OTICES OF THE
AMERICAN MATHEMATICAL SOCIETY
Newton's Principia Read 300 Years Later page 1148 V. /. Arno/'d and V. A. Vasi/'ev
1989 Annual AMS-MAA Survey page 1155
Los Angeles Meeting (November 18-19) page 1225
NOVEMBER 1989, VOLUME 36, NUMBER 9
Providence, Rhode Island, USA ISSN 0002-9920 Calendar of AMS Meetings and Conferences
This calendar lists all meetings which have been approved prior to Mathematical Society in the issue corresponding to that of the Notices the date this issue of Notices was sent to the press. The summer which contains the program of the meeting. Abstracts should be sub and annual meetings are joint meetings of the Mathematical Associ mitted on special forms which are available in many departments of ation of America and the American Mathematical Society. The meet mathematics and from the headquarters office of the Society. Ab ing dates which fall rather far in the future are subject to change; this stracts of papers to be presented at the meeting must be received is particularly true of meetings to which no numbers have been as at the headquarters of the Society in Providence, Rhode Island, on signed. Programs of the meetings will appear in the issues indicated or before the deadline given below for the meeting. Note that the below. First and supplementary announcements of the meetings will deadline for abstracts for consideration for presentation at special have appeared in earlier issues. sessions is usually three weeks earlier than that specified below. For Abstracts of papers presented at a meeting of the Society are pub additional information, consult the meeting announcements and the lished in the journal Abstracts of papers presented to the American list of organizers of special sessions. Meetings
Abstract Program Meeting# Date Place Deadline Issue 853 * November 18-19, 1989 Los Angeles, California Expired November 854 * January 17-20, 1990 Louisville, Kentucky October 11 December t (96th Annual Meeting) 855 * March 16-17, 1990 Manhattan, Kansas December 12 February 856 * March 23-24, 1990 Fayetteville, Arkansas December 12 February 857 * April 7-8, 1990 University Park, Pennsylvania January 25 March 858 * April 19-22, 1990 Albuquerque, New Mexico January 25 March 859 * August 8-11, 1990 Columbus, Ohio May 18 July I August (93rd Summer Meeting) November 2-3, 1990 Denton, Texas January 16-19, 1991 San Francisco, California (97th Annual Meeting) August 8-11, 1991 Orono, Maine (94th Summer Meeting) January 8-11 , 1992 Baltimore, Maryland (98th Annual Meeting) June 29-July 1, 1992 Cambridge, England (Joint Meeting with the London Mathematical Society) January 13-16, 1993 San Antonio, Texas (99th Annual Meeting) January 5-8, 1994 Cincinnati, Ohio (100th Annual Meeting) *Please refer to page 1238 for listing of special sessions. t Housing deadline is November 17
Conferences
January 16-17, 1990: AMS Short Course on Mathematical June 1990: AMS-SIAM Summer Seminar on Vortex Dynamics Questions in Robotics, Louisville, Kentucky. and Vortex Methods, location to be announced. June 7-July 4, 1990: Joint Summer Research Conferences in July 1990: AMS Summer Research Institute on Differential the Mathematical Sciences, University of Massachusetts at Geometry, University of California, Los Angeles, California Amherst, Massachusetts. Events Cosponsored by the Society
February 15-20, 1990: Section A (Mathematics) Sessions at the AAAS Annual Meeting, New Orleans, Louisiana. Deadlines
January Issue February Issue March Issue April Issue Classified Ads* Nov 27, 1989 Jan 10, 1990 Feb 8, 1990 March 6, 1990 News Items Nov 27, 1989 Jan 2, 1990 Feb 9, 1990 March 5, 1990 Meeting Announcements** Nov 20, 1989 Dec 21, 1989 Jan 29, 1990 February 27, 1990 * Please contact AMS Advertising Department for an Advertising Rate Card for display advertising deadlines. ** For material to appear in the Math~matical Sciences Meetings and Conferences section. OTICES OF THE
AMERICAN MATHEMATICAL SOCIETY
ARTICLES DEPARTMENTS 1148 Newton's Principia Read 300 Years Later V.I. Arnol'd and V. A. Vasil'ev 1147 Letters to the Editor The authors describe a theorem of Newton, and also some other new mathematical theorems, partially contained in the principia and partially 1216 News and Announcements suggested by Newton's text. 1220 Funding Information for the 1155 1989 Annual AMS-MAA Survey (First Report) Mathematical Sciences The first report on the 1989 Survey includes the 1989 survey of new 1223 Meetings and Conferences doctorates, starting salaries of new doctorates, faculty salaries, and of the AMS (Listing) a list of names and thesis titles for members of the 1988-1989 Ph.D. class. 1245 Mathematical Sciences 1189 A Differing View on Mathematics Education Reform Eleanor G. Palais Meetings and Conferences This article talks about current mathematics education reform and 1255 New AMS Publications whether efforts and money are being directed at the correct problems. 1261 AMS Reports and 1193 Survey of American Research Journals Communications This survey is our third cost-comparison study of mathematical Bylaws of the AMS, 1261 research journals, the first of which was published in 1983. We have AMS Funds, Prizes, Officers, brought that information up to date in this survey, expanded to include and Lecturers, 1266 comparisons between subscription years 1984, 1986, and 1988. 1276 Miscellaneous FEATURE COLUMNS Personal Items, 1276 Deaths, 1276 1199 Computers and Mathematics Jon Barwise 1277 New Members of the AMS This month's column contains two articles on TEX. one from a publisher's point of view and one from an author's point of view. 1278 Classified Advertising The column also contains three software reviews: a two-part review of PowerMath II; a review of Rubik's Algebra; and a review of Tarski's 1319 Forms World. 1211 Inside the AMS Accreditation of mathematics departments and small travel grants for mathematicians were two issues that raised lively debate at the recent meeting of the AMS Committee on Science Policy, held in Washington, DC in September. Allyn Jackson presents a synopsis of the Committee's discussion. 1214 Washington Outlook This month's column, written by Hans J. Oser, comments on the NSF Budget for FY 1990, a report released by D. Allan Bromley entitled ··Federal High Performance Computing Program;· and appointments made in the Department of Education.
NOVEMBER 1989, VOLUME 36, NUMBER 9 1145 Mentoring and the Mathematics Postdoc By most accounts, mathematics receives an improved report on the health of its postdoctoral program. Maybe mathematics does AMERICAN MATHEMATICAL SOCIETY not compare so well to disciplines in the natural sciences, but in sheer numbers it has shown a dramatic increase in postdocs since the first "David Report". Yet, data showing numerical increases
EDITORIAL COMMITTEE provide little insight into the health of the postdoctoral program in Robert J. Blattner, Michael G. Crandall mathematics. Indeed, mathematics as a discipline possibly has the Robert M. Fossum (Chairman) lowest expectations from the structure of its postdoctoral program Lucy J. Garnett, D. J. Lewis and, therefore, possibly one of the least effective postdoctoral Nancy K. Stanton, Robert E. L. Turner programs. In contrast to related disciplines, we do not view the MANAGING EDITOR postdoc as a continuing education/training period with a mentor but Donovan H. VanOsdol rather an opportunity to be free from non-research demands. ASSOCIATE EDITORS One of the reasons for the recent increase in the number of postdocs Ronald L. Graham, Special Articles Jeffrey C. Lagarias, Special Articles in mathematics is that, for statistical purposes, some funding agencies designate a researcher who receives financial support as a postdoc or SUBSCRIPTION INFORMATION Subscription prices for Volume 36 (1989) are a senior researcher simply by consideration of the number of years $1 081ist; $86 institutional member; $65 individual since the Ph.D. degree. (There have been some real increases with member. (The subscription price for members is the NSF Postdoctoral Research Fellowships and the various institute included in the annual dues.) A late charge of 10% of the subscription price will be imposed postdocs.) Apart from this relabelling, there is a rather established upon orders received from nonmembers after image of a postdoc appointment in mathematics. One is a postdoc January 1 of the subscription year. Add for post if one receives financial support for research (meaning, generally, a age: Surface delivery outside the United States and lndia-$10; to lndia-$20; expedited deliv reduced teaching assignment), one does not hold a "tenure-track" ery to destinations in North America-$15; else appointment at the same institution as the postdoc appointment, where-$38. Subscriptions and orders for AMS and one has a title that includes in it somewhere the word "postdoc" publications should be addressed to the Amer ican Mathematical Society, P.O. Box 1571, An or "fellow". nex Station, Providence, Rl 02901-9930. All or Postdoctoral appointments in mathematics, in general, have no ders must be prepaid. active component of mentoring. They function more as recognition ADVERTISING programs for the very select. Often the same individuals move Notices publishes situations wanted and classi from one postdoc appointment to the next, maintaining non-tenure fied advertising, and display advertising for pub lishers and academic or scientific organizations. track academic appointments for many years past the Ph.D. In the Copyright @ 1989 by the American Mathemat natural sciences, a postdoctoral appointment is ordinarily expected ical Society. All rights reserved. Printed in the upon earning the Ph.D. degree. There is a period of continuing United States of America. education/training with an active mentoring component and then The paper used in this journal is acid-free and falls within the guidelines established to ensure the opportunity for a postdoc no longer exists. This is not the case permanence and durability. €9 Most of this publi in mathematics. cation was typeset using the TeX typesetting sys tem. Should the postdoctoral position in mathematics be less-the-exception [Notices of the American Mathematical Society is and more-the-rule upon receipt of the Ph.D.? Should there be active published ten times a year (January, February, mentoring that not only concerns development of research potential March, April, MayjJune, July/August, Septem but emphasizes development of teaching skills and preparation for ber, October, November, December) by the Amer ican Mathematical Society at 201 Charles Street, the new Ph.D. to address the myriad of professional expectations? Providence, Rl 02904. Second class postage paid The whole subject of mentoring in the mathematics profession is at Providence, Rl and additional mailing offices. POSTMASTER: Send address change notices to being discussed by various groups in our community. In particular, Notices of the American Mathematical Society, the AMS Committee on Science Policy debated several aspects of Customer Service Department, American the issues mentioned above at their recent meeting. This subject will Mathematical Society, P. 0. Box 6248, Provi dence, Rl 02940.] Publication here of the Soci be a major topic of discussion at the Committee's next meeting, and ety's street address, and the other information in it is very likely that these discussions will lead to recommendations brackets above, is a technical requirement of the for Society action. U. S. Postal Service. All correspondence should be mailed to the Post Office Box, NOT the street William Jaco address. Executive Director
1146 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY In order to render the availability Policy on Letters to the Editor of results easier, we have planned to Letters submitted for publication in Notices Letters write a bibliography of publications are reviewed by the Editorial Committee, about stochastic orderings (in the whose task is to determine which ones are to the Editor broad sense) and applications. All suitable for publication. The publication schedule normally requires from two to the scholars who have written papers four months between receipt of the letter in in this area are kindly requested to Providence and publication of the earliest send us reprints (or, at least, a list of issue of Notices in which it could appear. Publication decisions are ultimately Comment on Report of NSF their relevant papers). Of course, we would greatly appreciate to receive made by majority vote of the Editorial Advisory Committee Meeting Committee, with ample provision for prior partial bibliographies, whenever they discussion by committee members, by mail The American Mathematical Soci exist. or at meetings. Because of this discussion ety exists to support mathematical Suggestions and indications of re period, some letters may require as much research. Such research requires pub searchers in the field are as welcome as seven months before a final decision is lication and papers. It is thus trou as reprints. made. Letters which have been, or may be, published elsewhere will be considered, but bling to find in these Notices (Vol. Karl Mosler the Managing Editor of Notices should be 36, No.5, MayjJune 1989, p. 541) a Fachbereich Wirtschafts- und informed of this fact when the letter is sub report of a meeting at the National Organisationswissenschaften mitted. Science Foundation of the NSF advi UniversiHit der The committee reserves the right to sory committee for Mathematics, in Bundeswehr Hamburg edit letters. Notices does not ordinarily publish which one of the members of that Postfach 70 08 22 complaints about reviews of books or arti committee "questioned the success D-2000 Hamburg 70 cles, although rebuttals and correspondence of the current system, which he says Federal Republic of Germany concerning reviews in Bulletin of the Amer 'produces papers but not people' ". email: [email protected] ican Mathematical Society will be consid I submit that no system can pro ered for publication. All published letters Marco Scarsini must include the name of the author. duce mathematical people without Letters should be typed and in legible producing the corresponding papers. Dipartimento di Scienze Attuariali form or they will be returned to the sender, The opposite opinion seems danger Universita "La Sapienza" possibly resulting in a delay of publication. ous and counterproductive-especially Via del Castro Laurenziano 9 Letters should be mailed to the Editor at this time when NSF support for 00161 Roma, Italy of Notices, American Mathematical Soci email: scarsini@irmunisa. bitnet ety, P.O. Box 6248, Providence, RI 02940, individual research is erratic, inade and will be acknowledged on receipt. quate, and apparently subservient to (Received July 19, 1989) the interest of industry, and when there is no mathematical scientist on the policy setting National Science Board. THE FLOWERING OF APPLIED MATHEMATICS IN AMERICA PETER D. LAX Saunders Mac Lane This perceptive and wide-ranging videotaped lecture provides University of Chicago a perspective on the development of applied mathematics (Received August 28, 1989) I in America from one who has been at the forefront of research in this field for almost forty years. Asserting that A Bibliography mathematics doesn't ··trickle down .. to the sciences but rather lives in partnership with them, Lax elucidates certain themes on Stochastic Orderings in applied mathematics by describing some of the field's Stochastic orderings and related top highlights in such areas as fluid dynamics, mathematical I physics, and optimization. He indicates the ways in which ics have been extensively studied other sciences have stimulated developments in mathematics and used in different disciplines like and describes some of the decisive mathematical contributions probability, statistics, operations re made by scientists from other fields. In addition, he turns his search, finance, economics, mathe experienced eye to issues of science policy, undergraduate matical physics, etc. It is often diffi education, and the role of computation in mathematical research. All prices subject to change. Shipment will cult for researchers to keep track of be made by surface. For air delivery add, 1980 Mathematics Subject Classification: 00 I st book $5, each additional book $3, maxi the developments of the field, since VHS format, approx. one hour, mum $100. Prepayment required. Order from results are published in many differ January 1989 American Mathematical Society, P.O. Box Price $59 1571, Annex Station, Providence, RI 02901- ent journals in seemingly unrelated 1571, or call toll free 800-321-4AMS to charge To order, please specify VIDLAX/ NA with VISA or MasterCard. areas.
NOVEMBER 1989, VOLUME 36, NUMBER 9 1147 Newton's Principia Read 300 Years Later
V. I. Arno/1d and V. A. Vasil' ev
Theorem 1 (Newton 1687, see [N], Lemma XXVIII). Abstract. Analyzing Kepler's law in two dimensions, Newton There exists no algebraically integrable convex nonsingu discovered an astonishingly modern topological proof of the lar algebraic curve. transcendence of Abelian integrals. Newton's theorem was not (There exist compact integrable algebraic curves, coo really understood by mathematicians at that time, since it was smooth at all their points but one, at which they have based on the topology of Riemann surfaces. Thus, it was in any prescribed finite number of derivatives. Example: contemporaries and for 20th comprehensible both for Newton's the curve century mathematician who were bred on set theory and the ym = x 1. Newton's Theorem on the Nonintegrability of Ovals An algebraic oval in the plane R2 is part of a real algebraic curve (i.e., the zero set of a polynomial), X homeomorphic to a circle. An oval is called nonsingular if it is C 00-diffeomorphic to the circle. An oval is called algebraically integrable if the area of its segment is an algebraic function of the secant line (i.e., there exists a nontrivial polynomial F ( V, a, b, c) which vanishes if V is the area cut by the line ax+ by = c). Fig. 2 An oval is locally algebraically integrable if the area of Newton's Proof. Let us fix a point 0 inside the oval, its segments coincides with an algebraic function in a and a ray with the origin 0. Consider the function on neighborhood of any line (but these functions may be the oval (or, equivalently, on the space of all the rays different for different lines). issuing from the origin), whose value at the point A equals the area of the sector bounded by the fixed ray, the radius OA and the oval, see Fig. 1. If the oval is integrable, this function is algebraic: a sector consists of the segment and a triangle, and the areas of both of these depend algebraically on the point A: this follows from the algebraicity and the integrability of the oval. Let us move the point A along the oval. After any complete cycle, the area of the sector increases by the area bounded by the oval. In particular, for the same point A this function has an infinite number of values which contradicts its algebraicity. Moreover, the same reasoning proves the following Fig. 1 stronger statement. 1148 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Newton's Principia Theorem 2 (see [AI], [A5]). There exists no locally alge Some of the above requirements on the oval may braically integrable nonsingular convex algebraic oval. be omitted. Newton himself does not require either Does there exist any obstacle to applying the preceding nonsingularity or convexity. He only indicates that the argument to a singular oval, e.g. to the curve of Fig. 2? oval should not touch any conjugate branch connecting Indeed, we have used the fact that the area of a sector it with infinity. (This requirement was added in 1713 is an analytic function of the point A. In the case of and appears only in the second edition of the Principia.) singular curves the area is, in general, nonanalytic: when Huygens wrote in a letter to Leibniz ( 1691) that Newton's A crosses the singular point, the area function may jump argument is wrong, because it may be applied even to from one local branch to another. a triangle (which is, of course, integrable). Leibniz had answered that a triangle may hardly be considered as an Lemma. Let the area of the sector (POA on Fig. I) in a oval. He suggested a more dangerous counterexample -smooth algebraic convex oval be a locally algebraic coo the Huygens lemniscate curve (described in one of function of the point A. Then this function is even his preceding letters to Leibniz). The lemniscate curve globally algebraic. evidently satisfies Newton's definition of an oval but it Proof. For a C 00-smooth oval, the area of the sector, con is algebraically integrable.* sidered as a function of the point A, has an asymptotic* Leibniz also conjectured the transcendence of the expansion area of almost any segment, which a line with rational (or algebraic) coefficients cuts from an oval, given by an (1) algebraic equation with rational coefficients. For instance, he conjectured the transcendence of the area 7C bounded near any point. Indeed, Newton discovered that any by a circle of radius 1. The general problem of Leibniz branch of an algebraic function has an asymptotic contains Hilbert's seventh problem, but, unlike Hilbert's Puiseux expansion problem, Leibniz' problem seems to be still unsolved. The requirement of algebraicity of ovals in Theorem 1 is unnecessary, since a smooth integrable oval is algebraic. near any point (it follows from the method of the Indeed, let us consider the zero set of the area "Newton parallelogram"). But, if such an expansion for function on the space of lines in R2• This set is a the graph of the area contains a term with a noniriteger (semi)algebraic curve C on the dual projective plane of degree oft, then our oval will not be smooth. It will also the plane where the initial oval lives. This initial oval is be nonsmooth if the expansions ( 1) for the two branches the envelope of the lines belonging to the algebraic set of this graph at two sides of our point are different. C of lines. Such an envelope (the dual curve of C) is However, a locally algebraic function, having an ex algebraic. pansion ( 1) at any point, is globally algebraic. Indeed, The algebraicity of the dual curve K of an algebraic in the opposite case there would exist a point on the curve C was evident to Newton. Indeed, the envelope two sides of which the graph would coincide with two is the limit for h --+ 0 of the curves Kh, formed by different algebraic curves. Both curves having the same the intersections of the lines belonging to C, having the expansion ( 1) now implies their order of tangency at angular coefficients t and t +h. The degree of the curves this point would be infinite. This contradicts Bezout's Kh being independent of h, the limit curve K is algebraic. theorem (formulated by Newton in the same paragraph The independence of the degree on h follows from of Principia): the number of (perhaps, confluent) inter the calculation of the degree of a resultant (that is, the section points of different irreducible algebraic curves is very calculation, which proves the "Bezout" theorem, majorized by the product of their degrees; this proves majorizing the number of intersection points of two the lemma. curves of degrees m and n by mn; this theorem is Newton was led to his theorem by a particular case: explicitly formulated and used by Newton on the same the position of a planet on the Kepler ellipse cannot page of the Principia that we discuss here). depend algebraically on the time (or on the area of Newton's theorem can be extended to nonconvex the sector, swept by the radii, which is proportional to curves, and also to multidimensional hypersurfaces. The the time according to the two-dimensional Kepler law). proofs are based on monodromy theory (or Picard Newton also noted that the length of an arc of an oval, Lefschetz theory), i.e., on the study of the ramification cut by a line, cannot be an algebraic function of the line. *In fact, this series converges in the neighborhood of the point, i.e., *Newton's argument proves the transcendence of the area function the area function is analytic; but in the proof that follows we only use for any oval, which is an immersed circle closed on its Riemann surface the existence of an asymptotic series. and which bounds a nonzero area on the plane. NOVEMBER 1989, VOLUME 36, NUMBER 9 1149 Newton's Principia of integrals along circles depending continuously on a around the critical values of the restriction of x to the parameter (see [Ph], [M], [AVG], [AVGL], [D], [F]). oval, consecutively in the order of the corresponding 2. Generalizations of Newton's Theorem to Hypersurfaces critical points on the oval. When t returns to its initial in Even-dimensional Spaces value along this path, the analytic continuation of the An ovaloid (a convex compact hypersurface) in Rn is area function increases by twice the area bounded by the called locally algebraically integrable, if the volume of the oval. segment cut off the ovaloid by a hyperplane, coincides with an algebraic function near any fixed hyperplane. Theorem 3 (V. A. Vasil'ev, see [AVGL]). For n even, there does not exist any smooth convex locally algebraically integrable ovaloid in Rn. We can choose a linear function x in Rn, whose restriction to the ovaloid has the nondegenerate (Morse) minimum m and maximum M. Let us consider a path, going around the interval mM on the complexification on the axis x (Fig. 3). L(k Fig. 4 m I Conjecture 1'. A path with this property exists for any even n. Fig. 3 3. Integrable Ovaloids in Odd-Dimensional Spaces Unlike the even-dimensional spaces, the odd-dimen Lemma 1. The increment along the path of Fig. 3 sional spaces contain algebraically integrable ovaloids. A of the volume V(t) of the segment x ~ t (or of the sphere in R3 is integrable (by a theorem of Archimedes). analytic continuation of this volume along the paths in The same holds for any ellipsoid in any odd-dimensional the neighborhood of the interval mM in the complex space; see [Ad. is twice as large as the volume bounded by the plane t) Conjecture 2. Any irreducible smooth locally algebraically ovaloid. integrable ovaloid in R2k+l is an ellipsoid. Theorem 3 follows immediately from this lemma, which is based on the following fact. Theorem 4. Almost all algebraic ovaloids of degree d ~ 3 in R2k+ 1, k ~ 1, are not algebraically integrable. Lemma 2. For n even, the analytic continuation of the The smooth algebraically integrable irreducible oval function V(t) along the small circles centered at the aids of degrees ~ 3 (if they do exist) are very special points m, M, equals correspondingly the functions - V(t), algebraic surfaces. For instance, their tangent planes at V(M)- V(t). their complex parabolic points should be tangent to words, the power series of the function V(t) In other the (complexified) ovaloid along the curves of parabolic of the points m, M contain only in the neighborhoods points, and so on (see [AVGL]). half-integer (but not integer!) degrees oft- m, M- t. The proof of Theorem 4 depends on the ramification Conjecture 1. For n even, there exist neither convex nor properties of the volume of the segment continued nonconvex smooth locally algebraically integrable ovaloids analytically to the complex projective space of the cutting in Rn. hyperplanes. The analytic continuation of the volume This is true for the usual ovals. The proof is similar function along a path X 1 in the space of hyperplanes to that of Theorem 3. We choose a more complicated is equal to the integral of the holomorphic differential path in the complex line x; see Fig. 4. This path turns n-form dx along an n-chain X1• This chain is bounded 1150 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Newton's Principia by the union of the complexified ovaloid hypersurface Theorem 6 ([N], Theorem XXXI). "With the same and the hyperplane X1• The ramification hypersurface assumptions, I affirm that a particle outside a spherical consists of those planes which are not general with surface is attracted to the center with the force inversely respect to the complexified ovaloid hypersurface. The proportional to its squared distance from the center." ramification at the tangents at the generic parabolic Proof. A spherically symmetric non compressible (of di points of the complexified ovaloid is logarithmical. Hence vergence zero) vector field decreases inversely propor the continuation of the volume function is infinitely tional to the squared distance to the center (since its multivalued. This implies Theorem 4. flows through all the spheres are the same). The at The difference between the cases of even and odd n traction field of any particle is noncompressible. Hence, is due to the n-dependent sign in the Picard-Lefschetz the attraction field of any body is noncompressible out formula, describing the ramification of the relative ho side this body. Thus, the attraction field of any sphere mology class of the chain X1• The same sign is respon is noncompressible outside the sphere. Being obviously sible for the existence of a sharp back front of a wave spherically symmetric, it coincides with the attraction in three space dimensions (and for its absence in a field of a particle in the center. two-dimensional space). The existence of a sharp back These theorems together with the corresponding front makes it possible to communicate acoustically in proofs hold in n-dimensional space, if the attraction the spaces of odd dimensions (and makes it impossible force is inversely proportional to the n - 1-th power of to communicate in even-dimensional spaces). the distance. The relation of Newton's theorem to the theory of Moreover, these theorems may be extended to the case hyperbolic POE's is deeper than it seems. The same of any ellipsoid in Rn, if the density of the distribution mathematical structure is even more transparent in of the matter on its surface is inversely proportional to another of Newton's creations-in his attraction theory. the length of the gradient of the quadratic form defining 4. Newton's Theorem on the Attraction by Spheres and this ellipsoid in the corresponding point. In this case, Hyperbolic Surfaces inside the ellipsoid the attraction is absent, and outside First we recall the following results of Newton. it is constant on the ellipsoids confocal with the initial one. (Ivory's theorem, [1].) Theorem 5 ([N], Theorem XXX). If toward the individual Newton's theorems on the attraction of ellipsoids may points of a spherical surface are directed forces decreasing be extended to hyperbolic surfaces of arbitrary degree in inversely proportional to the distances from these points, Rn. then a particle inside this surface is not attracted to any side. Definition. An algebraic hypersurface of degree d in Rn Indeed, for any infinitely narrow cone with the wedge is called hyperbolic with respect to a point x, if any real at this particle the intersections of the sphere with line containing this point intersects the surface exactly the opposite parts of the cone attract the particle with d times (possibly, at infinity). Such points x form the equal forces, since the areas of these intersections are hyperbolicity set of the surface. This set is a union of proportional to the squares of distances. some connected components of the complement to the hypersurface (see [ABG]); such components are called hyperbolicity domains. For example, an ellipsoid has one hyperbolicity do main, and a two-sheeted hyperboloid-two such do mains. A smooth hyperbolic surface given by a polynomial equation F = 0 partitions Rn into the components which we shall call zones. Let us order them according to the minimal number of intersections with the hypersurface of a path connecting a point of a component with a point of a fixed hyperbolicity domain. This hyperbolicity domain will be called the 0-th zone. The standard charge on the hyperbolic surface F = 0 is defined by the form dxfdF (i.e., as the limit of a homogeneous charge between the surfaces F = 0 and F = e with density 1I e and the signs equal to ± 1 depending on the parity of the number of the Fig. 5 corresponding component of the surface). NOVEMBER 1989, VOLUME 36, NUMBER 9 1151 Newton's Principia Theorem 7 (see [A2]). The standard charge on a hyperbolic intersection points are distinct and finite), then the .u-th surface does not attract the points in the hyperbolicity partial derivative (l.ul > q - d + r) of the potential is domain. Moreover, the same holds for the product of the given by the integral of a suitable differential form along standard charge and a polynomial of degree d - 2 (where a chain which consists of 2k small standard circles near d is the degree of the surface) some 2k of these intersection points-k points on any For an ellipsoid d = 2, hence only the standard line. The motion of the point x in the complex domain density is admissible, but for d = 4 we have many may only permute these points and the corresponding admissible densities. circles. If the degree of the polynomial-multiplier is m units more than the critical value d - 2, then the potential in the hyperbolicity domain is a polynomial of degree at most m; see [G]. The Newton-Coulomb potential (the attractive power in Rn is proportional to r1-n) may be replaced here by any Green's function Gin Rn- {0}, which is homogeneous of degrees- n (or, for s = n, proportional to the logarithm on any ray) and satisfies the equation G( -x) = ( -l)sG(x) (s being a natural number). In this case the critical degree d- 2 is replaced by d- s. I \ I \ Theorem 8 ([G)). A G-potential of the charge, which is the product of the standard one and of a polynomial of degree d - s + m, coincides with a po/ynonmial of degree 5 m in Fig. 6 the hyperbolicity domain. Is there any trace of the algebraicity of the potential in the other domains? {The simplest example is the 5. Magnetic Field Analogues of Newton's and Ivory's· logarithmic potential of a uniform circle in the outer Theroems domain.) In one other generalization of the theorems of Newton Theorem 9 (V. A. Vasil'ev). In the k-th zone of a and Ivory, the attracting ellipsoid is replaced by a hyper hyperbolic curve of degree d in R2, any partial derivative boloid of an arbitrary signature. In this case, the potential of the Newton potential of the standard charge coincides function is replaced by a differential form of a suitable with a sum of two algebraic functions, having at most c: degree (depending on the signature). Consider for in values. Moreover, the same holds for the partial derivatives stance the one-sheeted hyperboloid in three-dimensional of order q + 2 - d of the potential of the charge which is Euclidean space. It is fibered in a natural way into the product of the standard one and of a polynomial of two families of curves-the meridians and the parallels, degree q. diffeomorphic correspondingly to the lines and to the For instance, for the circle all the derivatives of circles (these curves are the traces on the hyperboloid the potential are single-valued functions so that our of the family of the ellipsoids and of the two-sheeted majorization of the number of the values ( q )2 = 4 is hyperboloids, confocal to it; they are also called the not attained. It is related with the fact that the functions elliptic coordinate curves). The family of meridians may F and G are not in general position: the singular lines be extended to the family of elliptic coordinate lines of the function G = lnlxl in C 2 are asymptotic with fibering into the lines of the interior of the hyperboloid. respect to the equation of the circle. In the case of a The family of parallels may be extended to an analogous typical ellipse our majorization is the best possible: the fibration of the exterior part of the hyperboloid into the analytic continuations of the derivatives of the potential closed elliptic coordinate lines. (See Fig. 7) are 4-valued functions. Theorem 10 ([A3]). There exists an electric current along The idea of the proof is very close to that for the meridians (along the parallels) of the hyperboloid, Theorems l-4 (although it provides the opposite answer). whose magnetic field vanishes in the interior domain and Namely, for any point x E R2 - {F = 0}, consider two is directed along the parallels in the exterior one (vanishes complex lines {~llx-~1 = 0} (i.e., (x 1 -~ 1 ) 2 +(x2 -~2) 2 = in the exterior domain and is directed along the meridians 0) and the intersection set of these lines with the surface in the interior one). { F = 0} ~ C 2• This set consists of 2d points (possibly, In [VS] this result is extended to the case of hy infinitely distant): d points on any line. If x belongs perboloids of arbitrary signatures in spaces of arbitrary to the k-th zone and is "generic" (i.e., all these 2d dimensions. 1152 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Newton's Principia It would be interesting to transfer these "magnetic" Proof. The Zhukovsky function w = c; + c;- 1 transforms generalizations of Newton's and Ivory's theorems to the a circle 1c;1 = r > 1 into a Hooke's ellipse centered at 0 case of the "generalized hyperbolic" surfaces of higher with foci ±2. But w2 = c;2 + c;- 2 + 2-the squaring of w degree. translates the focus of the ellipse to the origin. Remark 1. The motion of a free point (along a straight line on the plane) may be considered as the motion in the zero field of arbitrary degree. Applying Theroem 11, we obtain special orbits of the motion in a central field of an arbitrary degree A on the plane. These orbits are obtained from the straight lines by the mapping wpAw'\ a= 2/(A + 3). In the case of the universal attraction law these special trajectories are parabolas (a = 2). In the general case, the equation of these generalized parabolic orbits in the polar coordinates is ru = seen¢. I \ Fig. 7 -5 a I 6. Duality Between the Attraction Laws I I action Consider a point moving on a plane under the I " / of an attractive force directed toward the origin and I " ------J ~ !l.=~t~- proportional to the a-th degree of the distance from the ,.-": origin. It turns out, that for any such attraction law there " I " I -5 exists a dual one; the orbits of the motion under the dual I force fields are related by a simple conformal mapping. I I For instance, the universal attraction law and Hooke's I law are dual to each other. Let us introduce on the plane I a complex coordinate w. Theorem 11 ([A4], [A5]). Any orbit of the motion of the Fig. 8 point w on the plane of complex numbers in a central attraction field in which the force is proportional to wa, is Remark 2. Newton had considered in the Principia the transformed into an orbit of the motion in a central field values a= 1, -1, -2, -3, -5. The values a= -1 and -5 proportional to zA by the map z = wu, provided that are special for the duality law (2) as the self-dual ones. For a= -5, the formula (2) gives a= -1. (2) (a+ 3)(A + 3) = 4, a= (a+ 3)/2. Corollary. The orbits of motions in a central field, whose The proof is an immediate calculation. (See Fig. 8) force is inversely proportional to the 5-th degree of the Theorem 11 is not formulated in the Principia. But distance from the origin, are transformed by the inversions is was guessed thanks to Newton's formula for the angle to the orbits of the same kind. between the consequent apocenters of an almost round Example. The straight lines of motion in the zero field orbit. which do not contain the origin are transformed by the Example. If a = 1 (Hooke's law) then formula (2) gives inversion into the circles containing the origin. Hence A = -2 (the universal attraction law) and a = 2. We the motion along a circle containing the attracting point get Theorem 12 (Bohlin, see [B]). The transformation is possible in a field inversely proportional to the 5-th wpAw2 transforms an ellipse centered at the origin of the degree of the distance-this corollary is also due to complex plane into an ellipse having a focus at the origin. Newton [N]. NOVEMBER 1989, VOLUME 36, NUMBER 9 1153 Newton's Principia References [P] Petrovsky, I. G., On the diffusion of waves and the lacunas for hyperbolic equations. Matern. Sbornik, 1945, 17(59), 289- (Ad Arnol' d, V. I., A topological proof of transcendence of 370. des singu Abelian integrals in Newton's Principia. Quant 1987, No. 12, [Ph] Pham, F., Introduction a !'etude topologique 1967, ii 142 pp. 1-15. larites de Landau. Paris, Gauthier-Villars, + Z., Multidimensional [A2] Arnol'd, V. 1., On the Newtonian Potential of Hyperbolic [VS] Vainshtein, A. D. And Shapiro, B. and Ivory theorems. Funtional Anal. Layers. Selecta Math. Soviet., 1985, Vol. 4, No. 2, I 03-106. analogues of the Newton (A3] Arnol' d, V. 1., Magnetic field analogues of the theorems Appl., 1985, Vol. 19, No. I. local Petrovsky condi of Newton and Ivory. Uspekhi Mat. Nauk, 1983, Vol. 38, No. [V] Vasil'ev, V. A., Sharpness and the coefficients. Isvestija 5, 145, 145-146 (In Russian). tion for hyperbolic equations with constant 1986, Vol. 50, No. 2, 242-283. (A4] Arnol'd, V. 1., The 300th anniversary of mathematical Acad. Sci. USSR, Ser. Math. natural philosophy and celestial mechanics. Priroda, 1987, No. 8, 5-15 (In Russian). (As] Arnol' d, V. I., Huygens and Barrow, and Newton and V. I. Arnol' d is Professor of Mathematics at the Moscow Hooke-the first steps of the mathematical analysis and catas State University in the USSR. He was co-recipient of the trophe theory, from the evolvents to the quasicrystals. Birkhauser. Crafoord Prize of the Swedish Academy of Sciences and is [ABG] Atiyah, M. F., Bott, R. and Garding, L., Lacunas for a member of the USSR, USA and French academies of sci hyperbolic differential operators with constant coefficients. I, II. ence. His research interests include algebraic and symplectic Acta Math., 1970, 124, I 09-189; 1973, 131, 145-206. geometry and variational calculus. V. A. Vasil'ev, a student [AVG] Arnol'd, V. 1., Varchenko, A. N. and Gusein-Zadeh, C. of Arnol' d, received his Ph.D. from Moscow State Univer M., Singularities of differential mappings. II. Moscow, Nauka, sity in 1984. His thesis investigated the topic of asymptotic 1984. (English translation: ) behavior of exponential integrals in the complex plane. [AVGL] Arnol'd, V. 1., Vasil'ev, V. A., Goryunov, V. V. and Lyashko, 0. V., Singularities. II. Moscow, VINITI, 1989. (En glish translation: ) The series of Special Articles was created to provide a place (B] Bohlin, K., Bull. Astr., 1911, Vol. 28, No. 144. for articles on mathematical subjects of interest to the gen [BR] Brougham, H. and Routh, E. J., Analytical view of Sir eral membership of the Society. The Editorial Committee of Isaac Newton's Principia. London, 1855. the Notices is especially interested in the quality of exposi (D] Deligne, P. Equations differentielles a points singuliers tion and intends to maintain the highest standards in order reguliers. Lect. Notes Math., Springer, 1970, No. 163. to assure that the Special Articles will be accessible to math (F] Faltings, G., Endlichkeitssiitze fiir abelsche Varietiiten tiber ematicians in all fields. The articles must be interesting and Zahlkorpern. Invent. Math., 1983, No. 73, 349-366. mathematically sound. They are first refereed for accuracy [G] Givental, A. B., Polynomiality of the electrostatistical po and (if approved) accepted or rejected on the basis of the tentials. Uspecki Mat. Nauk, 1984, Vol. 39, No. 5, 253-254 (In breadth of their appeal to the general mathematical public. Russian). Items for this series are solicited and, if accepted, will (I] Ivory, J. On the attractions of homogeneous ellipsoids. Phi be paid for at the rate of $250 per page up to a maximum los. Trans., 1809, 99, 345-372. of $750. Manuscripts to be considered for this series should [M] Malgrange, B., Integrates asymptotiques et monodromie. be sent to Ronald L. Graham, Associate Editor for Special Ann. Sci. Ecole Norm. Sup., 1974, Vol. 7, 405-430. Articles, Notices of the American Mathematical Society, Post [N] Newton, I., Philosophiae Naturalis Principia Mathemat Office Box 6248, Providence, Rhode Island 02940. ica, London, 1687. 1154 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY 1989 Annual AMS-MAA Survey (First Report) Report on the 1989 Survey of New Doctorates, Edward A. Connors Salary Survey for New Doctorates Faculty Salary Survey Doctoral Degrees Conferred, 1988-1989 Highlights for description of groups). Table 1 provides the response rates for the 1989 Survey of New Doctorates. 1. 904 doctorates in the mathematical sciences were awarded by U.S. institutions in the period July 1, 1988 TABLE 1: Response Rates through June 30, 1989. This is a 12% increase over last Group I 39 of 39 year and an 18% increase over the average of the fall Group II 42 of 43 including 5 with 0 degrees counts for the last four years. Group III 73 of 84 including 19 with 0 degrees 2. 411 U.S. citizens received doctorates in the mathe Group IV 55 of 72 including 7 with 0 degrees matical sciences. This is only 46% of the total awarded by Group Va 12 of 16 including 2 with 0 degrees U.S. institutions, however. Group Vb 15 of 31 including 2 with 0 degrees 3. 24% of the U.S. citizen doctorates were awarded Group VI 24 of 29 including 6 with 0 degrees to women. This is the largest percentage ever and a Doctorates Granted significant increase over the 20 to 21% awarded in the last For the first time, we report separately the number of new six years. doctorates granted by U.S. and Canadian institutions. 4. Although women comprise 24% of the U.S. citizens These fall counts will, as is customary, be updated in the receiving doctorates, only 16% of the new doctorate hires Second Report of the 1989 Survey, to appear in a spring in the U.S. doctorate-granting departments were women. 1990 issue of Notices. 5. 9 of the 411 U.S. citizen doctorates were black, 7 of Doctorates, Fall Counts whom were women. Black women account for 7% of the TABLE 2A: New doctorates awarded to women U.S. citizens. 84-85 85-86 86-87 87-88 88-89 6. Median starting salary for new doctorates reporting u.s. 732 156 779 804 904 teaching (or teaching and research) employment was Canada 37 45 66 52 53 $30,500 (men) and $31,000 (women). Total 769 801 845 856 951 Report on the 1989 Survey TABLE 2B: New Doctorates, Fall and Spring Counts 84-85 85-86 86-87 87-88 88-89 of New Doctorates Fall/ Spring Fall/ Spring Fall/ Spring Fall/ Spring Fall/Spring Edward A. Connors u.s. 732 765 156 782 779 808 804 828 904 * Canada 37 42 45 45 66 66 52 55 53 * This report presents a statistical profile of new doctor Total 769 807 801 827 845 874 856 883 951 * ates in the mathematical sciences awarded by universities *To appear in a spring 1990 issue of Notices. in the United States and Canada during the period July 1, 1988, through June 30, 1989. It includes the employ In Table 2C we record the number of new doctorates ment status of recipients of 1988-1989 doctorates in the in the mathematical sciences in the U.S. and Canada mathematical sciences (as of August 31, 1989), an anal from the years 1984-1985, exclusive of Group Vb. The ysis of the data by sex, minority group, and citizenship, response rate for Group Vb, which includes departments and reports trends in the number of doctoral degrees in engineering and management science, is the lowest of for each of Groups I through V (see box on next page all groups. NOVEMBER 1989, VOLUME 36, NUMBER 9 1155 Annual AMS-MAA.Survey TABLE 2C: New Doctorates In rows 1 through 5 of Table 3A the numbers rep Awarded by Groups I-Va resent those who have accepted appointments in U.S. 84-85 85-86 86-87 87-88 88-89 doctorate-granting mathematical sciences departments I-Va 712 698 743 760 838** (Groups I-V). In the next two rows the figures represent ** This is a fall count. The other entries in Table 2C are spring those accepting appointments in U.S. mathematical sci counts. Table 2C will be updated to include a spring count for ences departments granting masters and bachelors as the 1988-1989 in a spring 1990 issue of Notices. highest degree. The information was initially obtained from the department granting the degrees and from data Employment Status of subsequently supplied by recipients themselves. New Doctorates, 1988-1989 Of the 619 new doctorates employed in the U.S. 68% Table 3A shows the employment status, by type of (422) assumed academic positions in university or four employer and field of degree, of the 957 recipients of year college mathematical sciences departments (a three doctoral degrees conferred by the mathematical sciences percentage point increase over last year), and 17% (103) departments in the U.S. and Canada between July 1, took employment in government, business, or industry 1988, and June 30, 1989. The names of these individuals (a four percentage point decrease). are listed with their thesis titles in a later section of this Table 3A shows as "not yet employed" about 4% of First Report of the 1989 Annual Survey. Again this year the 1988-1989 new doctorates, excluding those whose we present the employment status of the 179 women employment status is unknown. The data in Table 3A new doctorates in Table 3B. were obtained in many instances early in the summer of There was an increase in new doctorates hired in 1989 and do not reflect subsequent hiring; an update of Groups I-V (240 compared to 207 last year), with a sig Table 3A is planned for the Second Report in a spring nificant increase in those hired by Group I departments 1990 issue of Notices. A similar update last year revealed (100 compared to 73). There was a slight increase in that all but 11 new 1987-1988 doctorates found positions new doctorates hired by government and business ( 103 by fall 1988 (see Notices, November 1988, page 1303, compared to 96). Although women comprise 24% of the and MayjJune 1989, page 535). new doctorates, only 16% of the new doctorates hired by Groups I-V were women. Groups I and II include the leading departments of mathematics in This first report on the 1989 Survey includes a report on the 1989 the U.S. according to the 1982 assessment of Research-Doctorate survey of new doctorates, a report on salaries of new doctorates, Programs conducted by the Conference Board of Associated Re salary and on faculty members in four-year colleges and universi search Councils in which departments were rated according to the ties, and a list of names and thesis titles for members of the 1988- quality of their graduate faculty.' 1989 Ph.D. class. The report is based on information collected from Group I is composed of 39 departments with scores in the 3.0-5.0 questionnaires distributed in May to departments in the mathemat range. ical sciences in colleges and universities in the United States and Group II is composed of 43 departments with scores in the ·2.0- Canada, and later to the recipients of doctoral degrees granted by 2.9 range. these departments between July 1988 and June 1989, inclusive. A Group Ill contains the remaining U.S. departments reporting a doc second round of questionnaires was distributed in September, con toral program. Group IV contains U.S. departments (or programs) of statistics, cerneg with data on fall enrollments, majors, and departmental size. biostatistics and biometrics reporting a doctoral program. This data will appear in the second report on the 1989 Survey, in a Group V contains U.S. departments (or programs) in applied mathe spring 1990 issue of Notices. matics/applied science, operations research and management sci For these reports, departments are divided into groups accord ence which report a doctoral program. ing to the highest degree offered in the mathematical sciences. The Group Va is applied mathematics/applied science; Group Vb is op groups are described in the box in this report. erations research and management science. The 1989 Annual AMS-MAA Survey represents the thirty Group VI contains doctorate-granting departments (or programs) third in an annual series begun in 1957 by the Society. The 1989 Sur in the mathematical sciences in Canadian universities. vey is under the direction of the AMS-MAA Committee on Employ Gr~up M contains U.S. departments granting a master's degree as the highest graduate degree. ment and Educational Policy (CEEP), whose members are Donna L. Group B contains U.S. departments granting a baccalaureate de- Beers, Morton Brown, Stefan A. Burr, Edward A. Connors (chair), gree only. . Philip C. Curtis, Jr.; David J. Lutzer, and James J. Tattersall. The 1These findings were published in An Assessment of Research-Doctorate Pro questionnaires were devised by CEEP's Data Subcommittee whose grams In the United States: Mathematical and Physical Sciences, edited by members are Edward A. Connors (chair), Lincoln K. Durst (consul Lyle V. Jones, Gardner Undzey, and Porter E. Coggeshall, National Academy tant), John D. Fulton, James F. Hurley, Charlotte Lin, Don 0. Lofts Press, Washington, D.C., 1982. The information on mathematics, statistics gaarden, David J. Lutzer, James W. Maxwell (ex officio), Donald E. and computer science was presented in digest form in the Apri11983 issue of Notices, pages 257-267, and an analysis of the above classifications was McClure, and Donald C. Rung. Comments or suggestions regarding given in the June 1983 Notices, pages 392-393. For a listing of departments this Survey may be directed to the subcommittee. in Groups I and II see Apri11988 Notices, pages 532-533. 1156 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Annual AMS-MAA Survey TABLE 3A: Employment Status of 1988-1989 New Doctorates in the Mathematical Sciences fJ .. ~ ·!!! l#"' f ~ ~ ..,.,t' /! ! ~~ i~ .., ~§ I ~:§ ... "8.§ ... s-,., .ie{2 TABLE 3B: Employment Status of 1988-1989 New Doctorates in the Mathematical Sciences Females Only I I ~ ·!!! l! f t' ~ s.s ~ ~ .. /! ! fJ :f.§ .,~ c. I tJ ~.§ {!' ... ~: s-,., ~~ "' ~~ ~.~ NOVEMBER 1989, VOLUME 36, NUMBER 9 1157 Annual AMS-MAA Survey TABLE 4: Sex, Minority Group, and Citizenship of New Doctorates July 1, 1988-June 30, 1989 U.S. DEGREES MEN WOMEN TOTAL CITIZENSHIP CITIZENSHIP Not Total Not Total RACIAL/ETHNIC GROUP u.s. Canada Other Known Men u.s. Canada Other Known Women Asian, Pacific Islander 5 216 1 222 2 39 2 43 265 Black 2 8 10 7 3 10 20 American Indian, Eskimo, Aleut 1 1 1 Mexican American, Puerto Rican, or other Hispanic 4 1 18 23 4 7 11 34 None of those above 281 9 134 1 425 82 1 16 1 100 525 Unknown 21 2 15 13 51 3 2 1 2 8 59 Total Number 313 12 392 15 732 98 3 66 5 172 904 CANADIAN DEGREES MEN WOMEN TOTAL CITIZENSHIP CITIZENSHIP Not Total Not Total RACIAL/ETHNIC GROUP u.s. Canada Other Known Men u.s. Canada Other Known Women Asian, Pacific Islander 1 8 9 1 1 10 Black 1 1 1 American Indian, Eskimo, Aleut Mexican American, Puerto Rican, or other Hispanic 1 1 2 None of those above 15 9 24 2 1 3 27 Unknown 1 10 1 12 1 2 3 15 Total Number 1 26 19 46 4 3 7 53 Sex, Minority Group, and Citizenship Women comprise 24% of the U.S. citizens receiving of New Doctorates, 1988-1989 doctorates in the mathematical sciences, a three to four Table 4 presents a breakdown according to sex, minor percentage point increase over the 20 to 21% reported ity group, and citizenship of the new doctorates. The for the last six years. Table 6 presents data for the period information reported in this table was obtained from 1973-1974 through 1988-1989. departments granting the degrees and in some cases from Citizenship and Sex of the recipients themselves. U.S. Doctorates, 1973 to 1989 Of the 904 doctorates awarded by U.S. universities, is presented on the annual the citizenship is reported as known for 884 recipients, Again this year, information by U.S. universities to U.S. with 411 reporting U.S. citizenship. Thus, only 46% number of doctorates granted citizens since 1973 (Table 5). This number is divided of the doctorates awarded by U.S. institutions went to (Table 6). In Table 5 the U.S. citizens. The percentage of U.S. citizens receiving into male and female doctorates column headed Adjusted Total of Doctorates given by doctorates in the mathematical sciences, having declined U.S. Universities gives the number of doctorates granted consistently, from 73% in 1979-1980 to 45% in 1987- 30 of the indicated years 1988, now shows a slight increase, to 46%. For the first between July 1 and June Column 2 gives the number time since 1984-1985 the number of U.S. citizen doctor whose citizenship is known. and column 3 the percentage that ates is over 400. Refer to Table 5 and the accompanying who are U.S. citizens 6 the number in column 2 of graphs. this represents. In Table Table 5 is further divided into men and women. Note Among the U.S. citizens receiving doctorates in the to 1982-1983 include mathematical sciences, 9 were black (7 women, 2 men) that in both tables all years prior computer science departments. and 8 were Hispanic (4 women, 4 men). doctorates granted by 1158 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Annual AMS-MAA Survey TABLE 5: U.S. Citizen Doctorates Adjusted Total Total of of Doctorates Doctorates given by U. S. who are U.S. universities citizens % 1973-1974 938 677 72% Graph for Table 5: U.S. Citizen Doctorates 1974-1975 999 741 74% Total of Doctorates by Percent 1975-1976 965 722 75% % 1976-1977 901 689 76% 80 1977-1978 868 634 73% .