I. Lepowsky, Svetlana R. Katok, and Pe­ Sherman, Niky Kamran, and Luis Her­ Contributed Papers. There were ter Li. Each serves a three-year term. nandez, respectively. four sessions of contributed papers. Elected to three-year terms on the Special Sessions. By invitation of The session on Algebra was chaired Editorial Boards Committee are Bryan the same Committee, there were twelve by Liang-Cheng Zhang of Southwest J. Birch and Fan R. K. Chung. Special Sessions of selected 20-minute Missouri State University. The sessions Candidates elected to three-year papers. The topics and the names and on Combinatorics and Analysis were terms on the Nominating Committee are affiliations of the organizers were as chaired by George Matthew of South­ Vaughan F. R. Jones, Nancy K. Stanton, follows: west Missouri State University. and Jerome A. Goldstein. Harmonic Analysis, NAKHLE HABIB Committee. Clayton Sherman of All terms begin on February 1, 1993, ASMAR and STEPHEN JOHN MONTGOM­ Southwest Missouri State University su­ except those for the Nominating Com­ ERY-SMITH, University of Missouri, Co­ pervised local arrangements. mittee, which commence January 1, lumbia. Andy R. Magid 1993. The report of the tellers may Combinatorics and Discrete Geom­ be obtained by contacting the Secretary Associate Secretary etry, MARGARET M. BAYER, University of the Society. The full list of the Coun­ Norman, Oklahoma of Kansas, Lawrence. cil, the Trustees, and the Members of the Partial Differential Equations, WENG­ Executive Committee will appear in the The October-November Meeting XIANG CHEN and SHOU CHUAN Hu, February 1993 issue of the Notices. in Dayton Southwest Missouri State University. The 876th meeting of the Society was Robert M. Fossum Commutative Algebra, WILLIAM J. held in Dayton, Ohio at Wright State Secretary HEINZER and CRAIG HUNECKE, Pur­ University on October 30 and 31 and Urbana, Illinois due University, and KISHOR M. SHAH, November 1, 1992. There were 362 Southwest Missouri State University. registrants, including 266 members of The March Meeting The Geometry of Connections, LUIS the Society. In Springfield HERNANDEZ, University of Chicago, Invited Addresses. By invitation of The 873rd meeting of the Society was and ERNST RuH, Ohio State University. the Central Section Program Committee, held in Springfield, Missouri at South­ Lie Algebras, Cohomology, and New there were four invited addresses. The west Missouri State University on March Applications to Quantum Mechanics, speakers, their affiliations, and their ti­ 20 and 21, 1992. There were 347 reg­ NIKY KAMRAN, McGill University, and tles were as follows: MARTIN GOLUBIT­ istrants, including 236 members of the PETER J. OLVER, University of Min­ SKY, University of Houston, Symmetry Society. nesota. and Chaos; JONATHON I. HALL, Michi­ Invited Addresses. By invitation C* -algebras and Algebraic Topol­ gan State University, Finite methods in of the Central Section Program Com­ ogy, ELLEN MAYCOCK PARKER, DePauw infinite groups and discrete geometries, mittee, there were four invited ad­ University. Loms H. KAUFFMAN, University of Illi­ dresses. The speakers, their affiliations, Semigroups, BORIS M. SCHEIN, Uni­ nois at Chicago, From knots to quantum and their titles were as follows: ALEXAN­ versity of Arkansas. field theory and back; J. TOBY STAFFORD, DER EREMENKO, Purdue University, Re­ Fourier Analysis, VERA B. STANOJE­ University of Michigan, Ann Arbor, cent progress in value distribution the­ VIC, Southwest Missouri State Univer­ Noncommutative graded algebras and ory; JULIA KNIGHT, University of Notre sity. projective geometry. The speakers were

68 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ""lllllllllllllillllllllllllllillllllllllllllillllllllllllllillllllllllllllilllllllllllllliiiiiiiiiiiiiiBIIII""""~""~•-·•••••~··•••m•••••••••~•~•••••••• •••••••••••-•••••••••••••··~··••••••••••••-•••••••••••••••••••••••••••••••••••••• AMS Reports and Communications introduced by Lawrence Turyn, Daniel SVOBODY, Wright State University, and University of Cincinnati. Frohardt, Josef Przyticki, and Timothy SRDJAN D. STOJANOVIC, University of Contributed Papers. There were Hodges, repectively. Cincinnati. four sessions of contributed papers. Special Sessions. By invitation of Combinatorics and Graph Theory, The first session on Graph Theory was the same Committee, there were twelve ANTHONY B. EVANS and TERRY A. Mc­ chaired by Ann Farrell of Wright State Special Sessions of selected 20-rninute KEE, Wright State University. University. The second session on Graph papers. The topics and the names and Differential and Integral Equations, Theory and the session on Algebra were affiliations of the organizers were as MUHAMMAD N. ISLAM, University of chaired by David Miller of Wright State follows: Dayton, and LAWRENCE TuRYN, Wright University. The session on Analysis was Hyperbolic Manifolds, COLIN C. State University. jointly chaired by Steve Hoffman and ADAMS, Williams College, and ARA S. Knots and Toplogical Field Theory, Carl Maneri, both of Wright State Uni­ BASMAJIAN, University of Oklahoma. LoUis H. KAUFFMAN, University of Illi­ versity. Quantum Groups and Regular Al­ nois at Chicago. Committee. James T. Vance, Jr., of gebras, CAROLYN A. DEAN and J. TOBY Riccatti Equations and Transport Wright State University supervised local STAFFORD, University of Michigan, Ann Theory, HENDRIK J. KUIPER, Arizona arrangements. Among the amenities he Arbor, and TIMOTHY J. HODGES, Univer­ State University, and TAPAS MAZUM­ arranged were special guest accounts on sity of Cincinnati. DAR, Wright State University. the Wright State University computer to Operator Theory and Operator Al­ Topology of Affine Hypersurfaces allow meeting participants to remotely gebras, JOANNE M. DoMBROWSKI and and Related Number Theory, ANATOLY log on via the Internet to their home RICHARD MERCER, Wright State Univer­ S. LIGOBER, University of Illinois at machines. sity. Chicago, and STEVEN SPERBER, Univer­ Groups and Geometries, DANIEL E. sity of Minnesota, Minneapolis. FROHARDT, Wayne State University. Set-Theoretic Topology, JoE D. MASH­ Andy R. Magid Control Theory and Partial Differen­ BURN, University of Dayton. Associate Secretary Oklahoma tial Equations, LoP FAT Ho and THOMAS Function Theory, C. DAVID MINDA, Norman,

ADVANCES IN SOVIET MATHEMATICS Topics in Nonparametric Estimation R. Z. Khasminski't, Editor Volume 12

This book contains papers presented at the Seminar on Mathematical Statistics held at the Institute for Problems of Information Transmission of the Academy of Sciences in the former Soviet Union. The topics covered include density, regression, image estimation, adaptive estimation, stochastic approximation, median estimation, sequential experimental design, and large deviations for empirical measures. This collection is distinguished by the high scientific level of the papers and their modern approach. This book will be of interest to scientists and engineers who use probability and statistics, to mathematicians and applied statisticians who work in approximation theory, and to computer scientists who work in image analysis. 1991 Mathematics Subject Classification: 60, 62, 68 ISBN 0-8218-4111-4, 150 pages (hardcover), October 1992. Individual member $59, List price $99, Institutional member $79 To order, please specify ADVSOV/12NA

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JANUARY 1993, VOLUME 40, NUMBER 1 69 Miscellaneous

Personals Gail A. Schweiter, of Daniel H. VIsiting Mathematicians Cornelius 0. Horgan, of the University Wagner Associates, died on April 23, Supplementary List of Virginia, Charlottesville, was named 1992, at the age of 34. She was a Mathematicians visiting other institu­ a Fellow of the American Society of member of the Society for 12 years. tions during the 1991-1992 academic Mechanical Engineers (ASME). MichaeiJ. Seymour, of the Univer­ year have been listed in recent issues sity of New Hampshire, died on April of the Notices: October 1992, p. 960; 16, 1992, at the age of 39. He was a November 1992, p. 1129, and December Deaths member of the Society for 2 years. 1992, p. 1291. Ilya Bakelman, of Texas A&M Univer­ Earl W. Swokowski, of West Allis, Karl Barth (U.S.A.), University sity, died on August 30, 1992, at the age Wisconsin, died on June 2, 1992, at the College, England, Complex Analysis, of 63. He was a member of the Society age of 66. He was a member of the 1193-8/93. for 12 years. Society for 40 years. R. Miron (Romania), University of Peter A. Ruymgaart, of Leider­ Janet D. Thomas, of Rydal, Penn­ Tsukuba, Lagrange Geometry and Ap­ dorp, The Netherlands, died on June 11, sylvania, died on October 21, 1992, at plications, 4/92-5/92; and University 1992, at the age of 66. He was a member the age of 87. She was a member of the of Haifa, Differential Geometry, 5/92- of the Society for 26 years. Society for 59 years. 6/92.

Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications Donald St. P. Richards, Editor

This volume is based largely on lectures presented at a Special Session at the AMS meeting in Tampa, Florida, in March 1991 , which was devoted to hypergeometric functions of matrix argument and to fostering communication among representatives of the diverse scientific areas in which these functions are utilized. Accessible to graduate students and others seeking an introduction to the state of the art in this area, this book is a suitable text for advanced graduate seminar courses, as it contains many open problems.

1991 Mathematics Subject Classification: 33 ISBN G-8218-5159-4, 259 pages (softcover), November 1992 Individual member $26, List price $44, Institutional member $35 To order, please specify CONM/138NA

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

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

ORDINARY MEMBERS Yordan Perrov Miahev, Higher Peter N Zhevandrov, Center of Jeffrey A Dietrich Busuyi John Adewale, Osun-State, Institute of Forestry, Sofia, Investigations & Advanced Melissa Elaine Erwin Nigeria Bulgaria Studies, Mexico Chanelle Maria Jolly Vladimir Mikhalev, New York, NY Mara Alagic, South Burlington, VT Sheela Brammaji Kolluri Shivendu Mittal, Haryana, India Anthony M Barnes, Honolulu, HI Bret A Longman Merwin Gordon Beavers Jr, Abraham Neyman, State Univ of New York at Stony Brook RECIPROCITY MEMBERS Thomas Edward Morgenstern Clarksville, AR Hernando C Ombao Ping-Ying Chang, Berkeley, CA Iscander Nezhmetdinov, Kazan, Rep Australian Mathematical Society Phyllis Peterson Rahul Chattergy, Honolulu, HI of Russia Matteo J Paris, Cambridge, MA Michael S J Johnson RemaRaman Shuping Chen, Zhejian Univ, Erin Christine Pleva, Grapevine, TX Deutsche Mathematiker-Vereinigung Hangshou, People's Republic of Grzegorz Rempala Milja R Poe, Bedford, China MA e. V. Christine M Shutters Lisa R Pressler, Canton, MI Kay R DeVicci, Morristown, NJ Werner Varnhorn Cecelia St Anne Toulson Parthasarathi Raghavan, New York Terry Downs, Princeton, NJ Korean Mathematical Society Michelle Lynn Younker Univ Kurt 0 Ebner, Schenectady, NY Chunghyuk Kang John J Repcheck, Addison-Wesley Bryn Mawr College A I Filinkov, Ekaterinburg, Rep of Publishing Company, Reading, London Mathematical Society Abigail L Kay Russia MA Nicolaas P Landsman Hang Gao, Northeast California State University, Long Normal Univ, Albert Schwarz, Univ of California Jilin, People's Republic of Mathematical Society of Japan Beach China Davis Robert M Ginns, Polly W Sy Raymond Badalian New York, NY Jack L Shira, San Francisco, CA Yoshio Yamada James R Taylor A Charles Goetz m, Bridgeport, CT Vladimir Shpilrain, Technion-Israel Gildardo Guzman, Santander, Institute of Technology, Haifa Norsk Matematisk Foreningros Carnegie Mellon University Colombia J Eric Sims, Huntsville, TX Trygve Johnsen Sergio E Gutierrez Olga A Hachay, Institute of Vaclaw Snavsel, Palacky Univ Societe Mathematique Suisse Case Western Reserve University Geophysics, Ekaterinburg, Rep Olomouc, Czechoslovakia Max Albert Knus Barbara Haas Margolius of Russia Emily H Sprague, Manchester Jeffrey Allan Hall, Bantam, CT Center, VT Sociedad de Matematica de Chile Central Missouri State University Andrew G Jones, Sheffield Univ, Patricia A Startz, Runge, TX Carlos Lizama Keith Anthony Rogei:s England Jozef Joachim Telega, Polish Unione Matematica ltaliana Cheryl W Winter Rumena Kaltinska, Bulgarian Academy of Sciences, Warsaw Gabor Korchmaros Clarion University Academy of Sciences, Sofia Gulsen Tokat, Istanbul Technical Wiskundig Genootschap Dipendra N Bhattacharya Zbigniew Kamo, Warsaw Univ, Univ, Thrkey Leendert J van Gastel Bialystok, Poland Christian Holger Valqui-Haase, Colorado College Henry J Kelly, Flushing, NY Lima, Peru Eric B Schwent Myoung-Nyoun Kim, Seoul National Helmat Voelklein, Univ of Florida, Colorado State University Univ, Korea Gainesville Jikyong C Adair Daniel Laks, Washington, NY Vadim Von Brzeski, Gilroy, CA NOMINEE MEMBERS David De Long Jiyue J Li, Goleta, CA Michael M Walker, Twentynine American University Miles R Porter Xi Lin, Jimei Navigation Institute, Palms, CA Constantinos D Charitou Xiamen, People's Republic of Shu Pei Wang, East China Normal Hippolyte P Fofack Brian E Skahill China Mark S Vincent Univ, Shanghai, People's Angelo State University Qing Rong Liu, Northwest Univ, Republic of China Louis D Kovari Duquesne University Xian, People's Republic of China Zvi Wiener, Weizmann Institute of John Robert Nichols Xiaoping Liu, Univ of South Florida, Science, Rehovot, Israel Arizona State University Tampa Cong Xin Wu, Harbin Institute of Matthias Klaus Gobbert East Carolina University David K Livingston, Personal Technology, People's Republic Kong Hong Qasim Y Abuhantash Care Health Management, of China Benjamin R Kuehn Zeyi Hua Champaign, 1L Ti Jun Xiao, Yunnan Normal Univ, Kathleen McCool Deborah E Kellog Dong Yang Long, Zhongshan Univ, Kunming, People's Republic of Derar Shafie Serhan Sarah Jane Pulley Guangzhou, People's Republic of China James Douglas Stanley Phyllis Rae Sawyer China Huan Min Yao, Harbin Institute of Erica Ryder Wogarnan Kurt Mehlhorn, Max Planck Institute Technology, People's Republic Bowling Green State University for Informatik, Saarbrucken, of China Marcus Alberto Agustin Eastern Washington University Germany D V Yurev, Moscow, Rep of Russia Clarke Lawrence Cummings David D Turner