-'~-----~- 1978-1979 596 74% 806 70 1979-1980 791 578 73% 1980-1981 839 567 68% 1981-1982 798 519 65% 60 1982-1983 744 455 61% 1983-1984 738 433 59% 50 1984-1985 726 396 55% 1985-1986 755 386 51% '.----~ 1986-1987 739 362 49% 40 1987-1988 798 363 45% 1973- 1978- 1983- 1988- 1974 1979 1984 1989 1988-1989 884 411 46% Graph for Table 5: U.S. Citizen Doctorates 1000 TABLE 6: U.S. Citizen Doctorates, Male and Female 900 . 'o Doctorates who are % -· U. S. Citizens Male Female Female 800 - .- . ' -·- 1973-1974 677 618 59 9% 1974-1975 741 658 83 II% 700 ;~,~ 1975-1976 722 636 86 12% 1976-1977 689 602 87 13% 600 ." '-, 1977-1978 634 545 89 14% ~- 1978-1979 596 503 93 16% ~ 1979-1980 578 491 87 15% 500 \ 1980-1981 567 465 102 18% 1981-1982 519 431 88 17% 400 1982-1983 455 366 89 20% "~~,_/ 1983-1984 433 346 87 20% 1984-1985 396 315 81 20% 1973- 1978- 1983- 1988- 1985-1986 386 304 82 21 o/o 1974 1979 1984 1989 1986-1987 362 289 73 20% ---- Adjusted Total of Doctorates Given by U.S. Universities 1987-1988 363 287 76 21% - -- Total of Doctorates Who Are U_S, Citizens 1988-1989 411 313 98 24% NOVEMBER 1989, VOLUME 36, NUMBER 9 1159 Annual AMS-MAA Survey Concluding Remarks [10] D. J. Albers, R. D. Anderson, and D. 0. Loftsgaarden, We view with guarded optimism the small increase in the Undergraduate Programs in the Mathematical and Computer number of U.S. citizens receiving doctorates in the math Sciences. The 1985-1986 Survey, MAA Notes, 7. ematical sciences. It is encouraging to note the increase [11] The Science and Engineering Pipeline, Policy Research Analysis Report NSF PRA 87-2, April 1987. in the number of women among the new doctorates, [12] The Underachieving Curriculum: Assessing U.S. School but it remains to be seen if this gain can be sustained. Mathematics from an International Perspective, Stipes Publish Perhaps the proportionately large number of women ing Co., Champaign, Illinois, January 1987. new doctorates hired by the Group B departments, the [13] Competition for Human Resources in the 1990s, Pro wellspring of American mathematics, will result in larger ceedings of a Symposium, Commission on Professionals in Sci numbers of women enrolling in graduate programs (35% ence and Technology, May 1988. of the new doctorates hired by Group B departments [14) Science and Engineering Doctorates: 1960-86, NSF 88- were women). 309, Washington, DC 1988. [15] Educating Scientists and Engineers: Grade School to Grad School, U.S. Congress, Office of Technology Assessment, Bibliography OTA-SET-377, Washington, DC, June 1988. [1) Nurturing Science and Engineering Talent: A Discussion Pa [16] Boon or Bane - Foreign Graduate Students in U.S. En per, July 1987. The Government-University-Industry Research gineering Programs, Institute of International Education Re Roundtable, NAS, Washington, DC. search Report Series, Number 15, 1988. [2] Undergraduate Science, Mathematics and Engineering [17] National Research Council. Summary Report 1986, Doc Education, NSB 86-100, March 1986. NSB Task Committee on torate Recipients from United States Universities, National Undergraduate Science and Engineering Education. Academy Press, Washington, DC, 1987. [3] The Future Workforce Conference Proceedings, Septem [18) Edward A. Connors, A Decline in Mathematics Threat ber 10-11, 1986, Goddard Space Flight Center, Greenbelt, ens Science-and the U.S., The Scientist, November 28, 1988. Maryland, NASA Office of Educational Affairs and NASA [19] Edward A. Connors, America's Scientific Future is Office of Productivity Programs. Threatened by the Decline in Mathematical Education, The [4) National Science Foundation. Science and Technology Chronicle of Higher Education, January 11, 1989. Data Book, (NSF 88-332). National Science Foundation, Wash [20] National Research Council. Everybody Counts: A Report ington, DC, 1989. to the Nation on the Future ofMathematics Education. National [5] Scientific Manpower-1987 and Beyond. Today's Budgets Academy Press, Washington, D.C., 1989. Tomorrow's Workforce. Proceedings of a Symposium, October [21] Elementary and Secondary Education for Science and 15, 1986, Washington, DC, sponsored by the Commission on Engineering. U.S. Congress, Office of Technology Assessment, Professionals in Science and Technology. OTA-TM-SET-41. Washington, D.C., December 1988. [6] Foreign Citizens in U.S. Science and Engineering: His [22] Higher Education for Science and Engineering: a back tory, Status and Outlook, NSF 86-305 Revised, (Washington, ground paper. U.S. Congress, Office of Technology Assessment, DC, 1987). OTA-BP-SET-52. Washington, D.C., March 1989. [7] Rand Publication Series. Reports on teaching and edu [23] Changing America: The New Face of Science and En cation: Beyond the Commission Reports: The Coming Crisis in gineering. Interim Report, Task Force on Women, Minorities, Teaching. R-3177-RC, July 1984. Steady Work: Policy, practice and the Handicapped in Science. September 1988. and the reform ofAmerican education. R-3574-NIE/RC, Febru [24] Commission on Professionals in Science and Technol ary 1988. The Evolution of Teacher Policy. JRE-0 1, March 1988. ogy. Occasional Papers, prepared by Betty M. Vetter. Look Assessing Teacher Supply and Demand. R-3633-ED/CSTP, May Who's Coming to School (89-0), December 1988. Women in 1988. Science. Progress and Problems (89-1), February 1989. [8] Teaching Assistants and Part-time Instructors: Recruiting Doctoral Scientists and Engineers (89-2), February A Challenge, MAA Notes, 1987. 1989. CPST, Washington, D.C. [9] Scientific and Technical Personnel in the 1990's: An Ex [25] Meeting the Needs of a Growing Economy: The amination of Issues and Information Needs. Proceedings of the CORETECH Agenda for the Scientific and Technical May 9-10, 1985 Conference, Washington, DC (Prepared for the Workforce. CORETECH, Washington, D.C. 1988. Scientific and Technical Personnel Studies Section, Division of [26] Measuring National Needs for Scientists to the Year 2000. Science Resources Studies, NSF, by the Council of Professional Report to the National Science Foundation. Commission on Associations on Federal Statistics, Katherine K. Wallmann, Ex Professionals in Science and Technology, Washington, D.C., ecutive Director). July 1989. 1160 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Annual AMS-MAA Survey Salary Survey for New Recipients of Key to Tables. Salaries are listed in hundreds of Doctorates, 1988-1989 dollars. Years listed refer to the academic year in which the doctorate was received. M and F are Male and The figures for 1989 were compiled from question Female respectively. One year experience means that the naires sent to individuals who received a doctorate in the persons had experience limited to one year or less in the mathematical sciences during the 1988-1989 academic same position or a position similar to the one reported; year from universities in the United States and Canada. some persons receiving a doctorate had been employed Questionnaires requesting information on salaries and in their present position for several years. (X+ Y) means professional experience were distributed to 769 recipients there are X men and Y women in the 1989 sample. of degrees using addresses provided by the departments Quartile figures are given only in cases where the number which granted the degrees. Of these, 8 were returned of responses is large enough to make them meaningful. by the postal service as undeliverable and could not be Graphs. The horizontal line represents the median forwarded. There were 406 individuals who returned salary for 1988 in hundreds of dollars. The points forms between late June and early September. The tables plotted are the relevant data for each year converted to below are based on the responses from 351 of these 1988 dollars using the implicit price deflator prepared individuals (269 men and 82 women). Data from 55 annually by the Bureau of Economic Analysis, U.S. responses were not used in the compilation of the tables Department of Commerce. Where available, first and below; forms with insufficient data, or from individuals third quartiles appear as boxes along the vertical lines. who had indicated they had part-time employment, were (Because the deflator is not yet available for this year, not yet employed, or were not seeking employment were the 1989 figures do not appear on the graphs.) considered unusable. Note that salaries for teaching, or teaching and re Readers should be warned that the data in this report search, have yet to return to their high point of 1970, are obtained from a self-selected sample and inferences although steady progress has been made since 1980. (For from them may not be representative of the population. further details, see Donald Rung's article, "A Fifteen For more comprehensive information on the recipients Year Retrospective on Academic Salaries of U.S. Doc of new doctorates granted last year in the mathematical torate Holding Faculty," in the November 1985 issue of sciences in the U.S. and Canada, see the preceding article Notices, pp. 772-773.) by E. Connors. Nine-Month Salaries Nine-Month Teaching Ph.D. Reported Year Min a, Median 03 Max Median in 600 1988 $ TEACHING OR TEACHING AND RESEARCH (162 + 35) 500 ~ 1960 49 65 80 255 .!!! 1965 70 80 105 287 0 Cl 400 1970 85 110 195 318 0 1975 90 120 128 135 173 262 "0 1980 105 155 171 185 250 242 "'Q) 1984 140 215 230 255 380 259 -g 300 r ------r- --- : . ---·-----li 1985 170 23 250 270 380 272 :J J: 0 • ! ~ '" 1986 170 250 269 290 400 287 1987 165 260 280 300 517 289 200 I 1988 200 275 293 314 575 293 1989 200 290 310 330 478 1986M 170 250 269 290 400 100 1986F 230 250 268 294 270 1987M 165 260 280 300 517 1987F 230 251 280 325 420 0 60 65 70 75 80 85 88 1988M 200 274 290 315 520 1988F 216 275 299 314 575 1989M 200 290 305 330 478 1989F 220 295 310 330 470 One Year Experience (145 + 43) 1989M 200 290 303 330 470 1989F 220 290 310 325 450 NOVEMBER 1989, VOLUME 36, NUMBER 9 1161 Annual AMS-MAA Survey Nine-Month Salaries Nine-Month Research Ph.D. Reported Year Min Median Max Median in 1988 $ RESEARCH (6 + 0) 1960 52 65 80 255 1965 71 81 90 291 1970 78 105 160 303 1975 100 110 1980 125 137 180 194 Graph omitted because 1984 205 205 205 231 sample size too small. 1985 205 235 250 257 1986 215 245 280 261 1987 250 300 300 309 1988 260 280 385 280 1989 235 270 330 1986M 215 250 280 1986F 240 240 240 1987M 250 300 300 1987F 1988M 260 280 385 1988F 1989M 235 270 330 1989F One Year Experience (6 + 0) 1989M 235 270 330 1989F Twelve-Month Salaries Twelve-Month Teaching Ph.D. Reported Median in Year Min Ql Median Q3 Max 600 1988 $ TEACHING OR TEACHING AND RESEARCH (40 + 14) 500 1960 ...... NO DATA ...... 104 121 373 ~ 1965 78 ~ ! 1970 95 128 200 370 0 400 0 I 1975 87 145 204 297 I 276 0 1980 143 195 350 C/) -~·-- -o 1984 134 260 450 293 Q) -m .~ 300 -o 1985 220 230 273 300 470 299 c:: :1 I 360 480 341 1986 220 265 320 I "' 1987 200 283 315 357 520 325 1988 220 313 330 360 480 330 200 1989 238 290 315 370 620 270 321 360 480 1986M 220 100 1986F 240 245 285 340 360 1987M 200 270 300 358 520 1987F 300 320 339 357 450 1988M 220 308 330 355 480 60 65 70 75 80 85 88 1988F 329 335 350 365 441 1989M 238 295 315 370 620 1989F 275 290 314 380 435 One Year Experience (34 + 10) 1989M 260 300 318 370 495 1989F 275 290 320 380 435 1162 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Annual AMS-MAA Survey Twelve-Month Salaries Twelve-Month Research Ph.D. Reported Year Min Ql Median Q3 Max Median in 600 1988 $ RESEARCH (19 + 7) 500 1960 97 105 140 412 ~ 1965 81 107 334 93 '6"' 400 ~~ 1970 90 120 205 347 0 II! 1975 90 119 180 243 0 1980 120 180 321 255 '0"' t ~ ~ 1984 145 261 415 294 ~ 300 .. ·-~---r---t--- . --.~' ---tl '0 c I 1985 190 295 342 400 520 374 ::> I 1986 160 240 300 325 510 296 I I 'i. ' I 1987 200 260 287 337 430 320 200 1988 200 245 295 331 505 295 1989 180 250 317 385 623 1986M 160 240 300 330 510 100 1986F 240 240 270 300 300 1987M 200 250 282 337 400 1987F 300 308 316 373 430 60 65 70 75 80 85 88 1988M 200 240 280 330 505 1988F 280 320 330 350 360 1989M 180 250 300 393 623 1989F 200 295 350 373 400 One Year Experience (16 + 7) 1989M 180 250 300 361 522 1989F 200 295 350 373 400 Twelve-Month Salaries Twelve-Month Government Ph.D. Reported Year Min Ql Median Q3 Max Median in 1988 $ GOVERNMENT 600 (10 + 0) 1960 72 93 130 365 1965 70 126 160 452 500 1970 100 150 223 433 ~ ~ 1975 78 182 247 372 0 501 345 1'1 ~ 1980 156 244 :: 400 'I I 1984 140 315 490 355 0 __J _ ___ ,[ l-J)I 1985 263 294 325 381 440 356 '0"' L --+--- 610 426 ~ .:1 1[1 1986 270 330 400 449 -g 300 1987 200 290 360 465 500 371 ::> I I 1988 240 298 343 405 436 343 1989 330 363 378 438 540 200 1986M 270 330 400 449 610 1986F 1987M 200 290 360 465 500 100 1987F 1988M 240 290 332 360 436 1988F 380 380 405 430 430 60 65 70 75 80 85 88 1989M 330 363 378 438 540 1989F One Year Experience (7 + 0) 1989M 330 367 375 403 540 1989F NOVEMBER 1989, VOLUME 36, NUMBER 9 1163 Annual AMS-MAA Survey Twelve-Month Salaries Twelve-Month Industry Ph.D. Reported Year Min Ql Median 03 Max Median in ···1100 1988$ BUSINESS AND INDUSTRY 11001 (32 + 8) 1960 78 110 150 432 1965 100 136 180 488 1970 96 170 235 491 600: 1975 114 187 240 383 !!! 1980 190 284 400 402 co I 1984 180 378 660 426 .. 500 I i , 1985 260 360 400 420 493 438 8 I 0 i 750 453 --~ 1986 324 373 425 477 (/) -c ·---+-l-- 1987 290 400 451 500 1500 464 f L .L 440 490 1100 440 ~ 400 \ I 1988 300 400 c: 250 420 464 505 5250 ::::J 1989 I 1986M 324 390 453 492 750 300 1986F 350 357 375 400 440 1987M 290 400 465 517 1500 1987F 300 394 424 466 502 200 1988M 300 400 431 490 1100 1988F 375 437 454 495 660 1989M 250 420 464 513 5250 100 1989F 375 430 470 500 516 One Year Experience (17 + 7) 1989M 250 420 450 510 580 60 65 70 75 80 85 88 1989F 375 430 480 500 516 Faculty Status Survey Acknowledgement Salaries The Annual AMS-MAA Survey attempts to provide an The questionnaire sent to departments in the math accurate appraisal and analysis of various aspects of the ematical sciences this year was substantially changed academic mathematical scene vital to the entire mathe from previous years. Departments were asked to report matical community. Yearly, collegiate departments in the the number of faculty whose academic-year salaries fell United States, and the doctorate-granting departments within given salary intervals. The charts on the following in Canada, are provided the opportunity to respond. four pages display data for all eight groups - faculty The quantity and quality of the responses directly de salaries by rank, mean salaries by rank, the number termine the quality of the information in these reports. within that rank, and the number of usable returns for Without the dedicated cooperation of the secretarial the group. Note that we no longer collect or report salary and administrative support staff in the mathematical information for two years. See Tables on the following science departments we would not be able to conduct a pages. survey, nor be confident in our analysis of its results. We are, unfortunately, unable to thank personally all Age the departmental assistants for their cooperation, but Age data collected on the Faculty Status questionnaire it is nonetheless appreciated. However, we are able to will be reported in the Second Report in a spring 1990 thank the administrative support staff of the AMS, espe issue of Notices, with other departmental information cially Marcia Almeida, Monica Foulkes, and James W. currently being collected. Maxwell, whose efforts are acknowledged and appreci ated. 1164 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Annual AMS-MAA Survey 50 GROUPI -Doc t ora e gran f mg depa rtmens 24 of 39 reporting (62%) Rank #Reported Mean salary Assistant Professor 130 $36,628 Associate Professor 196 42,825 Full Professor 660 62,876 40 10 I ,..., -.... 1.-. - Ia II n a ~ I I R - <20K 20-25K 25·30K 30·35K 35-40K 40-45K 45-SOK 50-SSK 55-SOK 60-70K 70-BOK 80-90K 90-100K 100-120K >120K 1989 SALARY 50 GROUP II - Doctorate granting departments 35 of 43 reporting (81%) Rank #Reported Mean salary Assistant Professor 223 $34,059 Associate Professor 345 48,492 40 Full Professor 679 57,162 1"1 I ~e c: :g i "j 10 I ;;- :::> l!l ]j I g 0 I E "'e I "'c. JO ~ ~ "5 ~ I LL I r I I I I I II I I I~ n ~ I I .. cs=s E.9!3 ESS E.e!S c.s=s E.9!3 'E.9!3 E.9!3 E.9!3 E.S:S E.933 RANK ~-~U.. .m -~ u. !!J.~u. ~-~1.1... ~~~ -~·~LL i·~LL .!·~ LL .!·~LL -i·~u_ ~-~LL .!·~ LL ~~~ -~ ~ -~ ~ -~ §} .!2!2 ~.!2 <..: !2,!2 ~~ !2!2 <..: !2!2 ~~ <..:"'"' !2,!2 <..: J~ <20K 20-25K 25-30K 30-35K 35·40K 40-45K 45-SOK 50-SSK 55-SOK 60-70K 70-BOK 80-90K 90-100K 100-120K >120K 1989 SALARY NOVEMBER 1989, VOLUME 36, NUMBER 9 1165 Annual AMS-MAA Survey 60 GROUP Ill - Doctorate granting departments 73 of 84 reporting (87%) Rank # Reported Mean salary Assistant Professor 490 $33,607 Associate Profes sor 524 37,588 I Full Professor 800 55,828 40 l I 10 I n ~. I Ill I r n ~ n I I E.9!3 cs=s c.s~=s ES!S '2.9!3 cs=s E.9!3 ES!S - .!!! .!!! lL I I ~-~LL ~-~~ ~-~u_ -!·~ u_ ~-~LL ~-~LL ~u ~-~u_ .!·~LL i~~ ~u -~ ~ ~:2 ~~ ~.:2 ~! .:2,!2 ~! .!2.!2 <20K 20-25K 25-:JOK 30-35K 35-40K 40-45K 45-50K 50-SSK 55-60K 6C-70K 70-80K 80-90K 90-100K 100-120K >120K 1989 SALARY 50 GROUP IV - Doctorate granting departments 49 of 70 reporting (70%) Rank #Reported Mean sala ry Assistant Professor 150 $36,38 0 Associate Professor 150 43,67 7 40 Full Professor 336 63,7 04 I 10 n- n~. ~- - I In n~ a ~ r> I - E.a!-s 'ES!"5 'E.S!:S E~f3• ~~~ RANK ~-~~ ~-~~ ~-~~ i-~~ ~~~ £1 -~ u. -~-~LL ~-aLL ·m ~ 'i>lfil -~·ilL -~ ~ ~! <20K 20-25K 25-:JOK 30-35K 35-40K 40-45K 45-50K 50-SSK 55-60K 80-lOK 70-80K 80-90K 90-lOOK 100-120K >120K 1989 SALARY 1166 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Annual AMS-MAA Survey 50 GROUP V - Doctorate granting departments 15 of 29 reporting (52%) Rank #Reported Mean salary Assistant Professor 37 $43,215 Associate Professor 35 50,588 40 Full Professor 106 69,959 10 lm !Ill II n ~ I I 'E.S!-s "E.9:!3 E.s!a:S 'E$3 cg=s C.$!=§ "EJ!:!S RANK ~ -~ lL ~.~LJ... lL ~.~U.. ~.~& ~-~ u. ~-~U.. ~.~& ~~~ ~~~ .~-~ ~~~ .., 5! ~~~ i~~ ~~~ ·~ ·~ u_ .., 5! -~ ~ -~ ~ ~~ ~~ .... ~~ ~~ ~~ .:2~ ~~ ~! ~~ ~~ .... ~~ ~! ~.!2 c20K 20-25K 25-30K 30-35K 3540K 40-45K 45-50K 50-55K 55-SOK 60-70K 70-SOK 80-90K 90-100K 100·120K >120K 1989 SALARY 40 GROUP VI - Canadian doctorate granting departments (Salaries reported in Canadian $) 20 of 29 reporting (69%) Rank #Reported Mean salary Assistant Professor 94 $34,643 Associate Professor 189 44,403 Full Professor 307 56,391 10 ~ ~ ~ ~ ~ 0 II I~ ~.I ll ~ I n n~ P"' I 'E.$3 ·E-933 'E.9:!3 'E.$!3 c.es RANK ~~~ ~~& .m ·~ u.. ~-~U.. j.~~ ~~~ ~~~ .ZI.~u.. -~~~ j.~~ ~~~ ~ .~LL .., 5! i~& i-~~ -m-~U.. ·~ ~ -~ ~ -~ ~ ·~ ~ "'" -~ ~ ·~ ~ .... ~:2 ...... !2,!2 ~~ ~~ ~~ .. .. ~! ~! .. .. ~~ .. .. ~~ c20K 20-25K 25-30K 30-35K 35-40K 40-45K 45-50K 50-55K 55-60K 60-70K 70-SOK 80-90K 90-100K 100-120K >120K 1989 SALARY NOVEMBER 1989, VOLUME 36, NUMBER 9 1167 Annual AMS-MAA Survey 50 GROUP M - Master's degree granting departments 151 of 260 reporting (58%) Rank #Reported Mean salary Assistant Professor 714 $32,200 Associate Professor 791 39,959 40 Full Professor 928 49,172 'ES:S 'E~:S RANK i·~LL ~-~LL ~~~ ~~ ~~ !! <20K 20-25K 25-30K 30-35K 35-40K 40-45K 45-50K 50-55K 55-SOK 60· 70K 70-BOK 80·90K 90·100K 100-120K >120K 1989 SALARY 40 GROUP 8 - Bachelor's degree granting departments 417 of 978 reporting (43%) Rank # Reported Mean salary Assistant Professor 940 $31,776 Associate Professor 817 42,324 ~ Full Professor 793 48,073 <::: e! ~ 30 "iii ~ 13 .!!! I ]i _g 'l5 C' ~ "'c. 20 "' ~"' "5 u.~ 10 I ~~ I ~. I I n n ~ ~ I ~ - 'E.9!3 'E.s!:S 'E~:S 'E.S:S RANK ~~~ ~-~LL i·uu.. -m-~1.1...... 5! i!~ !·~LL :2.::! ~! ~~ ~! !! ]§ <20K 20-25K 25-30K 30-35K 35-40K 40-45K 45-50K 50-55K 55-SOK 60-70K 70-BOK 80·90K 90-100K 100-120K >120K 1989 SALARY 1168 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Annual AMS-MAA Survey Doctoral Degrees Conferred 1988-1989 ALASKA MATHEMATICS The annual list of doctoral degrees in the University of Alaska ( 1) Feres, Renato, Geodesic flows on mani mathematical sciences and related subjects folds of negative curvature with smooth reports 957 degrees conferred between July MATHEMATICAL SCIENCES horospheric foliations. 1, 1988, and June 30, 1989 by 219 depart Huang, Sen-Wei, A fully two-dimensional ments in 151 universities in the United States Hasselblatt, Boris, Regularity of the transport algorithm for and Canada. Each entry contains the name of flux-corrected Anosov splitting and a new description the recipient and the thesis title. The number hyperbolic partial differential equations. of the Margulis measure. in parentheses following the name of univer ARIZONA Hauser, Kai, Independence results for sity is the number of degrees listed for that indescribable cardinals. university. University of Arizona (6) Verona, Maria Elena, Generic differentia APPLIED MATHEMATICS bility of convex functions and monotone Adachihara, Hatsuo, Modulational insta operators. bility in optical ring cavity. Stanford University ( 13) Elele, Nwabuisi N. 0., Mathematical modeling of multistep chemical combus ENGINEERING-ECONOMIC SYSTEMS ALABAMA tion: The hydrogen-oxygen system. Bell, Hanan S., A new approach to University of Alabama, Rajagopalan, Ramachandran, Bifurcation incentives for information creation and Birmingham (2) analysis of the structure of vortices in an distribution. univorm strain field. Braden, David Jean, Nonlinear pricing to BIOSTATISTICS AND BIOMATHEMATICS MATHEMATICS reduce demand uncertainty. Blackwood, Larry G., Contributions to Damianou, Pantelis Andrea, Nonlinear El-Masri, Joseph Elias, Risk allocation the theory and application of the Rasch Poisson brackets. and contract design in banking. model. Grainger, Gary, Left modules for left Fung, Robert, Structure composing for Hruska, Susan Irene B., Investigation of nearrings. situation assessment. a statistic to test for serial correlation Nabla spaces, the Lyon, Thomas Peyton, Supply contracts, within subject in analysis of variance. Griesan, Raymond, theory of the locally convex topologies regulatory lag, and cost disallowance in University of Alabama, (2-norms, etc.) which arise from the the natural gas industry. Tuscaloosa (8) mensuration of triangles. Nease, Robert Frank, Increasing the transparency of medical decision mak MANAGEMENT SCIENCES AND ARKANSAS ing. STATISTICS University of Arkansas (3) Chyou, Po-Huang, A comparison of MATHEMATICS misclassification probability estimating MATHEMATICAL SCIENCES Chua, Kok-Seng, Absolute gradient techniques in discriminant analysis. Bello, Mohammed Yahuza, An introduc bound for surface of constant mean Fink, Ross Lawrence, A knowledge-based tion to free and semi-free groupoids. curvature. approach to expediting in manufacturing Breen, Michael Almon, The semigroup of Eloranta, Kari Vaino, a-congruence for facilities. binary relations. billiards and Markov processes. Ford, Donnie R., An intelligent simula Grant, Angela G., Class groups ofZariski Greenhalgh, Andrew Simon, Random tion generator with a natural language surfaces. walks on groups with subgroup invari interface. ance properties. CALIFORNIA Park, Young-Hong, An expert system for Lawlor, Gary Reid, A sufficient criterion statistical analysis in simulation. California Institute of Technology (7) for a cone to be area-minimizing. Rao, Pamu Mohan, A knowledge-based APPLIED MATHEMATICS Leung, Ming-Ying, Probabilistic models methodology for productivity analysis. and computational algorithms for some Rom-Kedar, Vered, I. An analytical study problems from molecular sequence anal Shirley, Britt M., The distribution of of transport, mixing and chaos in an ysis. the number of vertices contained in unsteady vortical flow. II. Transport in randomly generated polyhedra. two dimensional maps. Papanicolaou, Vassilis G., The probabilis tic solution of the third boundary value Ward, Phillip John, Goodness of fit tests Rotenberry, James Michael, Effect of problem for the SchrOdinger equation for multivariate normality. compliant boundaries on weakly nonlin and its path integral representation. West, Mark Stephen, A quantile view ear shear waves in channel flow. of bootstrap confidence intervals for the Soibelman, Israel, A study of finite am Puente, Maria Jesus, Riemann surfaces mean. plitude bifurcations in plane Poiseuille of a ring and compactifications of semi flow. algebraic varieties. NOVEMBER 1989, VOLUME 36, NUMBER 9 1169 Annual AMS-MAA Survey University of California, Dinh, Hung The, Discrete product systems Weinstein, Barry Jay, On embeddings of Berkeley (57) and their C* -algebras. the 1-3-1 into the recursively enumerable Helen Giessler, The arith degrees. BIOSTATISTICS Grundman, metic genus of Hilbert modular three White, Samuel Pollard, Two applications Lindahl, Kenneth Q., Jr., Biostatisti folds. ofgalois theory: A group theory problem for estimating bark bee ca/ methods Izzo Alexander John, Uniform algebras of Harvey Friedman and Hodge rings Scolytidae) populations tle (Coleoptera: ge~erated by ho/omorphic and harmonic on CM Abelian varieties. and tree mortality. functions of one and several complex Zeeman, Mary Lou, Hopf bifurcations INDUSTRIAL ENGINEERING AND variables. in the competitive three-dimensional OPERATIONS RESEARCH Jagy, William Charles, Minimal subman Lotka-Volterra systems. Cosares, Steven Thomas, On the com ifo/ds foliated by spheres. Zubelli, Jorge Passamani, Differential plexity of some primal-dual linear pro Jones, Theodore Warren, Topological equations in the special parameter for gramming pairs. rigidity of horocycle flows. matrix differential operations of AKNS Doucet, Joseph Ambroise, Differential Kadison, Lars David, Cyclic homology type. pricing ofelectricity through interruption of extension algebras with application STATISTICS insurance. algebraic K-theory, to matrix algebras, Chiang, Yann-Tong (Tom), Tests for of operators. Goldschmidt, Olivier Pol, Deterministic and nest algebras exponentiality with censored data. and probabilistic aspects of the k-cut Adlao, Jr., Stable rank Laroco, Leonard Cutler, Adele, Optimization methods in problem. theorems in H 00 • and approximation statistics. Kim, Soo-Young, Resource-constrained Arthur, Solutions ofthe Latham, Geoffrey Cutler, David Richard, Efficient block production scheduling in project-ori associ Kadomtsev-Petviashvili equation designs for comparing test treatments to ented production systems. commuting ordinary ated to higher rank a control in the presence of correlated Kim, Sung Chul, Bayesian calibration differential operators. errors. experimental designs based on linear Pete, A probabilistic LeBlanc, Emile Alvin Eudey, Lynn, Selection effects on regres models. for Bergman spaces. zero set condition sion models for clustered data. Monteiro, Renato Duarte Carneiro, In algorithm for computing the Li, Jing, An Fan, Jianqing, Contributions to the esti terior path following primal-dual algo matrix exponential. mation of nonregular functiona/s. rithms. Applications of de Branges' Li, Kin Yin, Khoshnevisan, Davar, Level crossings of Resende, Lucia Ignez Polverelli, Comput contained spaces. theory of contractively the uniform empirical process. ing network reliability using exact and John Edward, Analytic struc McCarthy, Kimanani, Ebi Kalahi, Statistical mod Monte Carlo methods. operators. tures for subnormal elling in pest management: Formulation Wee, Nam-Sook, A Bayesian model for Mess, Geoffrey, The Torelli groups for of a mosquito control model. determining optimal testing intervals for genus 2 and 3 surfaces. computer software. Koo, Ja-Yong, Tensor product splines in Mrowka, Tomasz Stanislaw, A local the estimation of regression functions, Wood, David Joseph, A study of multi Mayer- Vietoris principle for Yang-Mills exponential response functions and mul plicative-strategy equilibria in second moduli. tivariate densities. price multi-component auctions. Nordmark, Henrik Olov, Higher order Lee, Keewon, Bootstrap methods in gen Yoon, Bok Sik, Approximation for the vortex methods with rezoning. linear models. of stochastic pro eralized transient behavior O'Cairbre, Fiacre Ailbhe, Ergodic actions and uniformiza Mo, Moxiu, Robust additive regression. cesses: Discretization of SU(2) x Ton operator algebras. tion. Mykland, Per, Bootstrap and edgeworth Pavone, Marco, Boundaries of discrete methods for dependent variables. MATHEMATICS operators, and exten groups, Toeplitz Rotnitzky, Andrea, Analysis of general Arsenovic, Milos, A C* -algebra of sin sions of the reduced C* -algebra. ized linear models for cluster correlated gular integral operations on the Poin Rainsberger, Robert Bell, On L 2 bound data. care plane. edness of psuedo-differential operators. Schader, Carl, The second moment in Balaban, David John, A geometric per Strain, John Andrew, Numerical study of equality and Gaussian extremes. spective of experimental design and dendritic solidification. So, Beong Soo, Asymptotically optimal parameter identification. Torre, Nicholas Goodrich, Minimal estimation in the semiparametric het Bell, George Irving, A model of vortex hypersurfaces in compact symmetric eroscedastic linear model. induced radiation in the beta plane. spaces. University of California, Berarducci, Alessandro, The interpret Totaro, Burt James, K-theory and alge Davis (8) ability logic of Peano arithmetic. braic cycles. Cai, Maohua, Boolean logic in artifi Walker, Kevin Michael, An extension of MATHEMATICS cial intelligence and Turing degrees of Casson's invariant to rational homology Cheung, Samson Hok-Chi, Convergence Boolean-valued sets. spheres. acceleration of hypersonic flow calcula Cawley, Elise Ellen, Smooth Markov tions. partitions and toral automorphisms. 1170 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Annual AMS-MAA Survey Gomulkiewicz, Richard Stephen, Ana Grafakos, Loukas Georgios, Endpoint Luo, Feng, Triangulations in conformally lytic investigations of diploid models estimates for singular convolution oper flat geometry. of evolution by female choice sexual ators. Merino, Orlando, Optimization over spaces selection. Horn, Werner, Semi-classical approxima of analytic functions. Goulart, Jose Antonio, Fisheries models tions for tunneling near the top of a Schwartz, Anne, Modular forms of weight of pelagic species. potential barrier and its application to 1/2 on products of p-adic upper half Lucchetti, Roberto Edoardo, Set con solid state physics. planes. verges with application to optimization Kawahigashi, Yasuyuki, One-parameter Zack, Maria Russell, Convergence to and probability. automorphism groups of the injective uniform on the finite Heisenberg group Riskin, Adrian, Polyhedral maps on the finite factor of type II. and applications to random number pinched torus. Kim, Sung-Ock, Noether-Lefschetz locus generators. Saleem, Mohammad, Spectrum analysis for surfaces. University of California, and convergence acceleration techniques Tan, Ser Peow, Representations ofsurface Santa Barbara ( 4) applied to implicit finite difference ap groups into PSL(2, R) and geometric proximations for Euler and Navier structures. MATHEMATICS Stokes equations. Wang, Shicheng, Several results on 2- and BonDurant, William Richard, Spinor Shao, Sai-Lai Sally, Asymptotic behavior 3-manifo/ds. norms of integral quadratic forms. for a Jean, A piece-wise linear of solutions of model problems University of California, Person, Laura coupled system. proof that the singular norm is the Riverside (3) Yang, Wei-Chi, The multidimensional Thurston norm. variational integral and its extensions. MATHEMATICS AND COMPUTER SCIENCE Yurekli, Osman, Identities, inequalities Bourezgue, Tarik, Completely non- and Parseval type relations on integral University of California, boundary normal operators in finitely transforms and fractional integrals. Irvine (2) connected domains. STATISTICS MATHEMATICS Michaelis, Rebecca Noelle, Straight sub AND APPLIED PROBABILITY lattices of Euclidean space. Ford, Richard Loren, The use of c5- Zhou, Xian, Goodness of fit tests based functions in scattering past an obstacle. STATISTICS on spacings, interpoint distances and Masters, Wen Chen, Regularity properties Namini-Asl, Hamid, On robustness of nearest neighbors. properties of relativistic and spectral designs, invariance properties of arrays, Schrodinger operators. University of California, and influential observations. Santa Cruz (2) University of California, University of California, MATHEMATICS Los Angeles ( 15) San Diego (12) Melko, Michael, On the focal variety of BIOSTATISTICS MATHEMATICS real Stiefel manifolds. Ayala, Rafael Flores, Regression pre Allen, Jeffery Crawford, Nonlinear anal Rumbos, Adolfo J., Applications of the diction of body fat in Guatemalan ysis and approximation theory: Five Leray-Schauder topological degree to agricultural workers. applications to Haar manifolds. boundary value problems for semilinear Gjertson, David William, Incorporation Bai, Chongen, Asymptotic properties of differential equations. of continuous measurement error into some sample reuse methods for predic University of Southern California (2) pedigree probabilities. tion and classification. Lee, Jiun-Kae, Estimation of the location Barcelo, Helene (Marie-Louise), On the MATHEMATICS parameter for censored paired data. action of the symmetric group of the free Engel, Joachim, Density estimation with Lewis, Steven, A simple measure of rela Lie algebra and on the homology and Haar series. tive quality offit in stepwise regression. cohomology of the partition lattice. Haghoo, Majid, Analysis of parallel ef Park, Jong-Soon Paik, A two-stage classi Carter, Ithiel, Circle packing and confor ficiency of a domain decomposition fication procedure for tree classification. mal mapping. technique. Vollset, Stein Emil, Exact and asymptotic Gao, Zhicheng, The number of triangula inference in a stratified one parameter tions of a surface. COLORADO conditional logistic model. Gove, David B., Modular forms of weight Colorado State University (9) MATHEMATICS one-half over class number one imagi nary quadratic number fields. MATHEMATICS Andretta, Alessandro M., Iteration trees. He, Zheng-Xu, An estimate for hexagonal Alvarez, Eileen E., Rational elliptic sur Bertram, Aaron James, A compactifica- circle packings. faces with infinite cyclic Mordell- Wei/ tion of the complement of a secant groups variety. Lin, Tzuemn Renn, The Hermitian-Yang Mills metrics and stability for holo Lundberg, Bruce, Multistep predictors Christ, Carol Shubin, Singularly per morphic vector bundles over compact in continuation methods and equality turbed integral equations. Kaehler manifolds. constrained optimization. NOVEMBER 1989, VOLUME 36, NUMBER 9 1171 Annual AMS-MAA Survey Refai, Mashhoor, Group action on finite Ye, Hong, Some properties of recursively DELAWARE CW-complexes. enumerable sets uniform for equivalence Rhayyel, Ahmad, Elliptic surfaces over relations. University of Delaware (8) an elliptic curve and over a hyperelliptic Yu, Wenhuan, Inverse problems in partial MATHEMATICAL SCIENCES differential equations. curve. Altekar, Maneesha, Shift detection on STATISTICS STATISTICS two-way arrays. Ahlbrandt, Robert A., Some methods for Carlin, Bradley Paige, Approaches for em Bodt, Barry Alan, Extreme quantile esti selection of predictors. pirical Bayes confidence intervals with mation on sensitivity analysis. Arora, Sanjay, Contributions to search applications. Fast, Stephen A., An optimization method designs. Judge, John Joseph, Multistage sampling for solving a radiation direction problem. Kinoshita, Keizo, Multivariate records techniques for selecting the best treat Gatica-Perez, Gabriel N., On the coupling and scaled limits of random samples. ment. of boundary integral and finite element Sen, Bhabesh, Confidence intervals on Miller, Daniel Stephen, Sequential proce methods for nonlinear boundary value ratios of variance components in the dures based on likelihoods for selecting problems. three stage nested unbalanced model. the best exponential population. Grynovicki, Jock 0., Variance component Vecchia, Dominic F., Permutation tests Moreno, Mabel Haydee, Multistage and estimation diagnostics and associated for equality of linear models. sequential minimum risk point esti distribution theory for all random and mation procedures for the means of mixed designs application to repeated University of Colorado, Boulder (2) U-statistics. measures. MATHEMATICS Schumacher, Phyllis Pella, Analysis of the Krishnamurti, Malini, Uncertainty and length of success runs in a two state duality in economic models and effects Ash, Leslie E., Counting the number of market chain. of policy on the West German dairy solutions in reactive flow problems. industry. Pierce, Donald C., Jr., The global struc Wesleyan University (4) Shi, Sheg Lan (Peter), Application of ture of positive linear maps between MATHEMATICS variational inequalities to anesotropic C* -algebras. Hidalgo, Melissa, Periodic points and Hele-Shaw flows. University of Northern Colorado (6) topological entropy of transitive maps of Tung, Sarah Tze-Ming Young, An expert the circle. MATHEMATICS AND APPLIED STATISTICS system for ANOV A based on the study Landry, Stephen G., Generalized mar of statistical consulting process. Culverhouse, John, Predicting error prone ginal problems. cases in a welfare program using the Macula, Anthony J., Jr., Archimedean DISTRICT OF COLUMBIA dollar error prone index method. vector lattices versus topological spaces Fenn, Ethel Ruth Kloos, An exploratory with filters. American University (6) data analysis of preschool handicapped Miller, Cheryl Chute, Automorphism MATHEMATICS, STATISTICS children's educational progress during groups of N.0-categorical structures with AND CoMPUTER SciENCE intervention. equal numbers of orbits on k and k + l Akbari-Zarin, Mansour, Computer as Effect ofreliablity and Kopriva, Rebecca, sets. sisted instruction and critical thinking: N size on stat hypotheses. Yale University (7) Developmental model. Liao, Tien-Fu, Relationships between Brown, Martha A., The relationships be family environment variables, children's MATHEMATICS tween levels of mathematics anxiety in efficacy, and participation atti political Bremner, Murray Ronald, On tensor elementary classroom teachers, selected data from Taiwan, Republic tudes using products of modules over the Virasoro teacher variables, and student achieve of China. algebra. ment in grades two through six. Malmanger, Curtis, A statistical word Goldberg-Rugalev, Maxim Jonathan, An Hayden, Linda Bailey, The impact of an the book of Hebrews as to its study of alytic dependence and functional calculi. intervention program for high ability authorship. Pauline Jing, Naihuan, Vertex operators, sym minority students on rates of high May, Douglas, Robustness considerations metric functions and their q-defor school graduation, college enrollment ofan M/M/1 queueing model on a local mations. and selection of a quantitative major. area network. Pritt, Mark Davenport, Homotopy theory Jacob, Thomas A., The two-treatment of minimal simplicial spaces. CONNECTICUT crossover experiment for clinical trials. Tan, Eng-Chye, On some geometrical Langdon, Joan M., The effects of the use University of Connecticut (8) properties of K-types of principal series of software on students' understanding representations. of selected statistical concepts. MATHEMATICS Tsai, Tian-Yue, Nonlinear evolutions of Taylor, Ann Dismuke, A study of fac Hong, Seong-Kowan, The generalized the Schrodinger operator in R2. tors influencing student performance in Gauss maps of a maximal surface in Xue, Xiao-xi, On the first Betti numbers mathematics on the Florida college-level Lorentzian space. of hyperbolic surfaces. academic skills test (CLAST}. 1172 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Annual AMS-MAA Survey George Washington University (3) MATHEMATICS Allen, William Clay, III, Divide and conquer as a foundation for arithmetic. MATHEMATICS Bartolomeo, Jerry, Uniform stabilization of the Euler-Bernoulli equation with Lewis, Keith, Functional calculi, M Dajani, Karma, Simultaneous recurrence active Dirichlet and non-active Neumann spectra/ sets and invariant subspaces. of weighted cocycles. boundary feedback controls. Sollervall, Hakan L., Distribution of ze STATISTICS/COMPUTER AND Neal, David Kenneth, Optional stochas ros and polynomials and real analytic INFORMATION SYSTEMS tic integration in Hilbert space with functions. Hamdy, Mohammed Ismail, Approxi applicatiohns to nuclear spaces PUBLIC HEALTH SCIENCES mating the mean of the non-central STATISTICS Yang, Hui-ying, Segregation analysis of hypergeometric distribution and an al cleft lip and palate under the mixed Lee, Li-Chu, Empirical Bayes estimation ternative approach to pairwise multiple hypotheses with real and ofthe response function and multivariate model: Tests of comparisons. simulated data. Hammick, Patricia, Estimation of the regression model. prevalence of a rare disease using University of South Florida ( 1) IDAHO grouped data to preserve anonymity. MATHEMATICS Idaho State University ( 1) Howard University ( 4) Lo, Chi-Chang, Weak convergence in MATHEMATICS MATHEMATICS d x d bistochastic matricers and other Teets, Donald Alan, Convergence regions Issa, Abdulcadir S., Spaces of functions semigroups. for sequences of complex interpolating LP -differentiable in the local sense up to functions. GEORGIA a variable order and their stability under University of Idaho (4) pseudodijferentia/ operators. Emory University ( 1) Lisan, Amha Tume, The ideal structure MATHEMATICS AND APPLIED STATISTICS of the space of ultrafilters on a dis MATHEMATICS AND Azram, Mohammad, Graph theoretic ver- crete semigroup and related Ramsey COMPUTER SCIENCE sions of Reidemeister moves. theorems. Lindquester, Terri, The effects ofdistance Do, Tae, Dean cores for reaction-diffusion Steadman, Vernise, A theory of operators and adjacency conditions on Hamilton convection problems. on Banach spaces. ian properties in graphs. Lee, Young, Some singular perturbation Woodson, Leon, Infinite matrices, Cn Georgia Institute of Technology (4) problems in Hilbert space. functions and umbra/ calculus. Steenberg, Craig, On the octahedral MATHEMATICS group. FLORIDA Abell, Martha Louise, Symmetry reduc tion of Reynolds equation and applica ILLINOIS Florida State University ( 4) tions to film lubrication. Illinois Institute of Technology ( 1) MATHEMATICS Khadivi, Mohammed Reza, Operator the ory and infinite networks. MATHEMATICS Ernst, Claus, On knots and tangles. Lewellen, Gary Boyd, Topological inves Ghebremeskel, Kuflu, Some results in Williams, Roselyn Elaine, Finite dimen- iteration theory. sional Hopf algebras. tigations of self-similarity. Patterson, Wanda McNair, Problems in Illinois State University ( l) STATISTICS classical Banach spaces. Chiang, Yuang-Chin, A comparison oftwo MATHEMATICS University of Georgia (2) methods of bootstrapping in a reliability KonKar, Haifa Nassar, Graph theory as model. MATHEMATICS an introduction to methods of proof and Clair, James, Simultaneous quantile test- Wu, De Ting, A numerical study ofsecond problem-solving. ing. order Ito equations and of their additive Northern Illinois University ( 1) functiona/s. University of Florida (5) MATHEMATICAL SCIENCES STATISTICS INDUSTRIAL AND SYSTEMS ENGINEERING Gruenwald, Mark Edward, Strictly equicon Stewart, Frances P., Multidimensional tinuous subsets of the space of Bochner Rhee, Hahn-Kyou, Analysis of a control- blocking in experimental designs. integrable functions. lable M/M/2 queueing system operating (0, K, N, M) policy. under the triadic HAWAII Northwestern University (14) Wang, Kuo-Hsiung, Analysis and diffu ENGINEERING SCIENCE AND APPLIED sion approximation of the G/G/R ma University of Hawaii ( 5) MATHEMATICS chine repair problem with warm standby Braza, Peter Anthony, Singular Hopf bi spares. MATHEMATICS furcations in the laser with injected sig Agliano, Paolo, Algebras whose congru between bounded ence lattices are semimodular. nal and the transition and unbounded phase solutions. NOVEMBER 1989, VOLUME 36, NUMBER 9 1173 Annual AMS-MAA Survey Hobbs, Ann Kahlow, Mathematical mod Dix, Daniel Beach, Decay of solutions to Hopkins, Kevin Walter, Efficient quo elling of the properties of optical fibers: the Benjamin-Dna-Burgers equation. tient representations of meromorphic Bending loss, birefringence, and fiber Keel, Sean, Techniques for calculating functions. drawing. Chow rings. Lee, Chongsung, Lattice properties and Swietlik, Craig Edward, Rational least Lewis, James Welsh, Infinitesimal rigidity interpolation theory of the spaces A'P,q maximum approximation by weighted for the action of SL(nz) on TN. and M'¥. least squares. Napier, Terrence John, Convexity prop Pollack, David H., Nonlinear, condition boundary MATHEMATICS erties of coverings of smooth projective ally stable, singularly perturbed varieties. relation problems. Chen, Pengyuan, On the efficiency and Smith, Cameron Cotter, Dinatural trans complexity of computational and eco Pinney, Karen R., Complexity results for formations and polymorphic operators. nomic processes. domains in smooth projective varieties. Steinhart, Enid Marguerite, On the loca Closky, David, Infinitely many sinks for Stuck, Garrett, On the cocycles of char tion of zeros ofsolutions tow" +Aw = 0 a singular map. acteristic classes associated to certain ergodic group actions. for certain entire A". Dula, Giora, The conic structure of Thorn Tanner, Franz Xaver, On the smoothness spaces. STATISTICS of the Bellman function. Huang, Yenkun, Random sets for the Johnson, Valen Earl, On statistical image Wang, Gang, Some sharp inequalities for pointwise ergodic theorem. reconstruction. conditionally symmetric martingales. Hughes, Harry, Hitting time and place to Thomas, Neal, Jr., Designing an observa small geodesic spheres of Riemannian tional study using estimated propensity INDIANA manifolds. scores. Oakley, Patricia, Low frequency atmo Xu, Darning, Some divergence measures Indiana University (3) spheric acoustic propagation. models and their applica for time series MATHEMATICS Pant, Himanshu, Uncountably many tions. strictly ergodic models which are metri Wu, Berlin, On order statistics in time University of Illinois, Chicago (9) cally isomorphic but not almost topolog series analysis. ically conjugate. MATHEMATICS, STATISTICS AND Zarnowski, Roger Edward, A finite Schochat, Rainer, Two problems in scat CoMPUTER SciENCE difference scheme for the Navier-Stokes tering theory. Abughalous, Mansour M., Ranking and equations of one-dimensional isentropic fluid flow. Stafford, Matthew, Markov partitions for selection procedures for non-symmetric compressible the doubling map. models. Zasadil, Scott E., An asymptotic expan Vlasov-Poisson system of Van Newenhizen, Jill, The geometric Ganesan, Kothandaraman, Serre- Tate the sion of the investigation of voting techniques: A ory of ordinary K3 surfaces. equations. comparison of approval voting, posi Itai, Masanori, On the Strong Martin Purdue University (24) tional voting techniques and the Borda conjecture. ENGINEERING count. Job, Vanessa, On polyadic codes. INDUSTRIAL Xia, Zhihong, The existence of the non Johnson, Peter Malcolm, Gamma spaces Chou, Yon-Chun, Automatic design of collision singularities in Newtonian sys and loops of nilpotence class two. fixtures for machining processes. tem. Phanord, Dieudonne, Multiple scattering Gardner, Leah Leslie, Studies in 3- connect- Southern Illinois University, Carbon of elastic waves by a distribution of ed graphs: A decomposition theory and dale ( 4) identical spheres. Seeley, Craig Derrol, Nilpotent Lie al a decomposition-based optimization al MATHEMATICS gebras of dimension 7 over complex gorithm. Boukas, Andreas, Quantum stochastic numbers. Johnson, Mary Agnes, Phase distribu analysis: A non-Brownian case. Seif, Steven, Varieties and quasi tions: Selecting parameters for match Hering, Roger H., Roundedness and sta varieties of rings. moments. bility in functional differential equations. Srinivasan, Murali, Optimization prob- Kern, Dale, Optimal distribution net Keller, Timothy Paul, Witt groups of lems on posets and graphs. work configuration for the single-com elementary type. modity, single-supplier, W-distribution University of Illinois, Tankou, Victoire, Use of auxiliary infor- point, N-retailer system. Urbana-Champaign (9) mation in sampling theory. Lang, George, Aid for the user of a CAD MATHEMATICS system: CADCOACH-the expert tutor. University of Chicago ( 11) Benson, Steven Rex, Canonical invariants Moon, Young Bai, A framework for failure MATHEMATICS for corresponding residue systems in p recovery of automated manufacturing Bifet, Emili, On complete symmetric adic fields. cell components. varieties. Gurevic, Reuven Henry, Detecting alge Ouyang, Yew-Shing, Bimetal forming me Bradlow, Steven Benjamin, Vortices on braic (in)dependence of explicitly pre chanics with special reference to inden Kahler manifolds. sented functions. tation extrusion and upsetting. 1174 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Annual AMS-MAA Survey Song, Whey-Ming (Tina), Estimators Razenj, Vladimir, Low dimensional Prado, Humberto Eduardo, Local repre of the variance of the sample mean: groups over a-minimal structures. sentations of symmetric spaces and 0-S Quadratic forms, optimal batch sizes, Tsapogas, George, K- Theory of crystallo positivity. and linear combinations. graphic groups. Vera de Serio, Virginia, Spherical sym Upton, David, The operation of large metric rearrangements with respect to a computer-controlled manufacturing IOWA non-homogeneous mass density. systems. Iowa State University ( 15) KANSAS Venkatraman, Sekhar, Modeling mul tivariate populations with translation MATHEMATICS Kansas State University (2) systems. Martin, Andrew deLong, Topology MATHEMATICS MATHEMATICS posets and an unramified symmetric model for set theory. Mikhaeel, Nabila Nassief, A.-quasi partial Bhattacharya, Tilak, On some non Painted network planes and their logic. linear problems involving the p-Lapla Mehailia, Abdelghani, Zare-Chavoshi, Akbar, Topics in scatter cian. flows with weighted divergence. invariants and ing theory. Ferdinands, Ronald John Dave, Some Miliaras, George, Cardinal covering properties in topology. complex Grassmanian manifolds that KENTUCKY do not fibre nontrivially. Mughrabi, Tahsin Ahmad, Multi- transforms and Haji-Ghassemi, Kamran, On phase dimensional Laplace University of Kentucky (2) restrictions in differential applications. coordinate MATHEMATICS games. Nimmo, Steven Dale, Anticommutative rings. Wang, Tai-Lin, Implementation and ap Hung, Yu-Ching, On the convergence derivation alternator of the QR algorithm. restrictions of divergent power series. Park, Sang Ro, The phenomenon of plication in the presence of convection. Johnson, Craig Merle, Orientation-re quenching STATISTICS versing free actions on closed orientable STATISTICS Barker, Kerry, Analyzing repeated mea by finite groups. surfaces Beam, Craig Allen, The comparison of sures data with an autocorrelated struc Kim, Sung Sook, Characteristic numbers diagnostic tests when one is based ture. and group actions on homology spheres. upon a discrete separator variable and Notaris, Sotirios, An algebraic and nu the others are based upon continuous LOUISIANA merical study of Gauss-K ron rod quadra separator variables. Louisiana State University, ture formulae. Bayesian pre Carriquiry, Alicia Laura, Baton Rouge (7) Shah, Kishor Mohan, Coefficient ideals diction and its application to the genetic of the Hilbert polynomial and integral evaluation of livestock. MATHEMATICS closures of parameter ideals. Guo, Renkuan, Bayesian component reli Akkari, Safwan, On matroid connectivity. Sivaramakrishnan, Narayana, Quasidiag ability assessment with system data. Carpenter, Jenna Price, Finiteness theo- onality of direct sums of weighted shifts. Hong, Chong Sun, Granularity and effi rems for forms over number fields. Zhang, Shuang, On the structure of mul ciency. Chon, Inheung, Lie group and control tiplier algebras. Jensen, Karen Lorraine, Optimal adjust theory. STATISTICS ment in the presence ofprocess drift and Garcia, Josefa I., The congruence exten adjustment error. semigroups. Ananda, Malwane M. A., Estimating sion property for algebraic comparisons of functions of exponential parameters. Kim, Song-Ho, Stochastic Phenis, Patrick, On prime powers and order statistics. Burt, Jameson, Towards agreement: symbolic prime powers. Estimating the Bayesian experimental design. Mingoti, Sueli Aparecida, Reyes, Edgar Navarro, Ergodic actions of total number of distinct species when Mak, Kok-Sun, Adaptive tests and classi semi-direct product groups. quadrat sampling by elements is used. fication procedures. Russell, Robert, On the relative K2 of Nanayakkara, Nuwan, Heteroskedasticity Nalliah, Manohari, Estimating certain non-commutative rings. robust estimation of means. functions of normal parameters. Tulane University (3) Sung, Nae Kyung, L 1 Cramer-Rao ana University of Notre Dame (5) logues. MATHEMATICS MATHEMATICS University of Iowa ( 4) Joseph, George John, Stochastic numer ical optimization with application to Krueger, Andreas, Homogeneous Cauchy MATHEMATICS Riemann structures. seismic exploration. Cordero-Brana, Minerva, ?-primitive over Oates, Sarah Elizabeth, The jump degrees Lee, Sang Bum, Divisible modules planes. of groups. domains. Figueroa, Raul Franciso, On translation theory O'Driscoll, Hubert Peter, Isomorphisms Pickett, Douglas Dean, Scattering planes admitting a collineation group of higher order equations. of saturated subgroups of P06. for order q2 - I. NOVEMBER 1989, VOLUME 36, NUMBER 9 1175 Annual AMS-MAA Survey University of Southwestern Bryson, Noel, Multiobjective and large Brandeis University (3) Louisiana (6) scale linear programming. MATHEMATICS Casey, Stephen D., The boundary of the MATHEMATICS Maliakas, Mahalis, On the representation universal Teichmii.ller space and the Bers Beslin, Scott Jude, Number-theoretic equa of theory of the symplectic group. space of Schwarzians. tions, rings generated by units, GCD Mori, Andrea, Integrality of elliptic mod Cox, Stephen E., Nonlinear stability of matrices, and topological semigroups. ular forms via mass operators. traveling waves for a model of viscoelas Equivalence be STATISTICS tic materials with memory. Piovan, Luis Amadeo, tween integrable systems and Kummer Adams, Benjamin Michael, Economi Farsi, Carla, Index theory and positive varieties. cally optimal on-line quality control scalar curvature for orbifolds. procedures. Foster, Dean P., Conditional/east squares Harvard University (22) Lowry, Cynthia, Multivariate exponen for semi-Martingales. moving average control APPLIED SciENCEs tially weighted Myers, Margaret Elaine, Robustness of Cebuhar, Wenceslao A., Smoothing and charts. design in misspecified logistic regression. Hazem Diab, The effect of approximate linearization of discontin Maragah, Noon, Patrick James, The single layer on quality control charts. uous control systems. autocorrelation heat potential and Galerkin boundary Heddaya, Abdelsalam, Managing event Tracy, Nola Diana, Evolutionarily stable element for the heat equation. learning rules. based replication for abstract data types Papadakis, Panagiotis, Computational as in distributed systems. Vinyard, Bryan, Some extensions of con pects of the determination of the stress Kearns, Michael J., The computational struction techniques for fractional asym intensity factors in 2-dimensional elas complexity of machine learning. metrical factorial experiments. ticity. Krizanc, Daniel D., Merging and routing Plaut, Conrad P., Riemannian geometry MARYLAND on parallel models of computation. on non-Riemannian spaces. Johns Hopkins University (6) Rajasekaran, Sanguthevar, Randomized Shen, Yuan-Yuan, Units of real cyclic parallel computation. BIOSTATISTICS octic fields. Salzberg, Steven L., Learning with nested Albert, Paul S., Design and analysis of a Stephenson, Lawrence, Representation generalized exemplars. panel study for estimating durations and theory of nilpotent groups over local J., SIMD algorithms for point prevalence in a two-state recurrent fields of characteristic zero. Walsh, Robert image rendering. illness process. Walnut, David, Weyl-Heisenberg wavelet MATHEMATICAL SCIENCES expansions: Existence and stability in BIOSTATISTICS Benjamin, Arthur Todd, Turnpike struc weighted spaces. Archer, Linda Elise, The impact of tu for optimal maneuvers. mor lethality on statistical tests for tures MASSACHUSETTS Mathias, Roy Christopher, Matrix in carcinogenicity. equalities. Boston University (8) Begg, Melissa, The effects of model mis specification in regression, with applica MATHEMATICS MATHEMATICS tions to bioassay. Chiang, Yuan-Jen, Harmonic maps of Atela, Pau, Studies in dynamical systems: Lipsitz, Stuart R., Methods for analyzing V-manifolds. Collisions and codings. repeated categorical outcomes. Goloff, David, Controlling the dimension DiFranco, Donna Maria, Time-ordered Neuberg, Donna Shapiro, Enriching the of the space of rank-k holomorphic binary data with positive dependence. bootstrap, with application to incomplete mappings between compact complex Barbara, The dynamics Durkin, Marilyn data. manifolds. of the complex exponential function: A Spiegelman, Donna, The design and anal Leu, Ming-Guang, A class number prob mathematical and computer graphical ysis ofepidemiologic investigations when lem for real quadradic fields of R-D analysis. the exposure variable is mis-measured, type. Periodic points for Gole, Christopher, with application to the mis-measurement monotone symplectomorphism of Tn x University of Maryland, Baltimore ( 1) of obesity in models of diabetes, hyper Rn. MATHEMATICS tension and colon cancer incidence. Hathaway, Dale, Techniques for summa Liu, Jinn-Liang, Numerical methods for Spino, Catherine A., Rerandomization rizing longitudinal data. parabolic partial differential equation in algorithms for robust statistics and re Stephane, Exponential di which the diffusion coefficient changes Laederich, gression with an aggregate covariate. chotomies, non-linear partial differen sign. tial equations, and differential difference MATHEMATICS University of Maryland, equations. Kocherlakota, Rama Rao, Integral ho College Park ( 13) Sutherland, Scott, Finding roots of com mology of real flag manifolds and loop MATHEMATICS plex polynomials with Newton's method. spaces of symmetric spaces. Bonnetier, Eric, Mathematical treatment Terrin, Norma, The weak convergence of Li, Jun, The construction of stable vector of the uncertainties appearing in the for quadratic forms with long-range depen bundle on surface with low second Chern mulation of some models for plasticity. dence. class. 1176 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Annual AMS-MAA Survey Morelli, Robert, Hilbert's third problem Kilian, Joseph, Uses of randomness in Zhang, Weijiang, Center manifolds for and the K theory of toric varieties. algorithms and protocols. singularly perturbed discrete dynamical Prasad, Dipendra, Trilinear forms for Kim, Yeon Mi, Unique continuation systems and an application to multiple GL(2) of a local field and f.-factors. theorems for the Dirac operator and the coupling in chains of oscillators. Roberts, David P., Shimura curves anal Laplace operator. University of Massachusetts, ogous to Xo(N). Koch, Richard, An analysis of the perfor Amherst (8) Rockmore, Daniel, Fast Fourier analysis mance of interconnection networks for MATHEMATICS AND STATISTICS for finite groups. multiprocessor systems. Vakili, Pirooz, Three topics on perturba Lauer, Michael, Supersymmetric confor Acuna, Carmen Olga, Parameter estima tion analysis of discrete event dynamic mal field theory and superstrings. tion for stochastic texture models. systems. Lerman, Eugene, Symplectic fibrations Ding, Yi, The inverse power method for Zheng, Fanyang, Semipositive threefolds and weight multiplicities of compact semilinear elliptic equations in euclidean and threefolds with universal covering groups. space. c3. Lu, Ya Yan, Bifurcation to mean flows in Lin, Zongzhu, The structure of cohomol convection. ogy of line bundles on the flag varieties STATISTICS Malitz, Seth, Optimal and near-optimal for some groups of rank 2. Thoma, Hans Mathis, Factorization of results on book embeddings. Nee, Janpou, The motion of interaction belieffuntions. Messaoudone, Mohamed, The unit mass between two pair of vortices. Massachusetts Institute of Technol ball ofthree-vectors in R 6. Powers, Robert, Order theoretic classifi ogy (34) Meyer, David, The dimension of causal cation of percentile cluster methods. sets. Rising, Hawley, III, Applications of chaos MATHEMATICS Pemantle, Robin, Random processes with and dynamical systems ap- Bequillard, Alfredo, Estimates up to reinforcement. proaches to mixing in fluids. the boundary for certain subellliptic Pranata, I wan, Structure of Dixmier alge Rising, William Randolph, Exponential operators. bras. chains and generalized inverses: New Bertsimas, Dimitris, Probabilistic combi approaches to the approximate and exact Schick, Irvin, Robust recursive estimation natorial optimization problems. solution of Markov chain problems. of the state of a discrete-time stochastic Bressler, Paul, Schubert calculus in com linear dynamic system in the presence Yang, Yisong, Ginzburg-Landau equa plex cobordism. of heavy-tailed observation noise. tions: A revisit. Durso, Catherine, On the inverse spectral Smelt, James, Fixed point sets of nilpotent MICHIGAN problem for polygonal domains. elements acting on affine flag varieties. Edelman, Alan, Eigenvalues and condi Smith, Leslie, An upper bound with Michigan State University ( 12) tion numbers of random matrices. correct scaling laws for turbulent shear Edward, Julian, Spectral invariants of the flows. MATHEMATICS Neumann operator on planar domains. Snyder, Christopher, On the effects ofpar Ju, Hyeong-Kwan, Bifurcations of sym Fine, Dana, Quantum Yang-Mills on the tial equilibration and cumulus heating metric planar vector fields. two-sphere. on baroclinic instability. Kim, Young Ho, Submanifolds of eu Fortnow, Lance, Complexity-theoretic as Yang, Hu, Numerical simulation ofglobal clidean spaces with planar or helical pects of interactive proof systems. and antarctic ozone using a 2-D model geodesics through a point. Friedlander, Leonid, Determinants of in isentropic coordinates. McKenzie, Robert G., The ring of cy elliptic operators. You, Yuching, Soliton equations and clotomic integers of modulus thirteen is Gath, Eugene, Exact results in quantum infinite dimensional Lie algebras. norm-euclidean. field theory: The spinor Lehmann repre Zaslavsky, Alan, Representing the census Shen, Yun-qiu, Numerical methods of sentation in anti-de Sitter space and the undercount: Reweighting and imputa bifurcation problems via singular value superconformal Thirring ghosts. tion methods. decompositions and homotopy methods. Gerdes, Wolfram, Grassmannian homol Zworski, Maciej, High frequency scatter- Wei, Dongming, Numerical analyses of ogy, algebraic K-theory and higher Chow ing by a convex obstacle. some nonlinear partial differential equa groups for an infinite field. tions. Northeastern University ( 3) Harmse, Jorgen, On Lebesgue space esti STATISTICS AND PROBABILITY mates for the wave equation. MATHEMATICS Datta, Somnath, Asymptotically optimal Hess, Kathryn, A proof of Ganea 's con Burgos, L. Fernando, Inference after Bayes compound and empirical Bayes jecture for rational spaces. selection: Unequal variances and other estimators in exponential families with Hovey, Mark, A new definition of cocate results. compact parameter space. gory. Klimek, Jacek, Equations of nilpotent Dhar, Sunil, Minimum distance method Huang, Jing-song, The unitary dual of the conjugacy classes in classical Lie alge of estimation in an additive effects universal covering group ofGL(n,R). bras. outliers model. NOVEMBER 1989, VOLUME 36, NUMBER 9 1177 Annual AMS-MAA Survey Gunawardena, Kosgallana Liyana Durage, Chan, Kit Chak, Cyclic vectors in spaces MINNESOTA Extended rules for the classification of of analytic functions. dependent parameters. Ferlini, Vincent Joseph, The existence of University of Minnesota, Jung, Inna, Parametric empirical Bayes solutions to certain equations over cyclic Minneapolis ( 15) problems with cost for component obser groups. MATHEMATICS vations. Jung, II Bong, Dual operator algebras and Cohen, Robert Adam, Fractional step Rahbar, Mohammed Hossein, Sequential the classes Am,n. methods for liquid crystal problems. estimation offunctionals of the survival Keum, Jonghae, On Kummer surfaces. De Alwis, Tilak Ananda, Free minimal curve under random censorship. Kim, Myung-Ho, Toral actions on 4- resolutions and Betti numbers. Taraporevala, Arnavaz, Series represen manifolds and their classification. Gao, Wen-Jie, Boundary value problems tation for processes with infinite energy Kornhauser, Daniel Martin, Bounds for on Lipschitz domains for general elliptic and their predictions. the smallest integer solution of general systems. Yang, Song, Minimum Hellinger distance quadratic. Guo, Jong-Shenq, Nonlinear quenching estimation of parameters in the random Martin, Thomas Harry, Minimal theta problem and free boundary problem. censorship model. functions. Hofmann, Steven, Weighted weak-type University of Michigan, Ann Arbor (28) Montenegro Escovar, Carlos Hernando, (i,i) bounds for singular integrals with Combinatorics on large cardinals. BIOSTATISTICS non-smooth kernel. Shapiro, Michael David, Growth, almost Larson, Dean S., The integral cohomology Methods of Landenberger, Bryce David, convexity, and automatic structure in rings of split metacyclic groups. incorporating litter size in the analysis some geometric three-manifold groups. Li, On semilinear elliptic equations in of teratology. Yi, Staples, Susan Grace, Domains with a Rn. Lin, Danyu, Goodness-offit tests and local to global norm condition. Louisell, James Albert, Differential-delay robust statistical inference for the Cox Xin, Zhouping, Nonlinear stability of proportional hazards model. systems: A stability analysis for several rarefaction waves for systems of viscous classes of delay. Martin, Cathy Rose, Discrimination in hyperbolic conservation laws. volving the Markovian normal distribu McDaniel, Douglas Kelley, Siegel-Hilbert tion and discrimination with qualitative STATISTICS cuspforms attached to CM extensions data. Choi, Ki-Heon, An adaptive sequential and their application to periods of probability ratio test for autoregressive genus-2 Heeke eigenfunctions. INDUSTRIAL AND OPERATIONS Nelson, Gail, Bounds for the fundamental ENGINEERING process. Fong, Wai Kwan, A Bayesian approach solutions of degenerate parabolic partial Bischak, Diane, Weighted batch means to successive sampling with partial re differential equations. for improved confidence intervals for placement of units on two occasions. Peckham, Bruce Bartlett, The closing of steady-state processes. Rekab, Kamel, Asymptotic efficiency in resonance horns for periodically forced Kim, Yeong-Dae, An iterntive approach sequential designs for estimation. oscillators. for system setup problems of flexible Pohjanpelto, Petri Juha, Symmetries of manufacturing systems. Zoubeidi, Taoufik, Sequential tests for clinical trials of two treatments with Maxwell's equations. Lee, Hyo-Seong, Control policies for bounded deficiency. Rabau, Patrick, Emmeration on vector queueing and production inventory sys- spaces over a field extension. terns. Wayne State University ( 1) Sun, Min-Peter, A streamline-diffusion Lee, Woo-Jong, Tolerancing: computation MATHEMATICS method for miscible and immiscible on geometric uncertainties flow in porous media. Lai, Hong-Jian, Contractions and Eule- Maddox, Marilyn Johnson, Scheduling a rian subgraphs. Urbina, Wilfreda Oscar, On singular stochastic job shop to minimize tardiness integrals with respect to the Gaussian objectives. Western Michigan University (5) measure. Murray, Joseph, Stochastic initialization MATHEMATICS AND STATISTICS in steady-state simulations. MISSOURI Beckmann, Charlene E., The effect of Richter, Lori-Ann, Resource-constrained computer graphics use on student under project scheduling with preemption of University of Missouri, Columbia (2) standing of calculus concepts. jobs. MATHEMATICS Holbert, Karen S., Specified subgraphs Ryan, Sarah, Degeneracy in infinite hori and subgraph defined parameters in Girou, Mike, Locally H-closed spaces. zon optimization. graphs.; STATISTICS MATHEMATICS Johns, Garry L., Generalized distance in Pang, Ching-Fai, On the estimation of Brenner, Susanne C., Multigrid methods graphs. bath-tub shaped arrival rate. for nonconforming finite elements. Malde, Paresh J ., Chromatic partitions. Calvis, David Timothy, Domain con Witt, Lee, Measures of multiple determi stants of injectivity. nation based on R-estimates. 1178 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Annual AMS-MAA Survey University of Missouri, Rolla (I) NEW HAMPSHIRE Meziani, Abdelhamid, On the integrabil ity of singular differential forms in two MATHEMATICS AND STATISTICS Dartmouth College ( 5) complex variables. order re Guffey, James Michael, Some MATHEMATICS AND Rynes, Jean, Nonsingular affine K* stricted inferences in nonhomogeneous CoMPUTER SciENCE surfaces. Poisson processes. Atkinson, Leigh Louis, Jr., Embedded Tsukada, Haruo, String path integral Washington University (5) eigenvalues and resonances. realization of vertex operator algebras. Beery, Janet, Transitive groups of prime MATHEMATICS NEW MEXICO degree. Deiermann, Paul Jeffry, Some results on Bilaniuk, Stefan, Some results on Souslin univalent functions with quasiconformal New Mexico State University (3) trees. extensions. SCIENCES Bonin, Joseph Edmond, Structural prop MATHEMATICAL Deliu, Anca Liliana, IFS and functional erties ofDowling geometries and lattices. Golik, Wojciech Ludwik, Convergence equations. Wittbold, John Todd, Controlled sig of the integral methods and numerical El ghanmi, Abderrahim, Space/ike sur nalling systems and covert channels. solutions of Fourier problems. faces in Lorentizian manifolds. Ruch, David, Bideal theory. University of New Hampshire ( 1) Torres, Rodolfo Humberto, On the Zhao, Zhi-Yong, Edge detection with operators with boundedness of certain MATHEMATICS Q-B-spline operator. singular kernels on distribution spaces. Mathes, D. Benjamin, Invariant ranges Villamor, Enrique, On slowly increasing University of New Mexico ( 3) of operator algebras. unbounded harmonic funtions. MATHEMATICS AND STATISTICS NEW JERSEY MONTANA Knupp, Patrick, Robust grid generation on curves and surfaces. Princeton University (8) Montana State University (3) Pietsch, George William, Combinatorics MATHEMATICS in scattering theory. MATHEMATICAL SCIENCES Bluher, Gregory, Trisecants of certain Thomas, Edward Victor, Errors-in Doyle, Randy R., Sine methods for third-order Wirtinger varieties. variables estimation in multivariate cal problems. parabolic type Canary, Richard Douglas, Hyperbolic ibration with application to analytical Jonca, Andrzej Wilhelm, Confidence in structures on 3-manifolds with com chemistry. tervals for ill-posed problems. pressible boundary. Kachman, Stephen Daniel, Inference pro Fenley, Sergiu, Depth one foliations in NEW YORK cedures for fixed effects in multivariate hyberbolic 3-manifolds. Adelphi University (I) mixed models. Guan, Pengfei, Holder regularity of sub University of Montana (2) elliptic pseudodifferential operators. MATHEMATICS AND COMPUTER SCIENCE Lee, Chun-nip, Stable splittings of the Al-Kahby, Hadi, Reflection and dissipa- MATHEMATICAL SCIENCES dual spectrum of the classifying space of tion of vertically propagating acoustic Bolano de Ia Hoz, Alvaro Jose, Optimal a compact Lie group. gravity waves in an isothermal atmo control problems with state and control Minsky, Yair, Harmonic maps and hy sphere. constraints. geometry. perbolic CUNY, Graduate Center ( 1) St. George, Gregory Michael, Some as Saldanha, Nicolau, Analytic continuation pects of multiplicative commutation re is impractical. MATHEMATICS lations. Solovej, Jan Philip, Universality in the Cook, Michael, Crystallographic space von Weizacker model of groups and algorithms. NEBRASKA Thomas-Fermi atoms and molecules. Clarkson University (2) University of Nebraska ( 3) Rutgers University, MATHEMATICS AND (6) MATHEMATICS AND STATISTICS New Brunswick CoMPUTER SciENCE Gallagher, Richard Joseph, Scalarization MATHEMATICS Al-Humadi, Ala, Generalized state space of vector optimization problems and Capparelli, Stefano, Vertex operator rela control systems. properties of the positive cone in normed tions for affine algebras and combinato Ruzieh, Subhi, Some applications of vector lattices. rial identities. matrices related to graphs. Kulasekera, Karunarathna, Estimation of Kim, Suh-Ryung, Competition graphs Columbia University ( 10) change points in failure rate models. and scientific laws for food webs and Wei!, Pascal, Inverse monoids and the other systems. MATHEMATICS dot-depth hierarchy. Liverani, Carlangelo, Quantum systems Anshel, Iris, A Freiheitssatz for a class of in contact with a thermal environment: two relator groups. Rigorous treatment of a simple model. NOVEMBER 1989, VOLUME 36, NUMBER 9 1179 Annual AMS-MAA Survey Avidon, Michael, A method for deriving Meyer, Gabriele Elisabeth, Attracting and Hou, Jiashi, Formulation of synovial functional equations with applications to repelling point pairs for vector fields on fluid-articular surface interface condi the zeta and generalized theta functions. manifolds. tions, and asymptotic and numerical Hakim, Jeffrey, Distinguished nonar Xu, Jinchao, Theory of multilevel meth- analysis of squeeze film lubrication of chimedean representations for GL(2). ods. diarthrodial joints. Leon, Luis Enrique, The study ofthe spin Lascurain-Orive, Antonio, Fundamental New York University, odal region via the hodograph method. polygons for the Heeke congruence sub Courant Institute (13) groups. Szanc, Bohdan, The generalized comple Luttinger, Karl, Deformations and degen MATHEMATICS mentarity problem. erations of Riemannian manifolds of Alama, Stanley, An eigenvalue problem Turner, Todd, Non-smooth analysis of nonpositive curvature. and the color of crystals. infinite dimensional control sytems. Steiner, Michael, Gluing data and group Bell, Robert, Probabilistic number theory Wilder, Joseph W., Analytic solutions actions on R-trees. for normed free abelian semigroups. for electrochemical mechanisms involv To, Wing-Keung, Metric rigidity theo Bronsard, Lia, Reaction-diffusion equa ing coupled homogeneous and heteroge rems on locally symmetric Hermitian tions and motion by means curvature. neous chemistry. Steven, Kauffman networks: Cycle manifolds and quasi-projective embed Jaffe, SUNY at Binghamton ( 1) dings of non-compact complete Kahler structure of random clocked Boolean manifolds of positive Ricci curvature. networks. MATHEMATICAL SCIENCES Tsai, 1-Hsun, Holomorphic mappings be Knapp, Robert, Nonlinearity and local Norden, Jeffrey S., Homeomorphisms be tween Hermitian symmetric spaces. ization in 1-dimensional random media. tween Pixley-Roy spaces. Li, Yanyan, On second order fully nonlin Yeung, Sai-Kee, Compactifying Kahler SUNY at Buffalo (5) manifolds and integrality of characteris ear elliptic equations. tic numbers. Lowengrub, John, Convergence of the MATHEMATICS Zhang, Xingguo, Fixed points and auto- vortex method for vortex sheets. Chen, Pei-li, Existence and long time morphisms offree groups. Meth, Kalman, A vortex and finite differ behavior of solutions a diffusion model ence hybrid method to compute the flow for meylinated axon. Cornell University (II) of an incompressible viscous fluid past a Huang, Young-Ye, Topics on invariant APPLIED MATHEMATICS semi-infinite plate. means and weakly almost periodic func Gardner, Kenneth R., Investigation of Nachbin, Andre, Reflection and transmis tions on semigroups. channels population inversion in dense recombin sion of water waves in shallow Shiau, Lie-June, Degenerate Hopf bifur ing plasmas. with rough bottoms. cation and isolated periodic solutions Uniform regular Swindle, Glen H., A hydrodynamic limit Redondo, Juan Carlos, of the current clamped Hodgkin-Huxley sets ofpenalized solutions of of the contact process with large range. ity for level model. the obstacle problem. Ye, Zhongxing, On entropy and epsilon Yan, Gea-Gue, Bifurcation in a reaction Existence and stability entropy of random fields. Smyrlis, Yiorgos, diffusion system with reversible flow in of stationary profiles of the LW scheme. the time-independent system. BIOMETRICS Weinstein, Michael, An integro-differ STATISTICS Morris, Jeffrey David, Percentile and ential equation model of anovulatory percentile ranking estimation in single states in mammals. Weng, Chung-Sing, On some asymptotic sample and regression settings with spe Zhu, Jingyi, An adaptive vortex method properties of the Bayesian bootstrap. cial attention to median unbiasedness. for two-dimensional viscous and incom SUNY at Stony Brook ( 11) pressible flows. MATHEMATICS APPLIED MATHEMATICS AND STATISTICS Polytechnic University ( 1) Barton, Susan Maureen, The real spec Araque Gonzalez, Jesus Rafael, Contri trum of higher level of a commutative MATHEMATICS butions to the polyhedral approach to ring. Yallaoui, EI-Bachir, Topological measure vehicle routing. Bielefeld, Benjamin Martin, Changing theory: A study of repleteness and mea Buonincontri, Stephen, Multidi- the order ofcritical points ofpolynomials sure repleteness. mensional traveling wave solutions to using quasiconformal surgery. Rensselaer Polytechnic Institute (8) reaction diffusion equations. Brady, Thomas Gerald, The integral Gonalez, Jaime, The role of signatures cohomology ojOut+(F3). MATHEMATICAL SCIENCES and strong spanning trees. Kiralis, Geoffrey William, Pseudo-iso Covey, David, Parallel ellipsoid algo He, Mei-Qi, On estimating the parametric topies of irreducible three-manifolds. rithms in nonlinear programming. part of the shape invariant model. Low, Mark Gordon, A unified asymp Cox, Steven, Extremal eigenvalue prob Joh, Tenshang, The performance offactor totic minimax theory for nonparametric lems for composite membranes. analysis on linear recursive path model. density estimation and non parametric Hejna, Matthew James, Curves con regression. structed by geometrically based algo rithm. 1180 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Annual AMS-MAA Survey MATHEMATICS STATISTICS University of North Carolina, Dolan, Peter C., Spanning structures and Heckler, Charles, Estimators of the vari Chapel Hill ( 13) undecidability in random graphs. ance components and the mean of the BIOSTATISTICS Horwitz, Alan, Foliations with Ehres three fold nested random effects model. Cosmatos, Dennis, Methods for modeling mann connections. McDermott, Michael Paul, A new ap disease risk using probability ofexposure proach to statistical analysis subject to Hu, Bizhong, H-Cobordisms over certain measures. non-positively curved spaces. order restrictions. Hafner, Kerry B., Analysis of nonlin Llarull, Marcelo, Sharp estimate and NORTH CAROLINA ear regression models with compound Dirac operator. symmetric error covariance structure. North Carolina State University, Park, Efton, The index theory of Toeplitz Origasa, Hideki, Statistical methods for Raleigh ( 16) operators on the skew quarter plane. the analysis of longitudinal data with Santiago, Freddie, The Willmore prob- MATHEMATICS binary responses. lem. Feng, Wei, Coupled system of reaction Samsa, Gregory Paul, Regression to the Syracuse University ( 6) diffusion equations and applications. mean with applications to the design and analysis of epidemiologic studies. INDUSTRIAL ENGINEERING Mattingly, Robert Bruce, Vector and AND OPERATIONS RESEARCH parallel algorithms for computing the Trost, Donald Craig, Comparison of stationary distribution vector of an irre the probabilities of misclassification Foroudi, Amir David, The solution struc ducible Markov chain. for the estimated linear, quadratic ture of the mixed integer network flow and unbiased-density discriminant func problem. Ruan, Weihua, Reaction-diffusion sys tems with nonlinear boundary condi tions using asymptotic expansions. MATHEMATICS tions. Williams, Rick L., Large sample theory Dezern, David H., Fourier series on Singh, Daya Shankar, Transitive maps for U-statistics in unequal probability Vilenkin groups. from linearly ordered sets to Dynkin samples. Farrell, Ken H., Solution of a congruence diagrams. MATHEMATICS for a pair of polynomials with applica Yaemsiri, Naulchand, The structure of tions to certain convolutional operators. solvable K-Lie algebra. Calvetti, Daniela, A stochastic round off error analysis of the fast Fourier Rajagopalan, Shekhar, The multicom OPERATIONS RESEARCH transform. modity flow problem. Choi, Munkee, Multiclass queueing net Sutton, Michael, Equivalence of particle Rieders, Eric Forrest, Strong laws of works with finite buffers. Lagrangians under contact transforma large numbers for certain sequences and arrays of dependent random variables. Cruz, Jose, Perturbation analysis and tions. design of networks of queues. Thongyoo, Sutep, A study of using micro OPERATIONS RESEARCH AND Ferrell, William Garland, Jr., System computer software to enhance calculus SYSTEMS ANALYSIS dynamics in quality assurance. instruction. Bartroli, Marcelo, On the structure of Jun, Kyung-Pyo, Approximate analysis of optimal control policies for networks of University of Rochester (8) open queueing networks with blocking. queues. Shapiro, Gerald, Flow controls with MATHEMATICS Ware, Keith Alan, Some polytopes related packet fragmentation. Conklin, James E., The discrete Laplacian to the Steiner tree problem. applications to random walk and inverse STATISTICS STATISTICS problems on weighted graphs. Hernandez-Santiago, Jaime Luis, Testing Dong, Xiaoying, Families of functions for genetic disequilibris. Chao, 1-Feng, Capacity of Gaussian chan nels with jamming. whose Julia set is C and some related Kianifard, Farid, Using recursive resid results. uals. calculated on adaptively ordered Selukar, Rajesh, On estimation of Hilbert Eron, Mary Bernadette, Algorithms for observations, to identify outliers in linear space valued parameters. finding generators and relations for some regression. Sengupta, Debapriya, Improved estima cyclic quotient singularities of C2 and Liddle, Roger F., Stochastic approxima tion in some nonregular situations. c3. tion for optimization of integrals. OHIO Northshield, Samuel Woodworth, Marr, Raymond Lloyd, A normalized Schrodinger operators on infinite uniform test for serial correlation of Bowling Green State University ( I) graphs. regression model disturbances. Stahl, Cynthia Lynne, Some generaliza Prasetyo, Hardi, Effects of selection and MATHEMATICS AND STATISTICS tions of total boundedness and char crossbreeding on growth and fat deposi Ofori-Nyarko, Samuel, Improved esti- acterizations of compactness in normal tion in mice. mation of the covariance matrix, the spaces. Schaalje, Gary Bruce, Models for state precision matrix and the generalized Zhou, Xin, Inverse scattering transform structures insect populations affected by variance. on the line with arbitrary spectral singu pesticides with applications to pesticide larities. efficacy trials. NOVEMBER 1989, VOLUME 36, NUMBER 9 1181 Annual AMS-MAA Survey Case Western Reserve University (8) STATISTICS University of Toledo ( 1) OPERATIONS RESEARCH Chan, Shih-Huang, Polynomial spline MATHEMATICS regression with unknown knots and Bakshi, Sudhansu Kumar, Portfolio man Murthy, Nistala V., Essentially algebraic AR(I) errors. agement and resource allocation in a categories ofpartial algebras. venture capital company. Chen, Yun-Shiow, The changepoint prob Cherikh, Moula, Optimal decision and lem in a multinomial sequence and its OKLAHOMA detection in the decentralized case. application. Herzberg, Meir, Replacement of equip Chi, Yunchan, Comparisons of several Oklahoma State University (3) goodness-offit tests for proportional haz ment in public telephone networks due STATISTICS to impact on digital technology-process ard models. and optimization. Lin, Meily, Construction of designs in Chae, Seong-San, A comparative study to predict the numbers of clusters in cluster Kim, Tai Pyung, A static design for input the presence of polynomial trends for analysis. selection in a shared resource facility. varietal or factorial experiments. Mauromoustakos, Andronikos (Andy), Leach, Cynthia Diane, Design of a Lordo, Robert Anthony, On the use of Models for proportions in a two-way multi-product, multi-period, distribution Friedman-type statistics in a randomly cross classification without interaction. network with fixed costs, for refined incomplete two-way design. petroleum products. Palettas, Panickos, Stochastic modelling Nagadeolekar, Madhuri, Fixed sample and approximate Li, Gang, An interactive Delphi-goa/ pro and predictions for fatigue crack propa selection procedures Kieffer- Weiss solution for negative bino gramming procedure for countertrade gation. negotiation decision systems. Rashid, Md Mushfiqur, Statistical infer mial populations. ence based on ranks for some repeated Park, Kil ju, A systematic approach to OREGON countertrade decision making analysis. measurement designs with exchangeable Wu, Yea-win (Peter), A graph theory ap errors within blocks. Oregon State University ( 4) proach to process planning for balanced Zubovic, Yvonne M., Algorithms and machine loading. bounds for rank estimators for several MATHEMATICS samples. Park, Tae-Soon, Nonlinear free boundary University (2) Kent State problems arising from melting processes. Ohio University (2) MATHEMATICAL SCIENCES STATISTICS Lennard, Christopher J ., Operators and MATHEMATICS geometry of Banach spaces. Huang, Yong Kang, Functional differen Abdelhafez, Mohamed, Bootstrap pre Selvaraj, Suguna, Matrix summability of tial equations with piecewise constant diction and tolerance intervals for the classes of geometric sequences. argument. Weibull regression model with censored data. Ohio State University ( 16) Wang, You-Qiang, The P-parts of Brauer character degrees in ?-solvable groups. Halawa, Adel, Testing for location after MATHEMATICS transformation to normality. Anghel, Nicolae, L 2-index theorems for University of Cincinnati (6) Hussien, Osama, Robust estimation for perturbed Dirac operators. EPIDEMIOLOGY AND BIOSTATISTICS the mean of skewed distributions. Fiedler, Joseph Robert, On cubic graphs Bregman, Dennis J., The normal epi- University of Oregon (6) that are edge-critical for the torus. demic curve. Jha, Shingwhu, Asymptotics for the solu Chen, Rongdean, Estimation ofscreening MATHEMATICS tions of systems of smooth recurrence biases and survival benefits of x-ray Beale, Stephen Alan, Rudiments of an equations and their applications to the screened population in the early lung arithmetic for profinite groups. orthogonal polynomials. cancer (ELC) study. Hendrick, Daniel Allen, Common recur Moussong, Gabor, Hyperbolic coxeter MATHEMATICAL SCIENCES rent points for noncommuting transfor groups. mation. Alfaro, Ricardo, State spaces and skew Munemasa, Akihiro, Nonsymmetric P of group rings. Legorreta, Leonardo, Diagonalization and Q-polynomial association schemes quadratic forms. Nassar, Manal, Characterization of mix and associated orthogonal polynomials. Meyer, Michael Josef, Submultiplicative Ramasinghege, Wimelaratna, Multi tures ofexponential and geometric prob ability distributions. norms on Banach algebras. dimensional geometric moduli and ex Saxe, Karen, Fredholm theory with appli terior algebra of a Banach space. Yang, Ting, On the parametric estima- tions with local bandwidth selections. cations to regular operators. Rzedowski-Calderon, Martha, Galois mod Simmons, Richard Duane, Order of uni ule structure of rings of integers and QUANTITATIVE ANALYSIS form approximation to analytic func automorphism groups ofcongruent func AND INFORMATION SYSTEMS tions by rational trigonometric and tion fields. Lee, Wonboo, Consideration of a query weighted rational functions. Villa-Salvador, Gabriel, Zp-extensions of methodology to identify natural lan global fields and semisimple differen guage texts that correspond to specified tials. topics. 1182 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Annual AMS-MAA Survey PENNSYLVANIA Pennsylvania State University (I O) STATISTICS Dating, Corazon, Missing data in AR Carnegie-Mellon University ( 13) MATHEMATICS processes: Fisher's information in an Coleman, Matthew, Approximating the MATHEMATICS order determination criterion. vibration frequencies of a homogeneous, Carducci, Olivia Marie, On balanced and isotroric retragular thin plate, using a University of Pittsburgh (7) perfect matrices. Legendre spectral method. BIOSTATISTICS Du, Qiang, Analysis of a model of Feng, Qi, A hierarchy of Ramsey cardi incompressible viscous flow and its finite nals. Patwardhan, Rita Nalavade, Inferential procedures for multistage models for element approximation. Ferreira, Fernando, Polynomial time carcinogenic risk assessment with appli Meade, Douglas Bradley, Interface computable arithmetic and conservative cations. problems in elastodynamics. extensions. Milic, Natasa, On non-equilibrium Hatzikiriakou, Kostas, Commutative al MATHEMATICS AND STATISTICS phase transitions in mixtures with inter gebra in subsytems of second order Chen, Yong Zhuo, Functions of bounded facial structure. arithmetic. upper means and some new classes of Ritchey, Nathan Paul, Semi-linear pro Hirst, Holly, N-step quadratic convergence Hardy spaces. gramming and the unidimensional sim in the conjugate gradiant method. Costigan, Timothy, Product-type proba iliarities problem. Rupert, Carl, Certain rational sets infor bility bounds. Tarabek, Michael Anthony, On one mal language theory. Dai, Ruixiu, Characterization and com dimensional nonlinear thermoelasticity Saito, Mutsumi, A localization theorem putation of foldsets for parameter with second sound: existence of globally for D-modules. dependent equations. smooth solutions. Stefansson, Gunnar, Pettis integrability Metry, Magdy, Positive dependence con Ziemer, William Karl, An eigenvalue of vector valued functions. cepts for empirical rank distributions. problem for the mean curvature operator Suchower, Stephan, Subfield permutation Sambamoorthi, Nethrasigamani, Infor in non-radial domains. polynomials in finite fields and combi mation theoretic criterion approach to STATISTICS natorial applications. dimensionality reduction in multinomial Crawford, Sybil Louise, An approximate Zhang, Shangyou, Multi-level iterative logistic regression models. Bayesian analysis of finite mixture dis techniques. Zeng, Wei-bin, On a convolution equa tion and characterization of probability tributions. Temple University (6) Goodman, Jay Howard, Existence of distributions. compromises in simple group decisions. MATHEMATICS RHODE ISLAND Lam, Ching Yee Teresa, Stochastic mod Xu, Yuan, Weighted mean convergence eling and analysis of loosely coupled of some interpolating processes. Brown University (I 5) parallel systems. Zhang, He, Solving linear systems using Santi, Mary, A generalization ofthe Rasch parallel and distributing computing. APPLIED MATHEMATICS Pereira De, Statistical model for items with a cross-classified STATISTICS Almeida, Murilo structure. inference for MRF with unbounded Gillespie, Brenda W., Topics in Kaplan Steffey, Duane Leon, Hierarchical mod continuous spins and applications to Meier estimation. eling of binomial data. texture representation. Ratnasabapathi, Doraisamy, Polynomial Wilkinson, Robert George, Bayesian Barat, Christopher Eugene, A quasi hazard models in survival analysis. analysis using autoregressive models. Gaussian model for real textures. Rom, Dror, Further contributions to the Cao, Yulin, Small solutions and slowly Lehigh University (5) theory of association models in the oscillating periodic solutions for scalar contingency tables. MATHEMATICS analysis of differential delay equations. Shahmaei, Ardeshir, Stock price behavior Gauss-Jacobi quadrature Don, Wai Sun, Theory and application Badr, Abdullah, and the arc-sine law. with approximate nodes of unrestricted of spectral methods for the unsteady multiplicity. University of Pennsylvania ( 4) compressible wake flow past a two dimensional circular cylinder. Lienhard, Clarence W., Randomly MATHEMATICS stopped binomial tests. Kirby, Michael Joseph, Application of Chang, Pei-Kun, Estimates on harmonic the Karhunen-Loeve expansion to the Monks, Kenneth G., Nilpotence and tor maps. structures. sion in the Steenrod algebra and its analysis of coherent of cohomology. Costa, Antone Robert, The modularity Lyberopoulos, Athanasios N., Asymptotic certain class number congruences. oscillations of solutions of scalar conser Xiong, Zhongcheng Bonnie, A new class A., Quaternion L-value laws with or without convexity of almost complex structures. Schmidt, Thomas vation congruences. under the action of a linear excitation. Yousef, Hassan, The spherical spectrum Parameter estima of a graded ring. Rebnord, David Allan, tion for two-dimensional grid structures. NOVEMBER 1989, VOLUME 36, NUMBER 9 1183 Annual AMS-MAA Survey Regala, Benjamin, Periodic solutions and Craig, Jean Buckner, Sample size de Percell, Cheryl Bosman, The effect of stable manifolds of generic delay differ termination in clinical trials consid caustics in acoustic inverse scattering ential equations. ering non-uniform patient entry, loss experiments. Tarman, Isik Hakan, An analysis of to follow-up, non-compliance and cost Torczon, Virginia Joanne, Multi-direc turbulent thermal convection. optimization. tional search: A direct search algorithm Vazquez-Abad, Felisa Josefina, Stochastic University of South Carolina (3) for parallel machines. recursive algorithms for optimal routing MATHEMATICS in queueing networks. MATHEMATICS Mealy, Jack G., Calibrations on semi- Erdelyi, Tamas, Inequalities for general MATHEMATICS Riemannian manifolds. ized polynomials and their applications. Friesen, Christian, Continued fractions Reese, Margaret Linley, An example Southern Methodist University (6) and real quadratic function fields. problem. related to the atomic space MATHEMATICS Kuwata, Masato, Mordell- Wei! groups Shim, Yong-Sun, Maximal function tech and elliptic K3 surfaces. niques in elliptic linear POE. Bourland, Freddie Jerald, II, Modulations Loe, Brian J., Scattering by potentials of ofthe phase shift for nonlinear oscillators unbounded support. TENNESSEE and dispersive waves and connections McLaughlin, Dennis, Sring structures on across a separatrix. loop space. Memphis State University (I) Li, Yong, The rate of convergence of the J(q, I) Block-Jacobi method. Zamboni, Luca, A Chern character in MATHEMATICAL SCIENCES cyclic homology. Roller, Towanna A., Recursive processes Hornor, William Edward, Limiting equa in linear and nonlinear compartmental University of Rhode Island (2) tions and invariance principles for analysis. nonautonomous functional differential MATHEMATICS Sheng, Liahua, Numerical solution of equations. Farrell, Kevin John, Neutral delay dif nonlinear least squares problems by a ferential equations with positive and University of Tennessee (3) class of Broyden-like methods. negative coefficients. MATHEMATICS OPERATIONS RESEARCH AND ENGINEERING MANAGEMENT Mayfield, Marie Elizabeth, Non-reflec Cohen, Elizabeth Bruce, Analysis of a tive boundary conditions for Schroe class of two step implicit Runge-Kutta Amini, Mohammad Mehdi, Network re- dinger's equation. schemes for second order systems for optimization: A computational compar ordinary differential equations. ison of algorithmic alternatives. SOUTH CAROLINA Guilbault, Craig R., Some results in the STATISTICAL SCIENCE study of non compact 4-manifolds. Clemson University (6) Li, Huaixiang, On the UMVU estimators Retnam, P. Xavier Raja, On a multiple MATHEMATICAL SCIENCES after using a normalizing transforma stochastic integral with respect to a tion. Domke, Gayla Sue, Variations of color strictly semi stable random measure. ing, coverings, and packings of graphs. Texas A & M University (8) Vanderbilt University (2) Fields, Mary A., Analysis of a model of MATHEMATICS oxygen storage. MATHEMATICS Diener, Dwight Allen, On the stability Nylen, Peter MacDougall, Submultiplica Rayburn, Paula Nell Kimmins, Local of the dimension of spaces of bivariate tivity and matrix product. refinements of connectivity. splines. Rice, Virginia A., Cohesion properties Snodgrass, James Tutt, III, Completely and graphs. norma/lattices. STATISTICS Schwartz, Kenneth Eugene, Group testing Al-Khalidi, Hussein Rashid, Aspects of with dependence among items. TEXAS quantitative cancer dose-response mod Thornton, John Richard, Two problems eling and the role of the lognormal Rice University (6) concerning robot arms: Product au distribution. tomaton based control and recursive MATHEMATICAL SCIENCES Alexander, William Pyle, Boundary ker optimization on a hypercube computer. Chiang, Jershan, Convergence rates for nel estimation of the two sample com parison density function. Medical University of South Carolina the variable, the multiplier, and the pair (2) in SQP methods. Ebaseh-Onofa, Benjamin Ovesuo, Mix Lewis, Robert Michael, Source-velocity ture models ofstochastic compartmental BIOMETRY identification for a layered model of systems. Berrier, Deborah Lane, A simulation reflection seismology. Grimshaw, Scott D., A unified approach study of variable selecting techniques in Li, Shou Bai, Global convergence of to estimating tail behavior. linear regression for predictors. trust region methods for minimizing a King, Dennis Wayne, Nonparametric pro nondifferentiable function. cess control procedures. 1184 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Annual AMS-MAA Survey King, Eileen Catherine, A test for the Blanchet, Altha Elizabeth, Function fields VIRGINIA equality of two regression curves based of generalized Brauer-Severi varieties. on kernel smoothers. Chun, Jang-Ho, Isomorphic ore exten University of Virginia (7) Onate, Julia Mercedes, Distribution of sions of automorphism type. APPLIED MATHEMATICS com residence times of some stochastic Finley, Davis Wallace, A new proof that Vaughan, Courtenay Thomas, The partmental models. 1-VLC implies tameness. SSOR preconditioned conjugate gradient Texas Tech University (2) Knaust, Helmut, On uniform structures method on parallel computers. in infinite dimensional Banach spaces. MATHEMATICS MATHEMATICS Parker, Mary Ruth, Multiparameter es Balakumar, Sivanandan, Detection and timation in normal distributions: The Cheng, Raymond, Strong mixing in sta estimation of a changepoint using non slightly unequal variance case. tionary fields. parametric procedures. Pearson, John Michael, Sobolev inequali D'Amour, Alain, Jordan triple systems of Koti, Kallappa M., Optimum stratified ties for ultraspherical polynomials. Hermitian type. sampling using prior information. Wang, Suojin, Saddlepoint approxima Dritschel, Michael Anthony, Extension theorems for operators on Krein spaces. University of Houston ( 4) tions in statistics, including resampling. Xu, Xiangsheng, The continuous de Johnston, William Wilbur, Spectral the MATHEMATICS pendence of solutions to the Cauchy ory for perturbed Toeplitz operators. Krupa, Martin, Bifurcations of critical problem ftA(u) + B(u) 3 f on A and Munoz-Maya, lsmael, Asymptotic expan group orbits. B and applications to partial differential sion of certain Markov process expecta Nicolas-Carrizosa, Alfredo, Numerical equations. tions for large time. aspects of some time dependent par Peterson, Chariyapoan, The completion University of Texas, Dallas (3) tial differential equation problems. of small categories. Waggoner, Sheila, Global existence for MATHEMATICAL SCIENCES Virginia Polytechnic Institute solutions of semilinear and quasilinear Brock, Kerry Gail, Topics on invertibility and State University ( 13) parabolic systems of partial differential of linear operators. INDUSTRIAL ENGINEERING AND equations. Approxima Goldthwait, Richard G., Jr., OPERATIONS RESEARCH Waller, William Alfred, Jr., Average dis tion of nonlinear control systems by pure tance in graph with prescribed order and feedback systems. Magalhaes, Marcos, Queues with a Markov renewal service process. independence number. Wilson, Edward P., Some lifting of Patuwo, Butje Eddy, The effect of the University of Texas, Arlington (8) Cauchy-Riemann geometry to Minkow ski space. dependency in the Markov renewal ar MATHEMATICS rival process on the various performance Alidaee, Bahram, Solution concepts in UTAH measures ofan exponential server queue. cooperative game theory. Ulular, Osman, A primal-dual conju Fritsche, Yaowaluk, A protocol analysis University of Utah ( 6) gate subgradient algorithm for large ofa frame-based mathematical problem MATHEMATICS scalejspecially structured linear pro solving. gramming problems. Austin, David Michael, S0(3)-instantons Wortman, Martin A., Vacation queues Golec, Janusz, Approximation ofsolutions on L(p,g) x R of stochastic differential equations. with Markov schedules. Bozicevic, Mladen, A geometric construc Ha, Sung Nam, Experimental numerical tion of resolutions offundamental series MATHEMATICS of natural studies on a supercomputer representations. Clemence, Dominic, Half-bound states of in an enclosure with localized convection Nordhaus, Thomas Herbert, Echo-cycles a one-dimensional Dirac system: Their heating. in coupled Fitzhugh-Nagumo equations. effect on the Titchmarsh-Weyl M(J..) Liu, Xinzhi, Stability analysis of nonlin Phelps, Frederick Martin IV, The sub function and the scattering matrix. ear systems in terms of two measures. stitutional genetic load and the neutral Fassari, Silvestro, Spectral properties of Moadab, Mohammad, Discrete dynami theory of milecular evolution. relativistic and non-relativistic Kronig cal systems and applications. Stromberg, Marc R., Solution of shock Penney Hamiltonians with a localized Pirapakaran, Ratmam, Some problems in problems by methods using Sine func impurity. impulsive differential equations. tions. Miller, Robert Edwin, Approximation of Prueitt, Paul Stephen, Some techniques Zabcic, Miljenko, Geometry of discrete the LQR control problem for systems in mathematical modeling of complex series. governed by partial functional differen biological systems exhibiting learning. tial equations. Utah State University ( 1) University of Texas, Austin (9) Stoytchev, Orlin, A study of super-KMS MATHEMATICS functionals. MATHEMATICS Scully, Daniel Joseph, Maximal rank-one Babich, Amy Juliet, Vorticist denizens of spaces of matrices over chain semirings. R 3 are tame. NOVEMBER 1989, VOLUME 36, NUMBER 9 1185 Annual AMS-MAA Survey STATISTICS WISCONSIN Leu, Ching Ho, Discriminant and cat Chengalur-Smith, Indushobha N., Vari egorical data analysis and variance Marquette University ( 1) able sampling in multiparameter She estimation in complex sample surveys. whart charts. MATHEMATICS, STATISTICS Lin, Kon-Jin Dennis, Small response Hockman, Kimberly Kearns, A graphi AND COMPUTER SCIENCE surface designs. cal comparison of designs for response Huang, Xun-Cheng, A mathematical Lu, Jye-Chyi, Bivariate Weibull models optimization based on slope estimation. analysis of population models. and inferences based on life test of system and components. Kim, Sang-Ik, Contributions to experi University of Wisconsin, mental design for quality control. Taam, Winson, A semi-parametric ap Madison (23) Koons, Bruce Karl, Parameter estimation proach to spatially correlated data. for rounded time series data. MATHEMATICS Wong, Wing-Keung, New time series Vining, Gordon Geoffrey, A graphical Bak, Jong-Guk, Restrictions of Fourier applications in business and finance. approach for evaluating the potential transforms to flat curves and surfaces. University of Wisconsin, impact of bias due to model misspecifi Chisholm, John A., Effective model theory Milwaukee (2) cation in response surface designs. vs. recursive model theory. MATHEMATICAL SCIENCES Choe, Boo Rim, Composition with bound WASHINGTON ed holomorphic functions on the ball. Kreczner, Robert J., Generalized cardinal series. University of Washington ( 13) Cho, Han Hyuk, Semigroups on Boolean matrices. Yang, Shaochen, Quasi-injective hulls of delta-modules and their semicritical so BIOSTATISTICS Fisch, Robert Dave, One-dimensional de series. Anderson, Garnet LaRae, Mismodelling cyclic cellular automata. covariates in Cox regression. Goggin, Eimear Mary, Weak convergence WYOMING Churchill, Gary, Stochastic models for of conditional probabilities. DNA sequence data. Goldsmith, Judith Anne, Polynomial iso University of Wyoming (6) Emerson, Scott, Parameter estimation morphisms and near-testable sets. MATHEMATICS following group sequential hypothesis Hansen, Scott Walter, Frequency-pro Koebbe, Joseph Vincent, II, Numerical testing. portional damping models for the Euler schemes for the immiscible displacement Zhao, Lue Ping, Multivariate analysis of Bernoulli beam. equations using a general polynomial binary data. Jafari, Farhad, Composition operators in framework for the saturation equation MATHEMATICS polydiscs. and mixed finite element methods for Jeske, Clement Thomas, Groups with Do, Chi Ngoc, Second-order nonsmooth the pressure/velocity. character degrees dividing P 2. analysis and sensitivity in optimization Smylie, Donald Lowell, A near optimal problems involving convex functionals. McMichael, John David, A covering order approximation to a class of two lemma for surfaces of infinite type. Jenne, Ralph William, A construction of sided non-linear degenerate parabolic conformally invariant differential opera Newcomb, Richard T., II, Existence and partial differential equations. correspondence of value functions and tors. STATISTICS viscosity solutions of Hamilton-Jacobi Kwon, Youngmee, The submartingale equations. Fox, David, Calibration models: Theory problem for Brownian motion in a cone and applications. with nonconstant oblique reflection. Silva, Elves Alves de Barros e, Criti Mortazaviizadi, Mira, Stochastic goal Pang, Myung-Yull, The structure of Leg cal point theorems and applications to differential equations. programming. endre foliations. Tang, Dalin, Peristaltic transport of a Muttlak, Hassen, Some aspects of STATISTICS heat-conducting fluid, existence, unique ranked set sampling with size biased Andersen, Lars Smedegaard, Classical ness, stability, asymptotic expansion and probability of selection. inference in spatial statistics. numerical results. Ziemer, Terry L., Construction and test Bruce, Andrew Gardiner, Diagnostics for Theron, D. Peter, An extension of the ing of an expert system for implementa time series analysis. concept of graphically regular represen tion of exponential smoothing forecast ing models. Burns, Patrick Joseph, Aspects of robust tations. Yoo, Yoon Jae, On singular area integrals. analysis in designed experiments. CANADA Gentleman, Robert Clifford, Exploratory STATISTICS methods for censored data. Dalhousie University ( 1) Chi, Eric Mao-Sung, Analysis of longi Millar, Russell Brian, Estimation of mix tudinal date with random effects and MATHEMATICS, STATISTICS ing and mixed distribution. autocorrelated errors. AND CoMPUTING SciENCE Kang, Gunseog, Topics in multiresponse Zhuang, Deming, Regularity and mini regression analysis. mality properties of set-valued structures in optimization. 1186 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Annual AMS-MAA Survey McGill University (2) Baribeau, Line, Quelques problemes sur MacDonald, Gordon Wilson, Invariant subspaces for weighted translation oper MATHEMATICS AND STATISTICS les multifonctions analytiques. ators. Lamarche, Fran<;ois, Modelling polymor- Derhem, Alssa, Capitulation dans les phism with categories. extensions quadratiques non ramifiees University of Waterloo ( 15) de corps de nombres cubiques cycliques. Morin-Wahaab, Danielle, On some func APPLIED MATHEMATICS tions of quadratic forms and related Fortier, Claude, Criteres de persistance topics. des diagrammes de bifurcation en Carillo, Sandra, Invariance properties and presence de symetrie. symmetry structure of integrable sys Queen's University ( 1) Roy, Damien, Sous-groupes minimaux et tems. MATHEMATICS AND STATISTICS questions arithmetiques. Czapor, Stephen Richard, Grabner basis methods for solving algebraic equations. Moisiadis, Alexandros, K-saturated University of Alberta (2) graphs with minimum number Drennan, William Melville, Accurate cal of edges. MATHEMATICS culations of the Stokes water wave. Jiang, Hong, Numerical techniques for Ottawa-Carleton Institute (6) Hughes, William Patrick, Entropy and large scale computer simulations. inequalities. MATHEMATICS AND STATISTICS Kumar, Ravinder, Analysis of differential Parris, Ralph, Asymptotic methods in Bannani, Faiz, Bounds on classical Ram equation models of mutualism with a the numerical solution of stiff ordinary sey numbers. food chain. differential equations. Bickis, Mikelis Gun tars, On the computa University of Manitoba (3) tion of size and power for toxicological COM BIN A TORICS AND 0PTIMIZATION bioassays. STATISTICS Calkin, Neil James, Sum-free sets and Huse-Eastwood, Vera Regine, On some Awuku-Darkoh, Emmanuel, On the ad measure spaces. nonparametric methods for changepoint missibility of the MLE of a matrix of Goddyn, Luis Armando, Cycle covers of problems. Poisson means under a multiplicative graphs. Mampitiya, M.A. Upali, Spectral asymp model for complete and incomplete data Liu, Weiguo, Extended formulations and totics for left-definite vector Sturm problems. polyhedral projection. Liouville problems. Schwarz, Carl, Post-release stratification McCuaig, William Dodd, Edge reductions Srinivasan, Rengarajan, Topics in state and migration models in band-recovery in cyclicially k-connected cubic bars. independent queues and queueing net and capture-recapture model. McGuinness, Sean, Random walks on works. Spiring, Frederick A., Statistical process graphs and digraphs. Wong, Kieh Yun, The minimal number control methodologies for quality im of generators of a group. provement. PURE MATHEMATICS Willard, Ross David, Varieties having Simon Fraser University (2) University of New Brunswick ( 1) Boo- MATHEMATICS AND STATISTICS MATHEMATICS AND STATISTICS lean factor congruences. Biech, Ted, On exact Shearing solutions Armenakis, Antonis, Structural approach STATISTICS AND ACTUARIAL SCIENCE of the nonstatic spherically symmetric to slippage problems. Einstein field equations. Chamberlin, Stephen Raymond, Logical University of Regina (2) Samaratunga, R. T., A study of sub foundation and application of inferential spaces of bounded sequences, sequential MATHEMATICS AND STATISTICS estimation. Dean, Charmaine B., Mixed Poisson completeness and methods of almost Li, Zhi-Feng, Contributions to the limit models and regression methods for count convergence. theory of extreme order statistics. data. Universite de Sherbrooke (2) Xing, Anqing, Mathematical program- Mantel, Harold John, Conditional infer ming and optimal control theory. MATHEMATICS/INFORMATION ence in a stratified model with nuisance Lessard, Francois, Une methode generate University of Saskatchewan ( 1) parameters. de compactification d'un ensemble et ap MATHEMATICS Munholland, Patricia Lynn, Statistical plications aux operateurs induits par des aspects offield studies on insect popula Altas, Irfan, Adaptive mesh generation. transformations ponctuelles continues. tions. University of Toronto (4) University of Western Ontario (5) M'Khalfi, Abdessalam, Autres approches MATHEMATICS de !'integrate generalisee de Riemann. APPLIED MATHEMATICS Bradley, Robert Emmett, Induced opera Universite Laval (5) tors and alternating sequences. Culumovic, Louis B., Operator regular ization and renormalization theory. MATHEMA TIQUES, STA TISTIQUES ET Goyo, John Octavius, The Sullivan model ACTUARIAT of the homotopy-fixed-point set. Kember, Guy C., Transient heat conduc Abdous, Belkacem, Etude d'une classe Kalajdzievski, Saso, Centralizers offinite tion: Circular pipe in a half-space. d'estimateurs a noyau de Ia densite subgroups of the automorphism groups Steele, Thomas G., QCD condensates, d'une loi de probabilite. of a free group. the OPE and the dynamical quark mass. NOVEMBER 1989, VOLUME 36, NUMBER 9 1187 Annual AMS-MAA Survey Yip, Handson, Predicting concentration FLORIDA MISSOURI values in environmental flows. Young, Peter Joseph, Steady asymmetric University of South Florida ( 1) St. Louis University ( 1) flow of a viscous fluid past a cylinder. MATHEMATICS MATHEMATICS AND COMPUTER SCIENCE University of Windsor ( 1) Levinson, Deborah Penick, Minimizing Hasting, Martha Emilie, Foliations with noise in trimmed resistors. Morse singularities and the theory of AND STATISTICS MATHEMATICS levels. Naeem, Rana Khalid, Computation of MASSACHUSETTS transonic flows using a streamfunction NEBRASKA coordinate system. Tufts University ( 1) University of Nebraska (2) MATHEMATICS Doctoral Degrees Conferred Couch, Alva Lind, Graphical represen MATHEMATICS AND STATISTICS 1987-1988 tations of program performance on Saleh, Os, A characterization of proper Supplementary List message-passing multiprocessors. minimal points as solutions of sub linear optimization problems. Stephen, Joseph B., Applications of The following list supplements the list of the automata theory to presentations of published in the November 1988 sis titles monoids and inverse monoids. Notices, pages 1314-1331, and the April1989 Notices, pages 383-384. UNIMODAL LOG-CONCAVE AND ; POLYA FREQUENCY SEQUENCES IN COMBINATORICS Francesco Brenti (Memoirs of the AMS, Number 413) In recent years, considerable research has focused on applied to any situation in which log-concavity and unimodality unimodal or log-concave sequences that are of combinatorial questions arise. The second part of the book is devoted to interest. Although these two properties have simple definitions, applications to several combinatorial situations, yielding many proving that a sequence is unimodal or log-concave is often a new results and solutions to some problems that had resisted difficult task requiring refined and sophisticated mathematical attack with other techniques. Both parts of the book point to tools from such areas as representation theory, algebraic many conjectures, open problems, and directions for further geometry, or classical analysis. study. The main purpose of this book is to show the theory of total 1980 Mathematics Subject Classifications: 05A20; 05A15, 05A10, positivity can be very useful in studying this area. In the 05C20, 06A10, 11873, 15A04, 26C10, 30C15 ~EM first part of the book, after discussing some combinatorial ISBN 0-8218-2476-7, LC 89-15137 ~~:'> -~l'tc-t motivations, the author studies some of the fundamental ISSN 0065-9266 ~~OI -~ September 1989 that preserve the log-concavity or P61ya 106 pages (softcover), .Q"('~~~\~ linear transformations Individual member $10, List price $17, ffi: (~ ~ ! ~ frequency properties of a sequence. This part forms the Institutional member $14 -=i \. ~- /, ~ theoretical core of the work and may be read independently To order, please specify MEM0/413NA ·~· from the rest. In fact, this rich and powerful theory can be 0 UNoED \'0 All prices subject to change. Shipment will be made by surface. For air delivery add, 1st book $5, each additional book $3, maximum $100. Prepayment required. Order from American Mathematical Society, P.O. Box 1571, Annex Station, Providence, RI 02901-1571, or call toll free 800-321-4AMS to charge with VISA or MasterCard. 