JANUARY 1993, VOLUME 40, NUMBER 1 71 ...... _...... M··~········••••m·.m.w••••c••m•,••• ········································ New Members of the AMS

Emporia State University David Brian Steinberg Rockford College Karen L Scott Jeffrey Lee Hum James D Strange Keiili D White Jo Ann Withers Chung-Yen Shih Yuehui Tao SUNY at Buffalo Wen Xu Florida State University Cheryl A Thompson Bettina Breunig Tufts University Laura A Boehm Karen Marie Trujillo Constantin Gonciulea Peter J Ciccarelli Sylwia Felcyn Wei Zhang Christopher John Grasso Fuchun Dong Lucius R Junevicus North Dakota State University, Fargo Jyh-horng Jeng Karen G Santoro Pamela Kroeger Todd R Marzinske Chas B Kullmann Debora F Tomaselli Konstantine Kurbatskii Svyatoslav V Sharapov Danilo Lawvere Tulane University Yangang Li Northeast Missouri State University Jun Ling Bisong Tao Steve Powley Constantin-Dan Cazacu John Currey Meerse University of Alabama-Tuscaloosa Natalya Trinko Philip Gerard Jones Fusheng Nie Ramana Andra Chihiro Oshima Karen Therese Watson Northern Illinois University Chacko Barrock Richard S Wilder George Mason University Brian Lee Adcock Michael S Brown Maria C Collier Depeng Bi Seton Hall University Xuming Chen Idaho State University Esther M H Billings Patrick J Duggan Randall L Harrison John J Brunette Lauren Sara Grubb Patricia P Hulsen Quan Ouyang Scott Stephon Searey Jenny E Jones Costanza Saliani Natesan Raghuram Indiana University at Bloomington Lori F Jones Shippensburg University of Pa Gong Song Jie Tao Cheryl D Juengel Liam R Keigher Mark P Horrell Joseph Brian Thomas William K Koerber Steven James Kifowit South Dakota State University Weichang Wang Vittorino Pata David B Klanderman Xiao Rong Feng Fan Xu Jacqueline S Roberts Amy Louise Landolt Southern Illinois University, Andrius Tamulis Ishita Majumdar Carbondale University of Arizona Adele Zucchi Joy Ann McPheters Jeffrey Thomas Bonn Hyunju Oh Angela Celeste Moore Steven A Wexler Indiana University, Southeast Sean T Borman William David Trunkhill Aaron Daniel Koch Robert A Brown University of Colorado, Boulder Guosheng Wang Cappelletti Sarada D Ganti Indiana-Purdue University, Fort Bryan J Northwestern University Robert J Matuschek Jr Wayne Susan E Cashin Christopher L Cox Steven R Raasch Mark C Cutshaw Klaus Ender Antonio Garcia Hakshing Ma Devon Reimer University of Colorado, Colorado David J Hilbert Sherry L Scarborough Weber Toney L Stirewalt Springs Kewen Yao Greg A Wade Randolph Scott Crupper Mankato State University Ohio Wesleyan University Hanping Wang Michele K Davis Timoiliy P Altier Shriram Krishnamurthi Sengfeng Xie Murali M Krishna Paul J DeMorett Methodist University William Michael Rainaldi Patrick Jerome Dempsey Princeton University Southern Scott James Everman Anton G Kamaukh Alec Y Polakov University of Connecticut, Storrs Lisa Jean Miller J onailian Pakianailian Southwest Missouri State University Christine Amorossi Chrisopher Smyili Simons Gary Lee Boyd David E Molnar Memphis State University Derek Alan Smiili Michael E Cagle Talvinder Singh Chawla University of Dallas Julie A Millett Umamaheshwari Ramamurthy Purdue University Paul M Flyrtn Wasfi Ghassan Al-Khatib Gary L Stafford Montana State University University of Delaware Youngjoon Cha University Joseph S Dennehy Southwest Texas State Evans A Momanyi Joseph Chan Dana Fay Izard Simon King James C Rothwell Arthur J Lindeman II Edward C McCrone Stephen F Austin State University University of Florida Randy P Lucero Kyle L Riley Bryan E Adams Jason Earl Abernailiy Naia Nenkova Martcheva Cary Paul Evanoff Naval Postgraduate School Thad W Beavers Manochehr Misaghian Moyeen Uddin McDonald Muhammad Zhaowei Du Patrick James Victor Jacob Olesen Stetson University Christopher Erhart Elmer New Mexico State University, Las Siu Hung Tang Julie Lynn Plocar James D Friess Cruces Alexandre B Tchernev A & M University University of Idaho John C Chamberlin Jin Zhang Texas B Emery David E Frey Jeff D Almeida David Reed College Bradley H Merrell John B Cowgill Daniel J Gagliardi Michael Jeffrey Drinen David L Harrar II Laura A Merrell University of Illinois at Rensselaer Polytechnic Inst Jing He Roy A Strader Urbana-Champaign Jennifer A Blue Suzanne M Hill Texas Tech University Ross A Christofferson Chen Huang Rice University Mitchell L Allen Anna S Fiehl er Chun-Sheng Huang Amy Beth Christner Kumari Chandrawansa Geri Hendrickson Hui-Chuan Huang Simrat M Ghumman Michael L Clark Hui-Chen Ho Diane M Martinez Ming Li Deanna L Dick Hung-Jen Hsll Gabrielle M Mcintosh David Paul Phillips Molly Mae Dickens Boris Iskra Richard R Reynolds Igor P Prokhorenkov Ben R Neelley Mary Catherille Joyce Denette L Sinclair Jun Tian Timoiliy H Orsak Soon-Yi Kang

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

William Kinney Patricia D Snell University of Toledo Sunu Kartik0 YJhsiang Liow Yuan Lou Jennifer S Stephens Chaojie Wang Dae Hyun Paek University of Missouri-Columbia Irene C Vasquez University of Vermont Gary S Salsbery Marc A Bledsoe Michael D Wesselink Daniel J Murphy Lawrence Keng Urn Tan Ronnie Dickson University of Saskatchewan University of Wise, Stevens Point Dekang Yang Amy R Feltenberger Sumedha Chaudhari Michelle Lynn Kollross University of Kansas Craig L Haile Bin Jian Chen Laurie L Wilken Steven C Abele Mark C Lammers Charles Nosakhare Edediri University of Wisconsin, Milwaukee Iaroslav Semenovytch Krylionk Andrew Boland Blair Charles E Less Mouchumi Bhattacharyya Paulhus Ai-jun Gao Christina Anne Morlan Marc McBeth Vassiliki Binga Enrique Gonealo Reyes Mark A Grindol Atsushi Nakamoto Jooyong Choi Scott A Smith Kendall Dean Ponder Chang-Cheng Yang Wiebke S Diestelkamp Qingde Yang Chao Yang Annela Rammer Hong Li Donald W Rogers Jr University of Manitoba University of Southern California LeiLu Rebecca J Schofield Yue Dai Joerg Raichle Guoqing Shao Amy Elizabeth Scott Gholamhossein Iraghi Achaiyar Ramakrishnan Mark J Waldschmidt Don Steiger Moghaddam Paul A Scholtz Vanderbilt University Deanna Wasman Mo Liang Harald Edwin Schwer Aaron C Beshears Michael Wickey Wan Lin Hidayathullah Ali Sulaiman Hoseung Lee Li Zhou MeiMeng Fengzhu Sun Xiaoyu Liu Dabin Wang University of Missouri-St Louis Miroslav Svetoslavov Tanushev Virginia Commonwealth University Jiang Wang University of Maryland Baltimore Chengfang Hang Jacqueline M Blei Bastian Wartenberg County Theresa L Maxwell Clifton E Webb Gong Chen Caleb R Miller Ping Wen Yan Zhuang Wake Forest University Peiyi Liu University of N Cat Wilmington Misha E Clark Zhiyuan Lzang Robin Leigh Glover University of Southern Mississippi Eric J Clymer Roman Sznajder Valerie J Melvin Ruhong Cai Janet Louise Drake Detong Zhang Yaqi Yang Nancy McBride Hartfield Kenneth M Elliott Yuming Zhang University of Nevado, Las Vegas Hongyu He Aaron Alan Sumner Haomiao Jia University of Minnesota-Duluth Ted L Butts Kelly A Vickers Zhiwu Mo John P Caouette Helena Murvosh Washington University Jian Chen Ingrid G Stewart University of Southwestern Louisiana Michelle Y Penner Qiongwen Chen Sally L Stewart Mark J Broussard Nathan K Risk Mark A Cotter Aimin Jiang University of New Hampshire Zhi-feng Zhang Bin Fu Shiying Ning M Ottone West Virginia University Duane J Gajewski Suzy Catherine E Wier University of Texas at Arlington Xiao-Ping Hu Isao Hiyane Donna L Flint Eric L McDowell Lynda B Hoffmaster University of North Dakota, Grand Hsiengwen Huang Patricia Michelle Perkins Sangho Jie Forks Stephanie L LaKeyy Temba Shonhiwa Jennifer A Kohn Robert L Fixen Alan D Walter Guoqing Weng Eric A Nielsen David L Harpster Haw-Dai Yang Chang Peng Rebecca M Maki Western Carolina University Zbigniew Jan Wdowiak Cheryl Kay Pankow University of Texas at Austin Karl E Hallowell University of Minnesota-Minneapolis Michael J Petty Michael Chad Oehrtman Roger C Hunt Tracey L Parks Ellen Bonner Oliver April Jane Giesler Michael J Simmers

JANUARY 1993, VOLUME 40, NUMBER 1 73 INSTITUTIONS NOT SUBJECT TO U.S. LAWS may be required to execute and submit a copy of this form with the text of recruitment advertisements for the Notices (see Policy Statement below). Publication of recruitment advertisements not accompanied by the completed form may be delayed or denied.

Em~oymentM------(Name oflnstitution) (City) (Country)

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

(Signature) (Date)

Name (please print) (Title)

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

AMS Policy on Recruitment Advertising

No listing for a position will be printed if it expresses or implies any preference, limitation, specification, or discrimination based on age, color, race, religion, sex, or national origin in contravention of any federal or state statute prohibiting discrimination in employment on the basis of these criteria The publisher reserves the right to edit any listing prior to publication which does not conform with federal or state law on discrimination in employment. All employers in the United States are required to abide by the requirements of Title VII of the Civil Rights Act of 1964, announcing a national policy of equal employment opportunity in private employment. without discrimination because of color, race, religion, sex, or national origin. All U.S.listings are accepted with the understanding that the employer complies with federal requirements. Advertisers not subject to U.S. laws may be required to sign a statement that they do not discriminate in employment on grounds of age, color, race, religion, sex, or national origin. Applicants should be aware that institutions outside the U.S. may not be legally bound to conform to these or similar requirements and the AMS cannot assume responsibility for enforcing compliance. Applicants are advised to inform themselves of conditions that may exist at the institutions to which they apply. In particular, readers should note that the Equal Employment Opportunity Act (42 U.S.C., §§2000e et seq.), which prohibits discrimination in employment on the basis of race, religion, sex, or national origin, contains (in §2000e-1) an exception from the provisions of the Act for any religious corporation, association, educational institution, or society with respect to employment of individuals of a particular religion to perform work connected with the carrying on by such corporation, association, educational institution, or society of its activities. The Age Discrimination Act of 1967 (29 U.S.C., §§621 et seq., as amended), makes it unlawful for an employer to discriminate against any individual between the ages of 40 and 70 because of age; Thus it is legal to seek as an employee someone who is "over 30,'' but not one "over 50"; neither is it legal to express a preference for someone who is "young," or is a "recent graduate," since the latter tend (on statistical grounds) to be young.

74 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ...... ______Classified Advertisements

SUGGESTED USES for classified advertising are positions available, books or lecture notes for the position is filled. CSU San Marcos is an sale, books being sought, exchange or rental of houses, and typing services. Affirmative Action/Equal Opportunity Employer. THE 1993 RATE IS $65 per inch on a single column (one-inch minimum), calculated from the The University has a strong commitment to the top of the type; $35 for each additional Ib inch or fraction thereof. No discounts for multiple ads or principle of diversity and, in that spirit, seeks a the same ad in consecutive issues. For an additional $10 charge, announcements can be placed broad spectrum of candidates including women, anonymously. Correspondence will be forwarded. members of minority groups and people with Advertisements in the "Positions Available" classified section will be set with a minimum disabilities. one-line headline, consisting of the institution name above body copy, unless additional headline copy is specified by the· advertiser. Advertisements in other sections of the classified pages will be set according to the advertisement insertion. Headlines will be centered in boldface at no extra charge. Classified rates are calculated from top of type in headline to bottom of type in body copy, including lines and spaces within. Any fractional text will be charged at the next 1b inch rate. Ads HUMBOLDT STATE UNIVERSITY (HSU) will appear in the language in which they are submitted. Prepayment is required of individuals but not of institutions. There are no member discounts Applications are invited for a temporary (one for classified ads. Dictation over the telephone will not be accepted for classified advertising. or more expected) one-year, full- or part-time, DEADLINES are listed on the inside front cover or may be obtained from the AMS Advertising assistant professor position for Fall 1993. Can­ Department. didates must possess an earned doctorate in U. S. LAWS PROHIBIT discrimination in employment on the basis of color, age, sex, race, a mathematical science at the time of ap­ religion or national origin. "Positions Available" advertisements from institutions outside the U. S. pointment, and must present experience or cannot be published unless they are accompanied by a statement that the institution does not training in either mathematical modeling, sta­ discriminate on these grounds whether or not it is subject to U. S. laws. Details and specific tistics, or mathematics education (elementary wording may be found near the Classified Advertisements in the January and July/August issues school teacher training preferred) with a com­ of the Notices. mitment to teaching excellence. HSU, located SITUATIONS WANTED ADVERTISEMENTS from involuntarily unemployed mathematicians on the California north coast, has an active are accepted under certain conditions for free publication. Call toll-free 800-321-4AMS (321-4267) mathematics faculty, a strong undergraduate in the U.S. and Canada for further information. major, and a masters program in mathemati­ SEND AD AND CHECK TO: Advertising Department, AMS, P. 0. Box 6248, Providence, cal modeling of environmental systems. Direct Rhode Island 02940. AMS location for express delivery packages is 201 Charles Street, inquiries to Search Committee, Department of Providence, Rhode Island 02904. Individuals are requested to pay in advance, institutions are not Mathematics, Humboldt State University, Ar­ required to do so. AMS FAX 401-455-4004. cata, CA 95521-4957. Application deadline 15 February 1993. HSU is an EO/AA employer.