1188 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY A Differing View on Mathematics Education Reform Here We Go Again ... Are We Directing Our Efforts and Money at the Correct Problems? Eleanor G. Palais well-intentioned, but they finally admitted that the New Eleanor G. Palais has a bachelor's degree in physics from Rad Math had to be modified so our young people could cliffe College, a master's degree in mathematics from Harvard learn and understand. Many years and many dollars were University, and a master's degree in public administration from again spent revising texts and curricula. the Kennedy School of Government at Harvard. She presently And so a whole new set of materials was prepared teaches mathematics at Belmont High School in Belmont, Mas for our schools. The texts were simple, colorful, and sachusetts, and at the Radcliffe Seminars Business Manage clearly directed at the various ability levels-usually ment Program. four or so ability tracks. Special care was taken to remove stereotypes in texts and to represent minorities in everyday as well as in unusual professional roles. I have an uneasy feeling of deja vu as once again there The books for the most part became more readable is talk of what's wrong with our math curriculum and for student and teacher alike. Theory was clear and why aren't our students doing better in their scores and not cumbersome. Teachers' department meetings and in their general math achievement and understanding. professional days were spent writing a new curriculum I was in the middle of this controversy in the sixties and, happily for me, one could divide again as I had when my adolescent children proudly came home from been taught! As technology advanced, the computer's role middle school (then junior high school) and announced in educating our students was acknowledged. We taught that I didn't know how to do long division any more. estimation; the use of calculators in some classes was They pulled out their workbooks and did what looked common (though many of us as teachers were concerned totally different from what years earlier I had learned. that our students might forget how to multiply or divide We both agreed on the final outcome, but their way without one!). Pascal and Basic programming courses seemed strange and awkward to me. Thank heavens we were developed ... and we felt that all was well in our now divide in the "old" way ... or is it the "new" way mathematics world. again? But during the past few years, and especially during Textbooks in the late sixties and seventies were overly this last year, we again are being deluged with statistics precise with set notation and theory and symbols. This showing poor performance by our students in mathemat had been ordained by groups of academic educators ics. Committees have met, new Standards and Guidelines mostly funded by government grants. Their mission was have been established and we are told that we should to make our young students more proficient and more stop doing "this" and do more of "that." Software and competent to lead the world in math and science. Text more audio-visual aids should be used routinely in the book companies and publishers of education journals classroom. Calculus in high school should be replaced, or buzzed with the excitement of the "New Math." Eco at least we should have a parallel track that emphasizes nomically, it was a boon for them and for many others. discrete math. And anyway, the place for calculus, we Teachers were advised by their school administrators are told, is really in college. We also must rethink the that the old curricula were obsolete. There were flurries calculus curriculum. Why teach students how to integrate of workshops, articles, and curriculum revisions. and differentiate when soon they can all buy calculators It's old news now that the New Math was far from that will do it for them? Why should pencils be used to totally successful. It had many strengths, but it went sketch curves? Many educators feel that students can do too far with formalization and rigor. New Math made much better with interactive learning using a computer. reading the text nearly impossible for many students and And so we are setting to work again. But this time the took the ease out of learning the subject matter and academic community has learned a lesson as planning obscured its beauty in the process. The experts had been groups are meeting, organized by colleges and universi- NOVEMBER 1989, VOLUME 36, NUMBER 9 1189 Mathematics Education Reform ties, to find out why math scores are so low. Millions of properly in the middle schools? It must be the fault of dollars of grant money is being made available to them the teacher down there. Why, our students in high school by the National Science Foundation with the following can't even add simple fractions!" Of course when we caveat: the school teachers must be included in this meet with our colleagues at the middle school we find phase of rewriting our math curriculum. Colleges have they have taught the subject each year. The question promised teacher training and professional developement must be rephrased as: "Why don't the students learn to help teachers learn the new skills they may need in what is being taught?" This same dialogue gets repeated the classroom. Ways are being devised to make math when college teachers ask why students still can not "do" more interesting, more exciting, and more meaningful, fractions after six years of high school. The implication such as teaching about the new chaos theory, so stu is always there: What is wrong with the high school dents can learn about subjects on the "cutting edge" of teachers? It's no surprise then to us that we also are mathematical research. The educators, publishers, soft gently (sometimes not so gently) advised not to teach ware companies, computer corporations and curriculum calculus to our brighter students. High school is not the developers are all abuzz once again. This time they will place for calculus we are told. For if students "taste" and teach our schools how to do it right! This time for sure "learn" calculus once, they will think they know it all they know what's wrong with our schools. Now they and will not learn and be excited when they do it again know why "Janie can't add, or do fractions, or percents, in college. Once again we get blamed for the fact that or by gosh, just learn math!" in college, the students are not doing well in calculus Well, here's one experienced teacher who's very un courses (perhaps this is the start of an "upward blame" easy about what's going on. For one thing, I worry effect!). about-that's right-throwing the baby out with the I firmly believe that calculus, if it is well taught to an bathwater. Why must we always start over with a totally appropriately selected group of students, is one subject new approach? Why don't educators look at what's good that has its proper place in high school. The subject about how we are teaching and make changes thought is certainly broad and deep enough to be seen more fully and cautiously, rather than with full-blown hysteria than once, and it finally gives students a most beautiful about teaching and curricula being completely wrong? application of some of the more complicated algebra, Another concern is that the professors who are in curve sketching, and function theory they have worked volved in the grant writing and the proposals are often, with for many years. I personally resent the idea that as they were before, unfamiliar with the "playing field." this subject, which flows so naturally from much of the Over ten years ago I attended a National Science Board math my students have learned, should somehow be kept meeting in Washington, representing the Association for sacred and secret until college. Women in Mathematics. About forty of us were there to Once again the question surfaces as to why students discuss the "Mathematics Curriculum for the Eighties." are not doing well. Don't get me wrong. I agree that Most of the distinguished members there were excellent the learning ability of our student body is often quite mathematicians from top universities and colleges. Only dismal. Students are not motivated and want only easy a very few of this powerful planning group who were to ways to get good grades without lifting a pencil. One compile this impressive report were high school teachers, has simply to walk into a public school math class and and most of the academics had never been in a public observe students with bored looks, slouched in chairs school classroom except as students. with arms folded. Often homework has not been done And so it is with today's academic planners. Many and the class must be invited to take notes, or even to have never observed public school classes, or when they open their books or to get a pencil. Why hasn't the focus have they neglect to account for the effect of their one of "Why are the students' scores so poor?" been more on time presence. The only high school graduates they do the students themselves, rather than on the schools, the see later are the top students they meet in their own teachers, and the curriculum? I believe our young people colleges. There is little conception of the actual spread of today are doing poorly in their school work because abilities of the elementary and secondary school students they have been brought up as passive listeners in a TV (in our school we have four algebra tracks, for example). generation. When I am teaching, my students are often Perhaps college and university faculty should actually glassy-eyed and watching what is happening as if I were teach in our classrooms, or at least do some prolonged a TV performer. The students do not receive what is being observation, before they advise and before they spend said! I even write boldly on the board: millions of tax dollars to find out what's wrong and how to change it. IMathematics is not a spectator sport! I Professors who teach our graduates must be aware that there is always a "downward blame" effect. High to try to get an active response. Students must be taught school teachers may ask: "Why don't fractions get taught about active listening and know how to distinguish it 1190 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Mathematics Education Reform from passive listening. This is where our major efforts A high tech direction for our schools means an must be placed if we are really going to improve our ever-increasing cost commitment, keeping machines and students' ability to learn. This is where our creative software current and in good repair. My reasonably education efforts and monies should go. We in science affluent school in suburban Boston has just this year and education are faced with a new experience. For the been able to afford its second Macintosh for the whole first time in history, we are teaching a generation of department to share. The first machine has already been students who for the most part have been brought up to dubbed by many as too slow because it has no hard disk. tune out whatever noise is going on around them-even Once the computer companies have this captive market if it's teaching. Have you ever seen a student who must they will be developing "new and better" machines and be surrounded by noise so he or she can tune out and software continuously. Is all of this technology in the concentrate? schools really necessary, or is it just a nice alternative For the first time, also, we have a generation in school to board teaching? Isn't it simply another tool in the who has not had to learn to survive. Many of our students teaching of mathematics? Granted, it's a new and exciting don't have the competitive worries people their age used tool, one with different strengths than chalk, pencil, and to have. They know they will be able to make it because board work. But shouldn't we proceed more cautiously they come from well-off families, while on the sadder before committing ourselves to sweeping and costly side, others feel that the world has become so upscale major changes? that they have little chance of making it no matter how I have an uneasy premonition as I look into the hard they work. In short, many feel that education is no future. After all the hard work, the curriculum writing, longer the guarantor of making it in the world. and the purchase of new equipment, will our students' Not only should we look to our students themselves achievement really improve? Are we looking at the right as a possible source of their low achievement, but also, in targets now for our changes? Will educators in the making broad, sweeping revisions of styles and methods twenty-first century again want a revision in the way we of teaching math, we should be more cautious with teach our students? The new math of the new century, our directions. For example, I enthusiastically endorse will that be the phrase? Will we then throw out all our the computer and software in the classroom as useful artificial learning aids, and remove all the machines? tools. But although there is greater interaction with the Perhaps then we will give students a sharpened pencil, computer than with a TV, I feel we are encouraging a notebook, and a printed set of words to learn from and the passive act of watching a screen. Once again, this is to understand. Hands-on knowledge will be the hallmark learning "TV style." Please, educators, keep the pencil, of this new math. Let them do it themselves with only the paper, and the mind still active. Mathematics is their expert teacher there to guide, influence, and excite learned by doing, not by watching! them. Turn off their TVs. Teach them to listen and to Technology in the classroom, a computer at every hear, to question and to probe. Let them know that an desk, or at least a computerized classroom, will also be answer is expected. This, I know, will be called the NEW a tremendous economic burden for the schools. Already Math, and we will be using a lot of the same methods schools are mourning tight budgets and the loss of we used before, when we divided like I still do. local aid. What should be the priority for our schools? There are a lot of caring, talented, enthusiastic, and Higher pay for teachers and scholarship incentives to knowledgeable teachers in the classroom. We are trained encourage talented young people to choose teaching as as teachers. We are not all stars but most of us teach well. a career must be a top economic priority in education. Now students must listen, they must listen to learn. Our We have an aging faculty in the schools, and unless country has shown its concern over our students' poor society dignifies our profession on a par with medicine achievement. It must now show it supports excellence and law we will very soon face a serious teacher shortage. in education by giving academic achievement the top Shouldn't teaching our youth be considered one of the priority in family life, and the education of our young most important professions, one into which we want to the top priority on local, state, and federal agendas. direct our best college graduates? NOVEMBER 1989, VOLUME 36, NUMBER 9 1191 ,----: I I ! ' I [] L______l' :____ j Computational Complexity Theory Juris Hartmanis, Editor L__ _j Computational complexity theory is the study of the quantitative laws that govern computing. During the last 25 years, this field has grown into a rich mathematical theory. Currently one of the most active research areas in com puter science, complexity theory is of considerable interest to mathematicians as well, since some of the key open problems in this field raise basic questions about the nature of mathematics. Many experts in complexity theory believe that, in coming decades, the strongest influence on the development of mathe matics will come from the extended use of computing and from concepts and problems arising in computer science. This volume contains the proceedings of the AMS Short Course on Computa tional Complexity Theory, held at the Joint Mathematics Meetings in Atlanta in January 1988. The purpose of the Short Course was to provide an overview of complexity theory and to describe some of the current developments in the field. The papers presented here represent contributions by some of the top experts in this burgeoning area of research. Contents: Juris Hartmanis, Overview of computational complexity theory Stephen R. Mahaney, The isomorphism conjecture and sparse sets Ronald V. Book, Restricted relativizations of complexity classes Neil Immerman, Descriptive and computational complexity Alan L. Selman, Complexity issues in cryptography Shafi Goldwasser, Interactive proof systems 1980 Mathematics Subject Classifications: 68,94 ISBN 0-8218-0131-7, LC 89-6857, ISSN 0160-7634, 140 pages, June 1989 Hardcover: List $33, Inst mem $26, Indiv mem $20 Softcover: List $28, Inst mem $22, Indiv mem $17 To order, please specify PSAPM/38NA (hardcover) PSAPMS/38ENA(softcover) .------Standing orders are accepted for any book series published by the AMS. Contact Customer Services at 401-272-9500 or 800-321-4AMS in the continental U. S. for details. Prepayment Required. Order from American Mathematical Society, P. 0. Box 1571, Annex Station, Providence, Rl 02901-1571 or call800-321-4AMS to use VISA or Master Card. All prices subject to change. Shipment will be made by surface. For air delivery, add, 1st book $5, each additional $3, ~------______j Survey of American Research Journals In November of 1982 the Board of Trustees of the AMS do not provide absolute figures, but rather suggest a decided that a cost comparison study of mathematical systematic basis for comparison among journals. research journals would benefit the entire mathemati At least two samples were taken for each journal. In cal community, in particular department chairmen and the first sample ten pages were selected, spaced evenly librarians. A year later the Notices of the American Math throughout the journal; these pages were chosen so as ematical Society published its first survey of American to contain no figures, diagrams, or blocks of text set research journals. We have brought that information up at a type size nonstandard for that particular journal. to date in this third survey, expanded to include compar The lines of text and display per page were counted. A isons between subscription years 1984, 1986, and 1988. characters-per-line figure was determined by averaging A companion to this survey, a study by the European the character count for the first and last full lines of Mathematics Council of prices of European journals, is text on the first three pages of our sample. (Spaces in preparation. between words were counted as one character; spaces in Selection and classification of journals. As before, mathematical expressions were not counted.) Averages the list of journals surveyed consists of those published for the two figures were multiplied to obtain a figure for in the United States and reviewed in their entirety in the characters per page. Mathematical Reviews, with the exception of some of A second sample was then taken of another ten pages, the translation journals, which may have been reviewed spaced midway between the pages chosen for the first only in part or in the original. Journals are listed in sample. The cost calculation is based on the mean of three classes: primary typeset journals, primary journals these two samples. For several 1984 journals in which published from author-prepared copy, and translation the variation between the first and second samples was journals. Production costs vary considerably for these greater than 1 5percent, a third sample of twenty pages classes of journals, with the subscription prices varying was taken; for these journals, the results of the three accordingly. samples for that year are reported separately. When the Counting methods. First the number of pages pub third sample fell between the first two, the mean of the lished for each subscription year was determined, exclud first and second samples has been reported in the table. ing front and end matter. Extrapolation was required for Questionnaire information. A questionnaire was sent some of the translation journals, since their nominal to each publisher, asking for verification of our observed volumes were incomplete at the time of the sampling. page counts and subscription prices for each year, as well The next problem was to determine the amount of as our calculated lines per page and characters per line. In material on a page, a difficult task when dealing with addition, we solicited the following information: 1984, mathematics journals. For this reason, readers are en 1986, and 1988 circulation figures; the availability of back couraged to examine actual copies of these journals when volumes; the journal's policies regarding page charges, considering these figures. Variations in the amount of offprints, and discounts; and information about any displayed material, additional spacing around displays sources of support that the journal might have in addition and enunciations, and the typesetting specifications of to circulation revenues. Much of that information is the particular journal all affect the amount of material reported in the following sets of tables, in order that per page. Also, character counts in journals printed from readers might draw their own conclusions regarding the author-prepared copy vary considerably from article to effect of any of these factors on production costs or article. Therefore, readers should keep in mind that the subscription prices. Blanks in the tables indicate that methods given below for estimating characters per page questionnaires were not returned by the publishers. NOVEMBER 1989, VOLUME 36, NUMBER 9 1193 Journal Survey Primary Typeset Journals list Price $US Pages Cents/1 000 Char Journal Publisher 1984 1986 1988 1984 1986 1988 1984 1986 1988 Advances in Applied Mathematics Academic Press 78 92 105 504 502 500 7.1 7.8 9.4 Advances in Mathematics Academic Press 340 400 528 1279 1285 1605 11.3 14.1 14.9 American Journal of Mathematics Johns Hopkins University Press 95 122 136 1512 1506 1188 3.1 4.1 5.5 AMS Bulletin, New Series American Mathematical Society 50 148 161 783 589 829 2.1 8.9 6.4 Annals of Mathematics, Ser. 2 Princeton University Press 140 140 140 1223 1239 1301 4.4 4.5 4.2 Annals of Probability Institute of Math. Statistics 62 80 100 1227 1431 1859 2.1 2.2 2.3 Annals of Statistics Institute of Math. Statistics 66 85 96 1596 1641 1741 1.5 1.8 1.9 Applied Math. and Computation Elsevier 206 354 560 756 1138 1412 12.2 13.8 18.6 Applied Math. and Optimization Springer-Verlag 70 85 205* 558 276 549 5.6 8.7 12.0 Comms. in Pure and Applied Math. Wiley & Sons 144 176 256 848 1181 1088 7.4 5.6 10.4 Complex Variables: Theory & Applic. Gordon & Breach, Science Publ. 201 266 428 372 384 379 28.6 34.5 52.0 Computers and Math. wf Application Permagon Press 200 500 840 477 2528 2128 T 4.4 9.8 Duke Mathematical Journal Duke University Press 110 120 240 1020 1130 1616 4.4 4.5 6.0 Ergodic Theory and Dynamical Sys. Cambridge University Press 180 190 245 646 644 1059 8.9 9.5 7.7 Houston Journal of Mathematics University of Houston 70 70 85 599 599 600 5.0 4.7 5.7 Illinois Journal of Mathematics University of Illinois Press 50 50 70 702 695 715 3.1 3.1 4.5 Indiana University Math. Journal Indiana University 80 95 95 926 928 934 3.6 4.2 4.4 Information and Control Academic Press 300 340 384 919 1021 1146 13.0 13.2 13.8 Information Sciences Elsevier 222 255 322 756 906 1078 11.3 11.7 12.1 Journal of Algebra Academic Press 525 700 816 3401 3938 4203 6.2 7.3 8.2 Journal of Algorithms Academic Press 96 105 118 613 604 602 5.8 6.6 7.7 J. of American Statistical Assoc. American Statistical Assoc. 55 70 85 965 1141 1243 1.0 1.0 1.2 Journal of Approximation Theory Academic Press 258 300 380 1193 1179 1445 10.6 12.1 12.3 J. of Assoc. for Computing Mach. Assoc. for Computing Machinery 60 75 75 906 829 1000 2.0 2.5 2.2 J. of Combinatorial Theory, A Academic Press 174 258 303 754 966 965 9.7 11.2 12.8 J. of Combinatorial Theory, B Academic Press 174 204 240 612 758 757 11.9 11.5 12.4 J. of Computer and System Sciences Academic Press 208 246 288 913 910 910 7.5 8.4 10.3 J. of Differential Equations Academic Press 420 490 588 2197 2203 2404 9.0 9.8 10.6 J. of Differential Geometry Lehigh University 160 190 190 1105 764 1107 5.9 9.1 6.5 Journal of Functional Analysis Academic Press 410 485 630 2111 2102 2722 9.0 10.3 10.8 Journal of Graph Theory Wiley & Sons 88 108 125 532 557 595 6.4 7.2 8.5 Journal of Integral Equations Elsevier 148 ** ** 556 ** ** 12.9 ** ** Journal of Logic Programming Elsevier 85 95 115 356 360 344 7.4 8.2 10.1 J. of Math. Analysis and Applic. Academic Press 693 912 1064 4205 4797 4808 T 10.0 10.3 J. of Multivariate Analysis Academic Press 150 224 336 804 997 1419 9.2 9.9 10.4 Journal of Number Theory Academic Press 180 273 318 850 1130 1130 9.8 11.0 12.6 Journal of Symbolic Logic Assoc. for Symbolic Logic 65 85 105 1485 1145 1344 1.4 2.2 2.5 Journal of the AMS American Mathematical Society ** ** 100 ** ** 697 ** ** 5.4 libertas Mathematics Amer. Romanian Acad. of Arts, Sci. 40 40 45 196 200 190 9.5 9.4 10.5 linear Algebra and its Application Elsevier 480 792 1134 2343 3481 3662 10.9T 10.3 16.9 Linear and Multilinear Algebra Gordon & Breach, Science Publ. 252 302 540 345 405 303 35.1 36.4 71.9 Mathematics of Computation American Mathematical Society 100 164 181 1349 1674 1542 2.7 3.1 3.8 Math. of Operations Research lnst. of Management Sciences 44 50 60 634 729 724 2.3 2.2 2.1 Mathematical Systems Theory Springer-Verlag 94 108 109* 356 354 254 9.9T 8.5 14.4 Michigan Mathematical Journal University of Michigan 30 30 40 379 443 480 2.8 2.3 3.0 Notre Dame J. of Formal Logic University of Notre Dame 35 40 40 393 605 581 2.8 2.0 2.1 Pacific Journal of Mathematics Pacific Journal of Mathematics 132 190 190 2970 2475 1498 2.0 3.4 5.7 Proceedings of the ,A.MS American Mathematical Society 250 369 401 1934 2176 2426 4.4 5.6 5.3 Quarterly of Applied Mathematics Brown University 40 45 50 512 799 792 2.7 1.9 2.1 Rocky Mountain Journal of Math. Rocky Mt. Math. Consortium 95 115 145 995 857 864 3.6 5.2 8.9 SIAM J. on Algeb. & Discrete Methods Soc. for lndust. & Appl. Math. 43 60 ** 632 644 ** 1.9 2.6 ** SIAM Journal on Applied Math. Soc. for lndust. & Appl. Math. 95 130 150 1258 1149 1901 2.6 3.8 2.2 SIAM Journal on Computing Soc. for lndust. & Appl. Math. 68 98 140 889 1194 1282 2.1 2.1 2.8 SIAM J. on Control & Optimization Soc. for lndust. & Appl. Math. 95 130 172 978 1334 1503 3.1 3.0 3.4 SIAM J. on Discrete Mathematics Soc. for lndust. & Appl. Math. ** ** 140 ** ** 559 ** ** 5.9 SIAM Journal on Math. Analysis Soc. for lndust. & Appl. Math. 102 156 225 1237 1524 1493 3.0 3.2 4.7 SIAM J. on Matrix Analysis & Applic. Soc. for lndust. & Appl. Math. ** ** 88 ** ** 592 ** ** 3.5 SIAM J. on Numerical Analysis Soc. for lndust. & Appl. Math. 95 136 160 1207 1302 1500 2.5 3.5 3.4 SIAM J. on Science & Stat. Comp. Soc. for lndust. & Appl. Math. 48 78 140 997 1417 1132 1.3 1.6 3.4 Studies in Applied Mathematics Elsevier 106 126 154 524 542 552 8.5 8.9 10.9 Technometrics Am. Soc. Qual. Cnti./Am. Stat. Assoc. 23 23 23 419 418 470 1.1 1.1 NA Transactions of the AMS American Mathematical Society 445 598 675 4984 4987 5142 3.0 4.2 4.3 actual prices are 205.50; 109.50 ** not applicable; not in publication T see description of sampling methods and table at end of survey NA not available 1194 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Journal Survey Primary Author-Prepared Journals List Price $US Pages Cents/1000 Char Journal Publisher 1984 1986 1988 1984 1986 1988 1984 1986 1988 Algebras, Groups & Geometries Hadronic Press 150 150 150 509 503 500 20.2 19.4 16.2 Applicable Analysis Gordon & Breach, Science Publ. 252 334 540 283 295 328 56.0 68.6 93.5 Comms. in Algebra Marcel Dekker 425 475 685 3110 2042 2683 9.8T 16.3 16.3 Comms. in Partial Diff. Equations Marcel Dekker 255 350 395 1494 1736 1621 12.6 16.3 15.2 Comms. in Stat.: Theory & Methods Marcel Dekker 490w 550 675 4104 3805 4460 6.3 9.1 8.0 Comms. in Stat.: Simul. & Comput. Marcel Dekker 490w ws 245 4104 1255 1558 6.3 7.9 8.9 Inti. J. of Math. & Math. Sci. Univ. Central FL/Caicutta Math. Society 40 so 60 825 832 832 1.8 2.8 2.6 Memoirs of the AMS American Mathematical Society 148 214 . 239 2722 2165 1917 2.9 4.7 6.5 Numerical Funct. Anal. & Optim. Marcel Dekker 57 86 250 378 643 248 9.4 8.4 52.5 Semigroup Forum Springer-Verlag 216v 172v 96v 1131 831 373 10.6 10.1 13.2 Stochastic Analysis Application Marcel Dekker 75 125 195 470 497 477 11.2 14.5 25.4 v priced by.vol. (1984 contained 3 vois., 1986 contained 2, and 1988 contained 1) w subscribers received both parts for the stated 1984 price; pages reflect parts A and B T see description of sampling methods and table at end of survey Translation Journals List Price $US Pages Cents/1000 Char Journal Publisher 1984 1986 1988 1984 1986 1988 1984 1986 1988 Algebra & Logic Plenum Publishing 360 445 495 481 468 482 24.3 30.2 33.8 Differential Equations Plenum Publishing 505 645 795 1525 1498 1475 9.5 12.9 14.3 Fluid Dynamics Plenum Publishing 500 640 795 1030 998 990 13.0 15.6 18.5 Fluid Mechanics- Sov. Research Scripta Publishing Company 319 410 455 863 864 865 11.0 19.0 19.7 Functional Analysis Application Plenum Publishing 410 495 595 349 338 340 28.8 35.0 37.3 Journal of Soviet Mathematics Plenum Publishing 1035 1345 1595 3315 2882 2473 9.2 13.6 16.1 Lithuanian Math. Journal Plenum Publishing 255 325 395 399 393 400 20.1 23.6 24.7 Magnetohydrodynamics Plenum Publishing 415 495 595 440 456 527 24.8 24.6 26.1 Math. Notes of Acad. of Sci., USSR Plenum Publishing 520 645 795 965 944 950 14.4 17.3 19.0 Mathematics USSR - lzvestiya American Mathematical Society 330 426 483 1244 1236 1320 8.4 10.8 10.9 Mathematics USSR - Sbornik American Mathematical Society 450 596 670 1738 1710 1688 8.5 11.6 12.0 Moscow Univ. Math. Bulletin Allerton Press 260 385 500 503 486 486 21.0 32.5 37.5 Proceedings, Steklov lnst. of Math. American Mathematical Society 226 350 393 1096 1099 1023 6.9 11.0 11.6 Selecta Mathematics Sovietica Birkhii.user Boston 98x 198x 244x 408 421 414 9.8 17.9 20.4 Siberian Mathematics Journal Plenum Publishing 625 795 955 985 961 950 16.9T 19.8 22.8 Soviet J., Automation & Info. Sci. Scripta Publishing Company 185 225 235 552 559 579 T 9.7 11.6 Soviet J. of Contemp. Math. Anal. Allerton Press 260 375 485 500 605 600 25.7 24.8 29.2 Soviet Mathematics - Doklady American Mathematical Society 350 465 530 1555 874 1459 9.8 15.2 10.7 Soviet Mathematics (lz. Vuz.) Allerton Press 335 475 595 1316 1389 1350 10.0 12.2 15.6 Theoretical & Math. Physics Plenum Publishing 500 625 775 1269 1258 1002 9.6 10.1 18.9 Theory of Probab. & Application Soc. for lndust. & Appl. Math. 160 216 250 860 740 758 6.0 8.5 8 .. 8. Theory Probab. & Math. Statistics American Mathematical Society 194 225 245 322 284 301 27.5T 33.9 32,3 Trans. of Moscow Math. Society American Mathematical Society 150 150 167 558 276 261 10.5 16.8 20.8 Ukrainian Mathematical Journal Plenum Publishing 500 625 745 618 683 660 24.6 25.6 25.8 Vestnik Leningrad Univ. Math. Allerton Press (as of 1985) 80 275 385 270 347 330 12.5 30.7 45.4 x prices based on Swiss franc; previously published by Birkhii.user Boston, now handled by Birkhii.user Verlag and considered a European journal T see description of sampling methods and table at end of survey NOVEMBER 1989, VOLUME 36, NUMBER 9 1195 Journal Survey Primary Typeset Journals CharjPage Circulation Current: Page Back Free Outside In st. Chgs Vols + Off- Support Disc. Journal Publisher 1984 1986 1988 1984 1986 1988 ($US) prints Y/N ++ Y/N Advances in Applied Mathematics Academic Press 2190 2340 2240 NG NG NG 0 p 50 N N Advances in Mathematics Academic Press 2350 2210 2210 NG NG NG 0 p 50 N N American Journal of Mathematics Johns Hopkins University Press 2010 1970 2070 1473 1467 1509 0 P,M 75 N y AMS Bulletin, New Series American Mathematical Society 3090 2810 3030 19465 20189 21194 0 P,M 50 N Yj Annals of Mathematics, Ser. 2 Princeton University Press 2580 2520 2550 1777 1748 1695 0 P,M 100 NG N Annals of Probability Institute of Math. Statistics 2460 2570 2340 3334 3238 3235 45 P,M 50 y Ygh Annals of Statistics Institute of Math. Statistics 2760 2850 2890 4664 4723 4771 45 P,M 50 y Ygh Applied Math. and Computation Elsevier 2230 2250 2130 392 404 415 0 P,M 0 N N y Applied Math. and Optimization Springer-Verlag 2230 3560 3120 700 700 700 0 P,M 25 N Comms. on Pure and Applied Math. Wiley & Sons 2290 2650 2260 1336 1284 1309 0 P,M 75 N Yf y Complex Variables: Theory & Applic. Gordon & Breach, Science Publ. 1890 2010 2170 NA NA NA 0 P,M Ob N Computers and Math. wj Application Permagon Press T 4510 4030 NG NG NG 0 P,M 25 N Yi Duke Mathematical Journal Duke University Press 2470 2360 2460 1255 1212 1177 0 P,M 100 Yu N y Ergodic Theory and Dynamical Sys. Cambridge University Press 3120 3120 3000 389 445 499 0 P,M 100 N Houston Journal of Mathematics University of Houston 2320 2510 2490 450 465 475 50 p 50c N N Illinois Journal of Mathematics University of Illinois Press 2320 2290 2200 1137 1086 1043 40 p 100 Yu N Indiana University Math. Journal Indiana University 2390 2440 2290 NG NG NG 40 p 100 NG N y Information and Control Academic Press 2530 2520 2420 NG NG NG 0 p 50 N Information Sciences Elsevier 2590 2410 2460 607 620 600 0 P,M 0 N N Journal of Algebra Academic Press 2490 2450 2380 NG NG NG 0 p 50 N N Journal of Algorithms Academic Press 2700 2630 2560 NG NG NG 0 p 50 N N J. of American Statistical Assoc. American Statistical Association 5600 6020 5540 18500 18500 18500 65 p Oc Ym N Journal of Approximation Theory Academic Press 2050 2100 2130 NG NG NG 0 p 50 N N y J. of Assoc. for Computing Mach. Assoc. for Computing Machinery 3390 3560 3400 15000 15300 14000 60 P,M 50 N J. of Combinatorial Theory, A Academic Press 2400 2380 2450 NG NG NG 0 p 50 N N J. of Combinatorial Theory, B Academic Press 2400 2350 2550 NG NG NG 0 p 50 N N J. of Computer & System Sciences Academic Press 3060 3200 3080 NG NG NG 0 p 50 N N J. of Differential Equations Academic Press 2120 2280 2300 NG NG NG 0 p 50 N N J. of Differential Geometry Lehigh University 2460 2740 2630 849 821 874 30 p 100a N N Journal of Functional Analysis Academic Press 2170 2240 2140 NG NG NG 0 p 50 N N Journal of Graph Theory Wiley & Sons 2570 2700 2480 706 700 694 NG P,M NG NG N Journal of Integral Equations Elsevier 2070 •• •• 260 •• •• 0 P,M 0 N N Journal of Logic Programming Elsevier 3210 3200 3320 434 873 1028 0 p 0 N N J. of Math. Analysis and Applic. Academic Press T 1900 2140 NG NG NG 0 p 50 N N J. of Multivariate Analysis Academic Press 2040 2280 2280 NG NG NG 0 p 50 N N Journal of Number Theory Academic Press 2170 2200 2240 NG NG NG 0 p 50 N N y y Journal of Symbolic Logic Assoc. for Symbolic Logic 3180 3310 3080 2600 2680 2740 30 P,M 50 Journal of the AMS American Mathematical Society •• •• 2660 •• •• 507 0 P,M 50 N Yj y Libertas Mathematica Amer.Romanian Acad.of Arts, Sci. 2150 2120 2250 200 175 175 0 p 25 N Linear Algebra & its Application Elsevier 1960 2200 1830 725 734 709 0 P,M 0 N N y Linear and Multilinear Algebra Gordon & Breach, Science Publ. 2080 2050 2480 NA NA NA 0 P,M Ob N Mathematics of Computation American Mathematical Society 2700 3200 3080 1964 1725 1708 0 P,M 50 N Yj Math. of Operations Research lnst. of Management Sciences 3040 3120 3950 3300 3000 2900 0 NG 0 NG N y Mathematical Systems Theory Springer-Verlag 2680 3590 3000 800 800 800 0 P,M 50 N Michigan Mathematical Journal University of Michigan 2860 2890 2810 NG NG 820 25 p 0 N N Notre Dame J. of Formal Logic University of Notre Dame 3160 3270 3260 822 772 812 0 p 50 N N Pacific Journal of Mathematics Pacific Journal of Mathematics 2230 2310 2225 1425 1425 1425 30 p 75d Yu N Proceedings of the AMS American Mathematical Society 2930 3040 3120 1409 1188 1312 0 P,M 50 N Yj Quarterly of Applied Mathematics Brown University 2850 3020 2990 1057 1052 1020 30 p 100c N N Rocky Mountain Journal of Math. Rocky Mt. Math. Consortium 2650 2590 1890 680 689 666 35 p 50 N N y SIAM J. on Algeb. & Discrete Methods Soc. for lndust. & Appl. Math. 3570 3600 •• 883 994 •• 64 P,M Ob Yj SIAM Journal on Applied Math. Soc. for lndust. & Appl. Math. 2950 3000 3570 2718 2670 2641 64 P,M Ob y Yj y SIAM Journal on Computing Soc. for lndust. & Appl. Math. 3580 3860 3950 1917 1956 2004 64 P,M Ob Yj SIAM J. on Control & Optimization Soc. for lndust. & Appl. Math. 3140 3230 3320 1859 1843 1879 64 P,M Ob y Yj y SIAM J. on Discrete Mathematics Soc. for lndust. & Appl. Math. •• •• 4250 •• •• 941 64 P,M Ob Yj y SIAM Journal on Math. Analysis Soc. for lndust. & Appl. Math. 2770 3240 3230 1367 1362 1436 64 P,M Ob Yj (table continued) 1196 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Journal Survey Primary Typeset Journals Char/Page Circulation Current: Page Back Free Outside lnst. Chgs Vols+ Off- Support Disc. Journal Publisher 1984 1986 1988 1984 1986 1988 ($US) prints YfN++ Y/N SIAM J. on Matrix Analysis & Applic. Soc. for lndust. & Appl. Math. •• •• 4250 •• •• NG 64 P,M Ob y Yj SIAM J. on Numerical Analysis Soc. for lndust. & Appl. Math. 3090 3000 3120 2698 2681 2644 64 P,M Ob y Yj SIAM J. on Science & Stat. Comp. Soc. for lndust. & Appl. Math. 3620 3490 3650 1507 1704 1844 64 P,M Ob y Yj Studies in Applied Mathematics Elsevier 2370 2610 2570 981 943 919 0 M Ob N N Technometrics Am. Soc. Qual. Cnti./Am. Stat. Assoc. 4900 5150 NA 5700 5800 6371 0 p Ob N N Transactions of AMS American Mathematical Society 2990 2880 3040 1228 1184 1190 0 P,M 50 N Yj + P = paper; M = microform ++ m =member dues; s =society/association; u =university •• not applicable; not in publication T see description of sampling methods and table at end of survey NA not available NG not given a two or more coauthors receive 50 offprints each b offprints available but not free c contingent on payment of page charges d two or more coauthors share 1 00 offprints f discounts to Courant Institute members only g second copies received at same location offered at half price h subscriptions to more than one journal discounted from total of list prices lower rates for multi-year subscriptions membership-based discounts Primary Author-Prepared Journals Char/Page Circulation Current: Page Back Free Outside In st. Chgs Vols + Off- Support Disc. Journal Publisher 1984 1986 1988 1984 1986 1988 ($US) prints Y/N++ Y/N Algebras, Groups & Geometries Hadronic Press 1460 1540 1860 NG NG NG 0 p 50 N N Applicable Analysis Gordon & Breach, Science Publ. 1590 1650 1760 NA NA NA 0 P,M Ob N y Comms. in Algebra Marcel Dekker 1390 1430 1570 NG NG NG 0 P,M 50 N N Comms. in Partial Diff. Equations Marcel Dekker 1350 1240 1600 NG NG NG 0 P,M 50 N N Comms. in Stat.: Theory & Methods · Marcel Dekker 1900 1590 1900 NG NG NG 0 P,M 20e N N Comms. in Stat.: Simul. & Comput. Marcel Dekker 1900 1860 1770 NG NG NG 0 P,M 20e N N Inti. J. of Math. and Math. Sci. Univ. Central FL/Calcutta Math. Societ 2660 2615 2760 250 275 300 20 p 50 Yu y Memoirs of the AMS American Mathematical Society 1860 2120 1930 634 623 617 0 P,M 50 N Yj Numerical Funct. Anal. & Optim. Marcel Dekker 1610 1600 1920 NG NG NG 0 P,M 50 N N Semigroup Forum Springer-Verlag 1800 2050 1950 500 500 500 0 P,M 50 N y Stochastic Analysis Application Marcel Dekker 1430 1730 1610 + P = paper; M = microform ++ m =member dues; s =society/association; u =university NG not given e free with orders of 1 00 j membership-based discounts Translation Journals Char/Page Circulation Current: Page Back Free Outside lnst. Chgs Vols+ Off- Support Disc. Journal Publisher 1984 1986 1988 1984 1986 1988 ($US) prints Y/N ++ Y/N Algebra & Logic Plenum Publishing 3080 3150 3040 Differential Equations Plenum Publishing 3500 3330 3780 Fluid Dynamics Plenum Publishing 3740 4120 4300 Fluid Mechanics- Sov. Research Scripta Publishing Company 3350 2500 2670 233 207 199 0 P,M 1 N N (table continued) NOVEMBER 1989, VOLUME 36, NUMBER 9 1197 Journal Survey Translation Journals CharjPage Circulation Current: Page IBack Free Outside llnst. Chgs Vols + Off- Support Disc. Journal I Publisher 11984 1986 1988 1984 1986 1988 ($US) prints Y /N ++ Y/N Functional Analysis Application Plenum Publishing 4080 4190 4690 Journal of Soviet Mathematics Plenum Publishing 3390 3430 4000 Lithuanian Math. Journal Plenum Publishing 3180 3510 4000 Magnetohydrodynamics Plenum Publishing 3800 4410 4320 Math. Notes of Acad. of Sci., USSR Plenum Publishing 3750 3960 4410 P,M 50 N Yj Mathematics USSR - lzvestiya American Mathematical Society 3170 3200 3360 455 424 426 0 P,M 50 N Yj Mathematics USSR - Sbornik American Mathematical Society 3030 3000 3320 440 420 423 0 p 0 N Yk Moscow Univ. Math. Bulletin Allerton Press 2460 2435 2750 NG NG NG 0 P,M 50 N Yj Proceedings, Steklov lnst. of Math. American Mathematical Society 2970 3240 3320 330 328 331 0 NG 30 N NG Selecta Mathematica Sovietica Birkhauser Boston 2450 2630 2890 NG NG NG 0 Siberian Mathematics Journal Plenum Publishing 3750 4180 4360 P,M NG N N Soviet J., Automation & Info. Sci. Scripta Publishing Company 3750 4140 3670 141 125 116 0 p 0 N Yk Soviet J. of Contemp. Math. Anal. Allerton Press 2020 2500 2770 NG NG NG 0 P,M 50 N Yj Soviet Mathematics - Doklady American Mathematical Society 3070 3490 3400 709 680 678 0 p 0 N Yk Soviet Mathematics (lz. Vuz.) Allerton Press 2550 2790 2825 NG NG NG 0 Theoretical & Math. Physics Plenum Publishing 4120 4920 4090 P,M Ob y y Theory of Probab. & Application Soc. for lndust. & Appl. Math. 3090 3440 3740 1072 1059 1080 64 0 P,M 50 N Yj Theory Probab. & Math. Statistics American Mathematical Society T 2340 2520 197 219 215 P,M 50 N Yj Trans. of Moscow Math. Society American Mathematical Society 2560 3240 3080 321 369 383 0 Ukrainian Mathematical Journal Plenum Publishing 3290 3570 4370 p 0 N Yk Vestnik Leningrad Univ. Math. Allerton Press (as of 1985) 2370 2580 2570 NG NG NG 0 + P = paper; M = microform ++ m =member dues; s =society/association; u =university NG not given T see description of sampling methods and the following table: 1984 Cents per 1 000 Characters sample 1 sample 2 sample 3 Computers and Math. wj Application 15.6 13.0 13.0 J. of Math. Analysis and Application 8.4 6.8 9.3 Linear Algebra and its Application 9.8 11.1 10.5 Mathematical Systems Theory 9.1 10.7 9.6 Comms. in Algebra 11.3 8.7 9.9 Siberian Mathematics Journal 15.3 18.8 17.3 Soviet Automatic Control # 7.5 9.4 9.4 Theory Probab. & Math. Statistics 30.5 25.1 28.5 b offprints available but not free j membership-based discounts k 35% on back volumes # now entitled ··soviet Journal of Automation and Information Sciences·· 1198 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics Edited by Jon Barwise Editorial notes (often just listening to the salespeople) and then mandates what the entire campus will buy. If a In a previous column 1, I wrote a short piece de department uses its money or grant money to scribing the differences between TEX, LHEX, and buy "unauthorized" hardware, the school will not A.MS-TEX. That article inspired a pair of articles on commit any resources to its support. TEX and mathematical typesetting, which appear in this month's column. The first is written by Martin Second there are times when quickly obtain Gilchrist, a mathematics editor for Oxford Univer ing so~e computing power is better than bei?g sity Press. The second is written by Michael Doob, promised the perfect system at a later date. Whlle a mathematician from the University of Manitoba, PCs and Macs aren't perfect, they are easily con and author of "A Gentle Introduction to TEX." These figurable to individual users, and have sufficiently articles should be read by anyone contemplating the powerful hardware and software that they are very use of TEX in writing mathematics. useful right now. Although they need improving, The column also contains three software reviews: they are at least proven (and affordable). a two part review of PowerMath II , by Yvonne Nagel and Phil Miles; a review of Rubik's Algebra, by Mark Sand; and a review of Tarski's World, by Mark Seligman. TFX and Typsetting - A Publisher's View Mark Sand replies to Alex Feldman Martin Gilchrist* In an earlier column2, in a review of NetWare by Novelle, Mark Sand described the computational envi ronment at Augustana College, part of which consisted Within the mathematical community (and increasingly of a system of networked PCs. In a later column3, in other disciplines too), TEXis now the de facto stan Alex Feldman responded to this by questioning the dard text-processing system. Throughout the world, decision-making that often leads schools to go the PC more and more mathematicians are using TEX for route. Mark Sand replies: writing preprints, papers, review articles, and books. Consequently, publishers are finding that these authors While I agree with much of what Alex Feldman would like to see the electronic fruits of their labour said in his recent letter, I'd also like to add a used in the production of journals and books. This couple of points to the debate. article is intended to provide something of an idea as to how mathematical publishers are responding to this make inde First, not every math department can challenge. . pendent decisions about what types of hardware We need to distinguish between word-processmg and software they want to use. At many smaller and text-processing: the former describes the activity colleges, the administration "studies" the options of inputting text to a computer and its subsequent editing; the latter describes the manipulation of text 1 Vol 36, 3 (March 1989) 2 Vol 36, 3 (March 1989) 247-251 3 Vol 36, 6 (July/ August 1989) 675-676 *Martin Gilchrist is a mathematics editor for Oxford University Press. NOVEMBER 1989, VOLUME 36, NUMBER 9 1199 Computers and Mathematics and its logical structure in order to reproduce it technique in turn has been supplanted by the use of for publication. For some purposes, a wide range phototypesetters: the original image is created not by of "What you see is what you get" (WYSIWYG) metal type, but by scanning high-quality photographic word-processing programs are just as good as TEX paper with a laser which, by switching on and off very at producing readable and tidy copy. Many authors rapidly, creates the image of each letter and symbol as are content to prepare the typescripts of papers and it scans down pages of photographic paper. These first books using straightforward word-processors and to "bromides" are then cut and pasted to make the pages leave it to the publisher to worry about the appearance and then photographed to make the printing plates. and typesetting of the final form. On the other hand, This is the technology known as phototypesetting publishers have over several years developed ways which is used to typeset almost all modern books. of using author-supplied discs containing the text of Critical to this process is the computer program which books and prepared them using simple mark-up codes is driving the laser phototypesetter and which contains (that is, codes inserted into the text which indicated all the information concerning the layout of the page, section headings, new paragraphs, footnotes, etc.). the shape of each letter and symbol, the distance However, mathematics and technical material has between letters, and between one line and the next. always posed very difficult problems in this regard. As Publishers may not necessarily own a phototypesetter authors turn to TEX for the more complex functions of or for that matter use one they own to exclusively text-processing, publishers in turn have had to come set their books. Normally, an academic publisher will to grips with the new possibilities this opens up to use buy typesetting from around the world depending on authors' electronic files. In general, journal publishing the price, availability and the nature of the task of faces different demands and pressures from those of typesetting for a particular job. book publishing, and the remainder of this article will The main output file that the TEX program gen be devoted to the problems of producing books from erates is known as the dvi (device independent) file. TEX. This contains the precise details of the layout of each Suppose that an author is using TEX in the pro page and therefore many publishers are able to use it duction of a typescript. Three main alternatives are for phototypesetting. Indeed, an author's laser-printer open to the publisher. The publisher may prefer to is in some respects simply a low-resolution phototype design and typeset the book once the typescript is setter (typically with a resolution of 300 dots per inch delivered because they would like the book to have a (dpi) as opposed to a commercial phototypesetting particular appearance. For example, frequently under machine which may have a resolution of 2400 dpi or graduate textbooks will be produced using a designer even higher). The advantages of using a phototype employed by the publisher to prepare the page design setter rather than a laser-printer will principally be and format. In this case, the author's use of TEX to one of quality in the print of the final book. It is prepare the typescript is helpful (since it will produce usually possible to tell by close examination whether neat and unambiguous copy for the typesetter) but laser-printed camera-ready copy or phototypesetting it is not critical. A second option is that the author has been used to create the image used to produce the provides a laser-printed typescript from TEX. This will printed page. provide perfectly adequate camera-ready copy which All publishers, authors, and readers of books will can be made up into printing plates by a simple care about how the printed page looks - how pleasing photographic process. For some purposes, such as it is to the eye, how easy it is to read, and how free conference proceedings, this is quite suitable since in from errors and misprints it is. How a book looks can this case the main priority will be to produce such markedly affect how well it sells and how happy people a volume rapidly and cheaply. The third option will will be to buy, recommend, and read it. A publisher be to use the electronic files created by the author to will want to take care that any book they publish "drive" a phototypesetting machine. reflects their standards of design and editorial quality. Perhaps a remark here about typesetting is in They will also want to ensure that a book looks right order. In days gone by, books were typeset by laying for its intended audience. Consequently, if an author out in racks the metal type that on inking and is proposing to use TEX, their publisher will want pressing to paper gave the printed page. With the them to follow certain ideas of layout and design. advent of lithographic offset-printing, the metal type For example, the publisher will have accumulated was used only to create a first image which was then experience about the right relationship between the photographically transferred on to plates and the page width of a line of text on a page, the type size, and sheets would then be printed from these plates. This the space (the leading) between lines. They will have 1200 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics developed a variety of designs for chapter headings, typescript of the book run out on his/her laser-printer section headings, running heads, the width and depth or whatever. The hard copy is then read through of text on a page, etc. Similarly, they will have styles thoroughly by a professional copy-editor. This will for numbering equations and providing references; involve the copy-editor checking the entire typescript these all form part of the publisher's "house style." for consistency of spelling and grammar, that the Different sorts of books will probably have different equation numbering is correct and consistent, that styles to suit their respective audiences. To ensure that names, dates, and other information are consistent in these qualities are preserved it will be important for the text and with the list of references, that the layout author and editor to discuss in some detail what is conforms to the guidelines given, and many other as involved at an early stage in the preparation of the pects that contribute to the accuracy of the typescript. typescript. On the other hand, authors themselves may The copy-editor will also be looking for stylistic points have strong views about how their book should look which they will suggest to the author for improving the and will want to influence the final outcome too! clarity of the work. The copy-edited typescript is then In TEX, the page layout of a document is usually returned to the author who is usually responsible for determined by a set of macros. These are sets of incorporating the suggested changes and corrections instructions which the TEX program can interpret into the electronic files. It is almost certainly more and which, if incorporated in the author's source efficient to have the author make these changes: they file (the file of ordinary ASCII characters which will know their way around the electronic files better is the input to the TEX program), will reproduce than anyone, they can check what affect changes will certain features such as running heads or section have (such as line and page breaks), and they are not headings or page dimensions in a particular style. left with the uncertainty of not knowing what changes Typically, these macros will be held together in a are being made. Once the author has made all the "style file", which is called up by the appropriate TEX corrections, he/she runs the source files one last time command. In common with some other publishers, through TEX to generate perfect (in principle) dvi files. Oxford University Press can now provide its authors These are then sent to Oxford for typesetting. with such style files in order to produce one of a A natural question to ask is: Why use the dvi file variety of "looks." These files are usually provided on rather than the source file created by the author? Sev a disc or can even be transmitted by electronic mail. eral academic publishers, including Oxford University It is important that the author and publisher Press, have some in-house capabilities for using and discuss what can be done using TEX. It will be useful editing TEX files. However, mathematicians will know to check at an early stage that the final electronic form that there are many variations of TEX available each of the dvi file which the author generates can be used with subtle variations concerning the range of macros, by one of the publisher's typesetters. This process will fonts, and symbols that they will recognize. A source involve ensuring that the typesetter can cope with the file which produces a particular piece of mathematics range of fonts and symbols that the author will be in one form of TEX, may produce a subtly different using (or if not, what substitutes will do). Very often a looking version in another (if indeed both versions sample electronic dvi file of a chapter or so is sufficient can accept the same set of macros and fonts used). to check that no problems will arise. If no suitable For a publisher to agree to use source files they would typesetter can be found, then other arrangements will have to be sure that they could match this bewil probably need to be made (for example, by using dering array with the same proliferation of machines the author's TEX source file in another system). Some and TEX variations. On the other hand, the dvi file publishers are working towards providing authors with is by definition independent of machine and should sets of fonts and font metrics which are suitable for be faithfully produced by any typesetting machine a predetermined typesetter though this brings with it that can interpret it. Often too, authors will have additional problems of compatibility at the stage when expectations about how a particular piece of material the author is producing drafts on his/her own printer will look, which may not be faithfully reproduced by or screen. Author and editor will also need to discuss another version of TEX. Using the dvi file ensures issues such as the production of figures, illustrations, that the author has had complete control over the tables, etc. niceties of layout such as particular page breaks or A publisher will still want to ensure that the final equation breaks that are important to them. This said, dvi file is as error-free as possible. Oxford University with appropriate planning it is of course feasible and Press proceeds as follows. When the author has com may sometimes be desirable to work with the author's pleted his/her book, he/she first sends in a complete source file. NOVEMBER 1989, VOLUME 36, NUMBER 9 1201 Computers and Mathematics What benefits will using TEX bring authors and marketing, promoting, and distributing the book, not publishers? The obvious advantage that typesetting to mention the direct costs of paper, ink, printing, and from TEX has is that the stage of manually rekeying binding. On the other hand, every publisher will be the work by a typesetter is avoided. Thus, there is no concerned to charge what is a reasonable going rate for danger of new errors creeping in (as otherwise they their books no matter what the production costs are, would inevitably do). In turn, this saves the author and to derive a respectable rate of return. Largely, the from having to read one or more sets of proofs, impact of TEX on the price of books will depend on and results too in some savings in money for the each publisher's policy for pricing and printing books publisher (though I shall return to this point later on). and this already varies wildly from one publisher to Book production can also be speeded up by the three another! to four months that typesetting and proof-reading TEX is making every academic publisher sit up and typically take. Inevitably it will involve the author take notice. The issues raised by TEX and other desk in more work earlier on because TEX requires more top publishing systems are having a fundamental affect effort to input and is more fiddly to change. It is on the publishing industry. Increasingly, a publisher's our experience too that whereas authors would often expertise will reside in their editorial and marketing let small mistakes in a typescript go (or handwrite skills rather than production. The impact of better corrections in) and pick them up at proof-stage, with and better commercially available laser-printers for TEX, authors can devote hours to the exact layout of departments and offices will enable authors to generate a table or equation because it is possible to do it! high-quality copy themselves. How will this affect What savings in cost will using TEX bring a the role of publishers? What will be the long term publisher? In the normal course of events, an author effects on the range of mathematical publications will usually be expected to bear the cost of preparing and on their print runs and sales? What affect will a conventional typescript. However, when they have email have on the communication of mathematical used TEX, an author will occasionally ask for some ideas and the use of books? If one mathematician fee to cover the additional costs (if any) which they can electronically transmit, say, a TEX source file to have incurred in preparing the typescript. Different another for processing at the recipient's department publishers will have very different policies regarding what impact will this have? How will journals cope any such payment (though a rate calculated per page with the different electronic forms of source or dvi of output is often agreed). It is much better to arrange files? TEX is also making its presence felt in other a straight fee rather than try to increase a royalty rate. academic disciplines too, and so it is not just the main This is because the publisher will want to regard any publishers of mathematics books who will have to such payment as part of their production costs for the come to terms with TEX. At the same time, typesetters book and often the author needs to pay a typing bill (particularly those who derive a large amount of their immediately rather than defer payment until a royalty business from mathematical and technical setting) are cheque arrives! When a typesetter can use a TEX dvi beginning to realise the implications of these changes file to drive a phototypesetting machine then they and the need to respond either by installing TEX usually charge considerably less per page of output themselves or by ensuring that their machinery can be than for books which they have manually rekeyed. made compatible. It also means that for typesetters There is still some charge since labour, machines, and the traditional skill requirements of fast and accurate materials are all being used. keying are being supplanted (or at least supplemented) What affect then will setting from TEX files have by an ability to edit and reformat electronic files to on the price of books? It is certain that TEX will certain specifications. This in turn will have an affect reduce publishers' typesetting bills. However, the costs on the demands for computer literacy in the labour of typesetting a book comprise only a (surprisingly force. Will the imminent availability of WYSIWYG small) proportion of the cover price of a book. Fur front ends to TEX increase the spread of TEX or ther, the cost of "keyboarding" (which is essentially simply the ease of use in its present user community? what the author is providing) is only a part of the So far, it is clear that TEX is having an enormous cost of the entire typesetting operation. Larger propor impact on mathematical publishing and will continue tions of the cover price may be taken up by the costs of to do so for the foreseeable future. 1202 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics 1FX and Typsetting - An Author's View These two options are the extremes that result in minimal author-publisher cooperation in the typeset Michael Doob* ting process; either the publisher or the author does everything. One of the great assets of TEX, as we The juxtaposition of this article with the previous shall see, is that it makes possible a greater level of one might cause one to believe that the publisher cooperation. and author have conflicting methods and goals that An appealing aspect of using a WYSIWYG system must somehow be resolved. This, of course, is not the is the combination of the ease with which changes can case: both the author and the publisher want to create be made and the immediate feedback after making an accurate, informative, and attractive volume. The these corrections. It is usually possible to pick up perspectives of the two are rather different, and this is objects and move them around the screen using a reflected in the possible use of TEX. mouse or some keyboard sequences. But, in this case, The highest priority of the author is to present the judgement of where to place objects is affected all of his or her results accurately and clearly. There by the resolution of the screen. Either there must are several options open to do so. One is to prepare be a magnification to see the object in all its detail a manuscript, either by a typewriter or by a fancier or there must be a loss of resolution compared to word processor, and then let the publisher typeset the a laser printer or other printing device. This makes pages in the traditional way. A second option is for precise work difficult. Further, for the publisher to use the author to do all the preparation on his or her the author's computer file, the software and hardware own as camera-ready copy. On the face of it, this is must be identical. A WYSIWYG system, at least at possible using a cleanly typed manuscript, but anyone the present time, by its definition is highly machine who has tried to read an entire book done this way dependent. soon realizes that it is much harder to digest than Now, this is meant to be in contrast to TEX, of is a book typeset in the normal manner. This is not course. TEX is a markup language, that is, instructions altogether surprising, for there are several hundred are encoded that, for example, set the layout of a years of typesetting experience behind the books we page, and the text is then typeset according to those read; the absorption of information is aided by the instructions. The disadvantage is obvious compared sometimes subtle cues in the typesetting and in the to WYSIWYG: you don't see the final result as you spacing of words. enter the text. To see the final result it is necessary to Some improvement over the typewritten copy oc create (type in) a source file, to run that file through curs when an author works with a WYSIWYG (what the TEX program to produce a dvi file (which is not you see is what you get) system, for a variety of human-readable), and then to take that file and use typographic tools becomes available. The author has, another program to produce legible output. That's a however, been turned into a graphic designer. Now I lot of work when compared to WYSIWYG. have never heard of an expert in the graphic arts say, What does the author get for this extra work? First "I think I'll write a few mathematical papers; after all, of all, there is a much more accurate placement of my intuition with numbers is really quite good." But, characters. The internal computations within TEX are in effect, mathematicians are saying exactly the same carried out to within a few Angstrom units. Printing thing when they use WYSIWYG systems. It seems devices don't work to that accuracy, of course, but that the lure of all those extra fonts is irresistible. Of the full capabilities of, say, a 2400 dots per inch course it is possible for the mathematician to study phototypesetter are used. A monitor screen has a some of the classic books on typesetting styles; but it resolution of about 100 dots per inch, so WYSIWYG is much more likely that, if the problem of typesetting is rather limited by comparison. Also, the author gets is considered at all, the author will look at a few books a large and standard set of fonts. The repertoire of and imitate what is there, thus producing, at best, mathematical symbols, in particular, is much greater a work which is an amalgam of different styles. To with TEX than with WYSIWYG systems. produce a first rate result, the help of the publisher is But much more importantly, the universality of certainly necessary. TEX allows the author to prepare his or her source file on one machine and the publisher to use that file on a different machine; the use of the intermediate *Michael Doob is a mathematician from the University of dvi file lets both the author and publisher work with Manitoba. printed copy that is identical up to the physical limits of each output device. The WYSIWYG route forces NOVEMBER 1989, VOLUME 36, NUMBER 9 1203 Computers and Mathematics the publisher and author to use identical hardware and The availability of electronic mail transfer has a software. So, either the publisher must have a myriad further implication for the distribution of the author's of computers with different versions of software and final result. The distribution of books on magnetic operating systems, or the author is forced to get rather than paper media is possible and, in fact, something that matches what the publisher already is being done with Mathematical Reviews already. has. The distribution via electronic mail would be easy. But since TEX has been implemented on all major Perhaps in the near future we will be ordering a book computers, this problem does not arise. This means, by electronic mail and receiving the electronic file by at least in principle, that the page layout can be done automatic reply the next day. The smallest and most primarily by the publisher, and the writing can be remote colleges will have the same access to new books done primarily by the author, but each can make as the largest and most prestigious urban universities. significant contributions to the other at whatever level Finally, we should note that TEX has some built-in is mutually desirable. protection against becoming outmoded by technologi The importance of the separation of the page cal change. The source code is in the public domain; layout from the writing of the mathematical text by and can be tested against any new machine or com TEX is crucial. If the text, for example, is supposed to piler that appears. Also, the use of the dvi file makes be 6.5 inches wide, the particular coding in TEX would the use of new printing devices relatively easy, and be \hsize = 6. 5 in. Once this instruction is given is independent of the TEX program itself. If, in the at the beginning of the file, this value will be used future, all libraries have 5000 dots per inch printing for typesetting the width of all of the lines and will devices available like photocopy machines are today, also be used for other calculations such as centering then the TEX file made today will be reproduced in lines; it will be in effect for all lines typeset until the full glory! end of the document or until the parameter \hsize is changed. There are many such parameters like \hsize, all of which have default values. The point here is that these values can be changed easily; if, for example, the text should be 16 centimeters wide instead, all one must do is put \hsize = 16 em at the beginning Reviews of Mathematical Software of the document instead. There is no need to go through the document reformatting page after page. The graphics designer can set these parameters while the author can enter the text. In fact this has become standard with TEX and specialized "style" files have PowerMath II become available from particular publishers and even particular journals. Yvonne Nagel* There is another indirect but important advantage for the author using TEX. Since the TEX source This is a review of PowerMath II, a computer algebra file uses only normal characters and no special control system for the Macintosh. I reviewed Version 2.5 of characters, the usual array of tools for creating indexes, this program. It was originally developed by Industrial tables of contents, tagging references, and spelling Computations, Inc. for the 128 K Mac and Lisa checking are available. But even more importantly, in 1985. Further enhancements were made in 1986 the source file may be sent by electronic mail, and and 1987. The current version was made in 1987. this makes the communication between the publisher It is available from Central Products Corporation, and author much easier. It may be that the planning 2211 Norfolk, Suite 518, Houston, TX 77098 (phone: between author and publisher is perfect when the 713-529-1 080). author starts to write; but it is more likely that there The PowerMath II manual describes it as the first will be some evolution as the project moves along. symbolic problem solving program for the Macintosh. This is especially true if there is more than one author. I was eager to try it since I had already tried Derive It is certainly possible and in fact practical for authors to write separately and then meld the results using electronic mail. The ease of glueing the contributions *Yvonne Nagel manages the computers in the Mathematics Department at UW Madison. She also taught pre-calculus courses of the authors and the publisher is a real advantage of there for several years. Her email address is [email protected]. using TF)(. 1204 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics on an IBM-PC compatible computer. Also, since I had agreed to work in a summer program for high school minority students at the University of Wisconsin, I thought I could test it on them to see their reaction to the program. After some practice, the user recognizes this as which Pow The level of mathematical problems 2x2 + (-Sy)x- 3y2 One can also solve simultaneous erMath II is capable of solving is very much below equations such as: that of Derive, Maple, Mathematica or Macsyma, which are other symbolic manipulation languages. In compensation, though, it has a user interface which x+y=4-A-3 and easier to understand for high is more appealing y+6=x-4 college students. The four school-aged or beginning Solve(x;y) minority students whom I worked with had never used a Macintosh or IBM PC before this summer. One of them had extensive programming experience Highlighting this set of commands and choosing on a VAX. Two of them had taken an introduc Evaluate Selection as described above produces the tory basic course using Apple lis. The fourth student correct answer in terms of the symbolic constant had no prior computer experience. Moreover, none A. Actually, the user has the option of selecting or of them had used symbolic manipulation programs deselecting a "learning mode". If you choose Show before. They tried some simple problems on the IBM Work from the Preferences menu you will see the PC using Matlab and Derive. Then they tried some following display on your answer slate: exercises on the Macintosh using PowerMath II. They all agreed that they liked PowerMath II best. However, the student with the most computer experience also x+y=4-A-3 remarked that perhaps PowerMath II might be more y+6=x-4 other programs. After working with limited than the Solve(x;y) PowerMath II for several days, I tend to agree with x+y=-A-3+4 him. Becomes A-3+x+y-4=0 y+6=x-4 The user Interface Becomes -x+y+10=0 I would like to begin by describing the most appealing A-3+x+y-4=0 part of PowerMath II, namely the user interface. It is Becomes : x=-A-3-y+4 easy to work with and obviously easy to understand -x+y+10=0 make for unsophisticated computer users. This might Becomes : A-3+2*y+6=0 or PowerMath II useful in a high school algebra A-3+2*y+6=0 pre-calculus course. Becomes : y=(-A-3-6)/2 When the user opens PowerMath II, he is presented Solution : with four "slates" - actually four rectangles on the X = (-A-3+14)/2 left of the screen - which are labelled Data Sets, y = (-A-3-6)/2 Problems, Answers, and Functions. A window titled Problem Slate occupies most of the screen. This is a "clean slate" on which the user is to enter his If you do not choose to Show Work you will just problems. get the answer: Following the manual, one can enter a problem such as: ? (2x+y)(x-3y) x = (-A-3+14)/2 y = (-A-3-6)/2 The user then highlights this line using the stan dard Macintosh click and drag technique and selects Evaluate Selection from the Control menu at the top of This is, of course, the kind of technique used the screen (or presses the cloverleaf and 'e' keys simul in a precalculus course. The method of solution can taneously). A window titled Answer Slate immediately be immediately comprehended by students in such a appears with the answer: course. However, there are other methods of solving NOVEMBER 1989, VOLUME 36, NUMBER 9 1205 Computers and Mathematics such a problem - even in a pre-calculus course and quadratics in a pre-calculus course, this is a definite an instructor who uses PowerMath II must take care drawback. that students do not start solving such problems in a PowerMath II is capable of differentiating andjor stereotyped way. integrating expressions. It is also able to give the first n The Data and Function slates can be used to terms of the Taylor expansion of an expression about define and store data and functions used in several a point. Unfortunately, the manual informs us that problems. Data can include such things as the values expression must be a polynomial. I suppose that this of variables and even matrices. Predefined functions is the reason that the program was named PowerMath include the standard trigonometric functions such as II - i.e. it only handles polynomials well. Of course, sin, cos, etc., log with different bases, integration and the user can create a function definition which tells differentiation, roots, Taylor series, absolute value and PowerMath II how to differentiate, say, sin or cos. powers. The user is encouraged to define his own He can then use this definition to illustrate the chain functions and store them on the Function slate for rule by differentiating, e.g. sin(x2 - 2x). This might later use. There is also a Plot command which allows be useful for a precalculus student who is also a you to view plots of one or two variable equations. The computer sophisticate, but would probably be beyond user must set the range of the independent variable most students in a precalculus course. and avoid curves with discontinuities. It is capable of doing multiple plots. Thus one can see a graphical Summary representation of the solutions of a set of simultaneous In summary, PowerMath II has the potential of devel equations. Apparently, PowerMath II is not capable of oping into a useful tool for precalculus and, perhaps, doing three-dimensional plots. There is also a warning beginning calculus courses. The user interface is ap that the speed of plotting is slow. pealing and simple enough for unsophisticated users. However, the mathematical capabilities must be ex The Documentation tended before it would· be worthwhile in a classroom The manual was well written with clear examples. The setting. Also, the retail price of $149.00 is high. Right examples were easy to follow and the descriptions of now, perhaps, Matlab or Derive on an IBM PC offers the user's actions were clear. However, I found myself better value for the money. wishing for an index and, perhaps, an appendix with a brief summary of PowerMath II commands. More on PowerMath II Like many computer users, I was eager to try out the software and did not want to read the book completely Phil Miles* before I could do so. An entire chapter is dedicated to the mechanics of the program. This is probably PowerMath as student useful to beginning Macintosh users - as the minority PowerMath, in its "symbolic constant" mode, solves students were, but could probably be skipped by an problems in a fashion emulating what we convention experienced Macintosh user. The chapters on Problem ally expect in student solutions. Arithmetic of rational Definition, Matrices, and Functions were devoted to numbers is done in terms of rationals, not their deci the mathematics which the program is capable of mal approximations. Solutions to quadratics are given handling. in terms of square roots, not decimal approximations. It cheerfully solves 1/r = 1/rl + lfr2 for rl in terms The Mathematics of r and r2 [recognizing r, rl and r2 as three differ Although PowerMath II has an appealing user inter ent variables]. PowerMath looks like a student when face, I feel that much work needs to be done to extend solving problems. its mathematical capabilities. For example, although I had PowerMath II take the lower end of our PowerMath II easily expands an implied multiplication placement test, with myself acting as amanuensis. It such as got 33 out of 75 questions correct, which places it into our intermediate algebra course. Had it appealed this decision, we would have let it try college algebra ?(2x-y)(x-3y)(4x+2y)(3x-7y) *Phil Miles is Professor of Mathematics at the University of a simple Wisconsin-Madison, where he is concerned with placement and It does not seem to be capable of factoring pre-calculus courses. His email address is [email protected]. quadratic. Since much time is spent in factoring 1206 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics (which, with trig, immediately precedes calculus). It PM, in its "show work" mode, does display its wouldn't pass college algebra in its present form. I steps on the way to the answer. The result is, from a guess that it could be enhanced to a point where pedagogic viewpoint, a bad implementation of a dull it could place directly into calculus, and that the idea. Any device [including text or lecturer] which amount of work to accomplish this would be no simply scrolls through the lines of a solution is of greater than its creators have put into getting it this little help in teaching algebraic manipulation. And the far. PowerMath II is excellent on algebra problems actual sequence of steps followed by PowerMath II is of the genus "simplify", and good [though slightly frequently far from the one which a student should quirky] on equations of linear or quadratic type. It is follow. In short, PowerMath II is more interesting as simply not there as regards geometry or most of trig. a student than as a tool for learning. Does it learn like a student? The relevant context [These strictures concern PM's relevance to ordi for this question is elementary calculus. PowerMath nary students; the student who investigates why Pow II comes already able to find derivatives of rational erMath II follows the steps it does will presumably functions and indefinite integrals of polynomials. The learn a lot] user can readily program in rules for derivatives or integrals of other functions - say the basic trig PowerMath and future math education functions, log, exponential and roots. Once this is The wise have, I think, been silent on the future of done, PowerMath II can use the chain rule to produce mathematics education. I will do the best I can and the derivative of any elementary function. If "learning" be terse. means what can be readily demonstrated to occur in Math education, as generally discussed, means the majority of students ["assessment learning"], then roughly math for non-mathematicians. For the educa PowerMath II learns the chain rule like a student tion of this group, the fundamental question (I claim) in a routine business calculus course. I was unable is finding the right role of "getting the answers" - to teach it implicit differentiation or integration by fundamental for both choice of content and for ped substitution. agogy. Under at least some answers to this question, I concur with Yvonne Nagel's remarks on the future students will be not people but person-machine friendliness of the interface. I started with no experi teams. I doubt that PowerMath in its present form is ence of either the Mac or PowerMath II and spent less what one would wish as the machine half of such a than three hours of unsupervised exploration of the team. But PowerMath does demonstrate an approach combination before doing the placement test; most of which deserves careful consideration when thinking that time could have been saved had I read the manual about the possible composition of such teams. more thoroughly. There were eight problems on the placement test Rubik Algebra where a different kind of user would, with PowerMath II, have gotten the answer. These were "word prob Mark Sand* lems", and the kind of user in question is one who computers into mathematics classes is eas can write down equations from a word problem but Integrating areas than in others, with Abstract Algebra can't deal with the equations thereafter. This kind of ier in some of the most difficult. One program which user is very rare in pre-calculus courses on my campus being one can help is Rubik Algebra by Charles G. Flemming but, by my guess, constitutes about 10% of the overall D. Halchin of Eastern Illinois University. undergraduate body. and Judy It is commonly known that the turns of the faces of cube can be identified as permutations on the PowerMath as learning tool a Rubik's "cubies" that comprise the cube. An introduction to PM's strong point is in getting the answers. In the of the operations that can be done on a cube context of conventional instruction, this ability is the study in Douglas R. Hofstadter's "Metamagical otiose. No computer, no matter how cheap - no was given column in the March 1981 issue of Scientific environment, no matter how friendly, will obtain Themas" Magazine. Using the same ideas and similar answers as readily as looking them up in the back of American Algebra enables the user to perform the text. The goal in conventional instruction is not notation, Rubik getting the answer but doing the problem. The central failing of conventional instruction in recent years has *Mark Sand is an Assistant Professor of Mathematics at Au been in convincing students of the validity of this gustana College (SD). He is working on a Ph.D. in potential theory goal. from the University of Minnesota. NOVEMBER 1989, VOLUME 36, NUMBER 9 1207 Computers and Mathematics face rotations, either by typing them in or recalling Although I have had a lot of fun and learned a lot them from a saved list, and analyze them as a product from using Rubik Algebra, I think I would not use it of disjoint cycles. for an extended time as a teaching tool in a classroom Initially, the cube is shown on the screen with situation. Instead, it is ideally suited to individual a menu of choices. Of these, the choice I use most investigation. Since it is very easy to use, a student often is "Perform face rotations." After entering the (or teacher, of course) could spend just a short while desired sequence of turns and the number of times with the program and gain significant understanding the sequence should be repeated, the cube is erased of some of the ideas of group theory. This would and re-drawn in its new state. It would be fun to spur short classroom demonstrations and discussion see the faces turn in animation, but I can think of without using class time to learn the program. at least two reasons why that isn't done. First, it One word of caution for users of Rubik Algebra. would be too slow, since repeating a move a few Since the main menu choices can be performed by hundred times (a reasonable thing to do, actually) can typing the first letter of the line, typing 'u' will execute last nearly a minute even without animation. Second, the operation "Unscramble the cube." However, 'u' Rubik Algebra is designed to be a small and simple also represents a clockwise turn of the "up" face program that doesn't require an extensive amount of of the cube, and is often typed after selecting the memory. "Perform face rotations" line. When typing quickly, Rubik Algebra is a lot of fun to use, however, I frequently hit 'u' before selecting the correct line, for fans of Rubik's cube or elementary group theory. which unscrambled the cube instead of proceeding The menu choices are extensive enough to allow any with the next move. This cannot be undone, so the move to be accomplished, and the program will do previous work is lost. some of the work. Other choices that are available Rubik Algebra is written for IBM-compatible mi for manipulating the cube cause it to be turned, or crocomputers with CGA (or better) graphics. It is scrambled, or unscrambled. Another menu line allows distributed as shareware, with a price of $10, and can the user to step forward or backward through the be obtained by writing to the authors at Department of moves that have been previously entered. This is a Mathematics, Eastern Illinois University, Charleston, good way to set up a sequence of moves that show the IL 61920. cube being gradually scrambled and unscrambled. Mathematically, the most important menu choice Tarski's World is "Cycle decomposition." This writes the most recent operation on the cube as a product of disjoint cycles, Mark Seligman* some of them cycles of corner cubies and the rest World is a software tutorial written to intro being cycles of edge cubies. This is more complicated Tarski 's duce first-order predicate logic. The program provides than it sounds, since a cubie has both a position on an interactive setting in which first-order sentences the cube and an orientation of its colors. There is for syntactic correctness a help screen that can be called up at this point to may be composed, checked model constructed by the user. summarize what the _cycle notation means. It is not and verified in a Tarski's World runs on Apple Computer's Macintosh extensive, but is adequate to remind the user of what machines. the cycle notation is representing. Through this process, the user can experiment with orders of elements, conjugates, and commutators, and The Product not worry about the algebraic expressions becoming World presents three main windows on the too long or unwieldy. For example, letting the com Tarski's Macintosh screen. The "sentence window" displays puter scramble the cube results in a randomly-chosen formulas of first-order logic which the user wishes to move of about 60 to 70 face turns (90 degrees each). provides a version of the The cycle decomposition of the move will show cycles test. The "keyboard window" keyboard in menu form; from it the user may compose of various lengths, with the least common multiple of the lengths being anywhere from a few dozen to many hundreds. Then repeating the move the proper num *Mark Seligman studied mathematics at the University of ber of times will return the cube to its unscrambled Michigan and the University of Chicago. His main interests lie in state. If the move is repeated a number of times that mathematical logic, topology and the theory of algorithms. He is also is only a proper factor of this least common multiple, interested in finding ways for computers to help mathematicians interesting patterns can result. and their students. He currently makes his living writing software. 1208 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics sentences in the sentence window. The "world win to use the program, introduces concepts in logic and dow" displays the model in which sentences are to be develops exercises for use with the sample files. Some interpreted. The model, or "world" as the documen of the exercises can be written and then graded. tation terms it, is a collection of three-dimensional shapes lying on a ruled plane. The sentences being Review analyzed, then, are to be thought of as statements about the shapes in the world window. The program ran well with exercises taken from the Worlds are built from objects, which can be cubes, documentation. Even long and complex sentences ran dodecahedrons, or tetrahedrons; objects are selected reasonably quickly; I did not attempt to find one long from icons and "dragged" onto the plane in the enough to make the program fail, however. There was display. Objects may also be labeled with a constant, no problem either reading or writing my own files, much as a constant may be bound to its semantic although the documentation cautions that additional interpretation. Worlds may be edited using mouse and disks will be needed to hold more than about twenty menu commands to move, remove and size objects. five new files. Worlds may be saved in files for later use. An option is Those not used to working on the Macintosh may given to allow worlds to be viewed two-dimensionally feel cramped by its small screen. At times I was from above, useful when an object obscures the view. frustrated by having to hide windows or resize then A user composes sentences using either the key when my sentences grew large or numerous. It would board or the menu in the keyboard window. Available be nice if Tarski's World were available for machines are the usual symbols of a first-order language, includ with larger screens. ing the existential and universal quantifiers, negation, I had some difficulty learning the meaning of equality, conjunction, disjunction and implication. Six the spatial relation predicates used by language of unary predicates, three relating to shape and three re Tarski's World. For instance, "between" always con lating to size, and seven binary predicates, relating to fused me. Checking the documentation, though, one relative positions, of objects are provided. There are finds exercises prescribed very early for mastering the also supplied six constant and six variable symbols interpretation of this and other predicates. and parentheses. As the sentence is built, it appears in There is perhaps one criticism of the game. If a the sentence window. Lists of sentences may be built. sentence is true, the game will confirm it to be true Like worlds, sentences may be edited and saved in period. As the game is intended to be a teaching tool, files. the user might expect to be able to step back through A menu within the sentence window selects tests the verification, to affirm that various pieces of the which may be made on any displayed sentence. A sentence are valid for the reasons she or he thinks they sentence may at any time be checked syntactically for are. It is not hard to conceive of a student choosing either of two criteria: Is it a well-formed-formula? Is a valid sentence on a hunch, with little confidence in it a sentence? The user may assert either the truth or the reasoning leading to the sentence. The only option the falseness of these criteria; the program will check appears to be to deliberately make a false claim and the assertion. A third test, intended for sentences step through its contradiction. about a model displayed in the world window, verifies The documentation is nearly an introductory text the sentence's interpretation in the model. This test, on first-order logic. After a brief introduction to the referred to as "the game", is the heart of the program. mechanics of building worlds, composing formulas The game is a type of interactive theorem checker. and using files (with references to Appendix 2 for It not only checks the truth of an assertion about those needing to learn more about Apple utilities), the model, but, in the case of false assertions, helps the first chapter concentrates on teaching logic. The the user identify flaws of reasoning. It does this by meanings of the logical symbols are discussed, then deft use of counterexample, prompting the user for the notions of free and bound variable, well-formed claims about the validity of subformulas it has chosen formula and sentence. Footnotes point to deeper from the sentence, then challenging the user to find an explanations in Appendix 1. object witnessing a false claim. Chapters 2 and 3 explore propositional and pred On the program disk are included files, most icate logic, respectively. Exercises advise playing the bearing the name of famous logicians, which contain game on various sample sentences in sample worlds example worlds and sentence lists to be used as and then on alterations on them. A common theme exercises. With the program comes a document of in these exercises is the examination of the expressive about one hundred pages. The document explains how power of a formal language versus that of a natural NOVEMBER 1989, VOLUME 36, NUMBER 9 1209 Computers and Mathematics language; often the user is asked to translate English 8022, Ventura, CA 93002-8022 (phone 800-235-6919, sentences. Many exercises are directed to the illustra from California: 800-292-6640 and from outside the tion of specific concepts in logic, such as a sentence's US at 805-652-4158. A new version of the program being vacuously true or being the consequence of, or is expected to be released by CSLI, Ventura Hall, independent of, other sentences. Oddly, though, the Stanford, CA 94305 by January 1990. notion of proof, although well motivated at this point, is not covered. Chapter 4 explores further topics, including con sistency, persistence through expansion or contraction of the model and elementary equivalence. Some of the exercises require proofs; one of them requests Mathematical Freeware a proof by induction on the length of a formula. Much emphasis is made here, too, on semantics in and Shareware the formal language-even the software's constraint on the permitted number of variables and constants is critically examined. Despite the large number of topics discussed in the documentation, proofs are not given. In that sense at least, the documentation is not a self-contained text, but rather, as it claims, a supplementary text. It is Freeware and Shareware certainly more than just a manual. A curiosity, though, is the authors' commitment to the word "world". They An enhanced version of CC introduce may of the terms used by logicians, but seem to shy away from "model". A new version of CC, the Calculus Calculator (re viewed Vol 36, 7 (Sept 1989)) is now available. Enhancements include symbolic derivatives, complex Conclusion functions, 3-D graphs of surfaces, vector operations, Because of the didactic process of verification which statistical functions, solutions to non-linear systems the game offers, the user has a tool to help work of equations, binary and hexidecimal arithmetic, and through mistakes. This might mean less time spent full programmability. CC is shareware and may be by an instructor on concepts more easily practiced by obtained by writing: a student with a machine. Tarski 's World certainly David Meredith presents the student with more than just a work book. Department of Mathematics Judging by the quality of the software and the San Francisco State University coverage of the accompanying text and considering 1600 Holloway Ave. the usual cost of textbooks or classroom time, I'd say San Francisco, CA 94132 that at fifteen dollars Tarski 's World is a steal. Tarski's World is currently available from the Requests should include two blank IBM-PC disks Kinko's Academic Courseware Exchange, P.O. Box and a postage paid return envelope. 1210 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Inside the AMS Science Policy Committee Looks at Accreditation and Travel Grants report, intended as a discussion document, focused The AMS Committee on Science Policy is a standing on accreditation as a way of setting standards for committee of 14 members. The Committee meets mathematics departments and for how they fit into twice yearly to discuss matters of science policy their institutions. In other fields, such as engineering, affecting the mathematical sciences community. In accreditation is fairly common. In fact, the report was addition, it makes recommendations to the AMS put together by "translating" accreditation standards Council and other Society committees for actions for other fields into standards that might be met by and projects pertaining to science policy issues. mathematics departments. As provost at Lehigh University, Committee mem ber David Sanchez has had experience with accredita Discussion of science policy typically goes two tion boards in many academic disciplines. He strongly ways: either the issues are so lofty that they inspire criticized the report, saying that 80% of mathematics nothing but platitudes, or they strike sufficiently close departments could not meet the standards it set forth. to home to bring out some lively debate. The latest For example, the report said the majority of faculty meet~ng of the AMS Committee on Science Policy, in any mathematics department should have doctoral held m September in Washington, DC, had its share of platitudes, but for the most part consisted of intense degrees, a standard Sanchez called "wonderland" for institutions with only BA programs in mathematics. discussion of some of the major issues facing the mathematical community today. He felt the report's recommendations about comput ing equipment were unrealistic, given today's tight The Committee's agenda covers a daunting breadth of topics, from getting President Bush's Science Ad budgets, and he questioned the blanket recommenda viser to speak at the Society's winter meeting to tion that mathematics majors comprise 1 1/2% of all baccalaureate recipients at a given institution. He was considering whether the AMS should sponsor a lecture especially concerned that the report did not clearly series for high school students. Nonetheless, the Com differentiate between two different roles of accred mittee has· found a fairly clear sense of purpose and is emerging as a powerful and articulate body having an itation, as a means of evaluation and as a means influence on a wide variety of Society affairs. Indeed, of advocating increased resources. He conceded that the meeting opened with a description of a number of the report contained some ideas that could serve as useful guidelines, but as a formal accreditation pro projects-such as awards for public service in math gram, he stated emphatically, "I would not support ematics (see Notices, October 1989, page 1103) and an opinion column in Notices-that the Society is this document at all." David Vogan of the Massachusetts Institute of pursuing on the advice of this Committee. Technology added that the problems in providing a useful undergraduate experience in mathematics Accreditation of Departments were not addressed in the report. "It's fine to give recommendations," he said, "but many of the best One topic that drew some spirited discussion was a departments would not want to deal with this partic report by a committee of the Mathematical Associ ular program." Hyman Bass of Columbia University ation of America that has been examining the pos was surprised that the report read less like a set of sibility of accreditation of mathematics departments. educational principles than like a set of fair labor Accreditation can have various meanings, depending and consumer advocacy laws, designed to insure that on the discipline and the kind of institution. The mathematics faculty have good working conditions NOVEMBER 1989, VOLUME 36, NUMBER 9 1211 Inside the AMS and that students are not shortchanged. He also noted sion by saying that an AMS member had suggested the that, while the document itself was not adversarial, at Society formulate a program to administer the travel tempts to meet the standards articulated in the report grants and submit a proposal to the NSF for fund could set departments in an adversarial relationship ing. The AMS would choose the awardees (possibly with their administrations. through panel review) and make the grants directly Accreditation programs can help a department ar to individuals, thereby avoiding the overhead costs gue for increased resources from its administration, that educational institutions charge on regular NSF but some felt accreditation could end up working grants. It's not clear the NSF would fund it, but against mathematics departments if the standards are simply submitting the proposal would force the NSF too high. For example, if the accreditation standards to take some action on an idea that would likely enjoy said that mathematics classes should have fewer than considerable grassroots support. 35 students, university administrations might con Bernard McDonald, deputy director of the OMS, clude that all mathematics faculty should teach twice raised a number of questions, such as what the return as many classes. In addition, Sanchez, noting that on the investment would be and how the success of some accreditation boards "develop a life of their the program would be evaluated. He also said that own," cited an influential engineering accreditation the AMS could receive 1000-2000 applications for board which has become so institutionalized that it perhaps 100 grants. "If you tum down 900 out of actually inhibits curricular innovation. Large engineer 1000 applicants, will that just create more problems?" ing schools can thumb their noses at the board, but he asked. Jaco conceded that, when the DMS rejection small schools don't have the clout to stand up to it. rate for regular grant proposals is around 50%, the As an alternative, he suggested a program whereby smaller grants should not have a higher rejection rate. a mathematics department can request that a team In addition, the ballpark figure for the program of evaluators be sent out to assess the department's seemed to hover between $500,000 and $1 million, strengths and to offer suggestions for improvement. and no new NSF funds would be likely to be available Despite the strong criticism, the Committee gener for it. This means that investigators near the "cutoff ally favored the idea of having some sort of standards level" for NSF grants may have to settle for a travel or guidelines for departments and felt the report made grant rather than a grant with salary support. In recent many useful recommendations. The issue of standards years, Foundation officials have emphasized increasing also surfaced later on, during their discussion of a the size of grants over increasing the number of report on preparation for college teaching. The Com grantees, so it may be difficult to sell a program like mittee decided to recommend that the AMS appoint this one, which spreads limited DMS resources more a committee to give advice on what action the Society thinly over a larger pool of researchers. should take to establish guidelines for mathematics John Polking of Rice University said that one departments. objection to such a program is that other disciplines will assume that, if mathematicians can get by on Small Travel Grants small travel grants, then they don't need summer salary support for research. Such perceptions can be The idea of small travel grants for mathematicians important in the political maneuvering for research has been circulating in mathematical policy circles for funding, but Jaco pointed out that they might be less some time now, but it has never materialized. The of a problem if the AMS administered the program Advisory Committee for the Division of Mathematical than if NSF did. Sciences (DMS) of the National Science Foundation The travel grants could also be leveraged by de (NSF) recently endorsed a recommendation for a partments. Frank Gilfeather of the University of New travel grants program of 200 grants of $2000 each. Mexico pointed out that, as a department chair, he However, it is politically difficult for the OMS to would find it relatively easy to kick in $500 for travel justify such a program within the NSF. Foundation to a person who already has received a $500 travel officials often perceive this kind of program as making grant. But would deans and other administrators begin "second class" grants to "second class" researchers, or to ask for their "share" in the form of indirect costs? as a way to "spread the wealth," rather than to focus Some thought this might be a problem, but others said on supporting the highest quality science. In addition, that, because the grants would carry no salary support, the administrative costs could prove unwieldy. indirect costs would not be an issue. At the Science Policy Committee meeting, AMS A few Committee members were adamantly op executive director William H. Jaco opened the discus- posed to the idea. Ronald Lipsman of the University 1212 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Inside the AMS of Maryland said the plan sounded like "welfare," and Among the other topics discussed was the update James Glimm of the State University of New York at of the David Report, now in preparation by the Stony Brook said such a program would create a class Board on Mathematical Sciences. The new report will of "double losers," those who were turned down for address such topics as the target funding levels for regular NSF grants and for the travel grants. Glimm mathematics set forth in the original report, ways said the idea has never been implemented partly be to insure adequate numbers of trained mathemati cause it "devalues" the structure of the mathematics cians, and current areas of intense research activity. research enterprise. Lawrence H. Cox, executive director of the Board, Some Committee members privately noted that was on hand to get the Committee's input on various most of the members of the Committee are senior aspects of the report. The Committee also considered researchers supported on regular NSF grants, so their several ways in which it could assist in the widespread misgivings about the idea may not reflect the views dissemination and use of the report, to insure that of the broader mathematical community; after all, mathematics departments across the country can use only about 1500 investigators are supported by the the report effectively in arguing for increased resources NSF, compared to the AMS membership of over from their administrations. 20,000. Nonetheless, on the whole, the Committee did support the idea and voted to recommend that the AMS put together a draft proposal in time for the Allyn Jackson next Committee meeting. Staff Writer The Collected Papers of /R. H. BING/ Sukhjit Singh, Steve Armentrout, Robert J. Daverman, Editors A powerful mathematician and a great historical background on Bing's life and 1980 Mathematics Subject Classifications: problem solver, R. H. Bing laid the achievements. 