is negotiable, preferably beginning by 7/1/93. ALABAMA A review of applications and materials will .begin on March 1, 1993 and will continue until OCCIDENTAL COLLEGE the position is filled. Applicants should submit a AUBURN UNIVERSITY Los Angeles, California Dean Search vita and the names of five references to: Dr. June Henton, Chair College of Sciences and Mathematics Applications are invited to a tenure-track posi­ Search Committee tion in the Department of Mathematics at the The Auburn University College of Sciences and 21 0 Spidle Hall assistant or associate professor level. Mathematics invites applications and nomina­ Auburn University, AL 36849 Excellence in teaching and substantial pro­ tions for the position of Dean. Auburn University Auburn University is an Affirmative Action, fessional achievement are the major expecta­ is the 1862 land-grant institution located in Equal Opportunity Employer. Women and mi­ tions. The department is involved in curricular east central Alabama. It enrolls approximately norities are encouraged to apply. reform and encourages innovative teaching. 21,500 students on the Auburn campus. The The normal teaching schedule is 5-6 courses College of Sciences and Mathematics consists per year. New faculty members are currently of the departments of Botany and Microbiology; released for one course during the initial year. Chemistry; Discrete and Statistical Sciences; CALIFORNIA Some institutional support for extended leaves Geology; Mathematics; Physics; and Zoology is available. and Wildlife Sciences. CALIFORNIA STATE Occidental College is a selective private with The Dean is the chief executive officer of UNIVERSITY SAN MARCOS college of the liberal arts and sciences the college and reports directly to 1he Provost. 1650 undergraduate students, a college faculty General responsibilities include: · California State University San Marcos, the of 133, and a mathematics faculty of nine. 1) provide creative leadership for teaching, newest campus in the CSU, seeks a Ph.D. Occidental is located in northeast Los Angeles, research, and extension programs; · mathematician in algebraic geometry, analytic easily accessible to USC, UCLA, and Caltech. 2) promote the academic unit, through ac­ geometry, computational geometry, differential Salary is competitive. An excellent benefits tivities including fundraising, with alumni and geometry, finite geometry, geometric analysis, package includes a choice of health care plans, external groups; or a related field of geometry. This entry-level, tuition grants for children of faculty, and a 3) effectively represent the position of the tenure-track Assistant Professor position will mortgage subsidy program. College faculty to the central administration; begin in August 1993. This position is subject to Completed applications must include a cur­ 4) continue to lead the College toward final administrative authorization. CSUSM seeks rent resume and three letters of reference (at national prominence. an individual with strong academic preparation least one evaluating teaching performance and Qualifications include: earned doctorate in who has an interest in teaching undergradu­ potential). Please include a clear statement of field appropriate for full professor and tenure ates. An application consists of a statement commitment to teaching in a liberal arts college in one of the departments in the College; of interest, a complete resume, and at least environment as well as indicating professional excellence in research and teaching; strong three letters of reference which should com­ goals. All materials should be received by Febru­ administrative and leadership capability, includ­ ment on the applicant's credentials in teaching, ary 16, 1993. Address all materials of Faculty ing effective personnel management and com­ research, and service. Applications should be Search Committee, Department of Mathemat­ munication skills; commitment to Affirmative sent to: Mathematics Search Committee, Cali­ ics, Occidental College, 1600 Campus Drive, Action/Equal Employment Opportunity. fornia State University San Marcos, San Marcos, Los Angeles, CA 90041. Twelve-month salary is competitive and com­ California 92096-0001. Review of applications Occidental College is an Equal Opportu­ mensurate with qualifications. Employment date will begin January 25 and will continue until nity/Affirmative Action Employer . and encour-

JANUARY 1993, VOLUME 40, NUMBER 1 75 ------r ···mmm••--···m·-···m••---··•·•··•····•···•··•·•·•···•••············ ...... Classified Advertisements

ages applications from women and ethnic mi­ Chair of the Recruitment Committee at the and arrange for three letters of recommendation norities. above address. We should receive the ma­ to be sent to: H.F. Kreimer, Chairman, De­ terial no later than February 15, 1993. The partment of Mathematics B-154, Florida State University of California is an Equal Opportu­ University, Tallahassee, Florida 32306·3027. nity/Affirmative Action employer committed to The deadline for applications is February 1, UNIVERSITY OF CALIFORNIA, BERKELEY excellence through diversity. 1993. Fellowships In Mathematics Florida State University is an affirmative and Molecular Biology action/equal opportunity employer. Women and minorities are encouraged to apply. The Program in Mathematics and Molecular CONNECTICUT Biology has graduate and postdoctoral fellow­ ship support available. Current topics in the UNIVERSITY OF CONNECTICUT UNIVERSITY OF NORTH FLORIDA Program include geometry, topology, and se­ AT AVERY POINT quence analysis of DNA, molecular dynamics, Dept. of Mathematics Assistant Professor of Mathematics and Statistics and mapping functions and algorithms for DNA Instructor in Mathematics and protein structure prediction. Other areas Applications are invited for an anticipated full­ will be considered. Fellowships can be .held at time position at the Assistant Professor level The Department of Mathematics and Statistics any university or college in the United States. for the Avery Point campus. The Avery Point invites applications for a nontenure-track renew­ Awards made assuming continuation of fund­ campus is located in the Groton-New London able position at the Instructor rank beginning ing. Deadline for Applications: March 1, 1993. area. A Ph.D. in Mathematics, experience in August 1993. Candidates must have a Masters Women and minorities are encouraged to apply. teaching at the college level, demonstrated tal­ degree in Mathematics or the Mathematical Apply to: PMMB, 103 Donner Lab, Univer­ ent in teaching undergraduates, and evidence Sciences and a history of excellent teaching sity of California, Berkeley, CA 94720. Email: of ability to contribute to the research mission at the undergraduate level. Additional consid­ sylviaj @violet.berkeley.edu. of the department are required. Salary will eration may given to experience with student be competitive, commensurate with qualifica­ mathematics organizations. The Department of­ tions. Screening will begin February 1, 1993, fers the B.A. and B.S. degrees in Mathematics and continue until the position and Statistics and the M.A. degree with con­ UNIVERSITY OF CALIFORNIA, IRVINE is filled. Send curriculum vitae and have at least three let­ centrations in Mathematics and Statistics. The Department of Mathematics ters of reference sent to: Professor Jerome University of North Florida is a growing state Irvine, CA 92717 Neuwirth, Department of Mathematics, Uni­ university with approximately 9,000 students. Degree programs are offered in the traditional Applications are invited for possible regular versity of Connecticut, U-9, 196 Auditorium Rd., Storrs, CT 06269-3009. We encourage ap­ areas. Send applications with vita and three faculty positions in the following four areas of letters of recommendation by March 5, 1993 research: 1) applied and computational math­ plications from minorities, women, and people with disabilities. (Search #3A111) to: Dr. Jlngcheng Tong, Search Committee ematics; 2) geometry and topology (includes Chairperson, Department of Mathematics geometrical analysis); 3) analysis and POE and Statistics, University of North Florida, (including mathematical physics); 4) algebra 4567 St. Johns Bluff Road, South, Jack­ and number theory (includes algebraic and FLORIDA sonville, FL 32224-2645. THE UNIVERSITY arithmetic geometry). Very strong promise in OF NORTH FLORIDA IS AN EQUAL OPPOR· research and teaching required. Positions are FLORIDA INTERNATIONAL UNIVERSITY TUNITY/AFFIRMATIVE ACTION EMPLOYER. budgeted at the assistant professor level. Ap­ MINORITY AND WOMEN CANDIDATES ARE plicants should send a resume, reprints and The Department of Mathematics announces ENCOURAGED TO APPLY. preprints, and (for assistant professor positions) tenure track positions beginning August 1993. dissertation abstract and ask three people to These positions are usually at the beginning send letters of recommendation to: Chair of the Assistant Professor level. Candidates must Recruitment Committee, at the above address. have a Ph.D. in Mathematics and a commitment THE UNIVERSITY OF SOUTH FLORIDA We should receive the material no later than to research · and quality teaching .. Qualified Department of Mathematics February 15, 1993. The University of Califor­ candidates in all areas of Mathematics will be We invite applications for two tenure-track po­ nia is an Equal Opportunity/Affirmative Action considered. sitions at the Assistant Professor level effective employer committed to excellence through di­ Teaching load consists of no more than August 1993, contingent on availability of funds. versity. five 3-credit courses per academic year. Send Applicants must have or expect to have a Ph.D. resume and arrange for 3 letters of recommen­ in mathematics upon assuming the position, dation to be sent to: Recruitment Committee, and must show evidence of strong research Department of Mathematics, UNIVERSITY OF CALIFORNIA, IRVINE Florida Interna­ potential. Candidates demonstrating research tional University, Miami, FL 33199. Department of Mathematics experience beyond the Ph.D. are particularly en­ Florida International University is an equal couraged to apply. The duties include research Irvine, CA 92717 opportunity/affirmative action employer. It is a activity and both graduate and undergradu­ member of the State University system of Subject to availability of resources and ad­ ate teaching. We encourage applications from Florida, with approximately ministrative approval, applications are invited 23,000 students. the following fields: Analysis, Discrete Math­ The department offers bachelor's for several one or two year Visiting Assistant and master's ematics/Foundations of Computing, Numerical degrees. Professor positions in the following areas of Analysis, and Probability. Applicants must indi­ research: 1) applied and computational math­ cate in which of these four fields they wish to be ematics; 2) geometry and topology (includes considered, although outstanding candidates in geometrical analysis); 3) analysis and POE (in­ FLORIDA STATE UNIVERSITY other areas may apply. cluding mathematical physics); 4) algebra and Department of Mathematics The University of South Florida is the sec­ number theory (includes algebraic and arith· ond largest state university in the Southeast, metic geometry); 5) logic and set theory, 6) The department invites applications for a tenure­ with more than 34,000 students enrolled. The probability. Strong promise in research and track position of assistant professor. Require­ Mathematics Department offers B.A., M.A., and teaching is required. Salary $30,50Q-$38,800. ments include a Ph.D. and demonstrated ex­ Ph.D. degrees. Teaching load: six quarter courses per year. cellence in research and teaching. Appointment To apply, send a letter of application, with Applicant should send a resume, reprints and would begin August 1993. a curriculum vitae, and arrange to have at preprints, dissertation abstract and ask three Applicants should submit curriculum vita, list least three letters of recommendation sent to: people to send letters of recommendation to: of publications, statement of research interests, Search Committee, Department of Mathemat-

76 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY -·-··············-·-···· ·······················-····· ·········-·········-··-··-··-··········· ...... ""1111B!!!!!!llll!!.!!'!!!!!!gll!!"!!·. II• BBBBMBBB!!!!!!gllB!!i!!&l i!i ...... Classified Advertisements

to ics University of South Florida, 4202 Fowler NORTHERN ILLINOIS UNIVERSITY lent research potential, and a commitment Av~nue, PHY 114, Tampa, Florida 33620-5700 Department of Mathematical Sciences quality graduate and undergraduate teaching. in (email: [email protected], FAX: (813) Some preference may be given to applicants 974-2700). Anticipated assistant professorship with a spe­ algebra, scientific computing and applied statis­ Applications, which may be submitted by cialization in Numerical Differential Equations. tics. However, strong applicants from all areas email or FAX, must be submitted by February 1 , Ph.D. or equivalent and strong potential in re­ of mathematical sciences are encouraged to 1993. USF is an Equal Opportunity/Affirmative search and teaching required. Application (vita) apply. Action Employer and follows ADA guidelines. plus three letters of reference and descrip­ IUPUI is a comprehensive urban university tion of research program should be sent to: with over 28,000 students. The department Numerical Differential Equations Position, c/o offers programs of study leading to Purdue Professor William D. Blair, Chair, Department University B.S, M.S and Ph.D. degrees and of Mathematical Sciences, Northern Illinois Uni­ we anticipate significant growth in our faculty versity, DeKalb, IL 60115 by February 15, 1993. during the next few years. The university of­ GEORGIA. EO/AAE fers competitive salaries and provides excellent fringe benefits. Send resume and three letters UNIVERSITY OF GEORGIA of recommendation to Prof. Bart S. Ng, Chair, Department of Mathematics Department of Mathematical Sciences, IUPUI, NORTHERN ILLINOIS UNIVERSITY Athens, GA 30602 1125 E. 38th St., Indianapolis, IN 46205-2820. Department of Mathematical Sciences Closing date: February 1, 1993. Late appli­ The department has one or more tenure-tra~k cations will be considered until positions are Anticipated assistant professorship with ~ spe­ positions available for the 1993-94 academic filled. cialization in Ring Theory. Ph.D. or eqwval~nt year at the assistant professor level. The salary IUPUI is an Affirmative Action/Equal Oppor­ and strong potential in research and teaching will be commensurate with the applicant's abil­ tunity Employer. Women and minority candi­ required. Application (vita) plus three letters of ities and experience. The principle requirement dates are encouraged to apply. reference and description of research program is excellence in teaching and research. Some should be sent to: Ring Theory Position, c/o preference will be given to areas in which the.de­ Professor William D. Blair, Chair, Department partment is already represented. Send curncu­ of Mathematical Sciences, Northern Illinois Uni­ lum vitae and four letters of recommendation to versity, DeKalb, IL 60115 by February 15, 1993. John G. Hollingsworth, Head (address above). EO/AAE Applications will be accepted until March 15, IOWA STATE UNIVERSITY UGA is an Equal Opportunity/Affirmative 1993. Department of Mathematics Action Employer. WOLFRAM RESEARCH, INC. Subject to budgetary approval, there will be Mathematics Research and Development two tenure-track positions starting in August 1993. The positions will be full time during the We are looking for more top quality mathe­ 9-month academic year; they require a Ph.D. or maticians to join the Mathematics research and equivalent. ILLINOIS development team. We anticipate openings in One position will be in numerical analysis, several areas. At present, a position is available and will be at the assistant professor or asso­ NORTHERN ILLINOIS UNIVERSITY in our algebraic computation group. Applicants ciate professor level. The successful candidate Sciences Department of Mathematical should be able to work in a fast-paced en­ should have a strong interest in teaching at both vironment and be capable of interacting well undergraduate level. He or Anticipated assistant professorship with a spe­ the graduate and with mathematicians and others. Applicants an active research program cialization in Functional Analysis, preferably she should maintain should have a broad knowledge of mathemat­ analysis. The can­ with an interest in optimization theory. Ph.D. in some branch of numerical ics. Research experience in algebraic geometry, to apply for externally or equivalent and strong potential in research didate will be expected complex analysis, or a related field is desirable. Senior candidates should have a and teaching required. Application (vita) plus funded grants. Applicants should have considerable progra~­ and grants. Start­ three letters of reference and description of strong record of publications ming experience: knowledge of MathematiCS up funds for a workstation will be available. The research program should be sent !~: Function~! is required; experience with C is prefer~ed. A qualifications. Analysis Position, c/o Professor Wilham D. Bla1r, salary will be commensurate with Ph.D. in mathematics (or equivalent expenence) will be in mathemat­ Chair, Department of Mathematical Sciences, The second position is required. at the assistant professor level. Northern Illinois University, DeKalb, IL 60115 by ics education, Send resumes to: Attn: Personnel Depart­ should have strong interest and February 15, 1993. EO/AAE Candidates ment WoHram Research, Inc., 100TradeCenter qualifications in teaching both mathematics Drive', Champaign, IL 61820 or send email ~o and mathematics education, the latter at both [email protected]. Wolfram Research, Inc. IS the graduate and undergraduate level. Th~y an affirmative action, equal opportunity em­ should maintain an active research program 1n ployer. mathematics education. The duties will include NORTHERN ILLINOIS UNIVERSITY teaching, advising, supervision of student teach­ Department of Mathematical Sciences ers, and participation in regional and national math ed activities. with a spe­ Anticipated assistant professorship INDIANA Iowa State University is an Affirmative Ac­ Topology or Differen­ cialization in Algebraic tion/Equal Opportunity Employer. Women and and strong tial Geometry. Ph.D. or equivalent INDIANA UNIVERSITY-PURDUE minorities are encouraged to apply. required. potential in research and teaching UNIVERSITY The department will begin screening appli­ three letters of reference Application (vita) plus AT INDIANAPOLIS (IUPUI) cations January 15, 1993; applications will be of research program should and description Department of Mathematical Sciences accepted, however, until the positions are filled. Position, c/o be sent to: Geometry/Topology Applications (vita, description of research plans, Blair, Chair, Department Professor William D. The Department of Mathematical Sciences at and three letters of recommendation) should be Northern Illinois Uni­ of Mathematical Sciences, IUPUI is seeking applicants for two tenure-tra~k sent to Stephen J. Willson, Chair, Department 15, 1993. versity, DeKalb, IL 60115 by February positions to begin in Au~.ust. 1993. R~nk IS of Mathematics, Iowa State University, Ames, EO/AAE open depending on quahf1cat1ons. Apphca~ts Iowa 50011. must have an earned doctorate by the startmg date, either a strong research record or excel-