57, 54, 26 foundation for a number of areas of ISBN 0-8218-0117-1, LC 88-14445 2 volumes, 1680 pages (hardcover), July topology. Many of his papers have This collection will appeal to mathematicians in all areas, and 1988 continued to serve as a source of major List price $162, Institutional member $130 , theoretical developments and concrete especially those in topology, as well as Individual member $97 applications in recent years. One students, historians, and educators in the To order, please specify COLBING/NA outstanding example was Michael H. mathematical sciences, for it provides Freedman's use of Bing's Shrinking a complete historical summary of the Criterion to solve the four-dimensional mathematical events in the life of the man and the mathematician, R. H. Bing. All prices subject to change. Shipment Poincare Conjecture. will be made by surface. For air deliv Contents: ery add, 1st book $5, each additional This two-volume set brings together I. R. H. Bing: An introduction; An editorial book $3, maximum $100. Prepayment over one hundred of Bing's research, preface; R. H. Bing; A study of his life, required. Order from American Mathe expository, and miscellaneous papers. by S. Singh; A chronology of R. H. Bing; matical Society, P.O. Box 1571, Annex These works range over a great variety of Ph.D. students of R. H. Bing; R. H. Bing; Station, Providence, RI 02901-1571, or topics in topology, including the topology October 20, 1914-April 28, 1986, by R. D. call toll free 800-321-4AMS to charge with VISA or MasterCard. of manifolds, decomposition spaces, Anderson and C. E. Burgess; Abstracts continua, metrization, general topology, by R. H. Bing; II. Papers of R. H. Bing; and geometric topology. In addition, III. Classifications of works of R. H. Bing; there are a number of papers in the Publications of R. H. Bing: Classified by the areas of convex functions, linearity, and year; Publications of R. H. Bing: Classified conformal varieties. The introductory by subject matter; Works not included in section in the first volume provides these volumes; Permissions. NOVEMBER 1989, VOLUME 36, NUMBER 9 1213 Washington Outlook bit more. As it happens, the Goddard Space Flight Center is This month's column is written by Hans J. Oser, who located in Maryland. is a consultant to the Office of Governmental and Pub Another big-ticket item is also on the way to congressional lic Affairs of the Joint Policy Board for Mathematics in approval. The superconducting supercollider (SSC) came out Washington, D.C. of the Senate-House conference committee with $225 mil lion, just $25 million less than what the administration had NSF Budget for FY 1990 asked for. $90 million is intended for continued research and development, the remainder will be used for final stud As this column is being written, the Senate Appropria ies on the Waxahachie site in Texas and the procurement of tions Committee has just voted out an appropriations bill for "long-lead" items such as tooling and power transformers. the HUD-Independent Agencies that differs from the House Senator Mark Hatfield (R-OR) recently spoke at a retreat bill passed last summer. The final word will come from a of senior staff of the National Research Council. With a few Senate-House conference expected to take place later this bold strokes he characterized the budget climate by compar month. This is where things stand right now for NSF: ing the changes over a ten-year period from 1980 to 1990. NSF Request House Senate Entitlement programs, now at $550 billion, grew 80% in con (in million dollars) stant dollars; Defense, now $300 billion, grew by 69%; inter Research 1,803 1,715 1,685 est payments on the national debt have risen 189% to $180 U.S. Antarctic Pgm. 156 74 156 billion, while everything else in the budget declined by 33% Facility Upgrade 0 0 20 to $180 billion. Since the science budget is in that "all others" Science Education 190 210 200 category, it is heartening to note that NSF was able to grow Total 2,149 1,999 2,061 from $912 million to approximately $2 billion, or roughly 39% in constant dollars. But these figures illustrate that sci The facility upgrade is a disputed item between Congress ence has to fight for a share of the most embattled part, that and the NSF, which did not ask for the money in its 1990 15% slice of the federal budget pie that suffered the most pre budget request. NSF's priority was for supporting people be cipitous decline in the last ten years. That fact must be kept fore buildings, a strategy favored by most scientists. The in mind when discussing federal science policy (or the lack House agreed with the NSF but the Senate bowed to pressure thereof). We could have done a lot worse if science had not from some universities and put in $20 million to upgrade re had its stout defenders in the federal appropriations process. search facilities. The way things stand right now, the Senate House conference will not take place until the second week in October. If the past is any guidance, the conference com High-Performance Computing mittee will most likely discover again the arithmetic mean as the appropriate formula to arrive at a compromise fig A rare concurrence has developed between the Con ure for the NSF budget. This would work out to an overall gress and those technical agencies of the executive branch increase of 9% in 1990 ( 6% for the research part, 17% for that are covered by the FCCSET umbrella. That acronym science education). The administration had proposed a 14% stands for Federal Coordinating Council for Science, Engi increase to implement the five-year budget doubling plan for neering and Technology. These agencies have been working NSF. Congress has now rejected this request for the third hard for the past 18 months to develop a program plan for year in a row. Sympathy for NSF is high in the authoriz cooperative research and development in the area of high ing committees of both houses, but they don't control the performance computing. money. Senator Barbara Mikulski (D-MD), chair of the sub In one of his first public acts as the new Science and committee responsible for the appropriations of HUD and Technology Adviser to the President, D. Allan Bromley re the Independent Agencies, was able to come up with $200 leased on 8 September a report entitled "Federal High Per million more than NASA had requested for the Space Sta formance Computing Program". This report is the culmi tion, but had only regrets for not being able to get NSF a nation of an 18-month effort by the FCCSET Committee 1214 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Washington Outlook on Computer Research and Applications. It sets out a five would go a long way to reap some of the benefits that should year program plan to make supercomputers available to a be expected from having invested over 40 billion dollars in broad community of users in academia, industry and gov our satellite programs over the past 20 years. ernment. INTERNET, which is managed by NSF, is a vast The House Subcommittee on Science, Research, and Tech collection of smaller networks. It currently lacks both the nology held further hearings on high-performance computing necessary bandwidth and the capacity to grow. Based on an on 3 October. D. Allan Bromley, the President's Science and earlier FCCSET report of November 1987, the new program Technology Adviser, testified for the first time since his Sen plan recommends that in order to maintain and extend U.S. ate confirmation hearings in July. With his strong statements leadership in high-performance computing, and to maintain he convinced the committee that he would be a very effective U.S. sources of production as well as to support U.S. compet spokesman in defending the FCCSET plan within the admin itiveness, a multidisciplinary effort should be undertaken in istration. (It's a pleasure not to have another cheerleader for these four areas: ( 1) High performance computing systems, SDI, the chairman said). Bromley refused to give any dol (2) Advanced software technology and algorithms, (3) ANa lar amounts until the President submits his 1991 budget to tional Research and Education Network, (4) Basic research Congress in January. and human resources. The program should be based on close cooperation be tween industry, government, and academia, the report states. Appointments in the FCCSET recommends that the present level of federal sup Department of Education port, now about $500 million, should approximately double within the next five years. Things are finally moving at the Department of Education, Agreeing with FCCSET that the U.S. must maintain its maybe even a little too fast. Secretary Lauro Cavazos has leadership in high performance computing, the authorizing nominated Leonard L. Haynes, III, to be assistant secretary committees in the House and Senate that deal with science for post-secondary education. Haynes is the first black to and technology introduced legislation in the 101 st Congress be appointed to a high post in the Education Department. under the title "High Performance Computer Technology Haynes comes from Louisiana where he was assistant super Act of 1989". Doug Walgren (D-PA), chair of the House intendent for academic programs in the state's department Subcommittee on Science, Research and Technology, held of education. It is expected that Leonard Childers will be hearings in June that produced a phalanx of supportive wit deputy assistant secretary to Haynes. nesses for this legislation. The President also sent to the Senate the nomination of On September 15, his counterpart in the Senate, Albert Christopher T. Cross for the position of assistant secretary of Gore (D-TN), who chairs the Subcommittee on Science, Tech education for educational research and improvement. Cross nology and Space, held hearings on S1067 and again assem is a former Republican staff director of the House Committee bled a very impressive list of witnesses who testified in favor on Education and Labor. In his new role he will be super of creating a high-performance network linking the nation's vising the department's Office of Educational Research and supercomputers to assure access for large numbers of users Improvement. in academia, industry and government. This broadband net Newsweek magazine reports on .2 October that Secre work would be called the National Research and Education tary Cavazos may be out of office before the end of the Network (NREN). Both the FCCSET plan and the congres year. Cavazos is considered by many a do-nothing educa sional bill call for adequate support to drive software and tion secretary. "Imagine what Bennett would have done with algorithmic developments together with adequate standards this [Charlottesville] summit?'', the magazine asks. Well, they and protocols to ensure the broadest access with a minimum did not ask Bennett, but he had a succinct comment any of inconvenience. Senator Larry Pressler (R-SD), whose state way: "Pap". The White House was not amused, and Marlin holds NASA's magnetic tape library, said at the hearing that Fitzwater reprimanded him publicly. As for Cavazos' suc 95% of all the Landsat images have never been seen by a hu cessor, two names are being mentioned: Tom Kean, outgo man eye ("never fired a neuron", as Senator Gore put it), but ing governor of New Jersey, and former Tennessee governor he believes that a broadband network capable of transmit Lamar Alexander. Also mentioned: the current undersecre ting these pictures to the laboratories of research scientists tary for education, John Theodore Sanders. NOVEMBER 1989, VOLUME 36, NUMBER 9 1215 News and Announcements Sunley Receives sition as Deputy Director. In 1986, derrepresentation of women in the Presidential Rank Award she received the first NSF Direc physical sciences, engineering, and tor's Award for Equal Opportunity mathematics. Judith S. Sunley, Director of the Achievement. The fund sets aside $3 million Division of Mathematical Sciences According to an internal NSF for each of 14 educational institu (DMS) at the National Science Foun document on Sunley's nomination tions designated by the late Clare dation (NSF), has received the Presi for the award, her leadership has Boothe Luce, whose bequest created dential Rank Award, one of the high been characterized by a flexible ap the fund to encourage women in est awards at the Senior Executive proach to dealing with infrastruc fields where there have traditionally Service level of government. Sunley's ture concerns within the mathemat been obstacles to their advancement. rank of Meritorious Executive, which ical community, uniformly excellent The awards range from $225,000 to carries a stipend of $10,000, recog management of the Division, excep $430,000 over a five-year period. nizes sustained accomplishment dur tional success in recruiting and train One of the program's professor ing her executive career. Awards are ing high-quality program staff, and ship awards went to VANESSA JoB, made to executives throughout the a strong commitment to equal op who has been named Clare Boothe government, but this is the first time portunity. The document ends by Luce Professor of Mathematics and such an award has been conferred on stating, "Her understanding of the Computer Science at Marymount Uni a member of DMS staff. mathematical sciences community, versity in Virginia. Job has done re her commitment to the goals of the search in the area of polyadic codes NSF, and her ability to meld these and is especially interested in coding into a forceful plan for action make theory, combinatorics, supercomput her an outstanding asset to the Foun ing, and complexity theory. She will dation." be the first female appointment to Sunley originally came to the Marymount's computer science de Foundation in 1980 as a Program Di partment. rector in Algebra and Number The Each institution receiving an ory. She received her Ph.D. from the award will use the income on the University of Maryland and was on funds to support the advancement the mathematics faculty of American of women in science and engineer University for lO years. ing. The designated institutions are: Georgetown University, University Luce Fund of Notre Dame, Boston University, for Women Scientists Colby College, Creighton University, Fordham University, Marymount The Henry Luce Foundation has an University (VA), Mount Holyoke Col Judith S. Sunley nounced the establishment of the lege, Mundelein College, Santa Clara Sunley has made many contribu Clare Boothe Luce Fund, a $70 University, St. John's University, Se tions to the management of NSF and million endowment that will pro ton Hall University, Trinity College has shown outstanding leadership of vide professorships, fellowships, and (DC), and Villanova School. In addi the DMS both in her current position scholarships to women scientists in tion to the professorships, the Clare as Director, which she has held since higher education. The fund is in Boothe Luce Fund has made possible 1987, as well as in her previous po- tended to respond to the historic un- fellowships in research at the Insti- 1216 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements tute for Advanced Study in Prince Council will sponsor a series of six The 1990 Annual Meeting of the ton. regional workshops this fall and a AAAS will be held February 15- The remainder of the income national convocation in the spring 20, 1990, in New Orleans. Section from the fund will be distributed in as part of its Making Mathematics A of AAAS, which is concerned specific grants for professorships, fel Work for Minorities project. Funded with mathematics, is sponsoring sev lowships, and scholarships for women by the Exxon Educational Founda eral outstanding expository talks by in science and engineering at other tion, the project is intended to help prominent mathematicians. institutions. Under the terms of reverse long-standing patterns of un Details about sessions on math Luce's will, the selection of recipi derachievement and underrepresen ematics at the 1990 AAAS meeting ents of awards is made through a six tation of minorities in the mathe can be found in the section on Meet member selection committee, three matical sciences. ings and Conferences of the AMS in members of which are named by the The workshops will seek to raise this issue of Notices. Henry Luce Foundation and three awareness of the problems, reach Section A knows that the increas by the Heritage Foundation. Only consensus on the directions of change ing representation and participation institutions, not individuals, will be in the teaching of mathematics, and of mathematicians at AAAS Annual invited by the Luce Foundation to point toward solutions that national, Meetings are an important means for submit applications for these awards. state, and local leaders can pur deepening public awareness and ap sue. The first workshop was held in preciation of the manifold ways that Nominations for the Atlanta in October. The remaining mathematics contributes to science Alice T. Schafer workshops will be held in Chicago, and society. The Section A Commit Mathematics Prize November 3-5; Seattle, November 9- tee needs and welcomes suggestions 10; Princeton, November 17-18; San for symposia topics and individuals In January 1989 the Association for Antonio, November 30-December 2; who might be able to organize them. Women in Mathematics established and Irvine, January 5-6, 1990. Please send, and encourage your col the Alice T. Schafer Mathematics The national convocation will be leagues to send symposia proposals Prize of $1000 to be awarded an held May 4-5, 1990 at the National for 1991 and future AAAS meetings nually, beginning in 1990, to an un Academy of Sciences in Washington, to Warren Page, Secretary of Section dergraduate woman for excellence in DC. The purpose of the convocation A, New York City Technical College, mathematics. All members of the will be to bring national attention CUNY, 300 Jay Street, Brooklyn, NY mathematical community are invited to exemplary programs for minori 11201. to submit nominations for the Prize, ties, highlight relevant research find The Section A Committee will to be awarded in April 1990. The ings, define national needs, produce meet in New Orleans from 4:00p.m. nominee may be at any level in her a national plan of action, and focus to 6:00 p.m. on February 15, in Marl undergrduate career. The letter of the imagination and commitment of borough BRoom of the New Orleans nomination should include, but not leaders in American education. Hilton. The committee meeting is be limited to, an evaluation of the For more information, contact open to all who are interested in ac nominee on the following criteria: Beverly Anderson, Project Director, tivities of the mathematical sciences quality of performance in mathe Making Mathematics Work for Mi within the AAAS. matics, exhibition of real interest in norities, Mathematical Sciences Ed mathematics, ability for independent ucation Board, 818 Connecticut Ave, Magazine for Math work, performance in mathematical NW, Suite 500, Washington, DC and Science Students competitions at the local or national 20006. level if any. Supporting materials With funding from the National should be enclosed with the nomi Science Foundation (NSF), the Na Call for Topics nations. Nominations must be post tional Science Teachers Association Section A (Mathematics) marked no later than March 1, 1990 will soon publish Quantum, a maga of the AAAS and sent to Patricia Cross, Executive zine for high school mathematics and Director, AWM, Box 178 Wellesley science students. College, Wellesley, MA 02181. The American Association for the Quantum will be patterned af Advancement of Science (AAAS) is a ter the successful Soviet magazine Regional Meetings broadly based organization devoted Kvant, which contains physics and Focus on Minorities to promoting research and educa mathematics articles and numerous tion in all areas of science. Re problem-solving activities. Articles The Mathematical Sciences Educa cently the Society has begun efforts from Kvant will be translated for tion Board of the National Research to strengthen its ties with AAAS. use in Quantum. NOVEMBER 1989, VOLUME 36, NUMBER 9 1217 News and Announcements Two editors-in-chief, one for math Edward E. David, Jr., EED, Inc., ence is open to all who are interested ematics and one for physics, together Mathematics in a World of Mega in these issues. with an advisory board of science Projects; Can it Survive?; Peter D. The conference has been planned and mathematics teachers and pro Lax, Courant Institute of Mathemat by an organizing committee headed fessors, will determine the content ical Sciences, Today's World and by Yervant Terzian, Chairman, De of Quantum, review all articles, and Mathematics; Jacques-Louis Lions, partment of Astronomy, Cornell Uni solicit articles from U.S. scientists Centre National d'Etudes Spatiales versity. Other members of the orga and mathematicians to supplement College de France, Pure and Ap nizing committee include: Wilson V. the articles from Kvant. William P. plied Mathematics: Examples; Ivars Kone, Associate Director for Admin Thurston of Princeton University has Peterson, Science News, The Math istration, Mathematical Sciences In accepted the position as mathematics ematical Tourist; Shmuel Winograd, stitute, Cornell University; Simon A. editor. IBM, Mathematics and Computers; Levin, Director, Center for Environ Two premiere issues will be pub Roger W. Brockett, Harvard Uni mental Research, Cornell University; lished in the coming year, one this versity, Mathematics and Intelligent Anil Nerode, Director, Mathemati month and another in April 1990. Systems; Mary F. Wheeler, Rice Uni cal Sciences Institute, Cornell Uni Sales of subscriptions and advertis versity, Relationships between Indus versity; Lars B. Wahlbin, Associate ing space, as well as corporate do try and Academics; Walter W. Hollis, Director for Research, Mathematical nations, will help support the cost Deputy Undersecretary of the Army Sciences Institute, Cornell Univer of producing Quantum. The NSF is for Operations Research, Mathemat sity; and Daniel Willard, Office of contributing $366,000, and non-NSF ics in National Security; Michael the Deputy Undersecretary of the funding totals $508,500. E. Fisher, University of Maryland, Army for Operations Reseach. Mathematical Rigor in Physics: To The symposium will be held at the News from the What End? Statler Hotel on the Cornell Univer Mathematical Sciences Institute John J. Hopfield, California In sity campus. For a registration packet Cornell University stitute of Technology, will deliver and general information about the a university-wide lecture on Friday conference, contact conference sec The Mathematical Sciences Institute evening, March 30, on Mathematics retary Diana Drake at the Math (MSI) is hosting a major confer in Neural Sciences. ematical Sciences Institute, Cornell ence on the state of mathematics in University, Ithaca, NY 14853-2602, the modern world. Titled "Modern The conference will conclude with 607-255-7740. Perspectives of Mathematics: Mathe a panel discussion designed to pro matics as a Consumer Good, Mathe vide commentary on and to sum News from the matics in Academia," the conference marize the previous presentations. Center for Discrete Mathematics will bring together influential math Chaired by Werner C. Rheinboldt, and Theoretical Computer Science ematics consumers, educators, and University of Pittsburgh, the panel Rutgers University researchers for a 3-day examination also will include George Metakides, of the nation's use and development President, European Strategic Pro As part of its program, the Center of mathematics resources. (Note: the gram for Research and Development for Discrete Mathematics and Theo conference has been previously an in Information Technology; Cath retical Computer Science (DIMACS) nounced under the title "Mathemat leen S. Morawetz, Courant Institute will sponsor a variety of activities ics as Art, Mathematics as a Con of Mathematical Sciences; Richard each year which revolve around a sumer Good.") S. Stepleman, Exxon Research and special theme. The special theme for Planned for March 29-31, 1990, Engineering Company; Rose Teukol the academic year 1989-1990 is dis at Cornell University, Ithaca, NY, the sky, Ithaca High School; and Daniel crete and computational geometry. conference will feature 11 lectures by Willard, Office of the Deputy Under A year-long series of research pro leaders in business and industry, gov secretary of the Army for Operations grams devoted to this theme has ernment, and academia. Malvin H. Research. been organized. These programs are Kalos, Director of the Cornell Uni Within the context of their in concerned with such topics as geo versity Center for Theory and Simu dividual topics, invited speakers and metric computation, geometric com lation in Science and Engineering will panelists are expected to address how plexity, probabilistic methods in dis deliver the keynote address, Impact to develop mathematics education crete and computational geometry, of Computers on Mathematics. and research in ways that will en arrangements and their realizations, Other invited speakers and their courage the interplay of mathematics and polytopes and convex sets. topics in order of their expected ap and its applications in business, in As part of the special year, the fol pearance at the conference include: dustry, and government. The confer- lowing workshops have been sched- 1218 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements uled. More information about these Courant Institute of the Mathemati tage of the emergence of the city of workshops can be obtained from the cal Sciences; Micha Perles, The He.:. San Diego as a major mathematical organizer whose name appears or brew University of Jerusalem; Ricky sciences community centered around from the DIMACS office. Pollack, Courant Institute of the the University of California at San Mathematical Sciences. Diego (UCSD). Special Year Workshops: There are also several postdoc The Communications Research toral fellows who have research inter Division will change its name to Cen Oct. 16-20: Geometric Complexity, ests in this area. Furthermore, there ter for Communications Research - Organizer: Subhash Suri 201-829- will be a very large number of vis Princeton effective January 1, 1990. 4042, email: [email protected]; itors, from periods of a week to Both centers will be operated by Nov. 11-27, Dec. 1: Probabilistic several months, who will be partici the Institute for Defense Analyses Methods in Discrete and Compu pating in the activities of the special in support of the mission of NSA. tational Geometry, Organizer: Peter year. The Center for Communications Re Shor 201-582-4435, email: Further information about the search- La Jolla will eventually grow [email protected]; events of the special year in discrete to approximately 25 mathetmatical Jan. 8-12: Polytopes and Convex and computational geometry can be scientists; Melvin Sweet is the Acting Sets, Organizer: Jacob E. Goodman obtained from the organizer, Bernard Director. 219-690-6 7 37, email: Chazelle, 609-258-5030; email: The Institute for Defense Analy [email protected] .edu; [email protected] or from the ses' establishment of the Center for Mar. 19-23: Arrangements and their DIMACS office 201-932-5928. Communications Research- La Jolla Realizations, Organizer: William represents another facet of NSA's Steiger 201-932-2083, email: efforts to stimulate mathematical re [email protected]; A New Center for search and to increase its interac Apr. 16-20: Practical Issues in Geo Communications Research tion with the mathematical and sci metric Computation, Organizer: entific communities. Vice Admiral pending; The Institute for Defense Analy William Studeman, the Director of May 21-25: Algebraic Issues in Geo ses (IDA) and the National Secu NSA, has repeatedly stressed his con metric Computation, Organizer: rity Agency (NSA) have announced cerns about the health and vitality of pending. the establishment of a new Center mathematics in the United States. In In addition to the workshops, sev for Communications Research at La January he addressed the Joint Math eral weekly seminars on discrete and Jolla, California modeled after the ematics Meetings in Phoenix on this computational geometry are being Communications Research Division subject (see Notices, March 1989, run. of IDA in Princeton, New Jersey. pages 237-240). Since assuming his During the special year, we will The new center will seek to foster duties, he has increased the Agency's have five visitors for the academic stronger technical interactions with grants program in support of aca year September to June. They are: the West Coast academic and in demic research and has urged Agency Jacob E. Goodman, The City dustrial research community. By lo mathematicians to play a more active University of New York; Carl Lee, cating the new Center in La Jolla, role in the national efforts to improve University of Kentucky; Janos Pach, NSA and IDA hope to take advan- mathematics education. NOVEMBER 1989, VOLUME 36, NUMBER 9 1219 Funding Information for the Mathematical Sciences Call for Proposals pilot projects in the areas of differ education or research of the fellow's for Calculus Renewal ential equations and linear algebra, choice. The deadline for submission as they pertain to the first two years of applications is January 12, 1990. The National Science Foundation has of college calculus. The deadline for For more information and a pro for the past two years sponsored a proposals is February 2, 1990. gram announcement, contact: Fel program to support projects aimed at The program announcement and lowship Office, GR420A, National revamping the college calculus cur more information are available from Research Council, 2101 Constitu riculum. Designed to stimulate the John S. Bradley, USEME Room 639, tion Avenue, NW, Washington, DC development of high-quality calculus National Science Foundation, 1800 20418. curricula, the program is managed by G Street, NW, Washington, DC 20550; the Division of Undergraduate Sci telephone 202-357-7051; electronic Grants for Women Mathematicians ence, Engineering, and Mathematics mail [email protected] (Internet) Education with the cooperation of or jbradley@nsf (Bitnet). The National Science Foundation the Division of Mathematical Sci (NSF) sponsors a number of activ ences. NRC-Ford Foundation ities to provide support for women Computer technology, more re Postdocs for Minorities researchers in all science and engi alistic applications, development of neering disciplines. As a participant mathematical intuition, laboratory ex The National Research Council in these efforts, the NSF's Division periences, increased student involve (NRC) plans to award approximately of Mathematical Sciences (DMS) en ment in the learning process, and 25 Ford Foundation Postdoctoral Fel courages women mathematicians to concepts rather than manipulation lowships for Minorities. This pro apply to the Research Opportunites of formulas have been some of the gram supports individuals showing for Women (ROW) program. emphases of the projects funded in great promise of future achievement Three kinds of awards are avail the first two years ofthe program (see in academic research and scholarship able through ROW. Research Plan Notices, September 1989, page 854, in higher education. The one-year fel ning Grants are for women who have and November 1988,page 1361). The lowships are available in mathemat not previously served as principal calculus program sponsored several ics, as well as a variety of scientific, or co-principal investigators on in workshops and also provided start engineering, and humanities fields. dividual federal research awards or up funding for the UME TRENDS The program is open to Native whose research career has been in newsletter on undergraduate math American Indians and Alaskan N a terrupted for at least two of the last ematics education reform, a joint tives (Eskimo or Aleut), Black Ameri five years. These grants provide lim project of the AMS, the Mathemati cans, Mexican AmericansjChicanos, ited support to facilitate preliminary cal Association of America, and the Native Pacific Islanders (Microne studies and other activities related to Society for Industrial and Applied sian and Polynesian), and Puerto Ri a research project. Career Advance Mathematics. In addition, the last cans. Applicants must be U.S. citi ment Awards assist in developing the round of awards included a project zens, hold the Ph.D. or Sc.D. degree, careers of women researchers. These to disseminate descriptions and sum and be preparing for or engaged in awards are intended for women who maries of a host of calculus reform college or university teaching. have an established research career projects. Tenure of a fellowship provides in their current field or in a new For the next round of awards, for postdoctoral research experience one. Women who have had previous the NSF will also consider funding at a not-for-profit institution of higher research support are eligible for the 1220 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Funding Information program, but this is not required. limited, but the DMS would nonethe Postdoctoral Fellowships The deadline for proposals for these less like to encourage more women in Spain two grants is January 15, 1990. who are qualified to apply. Research Initiation Awards are Peter W. Arzberger, the DMS pro The Council for International Ex one-time grants designed to provide gram officer in charge of the ROW change of Scholars (CIES) has an opportunities to women mathemati program, would be happy to provide nounced the opening of its compe cians to become actively engaged in program announcements and more tition for Quincentenary Postodoc research as independent investiga information. He can be reached at: toral Fellowships in Spain for U.S tors. Like the planning grants, these Division of Mathematical Sciences, researchers. Six to eight grants will awards are open to those women Room 339, National Science Foun be available for individual research mathematicians who have not been dation, 1800 G Street, NW, Washing in Spain during the 1990-1991 aca principal or co-principal investigators ton, DC 20550; telephone 202-357- demic year. on research grants before. The pro 3693; email [email protected] Applications are encouraged in cedure for applying for the Research on Internet (or use @nsf.arpa for several areas, including basic sci Initiation Award is the same as for a CSNET and @nsf for Bitnet). ences, logic, and mathematics. Pre regular research grant; checking a box ferred projects are those that pro on the proposal cover sheet indicates New Initiative at the Navy mote greater knowledge of the devel that the proposal should be consid opment of the U.S. and Spain during ered for funding under the ROW The Mathematical Sciences Division the last five centuries. of the Office of Naval Research has program. As with all research pro The basic eligibility requirements there announced a new Accelerated Re posals submitted to the DMS, for these awards are U.S. citizen on Random Fields is no deadline, but it's best to get search Initiative ship, the doctorate or its equivalent, Modeling. them in soon after the start of the for Oceanographic and sufficient competence in oral and The goal of this initiative is to fiscal year, that is, after October 1. written Spanish for the proposed re develop techniques for probabilis The Research Planning Grants search. Candidates will be selected Awards tic modeling and statistical infer and the Career Advancement on the basis of their aptitute for random functions have limits on both the size of the ence for acausal and experience in carrying through a of space which are also causally grant and on the amount of over major project of research and must particular interest head that the applicant's institution time-varying. Of show strong evidence of the need to writ is the study of the partial differential can charge. At the time of this be in Spain. ing, some of the program guidelines equations of physical oceanography, were being changed, so more precise in continuous or discretized form, Award periods are from two to information was not available. How in the presence of stochastic excita ten months during the period August ever, a new program announcement tion, stochastic boundary conditions, 1, 1990 through July 31, 1991. Ben should be available by the time this and/or observation noise. The issue efits include a monthly maintenance issue of Notices reaches its readers. of sparse and irregularly observed allowance of approximately $1800 to In addition, proposals for the Re data sets is especially relevant for the $2550, depending on the number of search Planning Grants and the Ca ocean modeling and prediction prob accompanying dependents, as well as reer Advancement Awards are han lem. New mathematical approaches funds for travel, insurance, and other dled differently from regular research are currently being sought for the miscellaneous items. grants, as they are reviewed by a initiative. The application deadline is Jan panel, rather than through mail re Proposals for the period begin uary 2, 1990. For information and view. The panel assessment assures ning October 1, 1990 are due on applications, contact: Program Of that these proposals compete only or before April 1, 1990. Proposals ficer, Spain Quincentenary Fellow among themselves. The format for should be sent to: Julia Abrahams, ships, CIES, 3400 International Drive, proposals also differs considerably Code 1111, Room 607, Mathemati NW, Washington, DC 20008-3097; from that for regular research grants, cal Sciences Division, Office of Naval telephone 202-686-6243. Requests so it may be wise to consult with Research, 800 North Quincy Street, for applications must be received by DMS staff before applying. Funds are Arlington, VA 22217-5000. December 15, 1989. NOVEMBER 1989, VOLUME 36, NUMBER 9 1221 Now Available ... Now you can access Mathematical Reviews Fixed Cost (MR) and Current Mathematical Publications (CMP) on CD-ROM (Compact Disc-Read Only The MathSci Disc annual lease fee includes Memory). The CD, called MathSci Disc, com the use of MathSci Disc for 12 months, the bines the searching features of online MathSci SilverPlatter search software for the IBM or the with the browsing ease of printed MR. 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MR Subscriber or Additional Lease 1,820 Individuals* 379 Easy-to-Operate *Individuals at institutions leasing MathSci Disc can order a copy for personal use at a 90% discount; add MathSci Disc is available for the IBM PC $35 for a Silver Platter search manual. and for the Macintosh. SilverPlatter's user friendly software with help screens and ~------menus makes MathSci Disc easy to use. Information Words and phrases in the text of the reviews and abstracts are searchable with an adja For more information on MathSci Disc or to cency operator. Records can be downloaded receive a copy of the lease agreement, from the CD to the hard disk for editing or for please contact Services Department processing with TEX software into typeset Database American Mathematical Society mathematics. form with P. 0. Box 6248 Providence, RI 02940 or call (800) 321-4AMS in the continental U.S. or (401) 272-9500. Telex: 797192; FAX: 401-331-3842. E-mail on Internet: TTK®MATH.AMS.COM SM - MathSci is a service mark of the American Mathematical Society ®- SilverPlatter is a registered trademark of SilverPlatter Information, Inc. Meetings and Conferences of the AMS FUTURE MEETINGS Los Angeles, California November 18-19 1225 Louisville, Kentucky January 17-20 1234 Invited Speakers and Special Sessions 1238 FUTURE CONFERENCES Joint Summer Research Conferences in the Mathematical Sciences University of Massachusetts, Amherst, June 7-July 4 1242 OTHER EVENTS COSPONSORED BY THE SOCIETY Section A (Mathematics) Sessions at the AAAS meeting 1244 NOVEMBER 1989, VOLUME 36, NUMBER 9 1223 JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY The Journal of the American Mathematical Society is a quarterly journal containing research articles of the highest quality in all areas of pure and applied mathematics. Editors Michael Artin H. Blaine Lawson, Jr. Richard Melrose Wilfried Schmid Robert E. Tarjan ISSN 0894-0347 Quarterly, Volume 3, 1990 Code 90JAMS/NA 1990 Subscription Prices: List $116*, Institutional Member $93*, Individual Member $70* * Add for postage: Surface delivery to destinations outside the U. S. and India -- $8; to India - $18. Expedited delivery to destinations in North America $12; elsewhere-- $25. Note: Subscriptions to AMS journals are sold only on a calender year basis (January-December); split year and multiple year subscription orders are not accepted. Subscription orders received from nonmember institutions and organizations after January 1 of the subscription year will be sold at list price plus a 10% late charge (rounded); the maximum late charge for any subscrip tion is $200. Subscription cancellations from nonmembers will not be accepted after March 1 of the subscription year. Cancella tion refunds are computed by deducting an $8 cancellation fee, and the price of each issue already shipped, from the price paid. To order: Prepayment required in U. S. funds. Mail to AMS, Annex Station, P. 0. Box 1571, Providence, Rhode Island 02901-1571 U.S.A. or call800-321-4AMS in the continental U.S. to use VISA or MasterCard. Los Angeles, California University of California, Los Angeles November 18-19 Program The eight-hundred-and-fifty-third meeting of the Ameri McGibbon, Mamoru Mimura, James E. Searl, Michael can Mathematical Society will be held at the University Slack, and Frank Williams. of California, Los Angeles on Saturday, November 18, Quadratic forms and simple algebras, DAVID J. SALT and Sunday, November 19, 1989. This meeting will be MAN, University of Texas, Austin, and MuRRAY M. held in conjunction with a meeting of the Southern ScHACHER, University of California, Los Angeles. Frank California Section of the Mathematical Association of Demeyer, Richard Elman, Timothy J. Ford, Mike Fried, America. Darrell Haile, Bill Jacob, T.-Y. Lam, David B. Leep, Victoria Powers, David Saltman, and A. R. Wadsworth. Invited Addresses Harmonic analysis, THOMAS H. WoLFF. Josefina Al varez, Christopher Bishop, Stewart Gleason, Peter By invitation of the Far Western Section Program Com Holden, Robert Kaufman, Margaret A. M. Murray, mittee, there will be four invited one-hour addresses. Donald Sarason, and J. Michael Wilson. The speakers, their affiliations, the titles of their talks, and scheduled times of presentation are: Contributed Papers BURTON I. FEIN, Oregon State University, Galois groups and rational division algebras, 10:00 a.m. Sunday. There will also be sessions for contributed ten-minute STEPHEN M. GERSTEN, University of Utah, Salt Lake papers. City, Automatic and hyperbolic groups, 10:00 a.m. Satur day. MAA Program NICOLAS SPALTENSTEIN, University of Oregon, Eu gene, Nilpotent orbits and the Weyl group, 2:00 p.m. The Southern California Section of MAA will meet on Sunday. Saturday, November 18. The MAA Business Meeting will THOMAS H. WOLFF, California Institute of Technol begin at 8:00 a.m. MAA invited speakers are THOMAS ogy, Recent work in potential theory, 3:00p.m. Saturday. M. LIGGETT, University of California, Los Angeles, In teracting particle systems: Equilibria and rates of conver gence, 11:00 a.m.; and GUNNAR E. CARLSSON, Princeton Special Sessions University and MSRI, The topology of some spaces of By invitation of the same committee, there will be four functions, 4:00 p.m. The noon luncheon speaker is URI special sessions of selected twenty-minute papers. The TREISMANN, Director, Charles A. Dana Center for Math topics, the names and affiliations of the organizers, and ematics and Science, University of California, Berkeley, the list of speakers, are as follows: Changing demographics and the future of our profession. Geometric methods in combinatorial group theory, A workshop on Calculus and the computer will be ROGER C. ALPERIN, San Jose State University, and presented at 8:30 a.m. by WILLIAM A. HARRIS, JR., KAREN VOGTMANN, Cornell University. Juan M. Alonso, University of Southern California; RoNALD J. MIECH, Martin R. Bridson, Robert Brooks, M. M. Cohen, Daryl University of California, Los Angeles; and AL SHENK, Cooper, Mark Feighn, Benjamin Fine, Ross Geoghegan, University of California, San Diego. Robert H. Gilman, Renfang Jiang, Frank Rimlinger, There will be a special session titled Equity issues and Paul E. Schupp, M. Shapiro, John R. Stallings, and Kay minority access to mathematics from 1:30 p.m. to 2:50 Tatsuoka. p.m. The moderator is PHILIP DARO, Executive Director, Algebraic topology, JAMES P. LIN, University of Cali California Mathematics Project and American Mathe fornia, San Diego. James P. Lin, John McCleary, C. A. matics Project, and the discussant is URI TREISMANN. NOVEMBER 1989, VOLUME 36, NUMBER 9 1225 Meetings 0 INFORMATION 0 ENTRANCE * EMERGENCY REPORTING SYSTEM(ERS)BOOTHS • ACCESSIBLE TO N THE DISABLED 1226 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings The speakers are RICHARD CERCI, Morningside High Queen bed $71 School; PHILIP C. CuRTIS, University of California, Los Two twin beds $71 Angeles; DAVID MoRIN, East Los Angeles Community Parlor room (sofa sleeper and kitchenette) $66 College; and RAY C. ScHIFLETT, California State Uni Two room suite (kitchenette, queen versity, Pomona. and sofa sleeper) $99 Registration Food Service The meeting registration desk will be located in the Faculty Information will be provided at the meeting registration desk distance. Lounge in the Mathematical Sciences Building. The desk will regarding availability of food service within walking be open from 8:00 a.m. until 4:00 p.m. on Saturday, and from 8:30 a.m. to noon on Sunday. The registration fees are $30 Travel for members of the AMS, $45 for nonmembers, and $10 for is located approximately 12miles north of students and unemployed mathematicians. There is a special The UCLA campus International Airport (LAX), which is served by one-day fee of $15 for MAA members on Saturday only. Los Angeles all of the major airlines. The taxi fare from the airport to the UCLA campus is approximately $20 plus tip. There is no extra Petition Table charge for additional passengers going to the same destination. A petition table will be set up in the registration area. Addi The Super Shuttle, which provides door-to-door service, can be tional information about petition tables can be found in a box summoned by dialing number 35 from the courtesy phones in in the Louisville meeting announcement in the October issue of the baggage claim area. The bus should arrive within 15 min Notices. utes; the fare is $12 for one passenger plus tip. For informa tion or advance reservations call 213-777-8000. From courtesy Accommodations phones dial number 35. The most economical transportation is via public bus from Blocks of rooms were held until until October 17 at the follow the LAX Transit Center at 96th Street and Vicksburg Avenue ing locations. Participants should make their own arrangements (1/4 mile northeast of the main airport exit). To reach the Tran directly with the hotel of their choice and be sure to mention sit Center from the terminal, wait next to the lower level road the meetings at UCLA. Note that the rates do not include appli way under a SHUTTLE BUS sign, which lists buses as A, B, cable taxes. The Claremont and Royal Palace hotels are located C, etc. Board the free C or Lot C bus and exit the airport, in Westwood Village within walking distance, adjacent to the getting off at its first stop outside of the airport just after it south side of campus. The UCLA Guest House is on the cam enters Parking Lot C. Walk 100 yards east to the LAX Tran pus. Participants must refer to the AMS-MAA meetings when sit Center. The fastest and most frequent service to UCLA is making reservations at the following hotels to obtain the rates by the RTD #560 bus, which takes approximately 30 minutes that are listed. to reach the campus and costs $1.20. (NOTE: Exact change in service to UCLA Claremont Hotel coins is required; no bills accepted!) Direct on the Culver City #6 1044 Tiverton Avenue, Westwood 90024 is also available Monday through Friday fare is 50 cents. Telephone: 213-208-5957 bus, which takes approximately 50 minutes; the All buses approach the campus from the south, up Westwood Single $35.50 Double $37.50 Boulevard, turning right (east) at LeConte Avenue. Exit the bus Twins $41.50 at the comer and walk north up Westwood to the Mathemati cal Sciences Building (Boelter Hall, approximately 3/4 mile on Royal Palace Westwood the right, beyond parking structure #9.) 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NOVEMBER 1989, VOLUME 36, NUMBER 9 1227 Look what's new in Mathematical Surveys and Monographs The Mathematical Smveys and Monographs series is one you're already familiar with. It's been around since 1943, when The Problem of Momenta byJ. A. Shohat andJ. D. Tamarkin was pub lished. The series has grown over the years and includes important mathematical monographs that cover a broad spectrum of areas such as function theory, analysis, approximation theory, algebra, and topology. Each of the books is designed to give a survey of the subject and a brief introduction to its recent developments and unsolved problems. The editorial committee••• Victor W. Guillemin M. Susan Montgomery (Chairman) David Kinderlehrer ------...invites you to participate in the development of this classic series by • consulting them as reference books • using books in this series in your courses • recommending them to your library • submitting manuscripts for publication to begin a standing order to the Director of Publication at the AMS New and Recent Publications in Mathematical Surveys and Monographs Each new title is exceptional. All are the high quality mathematical publications you've grown to expect in the Mathematical Surveys and Monographs series. Yet the variety of topics and areas of mathematical interest make them perfect reference books or possible textbooks for graduate level courses. [J Represeutation theory IIDd harmonic IUlalyllis on [J Asymptotic behavior of dissipative systems by aemiaimple Ue groups, edited by PaulJ. Sally, Jr. Jack K. Hale, 1988, 198 pp. (LC 87-33495; ISBN 0-8218- and David A. Vogan, Jr., 1989, 350 pp. (ISBN 0-8218- 1527-X). List $58, Inst. mem. $46, Indiv. mem. $35, 1526-1). List $88, Inst. mem. $70, Indiv. mem. $53, Code SURV /25NA Code SURV /31NA [J NoetheriiiD rings 11Dd their applications, edited by [J The Markhoff 11Dd LagriiDge spectra by Thomas W. LanceW. Small, 1987, 118pp. (LC 87-14997; ISBN Cusick and Mary E. Flahive, 1989, 96 pp. (ISBN 0- 0-8218-1525-3). List $41, Inst. mem. $33, Indiv. mem. 8218-1531-8). List $42, Inst. mem. $34, Indiv. mem. $25, Code SURV /24NA $25,CodeSURV/30NA [J Introduction to various aspects of degree theory in [J Amenability by Alan L. T. Paterson, 1988, 416 pp. Banach spaces by E. H. Rothe, 1986, 254 pp. (LC 86- (ISBN 0-8218-1529-6). List $95, Inst. mem. $76, 8038; ISBN 0-8218-1522-9). List $66, Inst. mem. $53, Indiv. mem. $57, Code SURV/29NA Indiv. mem. $40, Code SURV/23NA [J Direct IIDd Inverse ecattering on the line by [J Noncommutative harmonic IIDalysis by Michael E. Taylor, Richard Beals, Percy Deift, and Carlos Tomei, 1988, 1986, 344 pp. (LC 86-10924; ISBN 0-8218-1523-7). List 209 pp. (LC 88-14487; ISBN 0-8218-1530-X). List $74, Inst. mem. $59, Indiv. mem. $44, Code SURV /22NA $57, Inst. mem. $46, lndiv. mem. $34, Code SURV/28NA [J The Bieberbach conjecture: Proceedings of the symposium on the occasion of the proof, edited by [J Basic hypergeometric series IUld applications by Nathan J. Fine, 1988, 144 pp. (LC 88-6235; ISBN 0-8218- Albert Baemstein, David Drasin, Peter Duren, and 1524-5). List $42, Inst. mem. $34, Indiv. mem. $25, Albert Marden, 1986; reprinted 1987, 260 pp. (LC 86-10843; Code SURV /27NA ISBN 0-8218-1521-0). List $50, Inst. mem. $40, Indiv mem. $30, Code SURV /21NA [J Operator theory 11Dd arithmetic In II"" by Hari Bercovici, [J Partially ordered abeliiiD groups with Interpolation 1988, 275 pp. (LC 88-10344; ISBN 0-8218-1528-8). List by Kenneth R. Goodearl, 1986, 358 pp. (LC 86-7876; $71, Inst. mem. $57, lndiv. mem. $43, Code SURV /26NA ISBN 0-8218-1520-2). List $74, Inst. mem. $59, Indiv. mem.$44,CodeSURV/20NA Standing orders are accepted for this and aey other series published by the Society. Proforma invoices are sent to standing order customers prior to the publication of each new volume. Shipment is made upon receipt of payment and publication. To begin a standing order, please contact the Customer Services Department of the AMS. PREPAYMENT REQUIRED. Order from the American Mathematical Society, P. 0. Box 1571, Annex Station, Providence, RI 02901-1571, or call800-321-4AMS from within the continental U.S. (401-272-9500, elsewhere) to use VISA or Master Card. Prices subject to change. Free shipment by surface; for optional air delivery, please add: first book $5, each additional $3, $100 maximum. For information on numbers 1-19, please refer to the AMS Catalogue of Publications. Program of the Sessions The time limit for each contributed paper in the sessions is ten minutes. In the special sessions, the time limit varies from session to session and within sessions. To maintain the schedule, time limits will be strictly enforced. Abstracts of papers presented in the sessions at this meeting will be found in the November 1989 issue of Abstracts of papers presented to the American Mathematical Society, ordered according to the numbers in parentheses following the listings below. For papers with more than one author, an asterisk follows the name of the author who plans to present the paper at the meeting. 9:30a.m. Automatic structure and graphs of groups. Saturday, November 18 (5) M. Shapiro, Mathematical Sciences Research Institute, Berkeley and Ohio State University, Columbus (853-20-15} MAA Business Meeting AMS Special Session on Quadratic 8:00 a.m.-8:30 a.m. Room 3400, Boelter Hall Forms and Simple Algebras, I AMS Special Session on Algebraic Topology, I 9:00 a.m.-9:50 a.m. Room 5117, Mathematical Sciences Building 8:30 a.m.-9:50 a.m. Room 5128, Mathematical 9:00a.m. Rational singularities and the Brauer group. Sciences Building (6) Preliminary report. Frank Demeyer*, Colorado State University, 8:30 a.m. Two-torsion and homotopy-associative H-spaces. Tim Ford, Florida Atlantic University, and (1} James P. Lin, University of California at San Diego, Rick Miranda, Colorado State University La Jolla, and Frank Williams*, New Mexico State (853-13-12) University, Las Cruces (853-55-13} 9:30a.m. On the Brauer group of a localization. 9:00 a.m. Generalized Whitehead spaces with few cells. (7) Timothy J. Ford, Florida Atlantic University (2) Norio lwase and Mamoru Mimura*, Okayama (853-13-1 0) University, Japan (853-55-23) (Sponsored by James P. Lin) 9:30 a.m. Loop spaces with the same n-type for all n. AMS Special Session on Harmonic Analysis, I (3) Preliminary report. C. A. McGibbon*, Wayne State University, and Jesper Meller, University of Copenhagen, Denmark 9:00 a.m.-9:50 a.m. Room 5137, Mathematical (853-55-08) Sciences Building 9:00a.m. Representation theoretic rigidity in PSL(2, R). (8) Christopher Bishop*, University of California, MAA Workshop Los Angeles, and Tim Steger, University of Chicago (853-22-47} 8:30 a.m.-9:30 a.m. Room 4000, Mathematical 9:30a.m. Extension theorem for VMO. Sciences Building (9) Peter Holden, Florida International University (853-42-16) Calculus and the computer. AMS Invited Address AMS Special Session on Geometric Methods in Combinatorial Group Theory, I 10:00 a.m.-10:50 a.m. Room 4000, Mathematical Sciences Building 9:00 a.m.-9:55 a.m. Room 5118, Mathematical Sciences Building (10) Automatic and hyperbolic groups. S. M. Gersten, University of Utah (853-20-28) 9:00 a.m. Subgroups of proper free factors of free groups. (4} John R. Stallings, University of California, Berkeley (853-20-30) NOVEMBER 1989, VOLUME 36, NUMBER 9 1229 Program of the Sessions Saturday, November 18 (cont'd) AMS Special Session on Harmonic Analysis, II 11:00 a.m.-11:50 a.m. Room 5137, Mathematical MAA Invited Address Sciences Building 11 :00 a.m. Multipliers of some Hilbert spaces of 11:00 a.m.-11:50 a.m. Room 3400, Boelter Hall (18) holomorphic functions. Preliminary report. Benjamin A. Lotto, Michigan State University, (11) Interacting particle systems: Equilibria and rates and Donald Sarason*, University of California, of convergence. Berkeley (853-30-36) Thomas M. Liggett, University of California, 11:30 a.m. Regularity properties of commutators and layer Los Angeles (19) potentials associated to the heat equation. John L. Lewis, University of Kentucky, and Margaret A. M. Murray*, Virginia Polytechnic AMS Special Session on Geometric Methods Institute and State University (853-42-03) in Combinatorial Group Theory, II 11:00 a.m.-11:55 a.m. Room 5118, Mathematical MAA Luncheon Speaker Sciences Building noon-1:20 p.m. Student Union 11:00 a.m. Computation in virtually free groups. (12) Robert H. Gilman, Stevens Institute of (20) Changing demographics and the future of our Technology (853-20-14) profession. 11 :30 a.m. Constructing negatively curved groups. Uri Treisman, University of California, Berkeley (13) Preliminary report. Mark Feighn*, Rutgers University, Newark, and Mladen Bestvina, University of California, AMS Session on Algebra Los Angeles (853-57-33) 1:15 p.m.-2:55p.m. Room 5138, Mathematical Sciences Building AMS Special Session on Algebraic Topology, II 1:15 p.m. Combinatorial interpretations of the q-analogues 11:00 a.m.-11:50 a.m. Room 5128, Mathematical (21) of L2n+l· Preliminary report. Sciences Building A. K. Agarwal, Pennsylvania State University, Mont Alto Campus (853-11-53) 11 :00 a.m. A generalization of the torus theorem. 1:30 p.m. The heredity measure of an algebra. (14) Preliminary report. (22) Vlastimil H. Dlab, Carleton University Michael Slack, University of California at San (853-16-07) Diego, La Jolla (853-55-06) 1:50 p.m. Decompositions of modules over Hensel rings. 11 :30 a.m. Rational homotopy theory: The general nilpotent (23) Preliminary report. (15) case. Michael F. Siddoway, Colorado College James E. Searl, New York Institute of (853-16-18) (Sponsored by David W. Roeder) Technology (853-55-04) 2:10p.m. Neat algebras. (24) 1. Agoston*, V. Dlab, Carleton University, and T. Wakamatsu, Jobu University, Japan AMS Special Session on Quadratic (853-16-32) Forms and Simple Algebras, II 2:30 p.m. Finitistic dimensions of Noetherian rings. (25) Ellen Kirkman*, James Kuzmanovich, Wake 11:00 a.m.-11:50 a.m. Room 5117, Mathematical Forest University, and Lance Small, University Sciences Building of California at San Diego, La Jolla (853-16-40) 2:45 p.m. Ends and cohomology of amalgamated 11 :00 a.m. On the relative Brauer group of the funtion field (26) products and HNN-extensions. Preliminary ( 16) of a plan cubic curve over a number field. report. Preliminary report. Michael L. Mihalik* and Steven Tschantz, Darrell Haile, Indiana University, Bloomington Vanderbilt University (853-20-21) (853-16-29) 11 :30 a.m. Quadratic forms, biquaternion algebras, and (17) function fields. Preliminary report. David B. Leep, University of Kentucky (853-12-17) 1230 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Program of the Sessions 5:00 p.m. Number of equivalence classes of vertices on AMS Special Session on Algebraic Topology, Ill (33) R-trees. Renfang Jiang, Mathematical Sciences 1:30 p.m.-2:20 p.m. Room 5128, Mathematical Research Institute, Berkeley (853-20-52) Sciences Building 5:30 p.m. Semistability of finitely presented groups. (34) Ross Geoghegan, State University of New 1 :30 p.m. Homology operations and invariant theory. York, Binghamton (853-20-31) (27) H. E. A. Campbell, Queen's University, and John McCleary*, Vassar College (853-55-48) 2:00 p.m. On the homotopy commutativity of the three AMS Special Session on Quadratic (28) connective cover of sJ. Forms and Simple Algebras, Ill James P. Lin*, University of California at San Diego, La Jolla, and Frank Williams, New Mexico State University, Las Cruces 4:00 p.m.-5:20 p.m. Room 5117, Mathematical (853-55-22) Sciences Building 4:00 p.m. lndecomposible division algebras of prime (35) exponent. MAA Session Bill Jacob, University of California, Santa Barbara (853-16-26) 1:30 p.m.-2:50 p.m. Room 3400, Boelter Hall 4:30 p.m. Nilpotence in the Witt ring. Preliminary report. (36) Jon Arason, University of Iceland, Iceland, and minority access to mathematics. Equity issues and Richard Elman*, University of California, Los Angeles (853-11-25) An covers to AMS Invited Address 5:00p.m. Serre's problem on lifting (37) unramified An-covers. Mike Fried, University of California, Irvine 3:00 p.m.-3:50 p.m. Room 4000, Mathematical (853-12-02) Sciences Building (29) Recent work in potential theory. Thomas H. Wolff, California Institute of AMS Special Session on Harmonic Analysis, Ill Technology (853-42-35) 4:00 p.m.-5:20 p.m. Room 5137, Mathematical Sciences Building MAA Invited Address 4:00 p.m. Estimates for the kernel and continuity (38) properties of pseudo-differential operators. 4:00 p.m.-4:50 p.m. Room 3400, Boelter Hall Josefina Alvarez*, Florida Atlantic University, and J. Hounie, Universidade Federal, Brazil (30) The topology of some spaces of functions. (853-35-41) Gunnar Erik Carlsson, Princeton University and Mathematical Sciences Research Institute, 4:30 p.m. Hessian determinants of harmonic functions. Berkeley (39) Preliminary report. Stewart Gleason, Courant Institute of Mathematical Sciences, New York University AMS Special Session on Geometric Methods (853-31-34) in Combinatorial Group Theory, Ill 5:00 p.m. Cauchy integrals on terrible curves. (40) J. Michael Wilson, University of Vermont (853-47-54) (Sponsored by Thomas H. Wolff) 4:00 p.m.-5:55 p.m. Room 5118, Mathematical Sciences Building 4:00p.m. Limits of free G-actions on R-trees and (31) reducible automorphisms. M. M. Cohen*, Cornell University, and M. Lustig, Ruhr Universitiit, Federal Republic of Germany (853-20-37) 4:30 p.m. Commuting elements in free actions on R-trees. (32) Preliminary report. Frank Rimlinger, Columbia University (853-20-11) NOVEMBER 1989, VOLUME 36, NUMBER 9 1231 Program of the Sessions Sunday, November 19 AMS Invited Address 10:00 a.m.-10:50 a.m. Room 4000, Mathematical AMS Special Session on Geometric Methods Sciences Building in Combinatorial Group Theory, IV (48) Galois groups and rational division algebras. Burton 1. Fein, Oregon State University 9:00 a.m.-9:55 a.m. Room 5118, Mathematical (853-12-20) Sciences Building 9:00a.m. .X 1, diameter, and injectivity radius of manifolds AMS Special Session on Geometric Methods (41) and of graphs. Preliminary report. Robert Brooks, University of Southern in Combinatorial Group Theory, V California (853-58-05) 9:30a.m. Non-positive curvature in piecewise Euclidean 11:00 a.m.-11:55 a.m. Room 5118, Mathematical (42) complexes. Sciences Building Martin R. Bridson, Cornell University 11 :00 a.m. Combings of groups. (853-20-51) (49) Juan M. Alonso, Cornell University (853-20-44) 11:30 a.m. The domino problem, hyperbolic geometry and AMS Special Session on Quadratic (50) the logic of Fuchsian groups. Paul E. Schupp, University of Illinois, Forms and Simple Algebras, IV Urbana-Champaign (853-30-42) 9:00 a.m.-9:50 a.m. Room 5117, Mathematical Sciences Building AMS Session II 9:00a.m. Brauer Hilbertian fields. (43) Burton Fein, Oregon State University, David 11:00 a.m.-12:40 p.m. Room 5138, Mathematical Saltman*, University of Texas, Austin, and Sciences Building Murray Schacher, University of California, Los 11:00 a.m. A local direct theorem for a Bernstein-type Angeles (853-12-09) (51) approximation process. Preliminary report. 9:30a.m. Higher level orders and holomorphy rings in Yegnaseshan Sitaraman, Kentucky Wesleyan (44) skew fields. College (853-41-39) Victoria Powers, Emory University (853-12-49) 11:20 a.m. Heron's problem in the Minkowski plane. (52) Preliminary report. Mostafa Ghandehari, Naval Postgraduate AMS Session I School (853-52-01) 11:40 a.m. Transforms of support functions. Preliminary 9:00 a.m.-9:50 a.m. Room 5138, Mathematical (53) report. Sciences Building Mostafa Ghandehari and Christopher P. Sagovac•, Naval Postgraduate School 9:00a.m. Boundary localization of the normal family of (853-52-46) (45) holomorphic mappings. E. B. Lin, University of Toledo (853-32-55) noon Global convolution operations in binary (54) algebras. 9:20a.m. On orthogonality of Legendre's polynomials via C. R. Giardina, City College, City University of (46) its generating function. Preliminary report. New York (853-93-45) Sadanand Verma, University of Nevada 12:20 p.m. On the equivalence of laws in trigonometry. (853-33-56) (Sponsored by L. J. Simonoff) (55) Preliminary report. 9:40a.m. Success runs in Markov chains. Preliminary Tony S. Verma• and Tonia S. Verma, Clark (47) report. High School and University of Nevada Anant P. Godbole, Michigan Technological (853-98-57) (Sponsored by L. J. Simonoff) University (853-60-19) 1232 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Program of the Sessions AMS Invited Address AMS Special Session on Quadratic Forms and Simple Algebras, V 2:00 p.m.-2:50 p.m. Room 4000, Mathematical Sciences Building 3:00 p.m.-4:20 p.m. Room 5117, Mathematical Sciences Building (56) Nilpotent orbits and the Weyl group. Nicolas Spaltenstein, University of Oregon 3:00 p.m. Some recent developments in the theory of (853-22-58) (60) function fields of quadratic forms. Preliminary report. T.-V. Lam, University of California, Berkeley AMS Special Session on Geometric Methods (853-12-50) in Combinatorial Group Theory, VI 4:00 p.m. u-invariants in characteristic 2. Preliminary (61) report. P. Mammone, Universite de Mons, Belgium, R. 3:00 p.m.-4:25 p.m. Room 5118, Mathematical Moresi, CERFIM, Switzerland, J.- P. Tignol, Building Sciences Universite Catholique de Louvain, Belgium, 3:00 p.m. Negatively curved groups. Preliminary report. and A. R. Wadsworth*, University of California (57) Daryl Cooper, University of California, Santa at San Diego, La Jolla (853-12-38) Barbara (853-20-24) Lance W. Small p.m. Homology of certain Artin groups. 3:30 AMS Associate Secretary (58) Kay Tatsuoka, Rutgers University, Newark La Jolla, California (853-57-43) (Sponsored by Mark E. Feighn) 4:00 p.m. Algebraic analysis of groups F-type. (59) Benjamin Fine*, Fairfield University, and Gerhard Rosenberger, Universiti'it Dortmund, Federal Republic of Germany (853-20-27) Presenters of Papers Numbers following the names indicate the speakers' positions on the program. • AMS Invited Lecturer o MAA Invited Lecturer * AMS Special Session Speaker Agarwal, A. K., 21 *Ford, T. J., 7 o Liggett, T. M., 11 Siddoway, M. F., 23 Agoston, 1., 24 *Fried, M., 37 Lin, E. B., 45 Sitaraman, Y., 51 *Alonso, J. M., 49 *Geoghegan, R., 34 *Lin, J. P., 28 *Slack, M., 14 *Alvarez, J., 38 •Gersten, S.M., 10 *McCleary, J., 27 • Spaltenstein, N., 56 *Bishop, C., 8 Ghandehari, M., 52 *McGibbon, C. A., 3 *Stallings, J. R., 4 * Bridson, M. R., 42 Giardina, C. R., 54 Mihalik, M. L., 26 * Tatsuoka, K., 58 * Brooks, R., 41 *Gilman, R. H., 12 * Mimura, M., 2 o Treisman, U., 20 o Carlsson, G. E., 30 *Gleason, S., 39 *Murray, M. A., 19 Verma, S., 46 *Cohen, M. M., 31 Godbole, A. P., 47 *Powers, V., 44 Verma, T. S., 55 *Cooper, D., 57 *Haile, D., 16 * Rimlinger, F., 32 *Wadsworth, A. R., 61 *Demeyer, F., 6 *Holden, P., 9 Sagovac, C. P., 53 *Williams, F., 1 Dlab, V. H., 22 *Jacob, B., 35 * Saltman, D., 43 *Wilson, J. M., 40 *Elman, R., 36 *Jiang, R., 33 *Sarason, D., 18 • Wolff, T. H., 29 * Feighn, M., 13 Kirkman, E., 25 *Schupp, P. E., 50 • Fein, B. 1., 48 *Lam, T.-Y., 60 *Searl, J. E., 15 * Fine, B., 59 * Leep, D. B., 17 *Shapiro, M., 5 NOVEMBER 1989, VOLUME 36, NUMBER 9 1233 Louisville Meetings January 17-20, 1990 Supplement to Announcement in October Notices Please refer to the Preliminary Announcement for this be moderated by A. DuANE PoRTER of the University of meeting which appears on pages 1039- 1082 of the Oc Wyoming and will be held on Thursday, January 18, at tober 1989 issue of Notices. The Table of Contents and 8:30p.m. Important Deadlines from the preliminary announce ment are reproduced below for convenience. The forms AMS Prize Session for Preregistration/Housing, MAA Minicourses, and the Mathematical Sciences Employment Register are located The Council and the Board of Trustees of the Society at the back of this issue. have established an Award for Distinguished Public Ser vice that will be made for the first time at its Business AMS Invited Addresses Meeting in Louisville. This award will be presented every who has made a The title of the invited address by SuN-YUNG ALICE two years to a research mathematician the mathematical profes CHANG is Analysis of spectral invariants. distinguished contribution to sion through public service during the preceeding five years. The Council and Board of Trustees of the Society Other AMS-MAA Sessions have also established a Citation for Public Service, one to three of which will be presented annually for notable The undergraduate linear algebra curriculum: This topic contributions to the mathematical profession through was the partial focus of an NSF funded conference public service. These citations will be presented for the Matrix theory for applications during the summer of first time at the Business Meeting in Louisville. 1989. The main speaker at the conference was Charles R. Johnson of The College of William and Mary. This session will deal with reports made by subgroups of participants regarding the position of linear algebra in the undergraduate curriculum. A panel discussion will IMPORTANT DEADLINES follow. Panelists will be named later and will include mathematicians not at the conference. The session will AMS Abstracts For Consideration for Special Sessions Expired Of Contributed Papers October 11 WHERE TO FIND IT PAGE MAA Abstracts Of Contributed Papers Expired How to Preregister and Get a Room 1052 For Special Computer Session October 20 AMS-MAA Invited Addresses 1041 Employment Register Annual Meeting of the AMS 1041 (Applicants & Employers) November 17 EARLY Preregistration and Housing October 31 AMS Short Course 1080 ORDINARY Preregistration and Housing November 17 Annual Meeting of the MAA 1044 MAA Minicourse Preregistration November 17 Other Organizations 1050 FINAL Preregistration December 18 Other Events of Interest 1051 Motions for AMS Business Meeting December 18 Preregistration Cancellations (50o/o refund) January 3 1061 Timetable Housing Changes/Cancellations with Housing Employment Register 1076 Bureau December 15 Miscellaneous Information 1056 AMS Banquet (50o/o refund) January 3 NAM Banquet (50o/o refund) January 3 1234 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings MAA Special Report The speakers who will participate in the AWM panel discussion on affirmative action are BEVERLY ANDERSON, A special report on Developing the teacher's ability to University of the District of Columbia and the Math encourage creativity in students II will be given by ematical Sciences Education Board; LIDA K. BARRETT, ARNOLD E. Ross, Ohio State University. This report will Mississippi State University; MARY W. GRAY, American be given at 1:00 p.m. on Saturday, January 20. University; JILL P. MESIROV, Thinking Machines, Corpo ration (moderator); MELVYN B. NATHANSON, Herbert H. Activities of Other Organizations Lehman College, CUNY; and MICHAEL C. REED, Duke University. The Association for Women in Mathematics (AWM) The AWM Business Meeting will now begin at 4:35 Emmy Noether Lecture will be given by BHAMA SRINI p.m. following the panel discussion. VASAN, University of Illinois at Chicago on The invasion of geometry into finite group theory. NEW Reviews in Operator Theory 1980-86 Introduction by Paul R. Halmos Operator theory is the branch of mathematics that treats the classification between 1980 and 1986 appear in these objects of analysis (numerical valued functions and their volumes. Within each section, reviews are ordered by their limiting properties) by the methods of modem topology and MR number. Relevant cross-references are given with each algebra. While, roughly speaking, the area 46 deals primar review, and author and key indexes appear in the fourth ily with the objects (i.e., topological vector spaces) associ volume. ated with the category of topological linear algebra, the area 4 7 deals with the morphisms between these objects (i.e., the 4 volumes, 2639 pages, Softcover, July 1989 mapings-both linear and nonlinear-between these spaces). ISBN 0-8218-0135-X, LC 89-6551 Although functional analysis and operator theory developed List $196, Institutional member $157, as identifiable fields in the early part of this century they Individual member $118, Reviewer $98 have seen tremendous growth in the past few decades and To order, please specify REVOPE/86NA have found applications to diverse areas, both to purely mathematical areas and to other scientific disciplines. These volumes contain a wealth of information about linear SPECIAL COMBINATION OFFER: Reviews in Operator Theory, 1980-86 and operators, algebraic systems of linear operators, differential Reviews in Functional Analysis, 1980-86 and integral operators, and nonlinear operators. ISBN 0-8218-0139-2 List $314, Institutional member $251, All the Mathematical Reviews entries having operator theory Individual Member $188, Reviewer $157 (MR classification number 47) as a primary or secondary To order, please specify REVFA0/86NA Prepayment required. Review volumes are shipped by surface at no extra charge; contact the AMS for air delivery rates. Prices subject to change. Order from the American Mathematical Society, P. 0. Box 1571, Annex Station, Providence, RI 02901-1571 or call toll free 800-321-4AMS to charge with VISA or MasterCard. NOVEMBER 1989, VOLUME 36, NUMBER 9 1235 American Mathematical Society Short Course Series Introductory Survey Lectures on Mathematical Questions in Robotics Louisville, Kentucky, January 16-1 7, 1990 The following synopses and reading lists supplement quite difficult for humans to specify. Furthermore, robot those presented in the first announcement of the Short assembly programs are very sensitive to the details Course to be held at the Hyatt Regency, Louisville; see of geometry. Finally, reprogramming a general purpose the October 1989 issue of Notices, pages 1080-1082 for robot for a new assembly task can take time on the program and registration information. Speakers/topics order of man-months. For these reasons, we have been are: ROGER W. BROCKETT, Harvard University, Intro working on the automatic synthesis of motion strategies duction and Symbolic Description of Movement; MAD for robots. HUSUDAN RAGHAVAN, General Motors Research Labora Research in task-level planning is often characterized tories, Kinematics of Manipulators; JoHN B. BAILLIEUL, as theoretical robotics. There are several reasons for this; Boston University, Resolution ofKinematic Redundancy; the first is that much of the work has been concerned SHANKAR SASTRY, University of California, Berkeley, with constructing a theory of planning. In other words, Control and Programming ofMultifingered Robot Hands; the computational problem "task-level planning" is not and BRUCE R. DoNALD, Cornell University, Planning well-specified. Much of our work lies in specifying and Executing Robot Assembly Strategies in the Presence the computation precisely. Second, given some sort of Uncertainty. of decomposition of task-level planning into "planning problems", one is immediately driven to ask, What are the algorithms for these problems? Can plans, in general, be computed? How efficiently can planning algorithms Synopses and Reading Lists run? Historically, the nature of these questions has led researchers to apply tools from theoretical computer Planning and Executing Robot Assembly Strategies in science, computational geometry, and algebra. the Presence of Uncertainty (Bruce R. Donald). Research Recently, a great deal of attention has been focused in robot programming attempts to build robot planning on a particular robotics problem, called the find-path, or systems that can function at the task-level. A task-level generalized movers' problem. In this problem, we ask the specification of a robot plan might have the form, · purely kinematic question, can a robot system be moved Put together this disk rotor assembly. The planner is from one configuration to another, without colliding with given geometric models of the parts, and geometric or obstacles? This is a nicely-defined mathematical problem, analytic models of the robot dynamics. Beyond this, the and, after much research, at this point its computational specification, or input to the planner does not mention complexity is precisely known. the specific kinematic and dynamic constraints that the In fact, the neatness of this problem is deceptive, robot must obey; these are determined by the planner so much so that this formal problem has even been using geometrical computation. The goal of a task-level called "the" motion planning problem. From a task planner is to take a task-level specification and to produce level viewpoint, there is much hidden in the statement a runnable robot program-one which is fully specified in "Can the robot system be moved ...?" Specifically, the terms of force-control, kinematics, and dynamics-that find-path problem assumes that the robot has a perfect can accomplish the task. control system that can exactly execute the plan, and Major advances in task-level planning can enable that the geometric and analytic models of the robot and robotics to achieve its full potential in the assembly obstacles are exact. domain. Today, even existing robots cannot be exploited In reality, of course, robot control systems are subject to their full capacity. For example, assembly tasks require to significant uncertainty and error. Typical robots are compliant motion; however, compliance requires force also equipped with sensors-force sensors, kinesthetic control, and such force-control motion strategies are position sensors, tactile sensors, vision, and so forth. 1236 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Short Course Series However, these sensors are also subject to significant experiments. The talk is a blend of recent advances uncertainty. Finally, the geometrical models of the robot in our understanding of classical mechanics, computer and the environment (parts, obstacles, etc.) cannot be graphics as well as some neurophysiology. exact-they are accurate only to manufacturing toler In the first part I will discuss the modelling of ances, or to the accuracy of the sensors used to acquire the low-level control problem for a multifingered hand the models. Uncertainty is not a mere engineering de manipulating an object under a variety of contact types: tail; in particular, it is characteristically impossible to fixed, sliding, rolling and soft fingered or rhealogical. "patch" these perfect plans in such a way that they will The nonholonomies associated with rolling make it function once uncertainty comes into play. Uncertainty particularly interesting. We discuss the use of control is an absolutely fundamental problem in robotics, and laws for explicit linearization of these control systems plans produced under the assumption of no uncertainty under state feedback. We show simulations and discuss are meaningless. What is needed is a principled the implementation considerations. ory of planning in the presence of uncertainty. Such I will discuss in the second part of the talk how a theory must not only be computational, but must results from the (differential) geometric control theory also take uncertainty into account a priori. The overlap literature can be brought to bear on the problem of with exact motion planning algorithms can be stated changing grasps on an object. Some connections with roughly as follows: exact kinematic planning algorithms Berry's phase formula will also be given. Finally, I will provide a computational-geometric theory of holonomic discuss a neurophysiologically motivated environment constraints. In motion planning with uncertainty, we which we are developing for the specification, control exploit compliant motion-sliding on surfaces-in order and programming of multifingered hands. to effect a "structural" reduction in uncertainty. Such The talk is based on collaborative work with my compliant motion plans can be synthesized from a com students: Li Zexiang (NYU), Ping Hsu (University of putational analysis of the geometry of the holonomic Illinois), Arlene Cole (AT&T Bell Labs), John Hauser constraints. (USC), Richard Murray, Curt Dena and Kris Pister. We will present a precise framework for motion planning with uncertainty. In particular, given geometric L Z. Li and S. S. Sastry, Task Oriented Optimal bounds on the uncertainty in sensing and control, we de Grasping by Multifingered Robot Hands, IEEE Journal velop algorithms for generating and verifying compliant of Robotics and Automation, Vol. 4, No. 1, 1988, pp. motion strategies that are guaranteed to succeed as long 32-44. sensing and control uncertainties lie within the as the 2. D. J. Montana, Tactile Sensing and the Kinematics specified bounds. of Contact, Ph.D. dissertation, Div. of App. Sciences, 1. B. R. Donald, Error Detection and Recovery in Harvard Univ., Cambridge, Mass., 1986. Springer-Verlag, Lecture Notes in Computer Robotics, 3. A. B. A. Cole and J. E. Hauser, Kinematics and Science, ( 1989). Control of Multifingered Hands with Rolling Contact, IEEE Transactions on Automatic Control, Vol. 34, No. and Programming of Multifingered Robot Control 4, 1989, pp. 398-404. Hands (Shankar Sastry). In this talk, I will discuss the dynamics, control, planning of motions and de 4. Z. Li, P. Hsu and S. S. Sastry, Grasping and Co sign of multifingered hands. The talk will be in two ordinated Manipulation by a Multifingered Robot Hand, parts with extensive videotape footage (to be shown International Journal of Robotics Research, Vol. 8, No. after the talk) illustrating both animated simulations and 4, August 1989, pp. 33-50. NOVEMBER 1989, VOLUME 36, NUMBER 9 1237 Invited Speakers and Special Sessions Invited Speakers at the time this issue of Notices went to the printer. at AMS Meetings The section below entitled Information for Organizers describes the timetable for announcing the existence The individuals listed below have accepted invitations of Special Sessions. to address the Society at the times and places in dicated. For some meetings, the list of speakers is incomplete. January 1990 Meeting in Louisville, Kentucky Associate Secretary: Joseph A. Cima Deadline for organizers: Expired Louisville, KY, January 1990 Deadline for consideration: Expired Jon Barwise (AMS-MAA) Henryk Iwaniec Joseph A. Ball and Israel C. Gohberg, Linear operators, Sun-Yung Alice Chang Janos Kollar matrix functions and control Charles W. Curtis Israel M. Sigal Joseph G. Conlon, The Schrodinger equation (AMS-MAA) Barry Simon (AMS-MAA) Raul E. Curto and Paul S. Muhly, Multivariable George B. Dantzig Shlomo Sternberg operator theory (Gibbs Lecture) (Colloquium Lectures) Ethan S. Devinatz and Mike Hopkins, Homotopy Israel C. Gohberg Nolan R. Wallach theory Mike Hopkins (AMS-MAA) Robert S. Doran, Group representations and operator algebras Fayetteville, AK, March 1990 Bruce R. Ebanks, Functional equations and their ap Marcel F. Neuts Mark A. Stern plications Vladimer I. Oliker Jonathan M. Wahl Florence D. Fasanelli and Victor J. Katz, History of Manhattan, KS, March 1990 mathematics J. Brian Conrey Jean-Pierre Rosay Robert E. Fennell and Suzanne Marie Lenhart, Control Stewart B. Priddy Jang-Mei Wu of infinite dimensional systems Carl H. FitzGerald and Ted J. Suffridge, Geometric University Park, PA, Apri11990 function theory in one and several complex variables Robert T. Glassey Lowell Jones Gary D. Jones, Oscillation theory in ordinary differen Carsten Grove Gang Tian tial equations Columbus, OH, August 1990 Janos Kollar, Algebraic geometry Michael G. Crandall John Morgan Efim D. Khalimsky, Yung Kong and Ralph D. (Progress in (Progress in Kopperman, Topology in computer graphics and Mathematics Lecture) Mathematics Lecture) image processing Michael E. Taylor Inessa Levi and W. Wiley Williams, Semigroup theory Peter A. McCoy, Function theoretic methods in differ Denton, TX, November 1990 ential equations Avner D. Ash Lynn McLinden and Jay S. Treiman, Optimization Organizers and Topics and nonlinear analysis of Special Sessions Hugh L. Montgomery, Analytic number theory Peter A. Perry, Geometric spectral and inverse spectral The list below contains all the information about problems Special Sessions at meetings of the Society available 1238 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Invited Speakers and Special Sessions Philip E. Protter, Markov processes and stochastic April1990 Meeting in Albuquerque, New Mexico analysis Far Western Section Associate Secretary: Lance W. Small Deadline for organizers: Expired March 1990 Meeting in Fayetteville, Arkansas Deadline for consideration: January 4, 1990 Southeast Section Associate Secretary: Joseph A. Cima August 1990 Meeting in Columbus, Ohio Deadline for organizers: Expired Associate Secretary: W. Wistar Comfort Deadline for consideration: November 21, 1989 Deadline for organizers: November 15, 1989 Geraldo Soares De Souza and Gary Sampson, Singular Deadline for consideration: April 27, 1990 integral operators and related areas Eiichi Bannai, Thomas A. Dowling, Dijen Ray J. Duncan and A. L. T. Patterson, Banach algebras Chaudhuri and Neil Robertson, Combinatorics Colm A. O'Cinneide and ltrel E. Monroe, Probability Zita M. Divis and David Terman, Dynamics of bio- distributions of phase-type and applications logical systems Karl H. Hofmann and Jimmie D. Lawson, Semi-groups John S. Hsia and Warren M. Sinnott, Number theory in geometry and analysis S. P. Jain and T. Rizvi, Ring theory Dima Khavinson, On complex function theory of one Surinder K. Sehgal and Ronald Solomon, Group theory and several complex variables David R. Morrison and Jonathan M. Wahl, Algebraic November 1990 Meeting in Denton, Texas geometry Central Section Vladimir I. Oliker and Andrejs E. Treibergs, Geometry, Associate Secretary: Andy Roy Magid physics and nonlinear PDE's Deadline for organizers: February 15, 1990 Deadline for consideration: July 16, 1990 James G. Oxley, Combinatorics William L. Pardon and Mark A. Stern, Differential geometry Information for Organizers Special Sessions at Annual and Summer Meetings are March 1990 Meeting in Manhattan, Kansas held under the supervision of the Program Committee Central Section for National Meetings (PCNM). They are adminis Associate Secretary: Andy Roy Magid tered by the Associate Secretary in charge of that Deadline for organizers: Expired meeting with staff assistance from the Meetings and November 21, 1989 Deadline for consideration: Editorial Departments in the Society office in Provi Andrew G. Bennett, Harmonic analysis and probability dence. theory According to the "Rules for Special Sessions" of David J. Foulis and Richard J. Greechie, Orthostruc the Society, Special Sessions are selected by the PCNM tures from a list of proposed Special Sessions in essentially Kadosa M. Halasi and Qisu Zou, Numerical analysis the same manner as Invited Speakers are selected. The David H. Hamilton and John F. Rossi, Geometric number of Special Sessions at a Summer or Annual function theory Meeting is limited. The algorithm that determines the Lige Li, Partial differential equations number of Special Sessions allowed at a given meeting, Satyagopol Mandai, Commutative algebra while simple, is not repeated here, but can be found in Alexander G. Ramm, Inverse problems and scattering "Rules for Special Sessions" on page 614 in the April theory 1988 issue of Notices. Joseph M. Rosenblatt, Ergodic theory Each Invited Speaker is invited to generate a Spe Richard H. Schelp, Graph theory cial Session, either by personally organizing one or Ernest E. Shult, Groups and geometries by having a Special Session organized by others. Pro George E. Strecker, Applications of category theory posals to organize a Special Session are sometimes requested either by the PCNM or by the Associate Meeting in University Park, Pennsylvania April 1990 a Special Ses Eastern Section Secretary. Other proposals to organize Associate Secretary: W. Wistar Comfort sion may be submitted to the Associate Secretary in Deadline for organizers: Expired charge of that meeting (who is an ex-officio member Deadline for consideration: January 4, 1990 of the committee and whose address may be found Donald M. Davis, Algebraic topology below). These proposals must be in the hands of the PCNM well in advance of the meeting and, in any NOVEMBER 1989, VOLUME 36, NUMBER 9 1239 Invited Speakers and Special Sessions case, at least nine (9) months prior to the meeting at Central Section which the Special Session is to be held in order that Andy Roy Magid, Associate Secretary the committee may consider all the proposals for Spe Department of Mathematics cial Sessions simultaneously. Proposals that are sent University of Oklahoma 601 Elm PHSC 423 to the Providence office of the Society, to Notices, or Norman, OK 73019 directed to anyone other than the Associate Secretary e-mail: [email protected] will have to be forwarded and may not be received in (Telephone 405- 325-2052) time to be considered for acceptance. Eastern Section It should be noted that Special Sessions must W. Wistar Comfort, Associate Secretary be announced in Notices in such a timely fashion Department of Mathematics that any member of the Society who so wishes may Wesleyan University Middletown, CT 06457 submit an abstract for consideration for presentation e-mail: [email protected] in the Special Session before the deadline for such (Telephone 203- 34 7-9411) consideration. This deadline is usually three (3) weeks Southeastern Section before the Deadline for Abstracts for the meeting in Joseph A. Cima, Associate Secretary question. Department of Mathematics Special Sessions are very effective at Sectional University of North Carolina, Chapel Hill Meetings and can usually be accommodated. They are Chapel Hill, NC 27599-3902 e-mail: [email protected] selected by the Section Program Committee. The pro (Telephone 919- 962- 1050) cessing of proposals for Special Sessions for Sectional As a general rule, members who anticipate organizing Special Meetings is handled by the Associate Secretary for Sessions at AMS meetings are advised to seek approval at least the Section, who then forwards the proposals to the nine months prior to the scheduled date of the meeting. No Special Section Program Committee, which makes the final Sessions can be approved too late to provide adequate advance selection of the proposals. Each Invited Speaker at notice to members who wish to participate. a Sectional Meeting is invited to organize a Special Session. Just as for national meetings, no Special Information for Speakers Session at a Sectional Meeting may be approved so late that its announcement appears past the deadline A great many of the papers presented in Special Ses after which members can no longer send abstracts for sions at meetings of the Society are invited papers, but consideration for presentation in that Special Session. any member of the Society who wishes to do so may The Society reserves the right of first refusal for submit an abstract for consideration for presentation the publication of proceedings of any Special Ses in a Special Session, provided it is received in Prov sion. These proceedings appear in the book series idence prior to the special early deadline announced Contemporary Mathematics. above and in the announcements of the meeting at More precise details concerning proposals for and which the Special Session has been scheduled. Con organizing of Special Sessions may be found in the tributors should know that there is a limitation in "Rules for Special Sessions" or may be obtained from size of a single special session, so that it is sometimes any Associate Secretary. true that all places are filled by invitation. Papers not accepted for a Special Session are considered as ten-minute contributed papers. Send Proposals for Special Sessions to the Abstracts of papers submitted for consideration for Associate Secretaries presentation at a Special Session must be received by The programs of sectional meetings are arranged by the Associate the Providence office (Editorial Department, American Secretary for the section in question: Mathematical Society, P. 0. Box 6248, Providence, Far Western Section (Pacific and Mountain) RI 02940) by the special deadline for Special Sessions, Lance W. Small, Associate Secretary which is usually three weeks earlier than the deadline Department of Mathematics for contributed papers for the same meeting. The University of California, San Diego Council has decreed that no paper, whether invited or La Jolla, CA 92093 e-mail: [email protected] contributed, may be listed in the program of a meeting (Telephone 619-534- 3590) of the Society unless an abstract of the paper has been received in Providence prior to the deadline. 1240 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Invited Speakers and Special Sessions Electronic submission of abstracts is now available Number of Papers Presented to those who use the TEX typesetting system. Requests Joint Authorship to obtain the package of files may be sent electron Although an individual may present only one ten ically via the Internet to [email protected]. minute contributed paper at a meeting, any combina Requesting the files electronically will likely be the tion of joint authorship may be accepted, provided fastest and most convenient way, but users may also no individual speaks more than once. An author can obtain the package on IBM or Macintosh diskettes, speak by invitation in more than one Special Session available free of charge by writing to: Rosanne Gra at the same meeting. natiero, American Mathematical Society, Publications An individual may contribute only one abstract by Division, P.O. Box 6248, Providence, RI 02940, USA. title in any one issue of Abstracts, but joint authors When requesting the Abstracts package, users should are treated as a separate category. Thus, in addition be sure to specify whether they want the plain TEX, to abstracts from two individual authors, one joint AMS-TE)(, or the lt reviews in GLOBAL ANALYSIS Introduction by 1980-86 Anthony J. Tromba The term "global analysis" refers to the These five volumes contain the more 1980 Mathematics Subject Classification: 58 general area of analysis on manifolds, in than 18,000 reviews that appeared ISBN 0-8218-0104-X, LC 88-10565 which the methods of modern algebra, in Mathematical Reviews from 1980 5 volumes, 4060 pages (softcover), August 1988 analysis, geometry, and topology are through 1986 and have a primary or List price $307, Institutional member $246, blended. Although the beginnings of a secondary classification in Global Individual member $184, Reviewer $154 these ideas can be traced to the 17th Analysis (classification number 58). To order, please specify REVGL0/86PNA century, major contributions in this Relevant cross-references are provided direction were made by Lie, Riemann, with each review. The fifth volume and Poincare toward the end of the of this set contains author and key Combination offer. Reviews in Partial last century, followed by the work indexes, making it very easy to locate Differential Equations, 1980-86, and of G. D. Birkhoff, E. Cartan, and items written by a specific author or Reviews in Global Analysis, 1980-86 Morse in the early part of this century. to get information about collections or {REVPDE/86 and REVGL0/86). However, it is only in recent years that conference proceedings dealing with List $491, Institutional member $393, the subject has attained its present global analysis. Individual member $295, Reviewer $246. central position in mathematics. The To order, Please specify subject has many rich applications to Contents: REVPGL/86NA fields outside mathematics--such as Volume 1: Global analysis, analysis on mechanics, quantum physics, and general manifolds; General theory of differentiable relativity-as well as within mathematics manifolds; Infinite-dimensional manifolds; All prices subject to change. Shipment itself. Calculus on manifolds; nonlinear operators; will be made by surface. For air deliv Spaces and manifolds of mappings; ery add, I st book $5, each additional Today, this vital and active field is Volume 2: Variational problems in infinite book $3, maximum $100. Prepayment required. Order from American Mathe dimensional spaces; Ordinary differential undergoing a virtual explosion of new matical Society, P.O. Box 1571, Annex and important results. Reviews in equations on manifolds; dynamical systems; Station, Providence, RI 02901-1571, or Global Analysis makes information about Volume 3: Ordinary differential equations call toll free 800-321-4AMS to charge the most recent contributions to this on manifolds; dynamical systems; Volume 4: with VISA or MasterCard. rapidly growing field accessible both t"o Partial differential equations on manifolds; specialists working in global analysis, differential operators; Pseudogroups and and to those in other areas of pure and general structures on manifolds; Volume 5: applied mathematics. Series contents; Author index; Key index. NOVEMBER 1989, VOLUME 36, NUMBER 9 1241 Joint Summer Research Conferences in the Mathematical Sciences University of Massachusetts at Amherst, MA, June 7 to July 4, 1990 The 1990 Joint Summer Research Conferences in the Summer Research Conference Coordinator, Meetings Mathematical Sciences will be held at the University Department, American Mathematical Society, Post of Massachusetts at Amherst from June 7 to July 4. It Office Box 6248, Providence, RI 02940 or by E-Mail: is anticipated that the conferences will be supported [email protected] on the Internet. by grants from the National Science Foundation and Please type or print the following: other agencies. and dates of conference desired There will be six conferences in six different areas 1. Title 2. Full name of mathematics. The topics and organizers for the 3. Mailing address conferences were selected by the AMS-IMS-SIAM 4. Telephone number and area code for office and Committee on Joint Summer Research Conferences in home the Mathematical Sciences. The selections were based 5. Member of AMS, IMS, or SIAM? If AMS, please on suggestions made by the members of the committee give member code and individuals submitting proposals. The committee 6. Your scientific background relevant to the topic of considered it important that the conferences represent the conference diverse areas of mathematical activity, with emphasis 7. Financial assistance requested; please estimate cost on areas currently especially active and paid careful of travel attention to subjects in which there is important 8. Indicate if interested in attending if support is not interdisciplinary activity at present. offered. Indicate if support is not required. The conferences are similiar in scientific structure to those held throughout the year at Oberwolfach. The deadline for receipt of applications is February These conferences are intended to complement the 23, 1990. Requests for invitations will be forwarded Society's program of annual Summer Institutes and to the Organizing Committee for each conference for Summer Seminars, which have a larger attendance and consideration after February 23. Applicants selected are substantially broader in scope. The conferences are will receive formal invitations and notification of research conferences and are not intended to provide financial assistance from the AMS. Requests received an entree to a field in which a participant has not past the deadline will be returned. Funds available already worked. for these conferences are limited and individuals It is expected that funding will be available for who can obtain support from other sources should a limited number of participants in each conference. do so. Women and members of minority groups Others, in addition to those funded, will be welcome, are encouraged to apply and participate in these within the limitations of the facilities of the campus. conferences. In the spring a brochure will be mailed to all who Any questions concerning the scientific portion of are invited to attend the conferences. The brochure the conference should be directed to the chair or any will include information on room and board rates, the member of the Organizing Committee. residence and dining hall facilities, travel and local The Joint Summer Research Conferences in the information and a housing form to use to request on Mathematical Sciences are under the direction of campus accommodations. Information on off-campus the AMS-IMS-SIAM Committee on Joint Summer housing will also be included in the brochure. Par Research Conferences in the Mathematical Sciences. ticipants should make their own housing and travel The following committee members chose the topics arrangements. Each participant will be required to pay for the 1990 conferences: William B. Arveson, John nominal registration and social fees. A. Bums, Martin Golubitsky, Daniel J. Kleitman, Those interested in attending one of the confer Anthony W. Knapp, Ingram Olkin, Mary Ellen Rudin, ences should send the following information to the Stephen Simpson and Gregg J. Zuckerman. 1242 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Joint Summer Research Conferences Descriptions of the subject matter of each of the Members of the Organizing Committee: Ronald R. 1990 conferences appeared in the October Notices, Coifman (Yale University), Craig A. Tracy (University pages 1087 -1089; they were accompanied by lists of of California, Davis) and Stephanos Venakides (Duke members of the respective Organizing Committees. University). Thursday, June 14 to Wednesday, June 20 Thursday, June 7 to Wednesday, June 13 Deformation theory of algebras and quantization Probability models and statistical analysis with applications to physics for ranking data MURRAY H. GERSTENHABER (University of MICHAEL A. FLIGNER (The Ohio State University), Pennsylvania), Co-Chair Co-Chair, JAMES D. STASHEFF (University of North Carolina), JosEPHS. VERDUCCI (The Ohio State University), Co-Chair Co-Chair Thursday, June 21 to Wednesday, June 27 Thursday, June 7 to Wednesday, June 13 Strategies for sequential search and selection Inverse scattering on the line in real time DAVID SATTINGER (University of Minnesota, THOMAS S. FERGUSON (University of California, Los Minneapolis), Chair Angeles), Co-Chair The following description did not appear in the STEPHEN M. SAMUELS (Purdue University), Co-Chair announcement in the October issue. There has been much progress recently on inverse scattering theory in one and two dimensions. This Thursday, June 21 to Wednesday, June 27 conference will cover recent developments in the Schottky Problems field, including inverse scattering theory on the line, LEON EHRENPREIS (Temple University), Co-Chair Riemann-Hilbert problems, and inverse monodromy ROBERT C. GUNNING (Princeton University), problems. Multidimensional problems will be covered, Co-Chair using the so called f) methods. Applications to the Davey-Stewartson II and KP II equations will be treated. One day will be devoted to higher dimensional Thursday, June 28 to Wednesday, July 4 problems, and one day to applications of inverse scattering theory and inverse monodromy theory to Logic, local fields, and subanalytic sets problems in statistical mechanics. Lou VAN DEN DRIES (University of Illinois at Urbana-Champaign), Chair NOVEMBER 1989, VOLUME 36, NUMBER 9 1243 Mathematics Sessions at the AAAS Annual Meeting New Orleans, Louisiana, February 15-20, 1990 The 1990 Annual Meeting of the AAAS, February • Frontiers of physical sciences: A mathematics lec 15-20 in New Orleans, will feature many outstanding ture by FRANK MORGAN, Williams College. expository talks by prominent mathematicians. These • One day short course on Chaotic dynamical systems include the following symposia (three-hour sessions) by ROBERT L. DEVANEY, Boston University. and invited talks cosponsored by Section A (Mathe matics) of the AAAS and the Society. The names and Section A of the AAAS is also cosponsoring various affiliations of the organizers follow (speakers are given symposia that will be of interest to mathematicians in parentheses): and mathematics educators. These include: • Radon and Penrose transforms: Medical imaging • Chaos in the balance of nature to supersymmetry, organized by JAMES V. PETERs, • Symmetry: Its theory and application through sci Long Island University, C.W. Post Center, and ence TODD QUINTO, Tufts University. (Allan Cormack, Gabor Herman, Larry Shepp, Ron 0. Wells.) • Mathematical models in the social sciences • New directions in the philosophy of mathematics, • The contributions of R.A. Fisher to science (sym organized by REUBEN HERSH, University of New posium commemorating the centennial of R.A. Mexico. (Gian-Carlo Rota, Thomas Tymoczko, Fisher's birthday) Nicholas Goodman, Hao Wang, Martin Krieger, • Revitalizing science and mathematics education Michael Resnik.) through the use of technology • Computational and mathematical modeling: A study • Project approaches in developing new introductory of oil production and water resources, organized by physics, chemistry, and mathematics curricula JAMES G. GLIMM, New York University. (James • The development of pre-adult attitudes toward sci Richard Ewing, Brent Lindquist, Larry Glimm, ence and mathematics in Japan and the United David Wilkinson.) Lake, States. • Geometry today, organized by ERWIN LuTWAK, A meeting of the Section A Committee will take Polytechnic University of New York, and RALPH place from 4:00 p.m. to 6:00 p.m. on February 1S ALEXANDER, University of Illinois at Urbana. in Marlborough BRoom of the New Orleans Hilton. (George Francis, Vladimir Oliker, Herman Gluck, The committee meeting is open to all who wish to Gian-Carlo Rota.) stimulate interest and activities of the mathematical • Zero knowledge proofs and their applications, or sciences within the AAAS. ganized by SILVIO MICALI, Massachusetts Institute For details see the November 10, 1989, issue of of Technology. (Shaft Goldwasser, Manuel Blum, Science. Additional information on Section A activ Silvio Micali). ities can be found in the News and Announcements section of this issue of Notices. 1244 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY 1988-1989. Academic Year Devoted to Mathematical Sciences Operator Algebras, Mittag-Leffler Insti tute, Djursholm, Sweden. (Feb. 1988, Meetings and Conferences p. 307) 1989. 40th Anniversary of Kansas Gamma of Pi Mu Epsilon, Wichita State Univer sity, Wichita, KS. (Jan. 1989, p. 63) 1989. Concentration Year on Fluid Dy namical Aspects of Combustion Theory, lnstituto Per Le Applicazioni Del Cal colo, Rome, Italy. (Jan. 1989, p. 63) 1989-1990. Academic Year Devoted to Hyperbolic Geometry and Quasiconformal Mappings, Mittag-Leffler Institute, Djur sholm, Sweden. (Dec. 1988, p. 1584) THIS SECTION contains announcements of meetings and conferences of interest to some segment of the mathematical public, including ad hoc, local, or regional meetings, * 1989-1990. Special Year in Geometry, and meetings or symposia devoted to specialized topics, as well as announcements University of Maryland, College Park, of regularly scheduled meetings of national or international mathematical organizations. MD. (Information on meetings of the Society, and on meetings sponsored by the Society, will SPONSORs: The University of Mary be found inside the front cover.) AN ANNOUNCEMENT will be published in Notices if it contains a call for papers, land and the National Science Foun and specifies the place, date, subject (when applicable), and the speakers; a second dation. full announcement will be published only if there are changes or necessary additional CONFERENCE THEMES AND INFORMA information. Once an announcement has appeared, the event will be briefly noted in each TION: Activities besides the "Folia issue until it has been held and a reference will be given in parentheses to the month, tions conference in memory of Bruce year, and page of the issue in which the complete information appeared. Asterisks (*) Reinhart" (Jul./ Aug. 1989, p. 762) mark those announcements containing new or revised information. and the annual "Geometry Festival" IN GENERAL, announcements of meetings and conferences held in North America carry will include workshops on the topics: only date, title of meeting, place of meeting, names of speakers (or sometimes a general "Spaces of Riemannian manifolds" statement on the program), deadlines for abstracts or contributed papers, and source of further information. Meetings held outside the North American area may carry more - contact K. Grove, 301-454-7075; detailed information. In any case, if there is any application deadline with respect to "Moduli spaces" - contact B. Gold participation in the meeting, this fact should be noted. All communications on meetings man, 301-454-2929; "Cyclic Homol and conferences in the mathematical sciences should be sent to the Editor of Notices, ogy" - contact J. Schafer, 301-454- care of the American Mathematical Society in Providence. 3535. DEADLINES for entries in this section are listed on the inside front cover of each issue. In order to allow participants to arrange their travel plans, organizers of meetings are urged January 1-December 23, 1989. Math to submit information for these listings early enough to allow them to appear in more than ematisches Forschungsinstitut Oberwol one issue of Notices prior to the meeting in question. To achieve this, listings should be fach (Weekly Conferences), Federal Re received in Providence SIX MONTHS prior to the scheduled date of the meeting. public of Germany. (Apr. 1988, p. 629 and Nov. 1988, p. 1381) (Computer Science); nfw2@pace (Bit 19-25. Random Partial Differential Equa November 1989 net). tions, Oberwolfach, Federal Republic of Germany. (Jul./ Aug. 1989, p. 764) 15-1 7. Geometry of Manifolds, Research * 11. New York Graph Theory Day Eigh- 20-24. Seminaire Sud-Rhodanien de Ge Institute for Mathematical Sciences, Ky teen, Pace University, New York, NY. ometrie Differentielle, Marseille, France. oto University, Japan. (Jul./ Aug. 1989, (Jul./Aug. 1989, p. 764) SPONSOR: Mathematics Section, New p. 764) 26-December 2. Methoden und Ver York Academy of Sciences. 17-20. Workshop on Classical and Quan fahren der Mathematischen Physik, Ober INVITED SPEAKERS: N. J. A. Sloane tum Transport in Hamiltonian Systems, wolfach, Federal Republic of Germany. (AT&T Bell Lab.), W.T. Tutte (Uni Mathematical Sciences Institute, Cornell (Jul./Aug. 1989, p. 764) versity of Waterloo). University, Ithaca, NY. (May/Jun. 1989, ORGANIZING COMMITTEE: W. J. p. 600) 27-29. Computer Algebra and Its Ap Adams, M. L. Gargano, J. E. Houle, plication to Investigations for Mathemat 18-19. Far Western Section Meeting of J. W. Kennedy, S. M. Merritt, L. V. ics, Research Institute for Mathemati the AMS, University of California, Los Quintas, C. Wolf. cal Sciences, Kyoto University, Japan. Angeles, CA. INFORMATION: GTD XVIII, Mathe (Jul./ Aug. 1989, p. 764) matics Department, Pace Univ., New INFORMATION: W. Drady, AMS, P.O. 27-29. The Recent Developments of High York, NY 10038; Telephone: 212-346- Box 6248, Providence, RI 02940. Technology and Mathematical Science 1280 (Mathematics); 212-346-1336 (II), Research Institute for Mathemat- NOVEMBER 1989, VOLUME 36, NUMBER 9 1245 Meetings and Conferences ical Sciences, Kyoto University, Japan. ranek, and Newman; N.F. Maxem 13-15. Twenty-eighth IEEE Conference (Jul./ Aug. 1989, p. 765) chuk, AT&T Bell Labs.; O.K. Prad on Decision and Control, Tampa, FL. * 27-December I. Workshop on Proba han, Univ. of Massachusetts; A. (Oct. 1989, p. 1093) bilistic Methods in Discrete and Computa Prekopa, Rutgers Univ.; S. Provan, 17-23. Theory and Numerical Meth tional Geometry and Tutorial on Random Univ. of North Carolina; C.S. Rag ods for Initial-Boundary Value Problems, Sampling and its Applications, Rutgers havendra, Univ. of Southern Califor Oberwolfach, Federal Republic of Ger University, Piscataway, NJ. nia; D. Shier, College of William and many. (Mar. 1989, p. 314) Mary. 18-20. Waves and Turbulence in Stably SPONSOR: DIMACS. * INFORMATioN: DIMACS, Hill Center, Statified Flows, Leeds, England. INFORMATION: DIMACS, Hill Center, Busch Campus, Rutgers Univ., P.O. Busch Campus, Rutgers University, Box 1179, Piscataway, NJ 08855; 201- INFORMATION: Y. May, Conference P.O. Box 1179, Piscataway, NJ 08855; 932-5928; [email protected]. Officer, The Institute of Mathematics 201-932-5928. and its Applications, Maitland House, 3-9. Wiener-Hopf-Probleme, Topelitz Warrior Square, Southend-on-Sea, Es 29-December 1. Numerical Analysis and Operatoren und Anwendungen, Oberwol sex SS I 2JY, England. Scientific Computing, Research Institute fach, Federal Republic of Germany. for Mathematical Sciences, Kyoto Uni (Jul./ Aug. 1989, p. 765) * 18-20. Cryptography and Coding, Cir- Aug. 1989, p. 765) versity, Japan. (Jul./ 4-6. 1989 Winter Simulation Confer cencester, England. ence, Washington, DC. (MayjJun. 1989, INFORMATION: Y. May, Conference December 1989 p. 600) Officer, The Institute of Mathematics 4-6. Studies on Decision Theory and and its Applications, Maitland House, * 2-4. DIMACS Workshop on Reliability Their Related Topics, Research Institute Warrior Square, Southend-on-Sea, Es of Computer and Communication Net for Mathematical Sciences, Kyoto Uni sex SS1 2JY, England. works, New Brunswick, NJ. versity, Japan. (Jul./ Aug. 1989, p. 765) 27-31. Holiday Symposium on Braids Reliability problems arise on PROGRAM: 4-6. First International Conference and Knots, New Mexico State University, increasing frequency as our mod Databases, with Deductive and Object-Oriented Las Cruces, NM. (Sep. 1989, p. 914) ern systems of telecommunications, Kyoto, Japan. (Oct. 1989, p. 1093) information transmission, transporta 4-7. Research on Complex Analytic Ge tion, and distribution become more ometry and Related Topics, Research In and more complex. This workshop is stitute for Mathematical Sciences, Ky 1990. IMACS International Workshop designed to analyze the discrete math oto University, Japan. (Jul./ Aug. 1989, on Massively Parallel Methods in Com ematical methods which are relevant p. 765) putational Physics, Boulder, Colorado. identify the latest to these problems, 4-8. Fifth Aerospace Computer Secu (Sep. 1989, p. 914) and important open problems, trends rity Applications Conference, Tucson, AZ. 1990. IMACS Conference on Computer potential practical applica and survey (MayfJun. 1989, p. 600) Aided Design, Yugoslavia. (Sep. 1989, tions, with an emphasis on computer Theory, Research p. 914) and communication networks. 