JANUARY 1993, VOLUME 40, NUMBER 1 77 ······························································"·~···················"·····················------Classified Advertisements

Selection is based on demonstration and KANSAS promise of excellence in research, teaching and MASSACHUSETTS innovative applications. KANSAS STATE UNIVERSITY Minority and women candidates are encour­ BOSTON UNIVERSITY Department of Mathematics aged to apply. The Johns Hopkins University is an Affirmative Action/Equal Opportunity Em­ The Department of Mathematics at Boston Subject to budgetary approval, applications are ployer: University invites applications for a position invited for several tenure track and visiting Applicants are asked to furnish a curriculum (pending final approval) in the area of Dynamical positions commencing August 18, 1993; rank vitae, transcripts Qunior applicants only), reprints Systems. This position is a two year appointment and salary commensurate with qualifications. (if available), a letter describing professional for a visiting assistant professor. The successful All fields will be considered, but for some of interests and aspirations, and to arrange for applicant should have a strong commitment the tenure-track positions, preference will be three letters of recommendation to: both to research and teaching. Applications given to candidates in Differential Equations, Prof. John C. Wierman, Chair and three letters of recommendation should Geometry/Topology, Algebra, and Functional Department of Mathematical Sciences be sent to: Search Committee (Dynamical Analysis. Applicants must have strong research 220 Maryland Hall Systems), Department of Mathematics, Boston credentials and a commitment to excellence in The Johns Hopkins University University, 111 Cummington St., Boston, MA teaching. A Ph.D. in mathematics or a Ph.D. Baltimore, Maryland 21218-2689 02215. AA/EOE. dissertation accepted with only formalities to Applications are requested by January 15, 1993. be completed is required. Letter of application, Applicants whose primary research is in al­ current vita, description of research and three gebra, analysis, geometry, logic, number theory, letters of recommendation should be sent to: or topology will not be considered. MOUNT HOLYOKE COLLEGE Louis Pigno Mount Holyoke College seeks an innovative Department of Mathematics leader in mathematics education to assume the Cardwell Hall 137 position of Director of the Summer Math for Kansas State University Teachers Program. Since 1983, Summer Math Manhattan, KS 66506 UNIVERSITY OF MARYLAND for Teachers has been in the forefront of the It is expected that offers will begin on December UNIVERSITY COLLEGE mathematics education reform movement, intro­ 15, 1992, but applications for all positions will ducing primary and secondary school teachers be accepted until February 1, 1993, or until Teach in Asia or Europe to new pedagogy and helping them transform positions are closed. AA/EOE University of Maryland University College seeks. their instructional techniques. The Program con­ excellent teachers for openings on U.S. military ducts a series of summer institutes designed bases overseas. Appointments begin August to provide opportunities for about 100 teachers 1993. Requirements include M.A. or Ph.D., each year to explore selected mathematical WASHBURN UNIVERSITY recent college teaching experience, and U.S. concepts and reflect on their own learning Chair citizenship. Competence to teach in another dis­ processes. It also offers academic-year mathe­ cipline desirable. Benefits include transportation Applications are invited for the position of matics courses for local teachers. This full-time and military base privileges (PX, commissary, Chair, Department of Mathematics and Statis­ administrative position carries lecturer status etc.). Frequent travel and the cost of schooling tics. Tenure track, 12-month position to lead an in either psychology-education or mathemat­ make these positions difficult for those with 11 member undergraduate department. Starts ics. Responsibilities include teaching in and children. Send resume to: Dr. Ralph E. Millis, July 1, 1993. 6 credit-hours per semester teach­ directing the summer institutes and related pro­ Assistant to the President, Overseas Programs, ing load. Current programs include mathemat­ grams, budget and program management, and University of Maryland University College, Col­ ics, applied mathematics, mathematics educa­ preparation of grant proposals for programmatic lege Park, MD 20742-1642. AA/EEO. tion, and actuarial science. QUALIFICATIONS: and research support. The Director supervises Earned doctorate in Mathematics, Statistics, or the work of the Assistant Director and ten Mathematics Education with significant college summer institute staff and works collaboratively teaching experience. A strong commitment to with the Directors of SummerMath, a six-week excellence in teaching and a significant record summer program in mathematics for women of continued scholarly activity. Strong commu­ WASHINGTON COLLEGE in secondary school. A deep understanding nication, leadership, and interpersonal skills. Department of Mathematics of mathematics is essential for the position. Desirable attributes include administrative ex­ and Computer Science Candidates should have a Ph.D. or Ed.D. in perience and experience with applications of 300 Washington Avenue mathematics or mathematics education or the equivalent. Experience as a school teacher and technology in the classroom. Chestertown, Maryland 21620 Send letter of application, resume, tran­ administrative experience are highly desirable. scripts, and names, addresses, and telephone Washington College announces a tenure track Mount Holyoke College is committed to fos­ numbers of 3 references to Ann Ukena, Wash­ position at the assistant professor level. The tering multicultural diversity among its faculty, burn University, Topeka, KS 66621. APPLICA­ position begins in late August 1993. staff and students and especially encourages TION DEADLINE: March 1, 1993. Consideration Applications are invited from persons trained women and minorities to apply. The College is will continue until a suitable candidate is identi­ in mathematics or computer science, especially an AA!EO employer. Please send letter of in­ fied. AA/EO Employer. those with some training in both. A Ph.D. is terest, cv, and three letters of recommendation required. Applicants should send a letter of to Prof. Donal O'Shea, SummerMath Search application including a statement on teaching Committee, Department of Mathematics, Mount and learning mathematics in a liberal arts Holyoke College, South Hadley, MA 01 075 by February 22, 1993. MARYLAND setting, a resume, transcripts, at least three letters of recommendation to Dr. Albert w. THE JOHNS HOPKINS UNIVERSITY Briggs, Jr. at the address above. Evaluation of candidates will begin in Jan­ Department of Mathematical Sciences THINKING MACHINES CORPORATION uary and continue until the position is filled. We Technical Course Developernnatructor Applications are invited for 3 anticipated faculty will be at the San Antonio meeting. positions within the areas of Washington College is an equal opportunity Thinking Machines Corporation is the world 1) numerical linear algebra (Senior appli­ employer. leader in massively parallel processing. We cants preferred), 2) statistics, 3) operations design and manufacture the world's most pow­ research, 4) applied discrete mathematics. erful supercomputer systems. Our users are

78 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements

innovators and leaders in research, academia, applications will begin November 15, 1992, and Ed. D. degree and be able to teach undergradu­ government, industry, and commerce. In our continue until the positions are filled. AA/EOE. ate mathematics courses. commitment to making our customers unparal­ The successful candidates are expected to leled in their success we are currently seeking have strong teaching credentials and outstand­ an energetic, motivated individual to join our ing research potential. Appointment at the senior Education Group. level will require a strong research record. Du­ Join us as a key member of our fast-growing ties include teaching, service and research with technical training group developing and teaching GMI ENGINEERING & a normal teaching load of courses (6 to 8 hours) courses on parallel programming languages to MANAGEMENT INSTITUTE per quarter. Preference will be given to candi­ a high-powered customer base of scientists and Faculty Position In Mathematics dates who can complement existing research computer specialists. and Computer Science interests in the department. The requirements for this challenging po­ Send curriculum vitae, transcript and three sition are: an advanced degree in computer GMI Engineering & Management Institute in­ letters of recommendation to science or mathematics (specific mathematical vites applications for a tenure-track position in Alphonse Baartmans, Head knowledge of compiler theory, linear algebra, Mathematics and Computer Science. This posi­ Department of Mathematical Sciences and numerical analysis), several years of teach­ tion is at the Assistant Professor level, and it is Michigan Technological University ing experience, strong technical background intended that it be filled by July 1, 1993. 1400 Townsend Drive including in-depth knowledge of Fortran or C, GMI operates on a five-year fully cooperative Houghton, Ml 49931-1295 and strong verbal and written communication plan of education. The Science and Mathemat­ Review of applications will begin on Decem­ skills. Up to 30% travel required. ics Department offers a Bachelor of Science ber 1 , 1992. Applications will be accepted .until If you feel you are interested in a challenging degree in Applied Mathematics with areas of the positions are filled. opportunity in a fast-paced environment, please concentration in Applied Analysis, Computer MTU is an equal opportunity educational send or fax your resume to: Science, and Statistics. The department also of­ institution/equal opportunity employer. Elizabeth Mye fers courses at all levels in support of the various Human Resources Engineering and Management bachelor's and Thinking Machines Corporation master's degree programs. Department faculty 245 First Street typically teach 3 courses per term and are NEBRASKA Cambridge, Ma. 02142 expected to participate in curriculum develop­ Fax #: 617·234-4421 ment, research, and professional development, UNIVERSITY OF NEBRASKA-LINCOLN An Equal Opportunity Employer student advising and service activities. The Connection Machine ® is a registered The minimum qualifications for this position We invite applications for two Assistant Profes­ trademark of Thinking Machines Corporation. include an earned Ph.D. in either Mathematics sor tenure-track positions beginning in fall1993. or Computer Science with a strong background Candidates must have a Ph.D. in mathematics in the other field and evidence of effective by August 1993, and have excellent teaching communication skills in the English language. ability and outstanding research potential in TUFTS UNIVERSITY The successful candidate will be expected to an area that complements existing expertise in the department. Strong preference given to The Department of Mathematics invites applica­ show evidence of strong research abilities and a candidates in the areas of: (1) combinatorics tions for the following positions. strong interest in undergraduate teaching. Expe­ and graph theory; or (2) nonlinear partial differ­ Assistant Professorships, two or three po­ rience in undergraduate education, in industry, ential equations with emphasis on applications, sitions, to begin Sept. 1, 1993. Initial one-year or in computer-aided classroom instruction is dynamical systems, or numerics. Send vita contract, renewable to a maximum of three desirable. and three letters of recommendation to Search years. Ph.D., promise of strong research and Please send resume, statement of research Committee Chair, Department of Mathematics evidence of strong teaching ability required. interests, and three letters of reference to: and Statistics, University of Nebraska-Lincoln, Relation of research interests to those of mem­ Professor John W. Dulin, Search Committee Lincoln, NE 68588-0323. Women and minority bers of the department will be a consideration. Chair, Science and Mathematics Department, candidates are particularly encouraged to apply. Research interests preferred: For Position No. GMI Engineering & Management Institute, 1700 The University of Nebraska is committed to 1, probability and statistics; Position No. 2, Lie West Third Avenue, Flint, Michigan 48504- a pluralistic campus community through Affir­ group representations; Position No. 3, combina­ 4898. Review of applicants will commence mative Action and Equal Opportunity, and is torial group theory including braid theory. Send immediately and continue until the position is responsive to the needs of dual career cou­ application with Position No. and three letters filled. ples. We assure reasonable accommodation of recommendation by March 1 , 1993, to R. GMI is an affirmative action/equal opportu­ under the Americans with Disabilities Act. Con­ Weiss, Search Committee Chair. nity employer and actively seeks the candidacy tact AA/EO at (402) 472-3417. The review of As an EO/AA employee, Tufts encourages of women and minorities. Preference will be applications will begin February 1 , 1993, and applications from minority and women candi­ given to citizens and permanent residents of the continue until suitable candidates are selected. dates. u.s. Tufts University Math Department Medford, MA 02155 MICHIGAN TECHNOLOGICAL UNIVERSITY NEW HAMPSHIRE Department of Mathematical Sciences Houghton, Ml 49931 DARTMOUTH COLLEGE WILL-IAMS COLLEGE John Wesley Young Research Departrnent of Mathematics Applications are invited for four tenure track Instructorship In Mathematics Williamstown, Massachusetts 01267 positions as well as visiting and temporary positions starting August 1993. The John Wesley Young Research Instructor­ One or possibly two anticipated positions, one Subject to funding, the department antici­ ship is a two year post-doctoral appointment of them preferably in statistics, probably at the pates tenure track openings in the areas of for promising new or recent Ph.D.'s whose rank of assistant professor, for Fall 1993. Strong algebra (1 position), applied mathematics (2 research interests overlap a department mem­ commitment to both teaching and scholarship is positions) and mathematics education (1 posi­ ber's. Current departmental interests include essential. tion). Candidates for the positions in algebra areas in algebra, analysis, algebraic geometry, Please have a vita and three letters of and applied mathematics must have a Ph.D. in combinatorics, computer science, differential recommendation on teaching and research mathematics while candidates in mathematics geometry, logic and set theory, number theory, sent to Hiring Committee. Formal evaluation of education are expected to have a Ph.D. or probability and topology. Teaching duties of four

JANUARY 1993, VOLUME 40, NUMBER 1 79 Classified Advertisements

ten-week courses spread over two or three Ohio University is an Equal Opportunity/ quarters typically include at least one course NORTH CAROLINA Affirmative Action Employer. in the instructor's specialty and include ele­ mentary, advanced and (at instructor's option) NORTH CAROLINA STATE UNIVERSITY graduate courses. Nine-month salary of $34,000 Department of Mathematics THE OHIO STATE UNIVERSITY supplemented by summer (resident) research AT NEWARK stipend of $7,556 (two-ninths). Send letter of AppliCations are invited for an anticipated tenure application, resume, graduate transcript, thesis track junior level position in algebra. Of particular Lecturer, Mathematics abstract, description of other research activities interest are candidates with an expertise in The Ohio State University at Newark is seeking a and interests if appropriate, and 3 or preferably representation theory. Applicants must have a Lecturer for a full-time, nine-month, temporary, 41etters of recommendation (at least one should strong commitment to research and teaching. non-tenure track, one year position, with the discuss teaching) to Phyllis A. Bellmore, Math­ Please send a curriculum vitae, an outline possibility of renewal up to two additional years. ematics and Computer Science, 6188 Bradley of current research program, and arrange to DUTIES INCLUDE: Ability to teach courses Hall, Hanover, NH, 03755-3551. Applications have sent three letters of recommendation to from remedial levels through the calculus level. received by Jan. 15 receive first considera­ the Algebra Search Committee, Department of QUALIFICATIONS INCLUDE: Master's degree tion; applications will be accepted until position Mathematics, Box 8205, North Carolina State in mathematics or equivalent required; docu­ is filled. Dartmouth College is committed to University, Raleigh, NC 27695-8205. Women mented excellence in college teaching required. affirmative action and strongly encourages ap­ and minorities are encouraged to apply. AA/EOE Doctoral degree desired. SALARY: $25,080- plications from minorities and women. $28,200 with comprehensive co-pay benefits package. STARTING DATE: Autumn Quar­ ter, 1993. To assure consideration, send vita OHIO and three letters of reference by 4/16/93 to Chairperson, Lecturer, Mathematics Search, DARTMOUTH COLLEGE BOWLING GREEN STATE UNIVERSITY c/o Coordinator, Human Resources, The Ohio The Department of Mathematics and Computer Department of Mathematics State University at Newark, 1179 University Drive, Newark, OH 43055-1797. The Ohio State Science has an opening for a tenure-track As­ and Statistics sistant Professor in Differential Geometry, with University is an Equal Opportunity/Affirmative initial appointment in the 1993-1994 academic The department anticipates a position in (Ap­ Action Employer. Qualified women, minorities, year. A candidate for the position must be com­ plied Analysis/Computational Mathematics) and/ Vietnam-era Veterans, disabled veterans, and mitted to outstanding teaching at all levels of or (Group Theory or Combinatorics). We have individuals with disabilities are encouraged to the undergraduate and graduate curriculum and 33 faculty, 65 full-time graduate students, and a apply. must give evidence of a well-regarded research growing doctoral program (15 Ph.D.'s awarded program that shows real promise for the future. in the last three years). The selected candidate, Candidates with several years of experience who must have a Ph.D. in Mathematics, will be should in addition be ready to direct Ph.D. expected to pursue research, teach two courses OREGON theses. per semester, work with graduate students, and UNIVERSITY OF OREGON To create an atmosphere supportive of re­ eventually direct Ph.D. dissertations. Those with search, Dartmouth offers new faculty members postdoctoral experience are encouraged to ap­ Department of Mathematics grants for research-related expenses, a quarter ply. Candidates are expected to have a strong Eugene, Oregon 97403 of sabbatical leave for each three academic research record (or potential) in an area com• Frank W. Anderson, Head years in residence and flexible scheduling of patible with current faculty. Salary competitive. teaching responsibilities. The teaching respon­ Please provide a vita, publication list, official Assistant or Associate Professor tenure track sibility in mathematics is four courses spread transcript, and have three letters of recommen­ position in pure mathematics beginning Septem­ over two or three quarters. The department dation (one concerning teaching) sent by 2/1/93 ber, 1993. Preference given to person with encourages good teaching with a combination to: research interests that complement those cur­ of committed colleagues and bright, responsive Andrew Glass, Chair rently represented. Competitive salary with ex­ students. Mathematics & Statistics Dept. cellent fringe benefits. Send complete resume Though first priority is to appoint a differen­ Bowling Green State University and three letters. Closing date is January 18, tial geometer, our second priority is in algebra. Bowling Green, OH 43403-0221 1993. Women and minorities are encouraged Exceptional circumstances could lead to making EOE Employer. Female & minorities encour­ to apply. An EO/AA Institution committed to the appointment in some third field. To apply, aged to apply. cultural diversity. send a l~tter of application, curriculum vitae, and a bnef statement of research results and interests. Also arrange for four letters of refer­ PENNSYLVANIA ence to be sent, at least one of which addresses OHIO UNIVERSITY teaching, and, if the applicant's native language Department of Mathematics UNIVERSITY OF PITTSBURGH is not English, the applicant's ability to use Department of Mathematics and Statistics English in a classroom. All application materi­ The Department of Mathematics anticipates als should be addressed to Phyllis Bellmore, the appointment of two tenure-track assistant The department invites applications for the Recruiting Secretary, Mathematics and Com­ professors beginning September 1, 1993. One following position, Professor of Mathematics, puter Science, 6188 Bradley Hall, Dartmouth position is in operator theory or functional with specialty in Ring Theory. College, Hanover, NH 03755-3551. Applica­ analysis and the other in general topology This would be a tenured senior position. It is tions completed by February 1 will receive first or set theory with possible applications to dependent on funding. We anticipate that it will consideration. Dartmouth is committed to Affir­ topology. Salary is competitive dependent on be available in either Fall1993 or Fa111994. mative Action and encourages applications from the candidate's qualifications and experience, Requirements include outstanding research African Americans, Asian Americans, Hispan­ with a minimum of $29,000. Applicants must accomplishment commensurate with experi­ ics, Native Americans, and women. Inquiries have a Ph.D. in mathematics before September ence, and ability and interest in excellent about the progress of the selection process can 1, 1993. Send resume and have three letters teaching. be directed to Richard E. Williamson, Recruiting of recommendation sent to Shih-liang Wen, Applicants should send a resume to S. Chair. Chairman, Department of Mathematics, Ohio Hastings, Chairman, Department of Mathe­ University, Athens, Ohio 45701. The deadline matics and Statistics, University of Pittsburgh, for applications is January 31, 1993. Pittsburgh, PA 15260. Do not have letters of

80 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ······~---,.__Classified Advertisements ....

recommendation sent at this time. Applications UNIVERSITY OF SOUTH CAROLINA didates working in numerical fluid dynamics. which are received by January 20, 1993 are Department of Mathematics Another position will be offered in differential assured of complete consideration. equations, with preference given to those hav­ The University of Pittsburgh is an equal The Department of Mathematics invites applica­ ing expertise in the nonlinear qualitative theory opportunity/affirmative action employer. Women tions for expected tenure-track faculty positions of differential equations. Another position will be and minorities are especially encouraged to for Fall 1993, at all ranks. Applications in all offered in Stochastic Differential Equations and apply. areas of mathematics will be considered. Re­ related fields of Stochastic Analysis. Employ­ search is supported by excellent inhouse library ment begins August 1993. Substantial research and computing facilities. The Ph.D. degree or promise as well as dedication to teaching are its equivalent is required. Appointments will be paramount. Interested applicants should ar­ consistent with the Department's commitment range to have a vita, three reference letters, to excellence in research and in teaching at the and a research statement sent to Professor YORK COLLEGE OF PA undergraduate and graduate levels. A detailed John B. Conway, Mathematics Search, Univer­ resume, containing a summary of research ac· sity of Tennessee, Knoxville, TN 37996-1300. Tenure track position, assistant or associate complishments and goals, and four letters of [email protected]. Review of appli­ professor level. Applicants should be able to recommendation should be sent to: cations will begin December 1 and will continue teach jr/sr course in numerical analysis and have Dr. George F. McNulty, Chairman until the positions are filled. completed Ph.D. mathematics by Fall 1993. Department of Mathematics UTK is an EEO/AAmtle IX/Section 504/ADA Facility with computer languages or experience University of South Carolina Employer. in computer-aided instruction is a plus. Columbia, SC 29208 York College of PA is an excellent, pri­ The University of South Carolina is an Affirma­ vate mainly undergraduate institution with about tive Action/Equal Opportunity Employer. 3,000 full-time and 1900 part-time students. We VANDERBILT UNIVERSITY offer competitive salary and fringe benefits and a Department of Mathematics friendly working environment. Our department is 136 Stevenson Center mostly a service department but we have about Nashville, TN 37240 50 mathematics education majors and a new mathematics major. All full-time faculty teach UNIVERSITY OF TENNESSEE AT DISTINGUISHED OR NAMED PROFESSOR. two or three freshman level courses. As our CHATTANOOGA We are seeking someone with outstanding re­ major grows, there will be opportunity to teach Department Head search credentials in algebra. The interests of one or two jr/sr level courses per year. Pro­ our algebra group include universal algebra, set­ fessional/research activities and college service The University of Tennessee at Chattanooga theoretic algebra, abelian groups, semigroups, are also required. Send curriculum vita, three invites applications for Head of the Department ring theory, ordered algebraic structures, lattice letters of recommendation, and a cover let­ of Mathematics. A Ph.D. in a mathematical theory, and logic with applications to com­ ter expressing interest to: Mathematics Search science and at least five years of college puter science. Evidence of effective teaching is Committee, Department of Physical Sciences, mathematics teaching experience are required. required. Have vita and 5 letters of recommen­ York College of PA, York, PA 17405-7199. First Applicants should provide evidence of leader­ dation sent to Professor Glenn Webb. consideration to applications received by Feb. ship in curriculum development, teaching, public VANDERBILT UNIVERSITY IS AN EQUAL 15, 1993. York College of PA is an equal op­ service and research/scholarly activities. In this OPPORTUNITY/AFFIRMATIVE ACTION EM­ portunity employer. Women and minorities are primarily undergraduate institution, the faculty PLOVER. encouraged to apply. is expected to exhibit excellence in teaching while maintaining a strong commitment to re­ search and public service. The mathematics department has 22 faculty members including a Chair of Excellence in Applied Mathematics. Located in a very scenic metropolitan area of LAMAR UNIVERSITY 8100. 400,000, UTC has a student enrollment of Beaumont, Texas :::::-sou'fHcAR5LiNA""~- Send applications with current vita to: Dr. Irene Loomis; Chair of the Search Committee, Dept. The Department of Mathematics seeks appli­ coKER COLLEGE of Mathematics, UTC, Chattanooga, TN 37403- cations for a tenure-track Assistant/Associate 2598. Consideration of applications will begin Professor position beginning Fall 1993. Appli­ Coker College invites applications for a tenure­ November 1 , 1992, and will continue until the cants must hold an earned Ph.D., should be track position in mathematics/computer science. position is filled. Women and minorities are en­ active researchers in Analysis and/or Applied Candidates must have PhD and demonstrate couraged to apply. UTC is an Equal Opportunity Mathematics, and have a strong commitment to the potential for high quality teaching and con­ Employment/Affirmative Actionmtle IX Section tinuing scholarly activity. Duties begin August teaching. 504 Institution. Lamar is a state supported educational and 1993 and include teaching introductory level institution of approximately 12,000 as well as major courses in mathematics and research students. The Department, which is located courses necessary to support a computer sci­ the College of Engineering, offers the ence minor. Total teaching load is 12 semester UNIVERSITY OF TENNESSEE within B.A., B.S., and M.S. degrees in Mathematics hours per semester with some teaching respon­ Knoxville, Tennessee 16 full-time faculty. sibilities in evening and off-campus programs. and has For the approximately 250,000 people in Rank and salary commensurate with experi­ The Mathematics Department of the Univer­ area, there are eight muse­ ence. Coker College is a private, four-year sity of Tennessee, in an effort to significantly the Beaumont ums, a symphony orchestra, ballet, opera; and liberal arts college in Hartsville, South Carolina. improve its research position, seeks to fill 3 productions. Other facilities and Deadline for applications is February 1 , 1993. or 4 tenure-track assistant or beginning asso­ other theatrical are found in Houston 85 miles west. Send a letter of application, curriculum vitae, ciate professorships in several areas. A Ph.D. events outdoor recreational opportunities in­ and three references to: Professor Kaye Crook, is required. Some postdoctoral experience is Nearby of the largest freshwater lakes in Chair, Mathematics Search Committee, Coker preferred. There will be one and possibly two clude two the Big Thicket National Preserve, four College, Hartsville, South Carolina 29550. Affir­ positions available in Numerical Mathematics; Texas, the Gulf of Mexico, and a large mative Action, Equal Opportunity Employer. candidates should be well versed in the core national forests, areas of Numerical Analysis with research in­ inland saltwater lake. terests in the numerical solution of differential Salary and rank are commensurate with equations. Preference will be shown those can- qualifications and experience. Send a resume

JANUARY 1993, VOLUME 40, NUMBER 1 81 ······························································································································································-··········------Classified Advertisements

and three letters of recommendation to: Dr. John full vita, and arrange to have at least 3 letters of UNIVERSITY OF TEXAS R. Cannon, Chair, Department of Mathematics, recommendation sent to AT ARLINGTON Lamar University, P. 0. Box 10047, Beaumont, William Rundell, Interim Head Department of Mathematics TX 7n10. Full consideration will be given to Department of Mathematics completed applications received before March Texas A&M University The Department invites applications for two to 15, 1993. Lamar is an EEO/AA employer. College Station, Texas n843-3368 three anticipated tenure-track positions begin­ Texas A&M University is an Equal Opportu­ ning with the Fall Semester, 1993. We seek nity/Affirmative Action employer. Women and candidates in various .areas of Mathematics minority applicants are especially encouraged. which are complementary to those of the cur­ TEXAS A&l UNIVERSITY rent faculty and would enhance and support Department of Mathematics the goals of the Department. Salary and rank Subject to availability of resources and ad­ are commensurate with qualifications which ministrative approval, at least one tenure-track must include the Ph.D. degree (in hand or position at the Assistant Professor level or expected by September 1993). Assistant Pro­ fessor candidates must show strong potential higher will be available beginning with the Fall TEXAS TECH UNIVERSITY Semester 1993. Candidates must have a Ph.D. for excellence in teaching and research. For Department of Mathematics an Associate or Full Professorial appointment in Mathematics, tangible evidence of scholarly P.O. Box 41042 publications, and a strong commitment to su­ the candidate must have excellent teaching cre­ Lubbock, TX 79409 perior teaching. Salary is commensurate with dentials and a nationally established research record; some success in attracting outside fund­ experience. Send resume and three letters of The Department of Mathematics at Texas Tech recommendation to: ing is preferred. A resume with three letters of University anticipates openings for at least one recommendation should be sent to: Faculty Search Committee tenure track Assistant Professorship beginning Department of Mathematics Chairman in the fall semester of 1993. To qualify the Recruiting Committee Campus Box 172 applicants must: Texas A&l University University of Texas at Arlington 1. have a Ph.D. from a recognized university, Department of Mathematics Kingsville, TX 78363-8201 2. have a strong dedication to both teaching Applications completed by February 1, 1993 will Box 19408 and research, Arlington, TX 76019-0408 receive first consideration. Texas A&l is a part 3. exhibit research interests that are compat­ of the Texas A&M University System and is an The University of Texas at Arlington is an ible with ongoing programs in the department, Affirmative Action/Equal Opportunity Employer. equal opportunity/affirmative action employer. and 4. be willing and able to work with students at both the undergraduate and graduate level. TEXAS A&M UNIVERSITY To apply, please send a resume and have UTAH Research Instructorships In Mathematics three letters of recommendation sent to Harold Bennett, Chairman of Hiring Committee, Depart­ UNIVERSITY OF UTAH The department expects to have several Re­ ment of Mathematics, Texas Tech University, Department of Mathematics search instructorships available for the 1993- P.O. Box 41042, Lubbock, TX 79409 EOE/AA 1994 academic year. These are two year The University of Utah, Department of Math­ positions, and candidates should have recently ematics, invites applications for the following received their Ph.D., show promise of re­ positions: search excellence in an area of pure or ap­ 1. At least two full time tenure track plied mathematics, and have a commitment appointments on the professional levels. The to teaching. Preference will be given to appli­ THE UNIVERSITY OF Department is primarily interested in applicants cants whose expertise augments our existing TEXAS AT SAN ANTONIO who work in the research areas represented in research strengths. the Department and who received their Ph.D. Application material consisting of a vita The Division of Mathematics, Computer Sci­ degrees prior to 1992. Selection will be based which should include a statement of research ence, and Statistics will have one tenure-track on research and teaching ability. goals, and 3 letters of recommendation should position at the assistant professor level in 2. Two or more nonrenewable three-year be sent to Mathematics, beginning Fall 1993. Applicants Instructorships. Persons of any age receiving William Rundell, Interim Head must have the Ph.D. degree in Mathemat­ Ph.D. degrees in 1992 or 1993 are eligible. Department of Mathematics ics or a related area by September 1, 1993, Applicants will be selected on the basis of Texas A&M University and should demonstrate strong potential for ability and potential in teaching and research. College Station, Texas n843-3368 excellence in research and teaching. Respon­ Starting salary Will be $33,000; future cost of Texas A&M University is an Equal Opportu­ sibilities include research, teaching, direction of IMng increases are contingent on action by the nity/Affirmative Action employer. Women and graduate students, and contributing in program State Legislature. Duties consist of teaching five minority applicants are especially encouraged. development. courses during the three quarter academic year. Applicants should submit a resume and 3. One C. R. Wylie Instructorship. The arrange to have at least three letters of recom­ term of this instructorship is one year, but it TEXAS A&M UNIVERSITY mendation sent to may be renewed for up to three years. It will Department of Mathematics Chair, Search Committee be awarded either to an incoming Instructor or Division of Mathematics, Computer to one of the Instructors already in residence Applications are invited for one or more tenure­ Science, and Statistics on the basis of ability and potential in teaching track or tenured faculty positions beginning The University of Texas at San Antonio and research. The stipend is $37,000. Duties in the 1993-1994 academic year. Outstand­ San Antonio, Texas 78249 consist of teaching four courses during the three ing candidates in all fields of mathematics Email: math@ ringer.cs.utsa.edu quarter academic year. are encouraged to apply. Significant research The closing date for receipt of applications is 4. One or more visiting faculty positions of accomplishments or, in the case of a junior ap­ March 1, 1993. UTSA is an Equal Opportu­ one year or less in any of the professorial ranks. pointment, exceptional promise plus an earned nity/Affirmative Action Employer. We encourage Selection will be based on potential contributions Ph.D., together with evidence of good teaching women and minorities to apply. to the departmenfs research program, and on ability, will be expected of successful applicants. teaching ability. Salary will be commensurate with qualifications. It is expected that offers of Instructorships Candidates should send a letter of application, will begin on January 1, 1993, but applications

82 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY .. ~············································ Classified Advertisements

tor all positions will be accep~ed until ~an- plications completed by 111/93 will be included VIRGINIA POLYTECHNIC INSTITUTE AND ary 31 1993 or until all pos1t1ons are f1lled. in the first round of evaluations. Equal Opportu­ STATE UNIVERSITY ~pplications f~r any of these positions should nity/Affirmative Action Employer. The University Department of Mathematics include curriculum vitae, bibliogr~phy a~d t~ree takes its affirmative action mission seriously and letters of reference. (Instructorship apphcat1o~s is especially interested in receiving applications Applications are invited for an anticipated should also include an abstract of the thes1s from women and people of color. tenure-track appointment in Geometry (differ­ and either a list of graduate cou~s. ~ompleted ential or algebraic, or related areas) beginning or a transcript of graduate work.) V1s1t~ng faculty Fall1993. Because we seek applicants who will applications should indicate the port1on. of the be able to develop a strong case for eventual three-quarter academic year dunng which the VIRGINIA POLYTECHNIC INSTITUTE AND promotion and tenure, preference will be given applicant wishes to visit. Please send your ap­ STATE UNIVERSITY to those with postdoctoral or instructorship ex­ plication to Committee on Staffing, Department Department of Mathematics perience and established research programs. of Mathematics, University of Utah, SaH ~ke Please send vita and brief description of re­ CitY, Utah 84112. The Un~ersity ~f Utah IS an The Department of Mathematics is actively search and have three letters of reference sent Equal OpportunitY, Affirmative Act1on El!'pl~yer seeking applications for an anticipated tenure­ to Prof. William Floyd, Chair, Geometry Search and encourages nominations and apphcat1ons track position at the Assistant Pro~essor lev~l Committee, Department of Mathematics, Vir­ from women and minorities. in the area of discrete mathematiCS, combl­ ginia Tech, Blacksburg, VA 24061-o123. At natorics, and graph theory beginnin~ with the least one letter should address the applicant's 1993-94 year. A Ph.D. in mathematics, strong qualifications as a teacher. Applications will be research potential, and good teaching ~reden­ accepted until March 15, 1993, or until posi­ UTAH STATE UNIVERSITY tials are required. Preference will be g1ven to Department of Mathematics and Statistics tion is filled. Applications completed by January candidates with postdoctoral experience. Appli­ 1, 1993 will be included in the first round of cations will be accepted for as long as there evaluations. Virginia Tech is an Equal Opportu­ Applications are invited for ~ne or more te!lure­ is a possibility of making an appointment or track positions in mathematics at the ass1stant nity/Affirmative Action Employer. The University until until March 15, 1993. Those completed professor level, to begin September 1993. Re­ takes its affirmative action mission seriously and by January 1, 1993 will be included in the first is especially interested in receiving applications quirements include a Ph.D. (by Septemt>E;r round of evaluations. Applicants should send 1993) in mathematics or m~themat1cal SCI­ from women and people of color. a curriculum vitae and arrange to have three ences, potential for excellence m research, and letters of reference sent to Professor Charles demonstrated commitment to both undergrad­ Parry, Chair, Discrete Math Search Committee, uate and graduate teaching. Candidates with Department of Mathematics, VPI&SU, Blacks­ research interests in algebra or related areas, burg, VA 24061-0123. At least ~ne letter sh~uld WASHINGTON integrable or dynamical systems, or computa­ address the applicants teachmg credentials. tional optimization are especially encouraged to WASHINGTON STATE UNIVERSITY VPI&SU is an Equal Opportunity/Affirmative apply. . Department of Mathematics Action Employer. The University takes its ~ffir­ Utah State University, located m the Wasatch mative action mission seriously and is especially Range of the Rocky Mountains, offers compet­ The Department of Pure and Applied Mathe­ interested in receiving applications from women itive salaries and excellent medical, retirement, matics has a permanent, tenure track position and people of color. and professional benefits. available beginning fall, 1993. Assistant Profes­ Applications, including resume and three sor level, salary commensurate with qualifica­ letters of reference, should be sent to LeRoy tions and experience. Applications are invited Beasley, Search Committee, Departn:'ent . of VIRGINIA POLYTECHNIC INSTITUTE AND from individuals expert in dynamical systems with special interest in bifurcation analysis. Ap­ Mathematics & Statistics, Utah State Umversjty, STATE UNIVERSITY plicants should have significant mathematical Logan, UT 84322-3900 or em~il: lb~asley@ Department of Mathematics usu.edu. The selection process will beg1n ~~b":'­ research accomplishments and strong commit­ ary 1, 1993 and will continue until the pos1t1on 1s Applications are invited for an anticipated ment to teaching. The successful applicanrs re­ filled. tenure-track appointment at the Assistant ~ro­ search will be expected to complement existing department research strengths in mathematical Women and. minorities are particularly en­ fessor level in the general area of Dynam1~1 couraged to apply. EO/AAE. Systems beginning with the 1993-94 academ1c modelling, numerical analysis and optimization. The position requires a Ph.D. with competence year. A Ph.D. and strong research _pot~mtial are required. The likelihood of productive mter­ in teaching relevant graduate and undergradu­ action with current faculty members, such as ate courses in Mathematics. Applicants should send a curriculum vitae, a statement of current VIRGINIA the group in partial diffe!ential equa~ions ~nd continuum mechanics, Will be a cons1derat1on. research and long-term research interests to: VIRGINIA POLYTECHNIC INSTITUTE AND Position involves teaching duties of approx­ Prof. V.S. Manoranjan, Search Committee, STATE UNIVERSITY . imately six hours per week. Evidence that Department of Pure & Applied Mathemat­ Department of Mathematics candidate is or will become an effective teacher ics Washington State University, Pullman, should be included in application materials; in wa~hlngton 99164-3113. Screening of appli­ We are seeking applicants for an ~nticipated particular, at least one reference letter should cations will begin on February 1 , 1993. WSU tenure-track appointment at the A~1stant Pro­ address this issue. Send a vita and arrange is an EO/AA educator and employer. Protected fessor level in the area of Computational Math­ to have three letters of reference submitted group members are encouraged to apply. ematics/Numerical Analysis beginning with the to Kenneth Hannagan, Chair, Dynamical Sys­ 1993-94 academic year. We seek applicants tems Search Mathematics Department, Virginia with a strong research potential as we_ll as t~e Tech Blacksburg, VA 24061-o123. Applications abilitY to be an effective teacher. A vita, bnef will be accepted for as long as there is a possi­ WISCONSIN description of research interests, three lett~rs bility of making an appointment or until 3/15/93. of recommendation including at least one which Those completed by 1/1/93 will be included in UNIVERSITY OF WISCONSIN-MADISON addresses teaching, and any supporting mate~­ the first round of evaluations. Equal Opportu­ als should be sent to Janet S. Peterson, Cha1r, nity/Affirmative Action Employer. The University University of Wisconsin-Madison Computational Mathematics Search Committee, takes its affirmative action mission seriously and Department of Mathematics ICAM, Wright House, Virginia Tech, Blacksburg, is especially interested in receiving applications Hiring Committee VA 24061-o531. Applications will be accepted from women and people of color. 480 Lincoln Drive for as long as there is a possibility of making 223 Van Vleck Hall an appointment or until 3/15/93; however, ap- Madison, Wl53706

JANUARY 1993, VOLUME 40, NUMBER 1 83 Classified Advertisements

The Mathematics Department solicits applica­ Chair, Department of Mathematics, University of reference, should be completed by January 15, tions for a tenure-track Assistant Professor Wyoming, Laramie, Wyoming 82071. Applica­ 1993 and sent to: Dr. L. Hambleton, Chair or position in the area of applied mathematics with tions completed by January 1, 1993 will receive V.P. Snalth, Sc.D., FRSC, Britton Professor an emphasis on large-scale scientific computa­ first consideration. The University of Wyoming is of Mathematics, Department of Mathematics tion. The position would be available in the fall an equal-opportunity employer and encourages & Statistics, McMaster University, Hamilton, of 1993. All candidates should exhibit evidence applicants from women and minorities. Ontario, Canada, L8S 4K1 of outstanding research and a strong commit­ ment to good teaching. Application forms are available from the above address. The deadline UNIVERSITY OF ALBERTA for submission of applications is February 1, AUSTRALIA Department of Mathematics 1993. The University of Wisconsin is an Af­ firmative Action, Equal Opportunity Employer, THE UNIVERSITY OF MELBOURNE Applications are invited for a tenure-track posi­ and encourages women and minorities to apply. Department of Mathematics tion at the assistant professor level, beginning Unless confidentiality is requested in writing, Research Fellow Grade 1 July 1, 1993, subject to confirmation of funding. information regarding the applicants must be (Temporary) Requirements are a Ph.D. and proven ability or released upon request. Finalists cannot be Geometry and Topology Group demonstrated potential for research and teach­ guaranteed confidentiality. ing. Salary for assistant professor is currently Applications are invited for the above position $40,035-$57,003. Send vita and arrange for funded by the Australian Research Council three letters of reference to be sent to: (ARC). The grant held by Dr. K. Ecker and Prof. Professor R. Bercov, Chairman WYOMING J.H. Rubinstein is for a project entitled Minimal Department of Mathematics Surfaces and Evolution Equations. University of Alberta UNIVERSITY OF WYOMING Candidates should be familiar with nonlinear Edmonton, Alberta, Canada T6G 2G1 Department of Mathematics elliptic and parabolic POE theory as well as In accordance with Canadian Immigration re­ Tenure-Track Position in Analysis differential geometry. Additional knowledge of quirements priority will be given to Canadian geometric measure theory and/or low dimen­ citizens and permanent residents of Canada. The University of Wyoming Mathematics De­ sional topology would be of advantage. Closing date for applications is February 15, partment invites applications for a tenure-track The position will commence on 1 April 1993 1993. The University of Alberta is committed to position in Analysis starting August 1993. Ap­ or as soon as possible thereafter. The duration the principle of equity in employment. The Uni­ plicants must demonstrate strong ability in will be for one year initially with a possible versity encourages applications from aboriginal research, breadth of mathematical knowledge, extension for a further year subject to continued persons, disabled persons, members of visible interest in collaboration with mathematicians in funding. Candidates must have a Ph.D. or minorities, and women. other areas, strong commitment to high quality equivalent qualifications. undergraduate and graduate teaching, and will­ Salary: A$ 28,7oo-38,950 (Research Fellow ingness to supervise masters and doctoral stu­ Grade 1). dents. Preference will be given to researchers Further information UNIVERSrrE LAVAL with strength in the areas of functional, com­ Dr. K. Ecker (03) 344 5535 or Prof. J.H. Poste en Al~bre et Theorie des Nombres plex and harmonic analysis. The Mathematics Rubinstein (03) 344 5550. Department has 25 full-time faculty in applied Applications close: 15 February 1993. Le Departement de mathematiques et de statis­ mathematics, algebra/combinatorics, analysis Reference number: y/618/185. tique sollicite des candidatures pour un poste and mathematics education. Applications should be sent quoting three de carriere en algebra et theorie des nombres Complete applications consist of a vita, a referees to the Director, Personnel Services, qui sera disponible le 1er juin 1993. list of publications, a summary of research The University of Melbourne, Parkville Victoria, FONCTIONS interests, and three letters of recommenda­ 3052, Australia. •Enseignement des mathematiques aux tion sent directly to Professor Myron B. Allen, The University of Melbourne is an equal trois cycles, y compris dans des cours autres Chair, Department of Mathematics, University opportunity employer and has a smoke free que ceux des programmes de mathematiques. of Wyoming, Laramie, WY 82071-3036. Com­ workplace policy. •Direction d'etudiants de deuxieme et de pleted applications received by 1 January 1993 troisieme cycle. receive first consideration. Women and minori­ •Recherche fondamentale en algebra et ties are encouraged to apply. The University theorie des nombres. of Wyoming is an affirmative action/equal­ CANADA •Participation aux autres tAches universi­ opportunity employer. taires. McMASTER UNIVERSITY QUALIFICATIONS Department of Mathematics & Statistics eEtre titulaire d'un doctorat en mathematiques ou d'un diplOma juga equivalent. UNIVERSITY OF WYOMING Applications are invited for the Britton Post­ •Etre actif en recherche fondamentale et Department of Mathematics doctoral Fellowship In Mathematics. Named oeuvrer en algebra et theorie des nombres Tenure-Track Position In after Dr. Ronald Britton, the Britton Fellowship is ou dans un domaine relie a Ia theorie des Applied Mathematics intended for talented research mathematicians nombres. Manifester Ia volonte de developper who have recently completed the Ph.D. degree. l'equipe d'algebre et de theorie des nombres Applications are invited for a tenure-track po­ The Britton Fellowship is open to candidates du Departement et Ia composante a I'Universite sition in Applied Mathematics at the rank of of any nationality and selection will be based Laval du Centre interuniversitaire en calcul assistant professor. Candidates should demon­ upon the candidates research potential. In this mathematique algebrique. strate promise for excellence in both teaching year's competition, preference will be given to ePosseder des aptitudes pour l'enseignement, and research. Strong consideration will be given candidates working in algebraic number theory. y compris a de grands groupes. to, but is not limited to, numerical analysis and The Britton Fellowship is tenable for a period •Pouvoir enseigner en franQais. mathematical modeling. Salary is competitive of two years with effect from July 1, 1993 at a INFORMATION and commensurate with experience and quali­ salary of $35,000 per year plus a research grant L'Universite Laval applique un programme fications. The Mathematics Department has 25 of $5,000. In addition, the successful candidate d'acces a l'egalite qui consacre Ia moitie des full-time faculty members and about 35 M.S. will be considered for leave in 1993-94 to postes vacants a !'engagement de femmes. and Ph.D. students. Applicants should send participate in the "L-Functions" program at the Conformement aux exigences en matiere d'immi­ vita, three letters of recommendation, and brief Fields Institute for Research in Mathematical gration, cet avis de concours s'adresse en pre­ description of research plans to: Dr. Myron Allen, Sciences. Applications, including three letters of mier lieu aux personnes qui ont Ia citoyennete

84 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements

canadienne ou le statut de resident permanent tions. The deadline for applications is January au Canada. 15, 1993. An application should contain the cur­ HONG KONG Le salaire est determine par Ia conven­ riculum vitae of the candidate plus three letters tion collective suivant l'anciennete et le rang of reference sent directly from the referees. In THE CHINESE UNIVERSITY OF universitaire accordes. accordance with Canadian immigration regula­ HONG KONG Les personnes interessees sont priees de tions this advertisement is directed at Canadian faire parvenir, avant le ler mars 1993, a l'adresse citizens and permanent residents of Canada. THE CHINESE UNIVERSITY OF HONG KONG cidessous: The University of Waterloo encourages applica­ (founded 1963) offers comprehensive pro­ eune copie de leur curriculum vitae; tions from qualified women and men, members grammes up to the Ph.D. level in the Hu­ edes tires-a-part de quelques publications of visible minorities, native peoples and persons manities, Business Administration, Education, n~centes; with disabilities. All appointments are subject to Engineering, Medicine Science, Social Science, •deux lettres de recommendation temoignant the availability of funds. Please send applica­ and Architecture. Student enrollment is planned de leurs aptitudes professionnelles tant en en­ tions to: Dr. J.W. Lawrence, Chair, Department to expand to over 11 ,000 full-time equivalent seignement qu'en recherche. of Pure Mathematics, University of Waterloo, by 1994-95. The University is very active in Claude LEMAIRE, directeur Waterloo, Ontario, Canada, N2L 3G1. promoting research and consultancies and in Departement de mathematiques et de liasing with industry and the business sector statistique worldwide. English and/or Chinese are used in Universite Laval teaching and administration. Sainte-Foy (Quebec) Applications are invited for Canada G1 K 7P4 The Department of Mathematics GUAM The Department is seeking an outstanding candidate for a teaching position. Subject to UNIVERSITY OF GUAM qualifications and funding from the University, UNIVERSITY OF TORONTO this position may be filled at the rank of Department of Mathematics The University of Guam solicits applications to Lecturer or Senior Lecturer, or a higher rank. establish a list of eligibles for the following non­ Candidates in applied and pure mathematics are The Department solicits applications for a limited tenure track or tenure track, full-time positions encouraged to apply. Duties include teaching term Assistant Professorship at the Erindale (one-, two-, or three-year appointment subject and research, and candidates are expected to campus, for the three-year period from July to availability of funds): demonstrate excellence at each. 1, 1993 to June 30, 1996. This position is ASSISTANT PROFESSOR TO ASSOCIATE Salary subject to budgetary approval. Duties consist PROFESSOR Lecturer: HK$28,640 - 47,845 per month of teaching and research, and candidates must STATISTICS: 1 VACANCY; APPLIED MATH­ (US$44,062- 73,608 per year); Senior Lecturer: demonstrate clear strength in both. EMATICS: 1 VACANCY; PURE MATHEMAT­ HK$44,500 - 59,780 per month (US$68,462 Applicants should send their complete C.V. ICS: 2 VACANCIES - 91 ,969 per year); Reader: HK$46,425 - including a list of publications and any ap­ General Description: The Division of Math­ 61 ,675 per month (US$71 ,423 - 94,885 per propriate material about their teaching, and ematical Sciences offers a baccalaureate de­ year); Professor: HK$63,520 per month mini­ arrange to have at least four letters of reference gree in mathematics. The Division also has mum (US$97,723 per year minimum). sent directly to Professor K. Murty, Associate a large developmental program. Faculty are (approx. exchange rate: US$1=HK$7.8) Chair, Department of Mathematics, University of expected to participate in the developmental Conditions of Service Toronto, Toronto, Canada M5S 1A 1. At least one program. The nonnal faculty load is twelve (12) The University offers a competitive renu­ letter should deal with the candidate's teaching. credit hours per semester, of which at least three meration package. Starting salary will be com­ To insure full consideration, this infonnation (3) credit hours would be normally devoted to mensurate with qualifications and experience. should be received by February 28, 1993. the developmental program. Superannuable appointment benefits include The University of Toronto encourages both Educational and Professional Background: annual leave and long leave with full-pay, con­ women and men to apply. In accordance with A Ph.D. in the appropriate mathematical sci­ tributory superannuation scheme (University Canadian immigration requirements, priority will ence is required. An ability to teach a variety of 15%, appointee 5%), medical care, education be given to Canadian citizens and pennanent undergraduate courses is required. At least two allowances for children, housing benefit for eligi­ residents. years of teaching experience is preferred. ble appointee (with appointee contributing 7.5% ASSISTANT PROFESSOR $34,307.00- of salary towards the provision of housing). $50,765.00 per Academic Year; ASSOCIATE The University may also consider more flexible PROFESSOR $39,300.00-$59,307.00 per Aca­ terms for suitable candidates subject to mutual UNIVERSITY OF WATERLOO demic Year. (Salary will be commensurate with Department of Pure Mathematics agreement. qualifications and experience relevant to the Application Procedure position applied for by the applicant.) The Department of Pure Mathematics at the Send full resume in duplicate, with copies of Application Process: Submit current vi­ University of Waterloo invites applications for academic credentials (in duplicate) and recent tae, an official transcript sent directly from the one or more tenure track positions at the As­ publications, and arrange to have at least three institution awarding the highest degree and un­ sistant Professor level starting July 1 , 1993. For letters of reference sent directly to the Personnel official transcripts of other degrees earned, three its first appointment the Department is partic­ Office, The Chinese University of Hong Kong, current letters of reference sent directly from ularly interested in candidates whose research Shatin, N.T., Hong Kong (Fax: (852)603-5026) persons knowledgeable about the applicant's interests are related to Algebraic Geometry, before February 15, 1993. Quote reference academic and professional performances and Algebraic Topology or Differential Geometry. A number 113150912192 and mark "Recruitment" request for official application to: Prof. Martin second appointment (tenure track or definite on cover. De Beer, Chairperson, Mathematical Sciences term) may also be made in the above areas Division, c/o Personnel Services Division, UOG or in some area of Analysis. In order to be Station, Mangilao, Guam 96923. Deadline: considered for the position, a Ph.D. is required. March 1, 1993. An appointment will be offered only to someone For more infonnation, call UOG Personnel LEBANON with very strong research and teaching qualifi­ Services Division at (671) 734-9535, 734-91 09 cations. The University of Waterloo is committed or call Dr. John Rider, our representative on AMERICAN UNIVERSITY OF BEIRUT to increasing the number of its female faculty, the U.S. Mainland West Coast, Toll Free at Teaching Overseas and therefore applications from women mathe­ 1-800-821-9233. EEO/AAE maticians are particularly welcome. Duties will The Department of Mathematics at the American include research, and teaching at all levels. University of Beirut in Beirut, Lebanon (AUB) Salary will depend on the candidate's qualifica- invites applications for faculty positions at the

JANUARY 1993, VOLUME 40, NUMBER 1 85 ········-·······-·.-···· .. ····• ············ ··········-·-··------Classified Advertisements ---·--

level of Assistant Professor or above, available terests: operations research, statistics, and October 1, 1993. Candidates with specialization NEW PUBLISHER actuarial science. NE U.S. preferred. Available in the following fields are sought: Analysis, now. Neil Miller, 2 University Way, Princeton Jet, Probability Theory, and Topology. Applicants in SENDERO SCIENTIFIC PRESS NJ 08550. other disciplines will also be considered. Authors or potential authors of expository books Applicants should hold the Ph.D. degree and in mathematics and physics are invited to are expected to teach. undergraduate and to be PUBLICATIONS FOR SALE discuss· their plans and enquire about our committed to research . Postdoctoral experience in books accessible is preferred. services. We specialize to graduate students, though books on any Appointments are normally made for a three­ MATH SCI PRESS, 53 Jordan Rd ., Brook­ offer a unique approach are also year period. AUB is an EO/AA employer. level which line, MA 02146, 617-738-0307. Constrained We seek books which are the best Interested persons may send their curricula considered. Mechanics and Lie Theory and Geometric in their fields for their intended audiences. For vitae and three letters of recommendation before Structures in Nonlinear Physics, both by R. , see our ad on p. 1156 of the April15, 1993 to the Dean of Arts and Sciences, more information Hermann and $95. 44 titles. Write or phone for 1992 Notices or write to Stephen c/o New York Office of the American University November Special Sale Prices. Director, 1678 Shattuck Ave. , #70, of Beirut, 850 Third Avenue, New York, New Parrott, , CA 94709. York 10022, USA. Berkeley U.S. passports are presently invalid for travel to, in , or through Lebanon, and for residence in PUBLICATIONS WANTED Lebanon, by order of the Department of State, and therefore applications from individuals who Wanted: Mathematical books, journals, reprints, would travel to or reside in Lebanon on a U.S. POSITIONS WANTED ephemera. Contact R. K. Dennis, Math. Dept., passport cannot at this time be considered. White Hall, Cornell U., Ithaca, NY 14853-7901. : RESEARCH MATHEMATICIAN. PH.D., 1992, Tel: 607-255-4027, FAX: 607-255-7149. email BROWN UNIVERSITY. Specialty: Numerical [email protected] Analysis and Scientific Computing. Other in-

Advances in Soviet Mathematics Volume 11

Entire and Subharmonic Functions B. Ya. Levin, Editor The papers in this collection, written by participants of the Research Seminar on the Theory of Functions at Kharhov University, primarily address the theory of entire and subharrnonic functions. Founded in 1953 by B. Ya. Levin and still functioning today, this seminar ranges over different problems in the theory of functions, functional analysis, and related problems in calculus and mathematical physics. Entire and Subhannonic Functions contains works presented recently in the seminar.

1991 Mathematics Subject Class!ftcation: 14, 30, 31, 34, 42, 60 ISBN 0 - 8218-4110-6 , 275 pages (hardcover), October 1992 Individual member $88, List price $147, Institutional member $118 Your ordering code is ADVSOVI 11NA

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86 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Educ dlloll Improving Math And Science Education The Hong Kong University NCREL develops R&D resources to support lnstruclonalln.,rovements In elementary and aacondary schools In a 7-slate area. We have of Science and Technology recently established a Midwest Consortium for the Systemic Reform of Math & Science Educalon (MSC) to further the profeaalonal development of teachers and administrators. Help us will this vital task. Department of Mathematics Evaluator-Deslgntconduct activities for Int­ .& emal evaluation of the Consortium and A extemal evaluation of associated sites/ projects. A PhD in Educational Evalua­ tion or a related field, or an MS in evalu­ ation with 3 years related experience The Hong Kong University of Science and Technology is a new publicly­ required. Your professional expertise funded research University. Students have been admitted for October must ei'ICOI'f1)8IIS: case study and quall­ tatiwllquantltallve methods; survey re­ 1991 at both undergraduate and postgraduate levels, including the search; K-12 curriculum and Instruction doctorate. Enrollment is expected to grow to 7,000 FTE (on full-time issues as related to math/science; school change processes: strong writ­ equivalent basis) by 1995-1996. The medium of instruction is English. Ing skills and the ability to travel 30% of Applications are invited for the following positions: the time. llalhiScllnce Education Specialists. .& Assess needs and provide on-going as­ Professor: Minimum US$97,700 per annum -~~lnthe~~mplsmenlaoon Reader: US$71 ,400--US$94,900 per annum of Instructional ln.,rovements In math and 8Cience ecb:allon, and assist In de­ Senior Lecturer: US$68,500--US$92,000 per annum veloping professional development Ini­ Lecturer: US$44, 100--US$73,600 per annum tiatives. A Master's degree with a Math/ Science content specially, coupled with experience in NraVurban K-12 systems The Department will place major emphasis on applications with an or other underrepresented and underaefved populalions, requlracl. Pref­ appropriate component of pure mathematics to preserve the integrity of erence will be given to candidates fa· the discipline. Research areas will be highly interdisciplinary and will niliar with contempormy pedagogical theory/practice, expertise in profes­ include discrete mathematics, scientific computation, statistics, fluid and sional/Organizational development de­ solid mechanics, mathematical physics, analysis, algebra, geometry, etc. sign and the abHity to develop and re­ view proposals. Telecommunications/Database Applicants should have a PhD degree in the relevant fields. 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Sabbatical leave, if approved, will be at puler teleconferencing/on-line data­ baaes8IMfllal. full salary. Program Mllelant-Rasearch support. con­ .& ferwlce participation and delivery of pro­ Applications/nominations should be sent with a complete CV, together - fessional development programs are key accountabilities. A BS In Math/Sci­ with the name and address of at least three referees, to: ence and experie~ In primary/second­ my education required. Fanillarlty with cognitive approaches to math/scle~ The Director of Personnel education preferred. The Hong Kong University of Science and Technology Applicants must respond by Janumy 15,1993 Clear Water Bay to Doria Belknap, Personnel Director, NCREL, 1100 Spring Rd., Sula 300, Oek Kowloon Brook, IL SOU1·1480, Attention: Dept Hong Kong IISC. To be conaldered, the following is r• qulnld: cover latter, detailed ....,me or cur­ Fax No: (852) 358.0700 riculum vitae, and h1l8 references will phone numbers. An equal opportunity employer, we actively encotl'· The search will continue until suitable appointments are made. Appli­ age women cants interested in positions in the academic year 1993-1994 are, NCREIa.=!- and minorities -to apply. however, advised to send in their applications before 1 March 1993. ESSENTIAL MATHEMATICS FROM CAMBRIDGE Affine Lie Algebras and Discrete Groups and Geometry Quantum Groups Edited by W. J. Harvey and C. Maclachlan An Introduction, with Applications in Conformal London Mathematical Society Lecture Note Series 173 Field Theory 1992 248 pp. 42932-3 Paper $39.95 Jurgen Fuchs Categories and Computer Science Cambridge Monographs on Mathematical Physics R. F. C. Walters 1992 447 pp. 41593-4 Hardcover $89.95 Cambridge Computer Science Thxts 28 An Introduction to Copublished with the Carslaw Publications 1992 176 pp. 41997-2 Hardcover $49.95 Mathematical Cosmology 42226-4 Paper $19.95 J. 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FUNDAMENI'ALS OF THE THEORY PISOT AND SALEM NUMBERS LOOP SPACES, CHARACIERIS11C by M.J. BERTIN, Universit6 Pierre et Marie Curie, Paris, CLASSES AND GEOMEIRIC OF OPERATOR ALGEBRAS France, A. DECOMJIS.GUILLOUX, Universit6 Pierre at Marie Special Topies Curle,Paris,France,M.GRANDEI'-HUQOT,Universit6deCaen, QUANI1ZA110N Caen, France, M. PATHIAUX-GELEFOSSE, Universit6 Pierre by RICHARD v. KADISON, University of Pennsylvania, Phila­ by JEAN-We BRYUNSKI, The Penn State University, et Marie Curie, Paris, France & J.P. SCHREIBER, Universit6 delphia, PA & JOHN R. RINQROSE, University of Newcastle, University Park, PA Newcastle upon Tyne, UK d'Orieans, Orleans, France "This book organizes and makes accessible to a wide This book develops a Chem-Weil theory of character­ The many readers of the highly acclaimed treatise on istic classes ofgerbes. Gerbes(inventedbyGiraud)are which this volume is based will enthusiastically wel­ audience much material previously found only in the research literature. It is a fitting tribute to thase fiber bundles whose fibers are groupoids (certain cat­ come the authors' decision to share with them their egories). Gerbes arise naturally in geometry, for in­ mathematicians Charles Pisot and Raphael Salem detailed solutions to the stimulating and penetrating stance, whenever one has a family of symplectic exercises that appeared in the first volume. With whose work laid the foundation ofso much ofthe work described here ... " manifolds or a bundle of projective Hilbert spaces. A clarity, thoroughness, and depth, these solutions this -FROM TilE PREFACE BY DAVID W. BOYD, product of theory is a geometric construction of supplement the basic theory and provide an invaluable ordinary degree 3 cohomology of manifolds, with tool for students and researchers in mathelilatics and VANCOUVER, CANADA CONTENTS: Preface • Introduction • Compact Families of applications to loop spaces and loop groups, group theoretical physics and engineering. They provide Rational Functions • Meromorphic Functions D(O,I). 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VOLUME III: ofFonnal Power Series • Pisot Sequences, Boyd Sequences and Linear CONTENTS: Introduction • Complexes of Sheaves and Their Elementary Theory ·An E:urcille ApprtHit:h Recummce • Generalizations of Fisot and Boyd Sequences • The Cohomology • Line Bundles and Geometric Quantization • Kilhler Salem-Zygmund Theorem GeometryoftheSpaceofKnots•DegJee3Cohomology:TheDixmier• CONTENTS: Preface • Linear Spaces • Basics of Hilbert Space and Douady Theory • Degree 3 Cohomology: Sheaves ofGroupoids • Line Linear Operators • Banach Algebras • Elemental)' C"-Aigebra Theory 1992 291 PP. HARDCOVER ISBN Q.8176-284S4 Bundles over Loop Spaces • The Dirac Monopole • Index • Elementary von Newnann Algebra Theory · $124.00 1993 320 HARDCOVER ISBN Q.8176-3644-7 $49.50 1991 287 PP. HARDCOVER ISBN 0-8176-3497-5 $34.50 PP. PROGRESS IN MATHEMATICS, VOLUME 107 VOLUME IV: New Textbook! 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It is ideal for a full 1900, the work presents a. careful analysis and recon­ " .. .it is the clearest this reviewer has ever seen (of a year Ph.D. qualifying course and sufficiently self struction of how Russell wrote The Principles of great many expositions of Galois Theory that have contained for private study by non-specialists wishing Mathematics from 1898 to 1903. A detailed historical appeared in the lost fifty years). Paiticu/Qrly remark­ to survey the topic. analysis of how other historians have interpreted the able is theauthar' s avoidance ofall temptations to give CONTENTS: Topological Manifolds • The Local Theory of same events ("standard" interpretations as the author Smooth Functions • The Global Theory of Smooth Functions • Flows pretty proofs ofneatly arranged theorems at the cost of calls them) is a further feature of the book which, in clarity, a temptation that has been the bane ofGalois and Foliations • LieGroupsandLieAigebras • Convectors and 1-Forms • Multilinear Alsebra and Tensors • Integration of Forms and de Rham addition, examines how other paradoxes emerged as a theory. Highly recommended." Cohomology • Fonns and Foliations • Riemannian Geometry • Index consequence of Russell's influence. -GIAN-CARLO ROTA, TilE BULLETIN OF MATHEMATICS 1993 361 PP. (APPROX.) ISBN 0-8176-3626-9 1992 288 PP. 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HARDCOVER ISBN 0-8176-3522-X $49.50 VISIT: Your Local Technical Bookstore, or urge your This bookisaboutoperatorsofDiractypeonmanifolds librarian to Older for your department. with boundary. Part one presents the analytic pre­ liminaries and then focuses on the role of the Ptzy~MIIl CIJII "-made by clwcl:,lfiDMY ortkr or crtdit C4l'd. Pkase encltne $2.50 for shipping & lumdling for tlw first book ($1.00 for Grassmannian ofpseudo-differential projections. The each additiOIIIJ! book) and add appropriiJit! 141est

Mathematic a® Across the Curriculum Workshops at Vanderbilt University Tnmslatloas of Summer 1993 MATHEMATICAL MONOGRAPHS Volume 112 Mathematica8 software from Wolfram Research enables significant new approaches to teaching any discipline where mathematics is important. Vanderbilt University will host its second series of Introduction to the General Theory workshops-designed for collegiate faculty-on using Mathematica• in various disciplines. The sessions will be led by of Singular Perturbations Vanderbilt faculty with experience in using Mathematica• in S.A.Lomov instruction, several of who led the successful 1992 workshops. The workshops will make extensive use of Vanderbilt's electronic This book is aimed at researchers and students in physics, classroom. so each workshop must be limited to thirty participants. mathematics, and engineering. It contains the first systematic presentation of a general approach to the integration of singularly For more information, please write Mathematic a• Workshops, perturbed differential equations describing nonuniform transi­ Vanderbilt University, 419 21st Avenue South, Nashville, TN tions, such as the occurrence of a boundary layer, discontinuities, 37240-0007; call 615-322-2951; or e-mail InterNet, boundary effects, and so on. The method of regularization of [email protected]. For fust consideration, singular perturbations presented here can be applied to the asymp­ please make a reservation with Vanderbilt by March 19, 1993. The totic integration of systems of ordinary and partial differential workshop series is supported in part by a grant from the Pew equations. Charitable Trusts, and there is a $100 registration fee. Faculty from historically black institutions are especially welcome. 1991 Mathemntics Subject Classification: 34 ISBN 0-8218-4569-1, 375 pages (hardcover), Dec. 1992 June 6 - 11: Mathematics, including calculus, differential Indiv. member $121, List price $201, Inst. member $161 equations, &. linear algebra To order, please specify MMON0/112NA

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Technical reports have functioned as the preprint literature for the field of computer science. Over the past thirty years, Stanford University has collected these reports on a regular basis from approximately 100 computer science departments and research groups world~ wide. This publication is a listing of 36,364 reports in the Stanford collection. The reports are listed in order by institu­ tion name and, within the institution listings, by report number. In addition, there is a list of institution names and codes and an author index. This publication is useful to researchers in mathematics and com~ puter science, as well as to librarians and others needing access to this kind of bibliographic information. Computer Science Technical Reports is also available through the AMS online databa~e, Math Sci®. Contact AMS Database Services for more details.

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M. RENARDY and R.C. ROGERS, both of T. BECKER and V. WEISPFENNING in M. ENOCK, Universit6 Pierre et Marie Curie Virginia Polytechnic Institute and State cooperation with H. KREDEL, all of and J.-M. SCHWARTZ, both of Paris, France University, Blacksburg, VA Universitit Passau, Germany AN INTRODUCTION TO KAC ALGEBRAS AND GROBNER BASES DUALITY OF LOCALLY PARTIAL DIFFERENTIAL A ComputatioiUll Approach to EQUAnONS Commutative Algebra COMPACT GROUPS ! Algorithms using Grobner bases Develops the general theory of Kac Based on a four-semester course in lead to exact conclusions concerning algebras and their duality, with partial differential equations, this the solutions of systems of nonlinear emphasis on the analytical aspects text opens with an introduction to equations, such as the number of of the subject instead of the purely the subject matter and its character­ solutions or the dimension of the algebraic ones. The category of Kac istics which contain the Cauchy­ solution set, and the computation of algebras developed in this book Kovalevskaya Theorem and the solutions to arbitrary precision. fully answers the original duality Holmgren's Uniqueness Theorem. This book on Grobner bases, assum­ problem, but is not yet sufficiently Conservation laws and shocks are ing the mathematical background of non-unimodular to include quantum then covered, followed by maxi­ an advanced undergraduate, will be groups. This self-contained account mum principles and function spaces. both a reference manual for the of the theory will be of interest to all Linear elliptic equations and nonlin­ working mathematician or computer researchers working in quantum ear elliptic equations are also includ­ algebraist as well as an introductory groups, and more generally also to ed. The text concludes with energy textbook. those working in C* algebras or methods for evolution problems and theoretical physics. semigroup methods. This book 1993/592 pp., 50 tabs./Hardcover $49.00/ISBN 0.387-97971-9 provides a thorough introduction to 1992/257 pp./Hardcover/$98.00 Graduate Texts in Mathematics, Volume ISBN 0.387-54745-2 partial differential equations, bring­ 141 ing the students up to the level at which research can begin. Third Edition Second Edition 1993/app. 440 pp., 21 illus./Hardcover B. tKSENDAL, University of Oslo, Norway $42.00/ISBN 0.387-97952·2 F.W. ANDERSON, University of Oregon, Texts in Applied Mathematics, Volume 13 Eugene, OR; K.R. FULLER, University of STOCHAS'nC DIFFER· Iowa, Iowa City, lA ENnAL EQUAnONS Second Edition RINGS AND CATEGORIES An Introduction with AppUcations NEAL KOBUTZ, University of Washington, OF MODULES FROM THE REVIEWS: Seattle, WA A self-contained account of much of " ... The author, a lucid mind with a INTRODUCTION TO the theory of rings and modules. fine pedagogical instinct, has writ­ Following a brief outline of the ten a splendid text ... The book can be EI.LIPIIC CURVES AND foundations, the book moves on to an ideal text for a graduate course, MODULAR FORMS basic definitions and properties of but it is also recommended to ana­ rings, modules and lysts (in particular, those working in The theory of elliptic curves and differential equations and determin­ modular forms provides a fruitful homomorphisms. The remainder of the text gives comprehensive treat­ istic dynamical systems and control) meeting ground for such diverse who wish to learn quickly what areas as number theory, complex ments of direct sums, finiteness conditions. the Wedderbum-Artin stochastic differential equations are analysis, algebraic geometry, and all about." representation theory. This book Theorem, the Jacobson radical, the hom and tensor functions, Morita -ACTA SCIENTIARUM MATHEMATICARUM starts out with a problem from 1992/224 pp., 10 illus-/Softcover/$32.00 elementary number theory and equivalence and duality, decomposi­ ISBN 0.387-53335-4 proceeds to lead its reader into the tion theory, and semiperfect and Universitext modem theory, covering such topics perfect rings. This second edition as the Hasse-Weil L-function and includes a chapter containing many the conjecture of Birch and ' of the classical results on Artinian Swinnerton-Dyer. The second rings. 3 Easy Ways to Order: edition of this text includes an 1992/376 pp./Hardcover/$49.50 CALL Toll-Free 1-800-SPRINGER updated bibliography indicating the ISBN 0.387-97845-3 (1-800-777-4643) In NJ call 201-3484033. Graduate Texts in Mathematics, Volume 13 Please mention 5259 when ordering by phone. latest, dramatic changes in the WilliE to Sprireer-Ver1ag New York, Inc., direction of proving the Birch and Oept. #5259, PO Box 2485, Swinnerton conjecture. It also Secaucus, NJ 07096-2491. discusses the current state of knowl­ VISIT your local technical bookstore. Payment can be made by check, edge of elliptic curves. purchase order, or credit caret Please enclose for shipping addition­ 1993/248 pp., 25 illus./Hardcover $2.50 ($1.00 al books) & add appropriate sales tax if you $49.00/ISBN 0.387-97966-2 reside in NY, MA, PA, or CA. Graduate Texts in Mathematics, Volume 97 NJ, VT, Canadian residents please add 7% G5T. Instructors: Call or write for information on textbook examination copies! Remember ••• your 30-day return privilege is always guaranteed! 1/93 REFERENCE #: S259