6-9. Algebraic Number Ky ORGANIZERs: F. Hwang, AT&T Bell Institute for Mathematical Sciences, Japan. (Jul./ Aug. 1989, Labs.; C. Monma, Bell Communica oto University, January 1990 tions Research; F. Roberts, Rutgers p. 765) Oberwolfach, Univ. 9. Boston Celebration of the ASA150 1-6. Zeitreihenanalyse, of Germany. (Mar. INVITED SPEAKERS: D.P. Agrawal, Sesquicentennial, Boston, MA. (Sep. 1989, Federal Republic North Carolina State Univ.; G. Ash, p. 914) 1989, p. 314) AT&T Bell Labs.; F. Barlow, Univ. of 10-16. Asymptotic Methods for 3-5. International Symposium on Arti California, Berkeley; J-C. Bermond, Computer-Intensive Procedures in Statis ficial Intelligence and Mathematics, Fort Univ. of Paris-Sud; D. Bienstock, tics, Oberwolfach, Federal Republic of Lauderdale, FL. (Oct. 1989, p. 1093) Bell Comm. Res.; D. Blair, Rutgers Germany. (Mar. 1989, p. 314) 7-13. Mathematische Optimierung, Ober Univ.; F. Boesch, Stevens Institute 11-13. Fourth SIAM Conference on Par wolfach, Federal Republic of Germany. of Technology; P. Boland, Univ. Col allel Processing for Scientific Computing, (Mar. 1989, p. 314) lege, Dublin; R. Cardwell, Bell Comm. Chicago, IL. (Mar. 1989, p. 314) * 8-12. Workshop on Applications of Al Res.; Y. Cheng, AT&T Bell Labs.; 11-14. Number Theory - Studies Related gebraic Geometry, University of Puerto J. Cohen, Rockefeller Univ.; C. Col to Automorphic Forms, Research Institute Rico, Rio Piedras, Puerto Rico. bourn, Univ. of Waterloo; N. Crystal, for Mathematical Sciences, Kyoto Uni Bell Comm. Res.; W. Cunningham, PROGRAM: The workshop will fea versity, Japan. (Jul./ Aug. 1989, p. 765) on exponen Carleton Univ.; R. Evans, Durham, ture expository lectures 12-14. Second Australian Supercomputer variables, NC; A.G. Fraser, AT&T Bell Labs.; tial sums in one and several Conference, University of Wollongong, M. Grotschel, Univ. of Augsburg; F. and also current work on the Soviet NSW, Australia. (Sep. 1989, p. 914) Hwang, AT&T Bell Labs.; P. Ku Union on applications of algebraic bat, GTE Lab.; M. Lepp, Bolt, Be- geometry to coding theory. Particular attention will be focused on exploring 1246 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences and discovering new possible interac vey Mudd College, Claremont, CA. (Sep. Sumners, J.C. Wang, M.S. Waterman, tions between algebraic geometry and 1989, p. 914) J.H. White. different applied areas. * 13-16. The 1989-1990 Annual Associa CONFERENCE TOPICS: DNA polymor INVITED SPEAKERs: From the U.S.: N. tion for Symbolic Logic Meeting, Univer phism; helical repeat; DNA supercoil Katz, H. Lenstra, H.P. Mattson, A.M. sity of California at Berkeley, CA. ing, structure and function; higher Odlyzco, N.J.A. Sloanne,W. Schmidt, order DNA organization; invariants; S. Sperber, V. Pless; From the Soviet ORGANIZING COMMITTEE: K. Fine, L. DNA geometry and flexibilty; graph Union: S. Litsyn, A.N. Skorobogatov, Harrington, A.S. Kechris (Chair), A. ics; recombination and transposition; M.A. Tsfasman, S.A. Stepanov, S.G. Scedrov. sequencing, matching and mapping. Vladut; From Norway: T. Helleseth. INVITED SPEAKERS: G. Cherlin, M. CALL FOR PAPERS: Abstract deadline CALL FOR PAPERs: One page abstract Magidor, W. Just, L. Blum, C. is December 1, 1989. should be received by December 20, Jockusch, P. Scowcroft, P. Scott, M. INFORMATION: S.J. Spengler, Program 1989; include address and email if Fitting, N. Belnap, G. Boolos, E. in Mathematics and Molecular Bi possible. Hrushovski. ology, 214A Stanley Hall, Univ. of INFORMATION: 0. Moreno, Depart INFORMATION: C. Ward Henson, Sec California, Berkeley, CA 94720; Fax ment of Mathematics, University retary-Treasurer, Department of Math (415)643-9290; voice (415)643-7799; of Puerto Rico, Rio Piedras, Puerto ematics, University of Illinois, 1409 email: [email protected] or Rico, 809-765-5170, 809-765-3263; West Green St., Urbana, IL 61801. sylviaj@ucbviole. bitnet. email: [email protected] 14-20. Nonlinear Evolution Equations, 28-February 3. Regelungstheorie, Ober and Carlos Moreno Solitons and the Inverse Scattering Trans ([email protected]). wolfach, Federal Republic of Germany. form, Oberwolfach, Federal Republic of (Mar. 1989, p. 314) Germany. (Mar. 1989, p. 314) * 8-12. DIMACS Workshop: Polytopes 29-February 16. Second College on Vari and Convex Sets, Center for Discrete 15-26. Workshop on Composite Me ational Problems in Analysis, Interna Mathematics and Theoretical Computer dia and Homogenization Theory, Inter tional Centre for Theoretical Physics, Science, New Brunswick, NJ. national Centre for Theoretical Physics, Trieste, Italy. (May/Jun. 1989, p. 600) Trieste, Italy. (May /Jun. 1989, p. 600) PROGRAM: This is the third workshop 16-17. AMS Short Course on Mathe in the DIMACS Special Year on Dis matical Questions in Robotics, Louisville, February 1990 crete and Computational Geometry. KY. The plan is to have a small number of * 1-4. Topological and Measurable Dy- invited and contributed talks, in order INFORMATION: M. Foulkes, AMS, P.O. namics, Minneapolis, MN. to encourage more direct interaction Box 6248, Providence, RI 02940. ORGANIZERS: R. Ellis, H. Keynes, S. among the participants. N. Chow, M. Golubitsky, G.R. Sell. ORGANIZERs: L. Billera and J. E. 17-20. Joint Mathematics Meetings, Louisville, KY. (Including the annual INFORMATION: Institute for Mathe Goodman. matics and Its Applications, 514 Vin INVITED SPEAKERs: G. Kalai, Hebrew meetings of the AMS, AWM, MAA and NAM). cent Hall, 206 Church Street S.E., Univ.; V. K.lee, Univ. of Washing Minneapolis, Minnesota 55455; ton; C. Lee, Univ. of Kentucky; P. INFORMATION: H. Daly, AMS, P.O. Phone: 612-624-6066. Mani-Levitska, Univ. of Bern; M. Per Box 6248, Providence, RI 02940. les, Hebrew Univ.; R. Seidel, Univ. 3. Eighty-seventh Ontario Mathematics of California, Berkeley; R. Wenger, 21-27. Modelltheorie, Oberwolfach, Fed Meeting, Ottawa, Ontario, Canada. (Oct. DIMACS. eral Republic of Germany. (Mar. 1989, 1989, p. 1094) INFORMATION: DIMACS, Hill Center, p. 314) 4-10. Funktiontheoretische Methoden Busch Campus, Rutgers University, 22-24. ACM/SIAM Symposium on Dis Bei Partiellen Differential Und Integral P.O. Box 1179, Piscataway, crete Algorithms, San Francisco, CA. gleichungen, Oberwolfach, Federal Re NJ 08855; 201-932-5928; (Sep. 1989, p. 915) public of Germany. (Mar. 1989, p. 314) [email protected]. 22-26. Workshop on Applications of Al 4-10. Nukleare Frechet-Riiume, Ober Topology to Geometry and Analy 8-13. Workshop on Variational Meth gebraic wolfach, Federal Republic of Germany. Mathematical Sciences Research In ods in Hamiltonian Systems and Elliptic sis, (Mar. 1989, p. 314) Berkeley, CA. (May /Jun. 1989, Equations, L'Aquila, Italy. (Oct. 1989, stitute, 5-10. Eighth International Seminar on p. 1093) p. 600) Model Optimization in Exploration Geo Mathematical Approaches to 9-13. Stable Processes and Related Top * 24-28. physics, with a Workshop on Geophysical (Knot Theory, Topology, Geometry, ics Workshop, Ithaca, NY. (Oct. 1989, DNA Data Inversion in Environmental Research New p. 1093) Probability, Statistics), Santa Fe, and Planning, Berlin-West, Free Univer Mexico. sity of Berlin, Federal Republic of Ger 10-13. International Conference on Dif many. (Jul./ Aug. 1989, p. 765) ferential Equations and Applications to ORGANIZING COMMITTEE: N.R. Coz Biology and Population Dynamics, Har- zarelli, E. Lander, S.J. Spengler, D. 11-15. The Twenty-sixth Australian Ap plied Mathematics Conference, Coolan- NOVEMBER 1989, VOLUME 36, NUMBER 9 1247 Meetings and Conferences gatta, Queensland, Australia. (Sep. 1989, especially at the elementary and high 16-1 7. Central Section Meeting of the p. 915) school level, and discussions of related AMS, Kansas State University, Manhat 11-17. Funktiontheorie, Oberwolfach, issues and programs that effect math tan, KS. ematicians working in educational re Federal Republic of Germany. (Mar. INFORMATION: W. Drady, AMS, P.O. form. 1989, p. 315) Box 6248, Providence, RI 02940. 15-20. American Association for the INVITED SPEAKERs: K. Hoffman, Advancement of Science Annual Meeting, MSEB; A. Ross, Ohio State Univ.; P. 18-24. Masstheorie, Oberwo1fach, Fed New Orleans, LA. (Please note changes Wagreich, Univ. of Illinois at Chicago; eral Republic of Germany. (Mar. 1989, from Sep. 1989, p. 915) H. Keynes, Univ. of Minnesota; F. p. 315) Demana, Ohio State Univ.; U. Treis 18-24. Third Centenary Celebration of AAAS, 1333 H St., INFORMATION: man, Univ. of California at Berke the Mathematische Gesellschaft in Ham Washington, DC 20005; 202- N.W., ley; C. Mahoney, Denison Univ.; T. burg, BundesstraBe, Hamburg. (Oct. 1989, Sec 326-6640.For information about Berger, NSF; E. Fennema, Univ. of p. 1094) tion A (Mathematics) Activities, con Wisconsin-Madison. 19-22. Eleventh Annual National Graph tact Warren Page by calling 914-476- INFORMATION: N. Fisher, Associate ics Association Conference and Expo 6446. Director, MER Network, University sition, Anaheim, CA. (Jul./ Aug. 1989, of Illinois at Chicago, Office of Mathe and Group p. 766) * 17-19. Algebraic Geometry matics and Computer Education Meeting of Theory Conference/Inaugural (M/C 249), Box 4348, Chicago, IL 19-24. US-USSR Approximation Theory Palm Beach, the Ulam Quarterly, West 60680; telephone: 312-996-2439, Conference, University of South Florida, Florida. bitnet U37158@UICVM. Tampa, FL. (Jul./ Aug. 1989, p. 766) SPONSORs: Palm Beach Atlantic Col * 19-April 13. Mathematical Physiology lege and Ulam Quarterly. 4-10. Interval Methods for Numerical and Differential-Delay Equations, Min CALL FOR PAPERS: Deadline for Paper Computation, Oberwolfach, Federal Re neapolis, MN. public of Germany. (Mar. 1989, p. 315) Proposals: January 5, 1990. ORGANIZERS: S.-N. Chow, M. Golu 5-7. SIAM Conference on Applied Prob INFORMATION: P. Blass, Palm Beach bitsky, J. Hale, N. Kopell, M. Mackey, ability in Science and Engineering, New Atlantic College, Department of Math J. Mallet-Paret, R. McGehee, G.R. Orleans, LA. (Nov. 1988, p. 1389) ematics, P.O. Box 3353, West Palm Sell. Beach, FL 33402-3353; phone: 407- 5-7. Symposium on Symbolic Computa INFORMATION: Institute for Mathe 835-4353. tion (on the occasion of the sixtieth birth matics and Its Applications, 514 Vin day of Erwin Engeler), Ziirich, Switzer cent Hall, 206 Church Street S.E., 18-24. Mathematische Modelle in Der land. (Sep. 1989, p. 915) Biologie, Oberwolfach, Federal Republic Minneapolis, Minnesota 55455; 11-17. Mathematische Stochastik, Ober of Germany. (Mar. 1989, p. 315) Phone: 612-624-6066. wolfach, Federal Republic of Germany. 20-22. Association for Computing Ma (Mar. 1989, p. 315) 20-23. Directions in Matrix Theory, chinery 1990 Computer Science Confer * 12-16. Twist Mappings and Their Ap- Auburn, AL. (May/Jun. 1989, p. 601) ence, Washington, D.C. (MayfJun. 1989, plications, Minneapolis, MN. 23-24. Southeastern Section Meeting p. 601) of the AMS, University of Arkansas, 22-23. Twenty-first SIGCSE Technical ORGANIZERS: L.P. Kadanoff, K. Fayetteville, AR. Symposium, Washington, D.C. (MayfJun. Meyer, J. Moser, C. Robinson, E. 1989, p. 601) Zehnder, S.-N. Chow, M. Golubitsky, INFORMATION: W. Drady, AMS, P.O. Box 6248, Providence, RI 0240. 25-March 3. Eigenwertaufgaben In Natur R. McGehee, G.R. Sell. INFORMATION: Institute for Mathe Und Ingenieurwissensachaften Und lhre 23-24. University of Arkansas' Four matics and Its Applications, 514 Vin Numerische Behandlung, Oberwolfach, teenth Annual Lecture Series in Math cent Hall, 206 Church Street S.E., Federal Republic of Germany. (Mar. ematical Sciences, Univ. of Arkansas, Minneapolis, Minnesota 55455; 1989, p. 315) Fayetteville, Arkansas. (Oct. 1989, Phone: 612-624-6066. 26-March 2. IEEE Computer Society p. 1095) COMPCON Spring '90, San Francisco, 13-16. Twenty-first Annual Iranian 25-31. Kontinuumsmechanik der Festen CA. (Sep. 1989, p. 915) Mathematics Conference, University of Korper, Oberwolfach, Federal Republic Isfahan, Iran. (Jul./Aug. 1989, p. 766) of Germany. (Mar. 1989, p. 315) March 1990 14-19. East European Category Semi 26-29. Workshop on Number Theory and nar, Predela, Bulgaria. (May I Jun. 1989, Algorithms, Berkeley, CA. (Sep. 1989, p. * 1-4. Mathematicians and Education Re p. 601) 916) form Network, Ohio State University, 15-21. International Conference on Dif 26-April 6. Workshop on Group Theory Columbus, Ohio. ferential Equations and Mathematical from a Geometrical Viewpoint, Interna PROGRAM: The workshop features pre Physics, University of Alabama at Birm tional Centre for Theoretical Physics, sentations by mathematicians who ingham, Alabama. (Oct. 1989, p. 1094) Trieste, Italy. (May/Jun. 1989, p. 601) have developed "exemplary projects", 1248 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences * 28-29. Chaos in Praxis: The Application INVITED SPEAKERs: M. H. Kalos, E.E. PROGRAM COMMITTEE: L. van den of Nonlinear Dynamics in Social Realms, David, P.D. Lax, J.-L. Lions, I. Peter Dries, S.G. Simpson (Chair), L. Stan Battelle Conference Center, Seattle, WA. son, S. Winograd, M.F. Wheeler, J.J. ley. Hopfield, W.W. Hollis, M.E. Fisher. CALL FOR PAPERS: ASL members SPONSORs: Battelle Research Institute should submit abstracts of contributed (with the Department of Energy), papers by February 2, 1990 to S.G. Seattle and Antioch University, Seat April1990 Simpson at the address below. Ab tle. Spring Meeting, Baltimore, stracts should be no longer than one PuRPOSE: This conference will pro 1-4. ENAR MD. (Jul./ Aug. 1989, p. 766) page (300 words) and should be suit vide an overview of the concepts for eventual publication in the 1-7. Design and Codes, Oberwolfach, able of nonlinear science, and show how of Symbolic Logic as part of Federal Republic of Germany. (Jul./ Aug. Journal those concepts are being applied to a the meeting report. in 1989, p. 766) wide variety of current problems INFORMATION: S.G. Simpson, Math. Study Institute the social sciences. In addition, tech 1-14. NATO Advanced Dept., Penn State University, McAl in Groups niques for modeling the dynamics of on "Generators and Relations lister Building, University Park, PA Castelvecchio Pascoli social systems will be demonstrated. and Geometries", 16802. CONFERENCE TOPICS: Nonlinear math (Lucca), Italy. (Sep. 1989, p. 916) ematical models, self-organizing sys 4-7. Symposium on Distributions with 8-14. Arbeitsgemeinschaft Mit Aktuellem tems, fractal models of social behav Given Marginals (In Memory of Giuseppe Thema (wird in den Mitteilungen der ior, modeling the dynamics of orga Pompilj), Rome, Italy. (Oct. 1989, p. 1095) DMV Heft 1/1990 bekanntgegeben), Ober nizations, chaos and creativity, psy * 5-7. Twenty-fourth Annual Spring Topol wolfach, Federal Republic of Germany. chology of decision making, new di ogy Conference, Southwest Texas State (Jul./ Aug. 1989, p. 766) rections in global economic models, Univ., San Marcos, TX. * 9-13. Fifth Workshop on Mathemati future trends in modeling social phe cal Aspects of Computer Science, Magde All areas of topology will nomena. PROGRAM: sprung, German Democratic Republic. INVITED SPEAKERS: R. Abraham, Univ. be covered. Some areas of special in of California, Santa Cruz; J. Casti, terest are general, point-set, and geo INFORMATION: J. Dassow, Magdeburg Technical Univ. of Vienna; R. De metric topology, continua theory, and University of Technology, Depart vaney, Boston Univ.; W. Freeman, dynamical systems. ment of Mathematics, PSF 124 Magde Univ. of California, Berkeley; P. Rapp, ORGANIZING COMMITTEE: S. Singh, burg, DDR-3010, German Democratic Medical College of Pennsylvania; J. T. Thickstun, S. Wayment. Republic. Massachusetts Institute of INVITED SPEAKERs: J. W. Cannon, Sterman, 15-21. Mathematical Concepts of De Technology. W. G. Fleissner, C. Gordon, S. New pendable Systems, Oberwolfach, Federal FOR PAPERs: Deadline is Jan house, C. Pugh, A. Dranishnikov, D. CALL Republic of Germany. (Jul./ Aug. 1989, uary 31, 1990. Fried, L. Oversteegen, J. T. Rogers. p. 766) INFORMATION: T. Masters, Orion/ CALL FOR PAPERS: Fifteen-minute Annual Meeting of Wellspring, 900 Queen Anne Ave. talks in all branches of topology are 18-21. Sixty-eighth Council of Teachers of Math N. 308, P.O. Box 9080, Seattle, WA solicited. Send a type-written (camera the National UT. (Jul./ Aug. 981 09; phone: 206-283-8959. ready) abstract, consisting of two hun ematics, Salt Lake City, dred words or less, of your talk to the 1989, p. 766) 29-31. Modern Perspectives of Mathe address below. Abstracts should be * 19-21. Fourth National Conference on matics: Mathematics in Academia, Math received by March 1, 1990. Undergraduate Research, Union College, ematics as a Consumer Good, Cornell INFORMATION: S. Singh, Department Schenectady, NY. University, Ithaca, NY. (Please note of Mathematics, Southwest Texas PROGRAM: The conference is expected changes in name and content from State University, San Marcos, TX to attract about 1500 undergraduate Jul./Aug. 1989, p. 766) 78666; phone: 512-245-3421; email students and faculty members to dis ma_singh@swtexas. bitnet. PuRPOsE: Designed to examine the cuss their scholarly and creative ac nation's use and development of math 7-8. Eastern Section Meeting of the tivities in a range of disciplines. Re ematics resources, leaders from busi AMS, Pennsylvania State University, Uni search papers, exhibitions, and poster ness and industry, government, and versity Park, PA. (Note change in date sessions will be presented in the arts, academia will address how to develop from Oct. 1989, p. 1095) engineering, the humanities, mathe mathematics education and research matics and computer science, man in ways that will encourage the in INFORMATION: W. Drady, AMS, P.O. agement and business, the natural sci terplay of mathematics and its ap Box 6248, Providence, RI 02940. ences, and the social sciences. plications in business, industry and SPEAKERS: Joyce Carol Oates, * 7-8. 1990 Association for Symbolic INVITED government. Richard Voss. Logic Spring Meeting (in conjunction Helen Caldicott, and ORGANIZING COMMITTEE: Y. Terzian FOR PAPERs: Deadline for sub with a Spring meeting of the AMS and CALL (Chair), W.V. Kone, S.A. Levin, A. of abstracts is February 13, a MAMLS meeting), Pennsylvania State mission Nerode, L.B. Wahlbin, D. Willard. University, University Park, PA. 1990. NOVEMBER 1989, VOLUME 36, NUMBER 9 1249 Meetings and Conferences INFORMATION: NCUR-90, Wells 7-June I. College on Recent Develop should be sent in triplicate to A.V. House, 1 Union Ave., Schenectady, ments and Applications in Mathematics Fiacco. Abstracts should provide a NY 12308; phone 518-370-6649. and Computer Science, International Cen good technical summary of key re tre for Theoretical Physics, Trieste, Italy. sults, avoid the use of mathematical 19-22. 1990 Far Western Section, Uni (MayjJun. 1989, p. 601) symbols and references, not exceed Mexico, Albuquerque, versity of New 13-1 9. Abstrakte Konvexe Analysis, 500 words, and include a title and the Mexico. New Oberwolfach, Federal Republic of Ger name and full mailing address of each deadline for submission INFORMATION: W. Drady, AMS, P.O. many. (Jul./ Aug. 1989, p. 766) author. The is March 9, 1990. Box 6248, Providence, RI 02940. 14-18. Conference on Nonlinear Anal INFORMATION: A.V. Fiacco, Organizer, ysis and Partial Differential Equations, Conference on Analytic The George Washington University, 22-27. Tenth Rutgers University, New Brunswick, NJ. Poland. (Oct. 1989, Washington, DC 20052; phone: 202- Functions, Kozubnik, (Jul./ Aug. 1989, p. 767) p. 1095) 994-7511. 17-1 9. Interface '90 (formerly Computer Einhollende Algebren und Ringe 22-28. Science and Statistics: Symposium on In 25-31. Tenth International Conference Oberwolfach, Von Differentialoperatoren, terface), East Lansing, MI. (Sep. 1989, on Pattern Recognition, Resorts Hotel, Republic of Germany. (Jul./ Aug. Federal p. 916) Atlantic City, NJ. (Mar. 1988, p. 466) 1989, p. 766) 20-26. The Schrodinger Equation and 27-June 2. Lyapunov-Exponents, Ober Symposium on Value Distribu * 28-29. Its Classical Counterparts, Oberwolfach, wolfach, Federal Republic of Germany. in Several Complex Variables, tion Theory Federal Republic of Germany. (Jul./ Aug. (Jul./ Aug. 1989, p. 767) Univ. of Notre Dame, Notre Dame, In 1989, p. 767) of Complex Projec- diana. * 28-June 2. Geometry 21-24. The Simulation of Random Pro tive Varieties, Cetraro, Italy. SPONSOR: University of Notre Dame. cesses and Fields - Mathematics and ORGANIZING CoMMITTEE: F. Catanese, PuRPosE: The symposium shall por Applications, Portofino, Italy. (Sep. 1989, A. Conte, T. Fujita, J. Guenot, A. tray value distribution theorem in p. 916) M. Palleschi, A.J. Sommese, several complex variables, its devel Lanteri, 21-25. Eleventh United States National Struppa. opment, its connection to other fields, D.C. Congress of Applied Mechanics, Tucson, SPEAKERS: L. Badescu and its hope for the future. The Uni INVITED AZ. (Nov. 1988, p. 1389) F. Catanese (Pisa), C. versity of Notre Dame Press will pub (Bucharest), 23-25. 1990 International Symposium A. Conte (Torino), lish the proceedings. Ciliberto (Roma), on Multiple-Valued Logic, Charlotte, NC. (Ann Arbor), T. Fu INVITED SPEAKERs: S.-S. Chern (In I. Doglachev (Apr. 1989, p. 496) L. Gottsche (Bonn), C. vited Participant), D. Drasin, G. jita (Tokyo), on Mathe P. Ionescu Henkin, S. Lang, B. Shiffman, Y.-T. * 24-25. Twelfth Symposium Hulek (Bayreuth), with Data Perturba V. Iskovskih (Moscow), Siu, W. Stoll, P.-M. Wong, L. Yang. matical Programming (Bucharest), Univ., Wash (Paris), K. Ranestad (Oslo), INFORMATION: W. Stoll, Department tions, George Washington C. Peskine F. Sakai (Urawa), of Mathematics, University of Notre ington, DC. I. Reider (Norman), M. Schneider (Bayreuth), F. Serrano Dame, P.O. Box 398, Notre Dame, PuRPOSE: The symposium is designed (Barcelona), A.J. Sommese (Notre IN 46556. to bring together practitioners who Dame), F. Zak (Moscow). use mathematical programming opti 29-May 5. Gruppentheorie (Pro-Endliche mization models and deal with ques Logic Conference in Gruppen), Oberwolfach, Federal Repub * 29-30. Algebraic tions of sensitivity analysis, with re of Professor Don Monk, Boulder, lic of Germany. (Jul./ Aug. 1989, p. 766) Honour searchers who are developing tech Colorado. niques applicable to these problems. Depart CALL FOR PAPERs: Contributed pa INFORMATION: W. Taylor, May 1990 Box pers in mathematical programming ment of Mathematics, Campus 3-4. Twenty-first Annual Pittsburgh Con are solicited in the following areas: 426, Boulder, Colorado 80309-0426. ference on Modeling and Simulation, Uni re sensitivity and stability analysis 29-June 1. Eleventh Annual Conference versity of Pittsburgh, Pittsburgh, P A. solution sults and their applications, of the Canadian Applied Mathematics (Sep. 1989, p. 916) im methods for problems involving Society, Halifax, Nova Scotia. (Oct. 1989, Mathematik, Ober so 6-12. Geschichte der plicitly defined problem functions, p. 1096) wolfach, Federal Republic of Germany. lution methods for problems involv 29-June 2. Dynamical Theories of Turbu- (Jul./ Aug. 1989, p. 766) ing deterministic or stochastic param * lence in Fluid Flows, Minneapolis, MN. 7-9. 1990 IEEE Symposium on Research eter changes, solution approximation in Security and Privacy, Oakland, CA. techniques and error analysis. "Clini ORGANIZERS: S.-N. Chow, C. Foias, (Oct. 1989, p. 1095) cal" presentations that describe prob M. Golubitsky, R. McGehee, R. 7-10. SIAM Conference on Applications lems in sensitivity or stability analysis Temam. also of Dynamical Systems, Orlando, FL. (Sep. encountered in applications are INFORMATION: Institute for Mathe 1989, p. 916) invited. Abstracts of papers intended matics and Its Applications, 514 Vin for presentation at the symposium cent Hall, 206 Church Street S.E., 1250 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences Minneapolis, Minnesota 55455; Minneapolis, Minnesota 55455; * ll-15. NSF/CBMS Conference on Phone: 612-624-6066. Phone: 612-624-6066. Wavelets, University of Lowell, Lowell, MA. * 29-June 2. Workshop on Dynamical Sys 6-9. Fifth Annual Conference of the tems in Fluid Mechanics, Minneapolis, European Consortium for Mathematics INVITED SPEAKERS: I. Daubechies MN. in Industry, Lahti, Finland. (Apr. 1989, (Principle Lecturer), AT&T Bell Labs.; p. 496) R. Coifman, Yale; S. Mallat, Courant. INFORMATION: W. Miller, Institute INFORMATION: CBMS Wavelet Con for Mathematics and its Applications, 6-12. 1990 Barcelona Conference on Algebraic Topology, Centre de Recerca ference, Department of Mathemat University of Minnesota, 514 Vincent ics, University of Lowell, Lowell, MA Hall, 206 Church St. S.E., Minneapo Matematica, Barcelona, Spain. (Sept. 1988, p. l 060) 01854; phone: 508-934-2410; email: lis, Minnesota 55455. [email protected]. 6-15. Third Logical Biennial (in honour of S.C. Kleene), Chaika (near Varna), 13-15. Seventh Annual Quality and Pro June 1990 Bulgaria. (Oct. 1989, p. 1096) ductivity Research Conference, Madison, June 1990. AMS-SIAM Summer Sem 7-July 4. 1990 Joint Summer Research WI. (Mar. 1989, p. 315) inar on Vortex Dynamics and Vortex Conferences in the Mathematical Sci 13-22. Free Boundary Problems: Theory Methods, Location on the west coast ences, University of Massachusetts at and Applications, Centre de Recherches to be announced. Amherst, MA. Mathematiques, Universite de Montreal, Canada. (Jul./ Aug. 1989, p. 767) INFORMATION: B. Verducci, AMS, P.O. INFORMA noN: C. Kohanski, AMS, Box 6248, Providence, RI 02940. P.O. Box 6248, Providence, Rl 02940. * 14-16. Fifth Southeast Asian Conference on Mathematical Education (SEACME June/July 1990. International IMACS l 0-16. Reelle Algebraische Geometrie, 5), Gadong, Brunei Darussalam. Conference on Mathematical Modelling Oberwolfach, Federal Republic of Ger INFORMATION: D. Daniels, SEACME and Applied Mathematics, Vilnius, USSR. many. (Jul./ Aug. 1989, p. 767) 5 Secretary, University of Brunei (Sep. 1989, p. 917) * 10-16. Fourth Czechoslovak Symposium Darussalam, Gadong, Brunei Darus Prachtice, Czechoslo l-8. Third International Symposium on on Combinatorics, salam (SE Asia). Orthogonal Polynomials and Their Ap vakia. plications, Erice-Trapani (Sicily), Italy. INFORMATION: P. Liebel, MU CSAV, 17-23. Partial Differential Equations in (Please note change in name from Sep. 115 6 7 Praha 1 , Czechoslovakia. Complex Analysis, Oberwolfach, Federal 1989, p. 917) Republic of Germany. (Jul./ Aug. 1989, l-1 0. Fourth Annual Meeting of the 11-14. Fourteenth Rolf Nevanlinna Col p. 767) International Workshop in Analysis and loquium, University of Helsinki, Helsinki, 18-20. Joint WNAR-IMS Regional Meet its Applications, Dubrovnik-Kupari, Yu Finland. (Jul./ Aug. 1989, p. 767) ing, Montana State University, Bozeman, goslavia. (Oct. 1989, p. 1096) 11-14. World Organization of Systems MT. (Mar. 1989, p. 315) 3-6. 1990 Annual Meeting of the Sta and Cybernetics Eighth International Con 18-22. Fourteenth Mathematical Sci tistical Society of Canada, St. John's, gress, New York, NY. (Mar. 1989, p. 315) ences Lecture Series on Partially Ordered Newfoundland, Canada. (Sep. 1989, 11-14. Fifth SIAM Conference on Dis Sets, Johns Hopkins University, Balti p. 917) crete Mathematics, Atlanta, GA. (Sep. more, Maryland. (Oct. 1989, p. 1096) 3-9. Graphentheorie, Oberwolfach, Fed 1989, p. 917) * 18-29. Radar/Sonar, Minneapolis, MN. eral Republic of Germany. (Jul./ Aug. * 11-15. Chaotic Processes in the Geolog- ORGANIZERs: M. Bern4feld, R.E. 1989, p. 767) ical Sciences, Minneapolis, MN. Blahut, A. Grunbaum, R. Tolimieri. 4-7. Fifth Annual IEEE Symposium on ORGANIZERS: G.F. Carnevale, S.-N. INFORMATION: Institute for Mathe Logic in Computer Science, Philadelphia, Chow, M. Golubitsky, R. McGehee, matics and Its Applications, 514 Vin PA. (Sep. 1989, p. 917) R. Pierrehumbert, G.R. Sell. cent Hall, 206 Church Street S.E., 4-8. Workshop on Model Theory, Berke INFORMATION: Institute for Mathe Minneapolis, Minnesota 55455; ley, CA. (Sep. 1989, p. 917) matics and Its Applications, 514 Vin Phone: 612-624-6066. * 4-8. Nonlinear Phenomena in Atmo cent Hall, 206 Church Street S.E., spheric and Oceanic Sciences, Minneapo Minneapolis, Minnesota 55455; 24-30. Mathematische Probleme in der lis, MN. Phone: 612-624-6066. Nichtlinearen Elastizitiit, Oberwolfach, Federal Republic of Germany. (Jul./ Aug. ORGANIZERs: G.F. Carnevale, S.-N. 11-15. Third International Conference on 1989, p. 767) Chow, C. Foias, M. Golubitsky, R. Hyperbolic Problems, Uppsala, Sweden. 25-29. International Symposium on McGehee, R. Pierrehumbert, G.R. (Jul./ Aug. 1989, p. 767) Fuzzy Approach to Reasoning and Deci Sell, D. Yen. 11-15. Rigorous Results in Quantum Dy sion INFORMATION: Institute for Mathe namics, Liblice Castle, Czechoslovakia. Making, Bochyne, Czechoslovakia. (Oct. matics and Its Applications, S 14 Vin (May fJun. 1989, p. 602) 1989, p. 1096) cent Hall, 206 Church Street S.E., 27-30. Fourth International Congress on Algebraic Hyperstructures and Ap- NOVEMBER 1989. VOLUME 36, NUMBER 9 1251 Meetings and Conferences plications, Xanthi, Greece. (Apr. 1989, 8-14. Variationsrechnung, Oberwolfach, by May 1, 1990. Abstracts and man p. 496) Federal Republic of Germany. (Apr. uscripts should be sent in duplicate 1989, p. 497) following the guidelines for submis 9-11. "Universita'di Genova- The Ohio sion of articles found on the inside 1990 July State University Joint Conference" on front cover of any recent issue of The July 1990. AMS Summer Research Insti New Trends in Systems Theory, Genoa, Fibonacci Quarterly to the address tute on Differential Geometry, University Italy. (Jul./ Aug. 1989, p. 768) below. INFORMATION: G.E. Bergum, Depart of California, Los Angeles, CA. 9-20. Geometry and Topology of Four ment of Computer Science, South Manifolds, McMaster University, Hamil INFORMATION: W. Drady, AMS, P.O. Dakota State Univ., P.O.Box 2201, ton, Ontario, Canada. (May I Jun. 1989, Box 6248, Providence, RI 02940. Brookings, SD 57007-0194. p. 602) 1-7. Modulfunktionen In Mehreren Vari 15-21. Stochastic Image Models and Al * 31-August 2. Dynamics of Numerics ablen, Oberwolfach, Federal Republic of gorithms, Oberwolfach, Federal Republic and the Numerics of Dynamics, Bristol, Germany. (Apr. 1989, p. 497) of Germany. (Apr. 1989, p. 497) England. 1-15. International Symposium on Alge * 15-22. 1990 European Summer Meet INFORMATION: Y. May, Conference braic Topology - Adams Memorial Sympo ing (Logic Colloquium '90), University of Officer, The Institute of Mathematics sium, University of Manchester, England. Helsinki, Finland. and its Applications, Maitland House, (Sep. 1989, p. 918) ORGANIZING COMMITTE: J. Viiiiniinen Warrior Square, Southend-on-Sea, Es Session on 1-18. Twentieth Summer (Chair), I. Niiniluoto, A. Halko, H. sex SS1 2JY, England. Probability Theory, Saint-Flour (Cantal), Heikkila, L. Hella, T. Huuskonen, T. 315) France. (Mar. 1989, p. Hyttinen, K. Luosto, J. Oikkonen, H. August 1990 2-6. Tenth Australian Statistical Con Tuuri. ference/Second Pacific Statistical Con INFORMATION: Logic Colloquium cfo 5-11. Mathematical Methods in Tomog gress, Sydney, Australia. (Jul./ Aug. 1989, J. Viiiiniinen, Department of Mathe raphy, Oberwolfach, Federal Republic of p. 768) matics, University of Helsinki, Halli Germany. (Apr. 1989, p. 497) 2-6. The Jonsson Symposium, Laugar tuskatu 15, Finland. 5-11. International Conference on Ap vatn, Iceland. (Sep. 1989, p. 918) proximation Theory, Hungary. (Oct. 1989, Colloquium in Honor of Roland 2-6. Thirty-fourth Annual Meeting of the 15-23. Fraisse, Centre International de Recon p. 1097) Australian Mathematical Society, Towns tres Mathematiques, Luminy, France. 6-9. 1990 Joint Statistical Meetings, ville, Queensland, Australia. (Oct. 1989, 602) Anaheim, CA. (Mar. 1988, p. 466) p. 1097) (May /Jun. 1989, p. 16-20. SIAM Annual Meeting, Chicago, 8-11. Joint Mathematics Meetings, Ohio * 2-31. Time Series, Minneapolis, MN. IL. (Nov. 1988, p. 1389) State University, Columbus, OH. (includ ing the summer meetings of the AMS, ORGANIZERS: D. Brillinger, J. 22-28. Konvexgeometrie, Oberwolfach, AWM, MAA and PME). This is the 75th Geweke, R. Gnanadesikan, E. Parzen, Federal Republic of Germany. (Apr. of the MAA. M. Rosenblatt, M. Taqqu. 1989, p. 497) Anniversary Institute for Mathe INFORMATION: 26-29. International Conference on New INFORMATION: H. Daly, AMS, P.O. Applications, 514 Vin matics and Its Trends in Geometric Function Theory Box 6248, Providence, RI 02940. S.E., cent Hall, 206 Church Street and Applications, University of Madras, Minnesota 55455; 12-18. Algebraische Zahlentheorie, Ober Minneapolis, Madras, India. (Sep. 1989, p. 918) Phone: 612-624-6066. wolfach, Federal Republic of Germany. 29-August 4. Mechanik Und Algebrais (Apr. 1989, p. 497) 3-6. Eleventh Dundee Conference on Or che Geometrie, Oberwolfach, Federal Re 12-18. Pre-Congress Topology Confer and Partial Differential Equations, public of Germany. (Apr. 1989, p. 497) dinary ence, University of Hawaii, Honolulu, Dundee, Scotland. (Sep. 1989, p. 918) * 30-August 4. The Fourth International HI. (Feb. 1989, p. 183) 6-7. International Colloquium on Appli Conference on Fibonacci Numbers and * 13-16. Alaska Conference, Quo Vadis, of Mathematics (on the occasion their Applications, Wake Forest Univer cations Graph Theory?, University of Alaska, of the 80th birthday of Lothar Collatz), sity, Winston Salem, NC. Fairbanks, AK. (Oct. 1989, p. 1097) Hamburg, West Germany. SPONSORs: Fibonacci Association and 13-1 7. Fifth International Conference INVITED SPEAKERS: Ph. Ciarlet (Paris), Wake Forest University. on Hadronic Mechanics and Nonpoten D. Gaier (Giessen), R. Guenther (Cor CALL FOR PAPERS: Papers on all tial Interactions, University of Northern vallis), W.C. Rheinboldt (Pittsburgh). branches of mathematics and science Iowa, Cedar Falls, Iowa. (Jul./ Aug. 1989, INFORMATION: G. Opfer, University related to the Fibonacci numbers and p. 768) as well of Hamburg, Institute of Applied generalized Fibonacci numbers 13-17. Eleventh IFAC World Congress, and Mathematics, Bundesstrabe 55, D- as papers related to recurrences Tallin, USSR. (Sep. 1989, p. 918) 2000 Hamburg 13, West Germany. their generalizations are welcome. Ab stracts are to be submitted by March 15, 1990, while manuscripts are due 1252 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences 13-l 7. Algebraic Geometry and Ana 19-25. Mathematische Methoden Des 3-7. Representation des Groupes et Anal lytic Geometry, Tokyo, Japan. (Sep. 1989, VLSI-Entwurfs Und Des Distributed Com yse Complexe, Marseille, France. p. 919) putings, Oberwolfach, Federal Republic (Jul./ Aug. 1989, p. 768) 13-18. Institute of Mathematical Statis of Germany. (Apr. 1989, p. 497) 8-12. Neuronet-90: IMACS International tics Fifty-third Annual Meeting(jointly 21-2 9. The International Congress of Symposium on Neural Nets and Neu with the Second World Congress of the Mathematicians 1990, Kyoto, Japan. ral Computers, Prague, Czechoslovakia. Bernoulli Society), Uppsala, Sweden. (Sep. (Nov. 1988, p. 1389) (Please note change from May/ Jun. 1989, 1989, p. 919) 26-September 1. Komplexe Analysis, p. 602) * 13-18. Tsukuba International Confer Oberwolfach, Federal Republic of Ger 9-15. Surgery and L-Theory, Oberwol ence on Representations of Algebras and many. (Apr. 1989, p. 497) fach, Federal Republic of Germany. (Apr. Related Topics, University of Tsukuba, 28-30. IMACS European Simulation 1989, p. 498) Japan. Meeting on Problem Solving by Simula 10-0ctober 5. School on Qualitative Aspects and Applications of Nonlinear CoNFERENCE ToPics: Finite dimen tion, Esztergom, Hungary. (Mar. 1989, Evolution Equations, International Centre sional algebras over fields of Artinian p. 316) for Theoretical Physics, Trieste, Italy. rings, representations of finite groups, 28-31. Operations Research 1990, Inter (May !Jun. 1989, p. 602) representations of orders and their national Conference Operations Research, related fields. Vienna, Austria. (Jul./ Aug. 1989, p. 768) 10-14. Mathematiker-Kongress, Dres INVITED SPEAKERS: M. Auslander, G. 30-September 4. International Confer den, German Democratic Republic. Azumaya, S. Brenner, V. Dlab, G. ence on Potential Theory, Nagoya, Japan. (Jul./ Aug. 1989, p. 769) Michler, C.M. Ringel, A.V. Roiter. (May /Jun. 1989, p. 602) 16-22. Risikotheorie, Oberwolfach, Fed CALL FOR PAPERS: Anyone wishing eral Republic of Germany. (Apr. 1989, to talk at the conference should send p. 498) a one-page abstract to the address September 1990 17-22. DMV-Jahrestagung 1990, Bre below. September;october 1990. IMACS men, Federal Republic of Germany. INFORMATION: H. Tachikawa (Orga GAMM Conference on Computer Arith (Jul./ Aug. 1989, p. 769) nizer), Institute of Mathematics, Uni metic, Scientific Computation and 23-29. Random Graphs and Combinator versity of Tsukuba, Tsukuba, Ibaraki Mathematical Modelling, Bulgaria. (Sep. ical Structures, Oberwolfach, Federal Re 305, Japan. 1989, p. 919) public of Germany. (Apr. 1989, p. 498) 14-18. The Asian Mathematical Con IMACS Symposium on Modelling and 24-28. International Symposium on Math ference 1990, Hong Kong, China. (Sep. Simulation of Electrical Machines, EN ematical Theories, San Sebastian, Spain. 1989, p. 919) SEM- Nancy, France. (MayfJun. 1989, (Jul./ Aug. 1989, p. 769) p. 602) 15-l 9. International Conference on Knot 30-0ctober 6. Diophantische Approxi Theory and Related Topics, International 2-7. Twelfth International Conference on mationen, Oberwolfach, Federal Republic House, Osaka, Japan. (Apr. 1989, p. 497) Nonlinear Oscillations, Cracow, Poland. of Germany. (Apr. 1989, p. 498) (Sep. 1989, p. 919) * 15-20. Conference on Gaussian Random * 2-7. International Conference on Integral Fields (The Third Nagoya Levy Seminar), October 1990 Nagoya University, Nagoya, Japan. Equations and Boundary Value Problems, Yantai University, Shandong, People's 7-13. Arbeitsgemeinschaft Mit Aktuellem PROGRAM: On the occasion of the Republic of China. Thema, Oberwolfach, Federal Republic forty-fifth anniversary of Levy's Brow of Germany. (Apr. 1989, p. 498) nian motion with multi-dimensional ORGANIZERS: W. Guo-chun (Peking 14-20. Geometrie, Oberwolfach, Fed parameter, the conference will be held Univ., Yantai Univ.), Z. Zhen (Bei eral Republic of Germany. (Apr. 1989, and devoted to the theory of Gaussian jing Normal Univ.), H. Zong-yi (Fu p. 498) random fields and its applications; dan Univ.), L. Wei (Zhongshan Univ.), white noise approach and related top L. Jian-ke (Wuhan Univ.). 21-27. Mathematische Methoden In Der Ics. INFORMATION: W. Guo-chun, Depart Robotik, Oberwolfach, Federal Republic INVITED SPEAKERS: D.A. Dawson, L. ment of Mathematics, Peking Uni of Germany. (Apr. 1989, p. 498) Gross, LA. Ibragimov, G. Kallianpur, versity, Beijing, People's Republic of 21-27. Arithmetik der Korper, Oberwol H.-H. Kuo, Y.A. Rozanov, B.L. Ro China l 008 71. fach, Federal Republic of Germany. (Oct. 1989, p. 1098) zovskii, L. Streit. 2-8. Topologie, Oberwolfach, Federal INFORMATION: T. Hida, Department Republic of Germany. (Apr. 1989, p. 497) 21-2 7. International Functional Analysis of Mathematics, Nagoya University, Meeting on the Occasion of the Sixti 3-6. Fourth Asian Logic Conference, Chikusa-ku, Nagoya (464), Japan. eth Birthday of Professor M. Valdivia, Tokyo, Japan. (Mar. 1989, p. 316) Pefiiscola, Spain. (Oct. 1989, p. 1098) 16-18. SIGAL International Symposium IMACS Symposium on Intelligent 3-7. 28-November 3. Mathematical Eco on Algorithms, Tokyo, Japan. (Oct. 1989, Systems Simulation, Brussels, Models in nomics, Oberwolfach, Federal Republic p. 1097) Belgium. (Mar. 1989,p. 316) of Germany. (Apr. 1989, p. 498) NOVEMBER 1989, VOLUME 36, NUMBER 9 1253 Meetings and Conferences IMACS World Congress is expected to follow a similar format. 1990 January 1991 November CALL FOR PAPERS: Under the gen 2-3. Central Section Meeting of the 16-19. Joint Mathematics Meetings, eral theme of computation and ap AMS, University of North Texas, Den San Francisco, CA. (including the an plied mathematics, preliminary man ton, TX. nual meetings of the AMS, AWM, MAA, uscripts (original contributions or sur and NAM) vey papers) and proposals for the W. Drady, AMS, P.O. INFORMATION: organization of sessions are solicited INFORMATION: H. Daly, AMS, P.O. Box 6248, Providence, RI 02940. in the following areas: theory, appli Box 6248, Providence, RI 02940. 4-10. WahrscheinlichkeitsmaBe auf Grup cations, new tools in computation, pen, Oberwolfach, Federal Republic of contributions to scientific comput Germany. (Oct. 1989, p. 1098) June 1991 ing coming from nonnumerical dis 5-7. Second SIAM Confernce on Linear ciplines, and history of computing * 10-14. Bernoulli Society Twentieth Con and applied mathematics. Algebra in Signals, Systems & Controls, ference on Stochastic Processes and their San Francisco, CA. (Sep. 1989, p. 920) Applications, Nahariya, Israel. 12-16. Supercomputing '90, New York, August 1991 Industrial NY. (Sep. 1989, p. 920) INFORMATION: R. Adler, Engineering & Management, Tech 8-11. Joint Mathematics Meetings, Uni 18-24. Komplexitiitstheorie, Oberwol nion, Haifa, 32000 Israel; Tel: versity of Maine, Orono, ME. (including fach, Federal Republic of Germany. (Apr. 972-4-294503; email: the summer meetings of the AMS, AWM, 1989, p. 498) [email protected]. MAA, and PME) 25-December l. Stochastische Approx imation Und Optimierungsprobleme In * 17-21. 1991 International Symposium INFORMATION: H. Daly, AMS, P.O. Der Statistik, Oberwolfach, Federal Re on the Mathematical Theory of Networks Box 6248, Providence, RI 02940. and Systems (MTNS-91), International public of Germany. (Apr. 1989, p. 498) 19-22. 1991 Joint Statistical Meetings, Conference Center Kobe, Kobe, Japan. 25-December l. Lineare Modelle und Atlanta, GA. (Mar. 1988, p. 466) Multivariate Statistische Verfahren, Ober CONFERENCE TOPICS: Mathematics for wolfach, Federal Republic of Germany. Control, System and Circuit The (Jul./ Aug. 1989, p. 769) ory; System Theory-Modelling, Re January 1992 alization and System Identification; 8-11. Joint Mathematics Meetings, Bal System; December 1990 Control of Linear/Nonlinear timore, MD. (including the annual meet Specific Applications. ings of the AMS, AWM, MAA and NAM) 2-8. Multigrid Methods, Oberwolfach, INFORMATION: H. Kimura, Depart Federal Republic of Germany. (Apr. ment of Mechanical Engineering for INFORMATION: H. Daly, AMS, P.O. 1989, p. 498) Computer-Controlled Machinery, Fac Box 6248, Providence, RI 02940. 3-5. First International Symposium on ulty of Engineering, Osaka Univer Uncertainty and Analysis: Fuzzy Reason sity, Yamada-oka, Suita, Osaka 565, June 1992 ing, Probabilistic Methods and Risk Man Japan. agement, College Park, Maryland. (Oct. 29-July l. Joint Meeting with the Lon 1989, p. 1098) don Mathematical Society, Cambridge, July 1991 England. 3-7. 1990 Australasian Conference on Combinatorial Mathematics and Comput 8-12. Second International Conference INFORMATION: H. Daly, American ing, Palmerston North, New Zealand. on Industrial and Applied Mathematics, Mathematical Society, Post Office Box (Feb. 1989, p. 183) Washington, DC. (Nov. 1988, p. 1389) 6248, Providence, Rhode Island 02940. 9-15. Allgemeine Ungleichungen, Ober * 22-26. Thirteenth IMACS World Con gress on Computation and Applied Math wolfach, Federal Republic of Germany. January 1993 (Apr. 1989, p. 498) ematics, Trinity College, Dublin Uni 16-22. Mathematische Logik, Oberwol versity, Dublin, Ireland. (Please note 13-16. Joint Mathematics Meetings, San fach, Federal Republic of Germany. (Apr. changes from Mar. 1989, p. 316) Antonio, TX. (including the annual meet 1989, p. 498) CHAIRMAN: J.H. Miller, Trinity Col ings of the AMS, AWM, MAA, and NAM) 25-January 1. Lineare Modelle Und Mul lege, University of Dublin. tivariate Statistische Verfahren, Oberwol PROGRAM: The last IMACS World INFORMATION: H. Daly, AMS, P.O. fach, Federal Republic of Germany. (Apr. Congress, (the 12th, held in Paris in Box 6248, Providence, Rl 02940. 1989, p. 498) 1988), featured about 800 technical papers on a wide variety of subjects, and was attended by 1100 participants coming from 52 countries. The 13th 1254 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY New AMS Publications Contents THE CONNECTION BETWEEN INFINITE R. Temam, Dynamical systems in infinite dimension DIMENSIONAL AND FINITE DIMENSIONAL P. Constantin, A construction of inertial manifolds DYNAMICAL SYSTEMS M. Tabor, Analytic structure of dynamical systems Basil Nicolaenko, Ciprian Foias and Roger G. Sell, Hausdorff and Lyapunov dimensions for gradient Temam, Editors systems (Contemporary Mathematics, Volume 99) D. Armbruster, Persistent homoclinic orbits M. S. Jolly, Orientation of saddle connections for a The last few years have seen a number of major developments reaction-diffusion equation demonstrating that the long-term behavior of solutions of a C. R. Doering, J. D. Gibbon, D. D. Holm and B. Nicolaenko, very large class of partial differential equations possesses Finite dimensionality in the complex Landau-Ginzburg equation a striking resemblance to the behavior of solutions of finite J. M. Ghidaglia and R. Temam, Periodic dynamical systems dimensional dynamical systems, or ordinary differential with applications to Sine-Gordon equations: Estimates of the equations. The first of these advances was the discovery fractal dimension of the universal attractor that a dissipative POE has a compact, global attractor with B. Nicolaenko, Inertial manifolds for models of compressible finite Hausdorff and fractal dimensions. More recently, it was gas dynamics shown that some of these PDEs possess a finite dimensional W. W. Zachary and T. Gill, Existence and finite-dimensionality inertial manifold-that is, an invariant manifold containing the of universal attractors for the Landau-Lifschitz equations of attractor and exponentially attractive trajectories. ferromagnetism M. I. Weinstein, The nonlinear Schrodinger equation With the improved understanding of the exact connection singularity formation, stability and dispersion between finite dimensional dynamical systems and various A. Mazer and T. Ratiu, Formal stability of two-dimensional classes of dissipative PDEs, it is now realistic to hope that the self-gravitating rotating disks wealth of studies of such topics as bifurcations of finite vector fields and "strange" fractal attractors can be brought to bear E. Van der Groesen, A deterministic approach towards on various mathematical models, including continuum flows. self-organization in continuous media Surprisingly, a number of distributed systems from continuum L. Sirovich, Low dimensional description of complicated mechanics have been found to exhibit the same nontrivial phenomena dynamic behavior as observed in low-dimensional dynamical E. Kostelich and J. Yorke, Using dynamic embedding methods systems. As a natural consequence of these observations, to analyze experimental data a new direction of research has arisen: detection and I. G. Kevrekidis and R. Ecke, Global bifurcation in maps of the analysis of finite dimensional dynamical characteristics of Plane and Rayleigh-Bernard convection infinite-dimensional systems. E. Knobloch, A. Deane and J. Toomre, A model of double-diffusive convection with periodic boundary conditions This book represents the proceedings of an AMS-IMS-SIAM K. Gustafson, K. Halasi and R. Leben, Controversies Summer Research Conference, held in July, 1987 at concerning finite/infinite sequences of fluid corner vortices the University of Colorado at Boulder. Bringing together mathematicians and physicists, the conference provided a 1980 Mathematics Subject Classifications: 34C, 35K, 70K, 76 forum for presentations on the latest developments in the field ISBN 0-8218-5105-5, LC 89-15158 ISSN 0271-4132 and fostered lively interactions on open questions and future 376 pages (softcover), November 1989 directions. With contributions from some of the top experts, Individual member $25, List price $41, these proceedings will provide readers with an overview of Institutional member $33 this vital area of research. To order, please specify CONM/99N Use the order form in the back of this issue or call 800-321-4AMS to use VISA or MasterCard. NOVEMBER 1989, VOLUME 36, NUMBER 9 1255 New AMS Publications for each point, the set of all predecessors of that point is SOME MATHEMATICAL QUESTIONS IN linearly ordered. The theory appears to be a natural extension BIOLOGY: THE DYNAMICS OF EXCITABLE of the theories of linearly ordered topological spaces and GO-spaces. The author applies the theory to solve some MEDIA problems in general topology and the theory of uniquely Hans G. Othmer, Editor arcwise connected continua. (Lectures on Mathematics in the Life Sciences, Volume 21) Contents This volume contains the proceedings of the 22nd annual Order topologies on pseudo-trees Symposium on Some Mathematical Questions in Biology, held Compactness properties in May, 1988 in Las Vegas. The diversity of current research in the dynamics of excitable media is reflected in the six papers Connectedness properties; uniquely arcwise connected in this volume. The topics covered include a mathematical spaces and dendritic spaces treatment of phase-locking, numerical results for models of A class of topologies on pseudo-trees synchronization in the mammalian sinoatrial node, simulations of a model of the hippocampus, and wave propagation in Universal pseudo-trees excitable media. Both experimental and theoretical aspects Dendrons are treated. Aimed at mathematicians, physiologists, and cardiologists, the book requires only background in differential Dendroids equations. Readers will gain a broad perspective on current Hereditarily indecomposable continua and hyperspaces of research activity in the modeling, analysis, and simulation of their subcontinua systems with excitable media. 1980 Mathematics Subject Classifications: 54F05, 54F20; 54A 10, Contents 54H12, 06F30 J. C. Alexander, E. J. Doedel and H. G. Othmer, Resonance ISBN 0-8218-2479-1, LC 89-17764 and phase-locking in excitable systems ISSN 0065-9266 124 pages (softcover), November 1989 Jose Jalife and Donald C. Michaels, The initiation of the Individual member $11, List price $19, heart beat as a dynamic consensus of electrically coupled Institutional member $15 pacemaker cells To order, please specify MEM0/416N Roger D. Traub, Richard Miles and Robert K. S. Wong, Collective behaviors of the hippocampal CA3 region P. B. Monk and H. G. Othmer, Relay, oscillations, and wave propagation in a model of Dictyostelium discoideum Robert Plonsey, The use of a Bidomain model for the study of COMPLETING THE RIESZ-DUNFORD excitable media FUNCTIONAL CALCULUS J. P. Keener and F. M. Phelps, IV, Consequences of the John B. Conway, Domingo A. Herrero and cellular, anisotropic structure of myocardium Bernard B. Morrel 1980 Mathematics Subject Classifications: 92A07, 92A09 (Memoirs of the AMS, Number 417) ISBN 0-8218-1171-1 , LC 89-17794 ISSN 0075-8523 In the classical context, the Riesz-Dunford functional calculus 192 pages (softcover), November 1989 Individual member $20, List price $34, analyzes the functions of a given, fixed operator. In this Institutional member $27 work, the authors take a different tack, by treating the To order, please specify LLSCI/21 N case in which the function f is fixed and the operator T is allowed to vary over all operators for which it makes sense to define f(T). More precisely, the authors take f analytic in TOPOLOGIES ON PSEUDO-TREES AND some neighborhood of a fixed, nonempty subset E of the plane and analyze the topological properties of the set of APPLICATIONS all operators of the form f(T). In this case, T runs over all Jacek Nikiel (bounded linear) operators acting on a complex, separable, (Memoirs of the AMS, Number 416) infinite-dimensional Hilbert space such that the spectrum of T is contained in the original set E. One of the book's main The main purpose of this monograph is to build a theory results is a characterization of the closure and interior of the of natural topologies of psuedo-trees. Pseudo-trees are set of all such f(T) in terms of spectral and function-theoretic partially ordered sets fulfilling the acyclicity condition that properties alone. The results and proofs provide an interesting Use the order form in the back of this issue or call 800-321-4AMS to use VISA or MasterCard. 1256 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY New AMS Publications interplay between operator theory and function theory, and Contents pathologies. several key examples illustrate the possible The trace formula for Heeke operators Contents Twisting newforms Spectral preliminaries Theta series The closure of f( S (c)) A representation-theoretic definition of Brandt matrices Examples Trace identities Compact perturbations Cuspidal theta series and newforms The interior of f(S(t')) The basis problem Connections with representation theory The closure of the interior of f ( S(c)) 11 F11; 11 E45, 11 R52, The interior of the closure of f(S(c)) 1980 Mathematics Subject Classifications: 11545, 16A18 Further iterations of the interior and closure ISBN 0-8218-2481-3, LC 89-17739 ISSN 0065-9266 1980 Mathematics Subject Classifications: 47 A60, 47 A05, 47 A 10 168 pages (softcover), November 1989 ISBN 0-8218-2480-5, LC 89-17740 Individual member $12, List price $20, ISSN 0065-9266 Institutional member $16 124 pages (softcover), November 1989 To order, please specify MEM0/418N Individual member $10, List price $17, Institutional member $14 The following videotape is now available through the AMS. To order, please specify MEM0/417N THE BASIS PROBLEM FOR MODULAR THE BEAUTY AND COMPLEXITY OF THE FORMS ON ro{N) MANDELBROT SET Hiroaki Hijikata, Arnold K. Pizer and Thomas John Hubbard R. Shemanske A Science Television Production (Memoirs of the AMS, Number 418) Providing an accessible introduction to the basics of fractals, Requiring a basic knowledge of number theory and modular this videotape presents an appealing balance of the theoretical forms, this work will provide readers with an understanding of and aesthetic aspects of the Mandelbrot set. Viewers will the explicit connections between the arithmetic of quaternion appreciate the clarity of exposition as John Hubbard uses algebras and the theory of modular forms on r 0 (N). The a combination of lecture, boardwork, Macintosh computer book explores the "basis problem" for modular forms. Simply demonstrations, and colorful computer-generated films and posed, the problem is to construct a basis for all spaces pictures to bring the concepts to life. Part I focuses on Sk( N, x) of cuspforms of integer weight k ~ 2 and character x iteration and Julia sets, while Part II addresses Mandelbrot on r 0(N) whose elements are "arithmetically distinguished" in sets. Part Ill examines a way of using the concept of electric that the coefficients in their Fourier expansions are explicitly field lines to understand these fractal sets. The concluding computable. The authors consider two kinds of spaces remarks round out the lecture by pointing to a philosophical (certain spaces of explicitly computable theta series and framework that relate these sets to phenomena occurring in spaces of cuspforms called primitive neben spaces) which the natural world. Requiring only a background in calculus, provide a complete solution to the basis problem, in the this videotape will prove a useful tool in classrooms and sense of providing an explicit decomposition of any space of would be an excellent addition to a videotape library. newforms s~ew(N, x) into a direct sum of character twists of 1980 Mathematics Subject Classification: 58 these two types of spaces. The book concludes with many VHS format, approx. one hour, numerical examples illustrating various aspects of the theory October 1989 of Brandt matrices, theta series, twists of newforms, and the Price $59 basis problem. To order, please specify VIDHUBBARD/N Use the order form in the back of this issue or call 800-321-4AMS to use VISA or MasterCard. NOVEMBER 1989, VOLUME 36, NUMBER 9 1257 New AMS Publications Assistantships and Graduate Fellowships brings together a EIGHT PAPERS TRANSLATED FROM THE wealth of information about resources available for graduate RUSSIAN study in mathematical sciences departments in the United States and Canada. For each department listed, it provides the S. G. Dalalyan, I. I. Danilyuk, A. T. Fomenko, number of faculty, graduate students, and degrees awarded S. G. Gindikin, M. L. Gorbachuk, V. I. (BAs, MAs, and PhDs). Stipend amounts and the number Gorbachuk, M.G. Krein, V. P. Palamodov, of awards available are given, as well as information about I. V. Skrypnik, Dao Chong Tkhi foreign language requirements for the mathematics PhD and (American Mathematical Society Translations, whether or not the department accepts critical, expository, Series 2, Volume 145) or historical theses. Numerous display advertisements from mathematical sciences departments throughout the country The papers in this collection range over topics in such areas provide additional information. as algebraic geometry, partial differential equations, Fourier Also listed are sources of support for graduate study and analysis, functional analysis, operator theory, differential travel, summer internships, and graduate study in the U.S. geometry, and global analysis. for foreign nationals. Finally, a list of reference publications for fellowship information makes Assistantships and Graduate Contents Fellowships a centralized and comprehensive resource. S. G. Dalayan, On tetragonal curves 1980 Mathematics Subject Classification: 00 pointwise estimates of some capacity I. V. Skrypnik, On ISBN 0-8218-0141-4 potentials ISSN 1040-7650 V. P. Palamodov, Some singular boundary value problems for 144 pages (softcover), November 1989 partial differential equations Individual member $9, List price $15, V. I. Gorbachuk and M. L. Gorbachuk, Trigonometric series, To order, please specify ASST /90N generalized periodic functions and boundary value problems of mathematical physics M. G. Krein, On determinants of a perturbation and a trace formula for some classes of pairs of operators S. G. Gindikin, Nonlinear equations of integral geometry SOCIETE MATHEMATIQUE DE FRANCE, ASTERISQUE [rational curves on a two-dimensional manifold] Dao Chong Tkhi [Dao Trong Thi] and A. T. Fomenko, The AMS distributes Asterisque only in the U.S., Canada, and Mexico. Topology of absolute minima of functionals of volume type and Orders from other countries should be sent to the SMF, B.P. 126-05, the Dirichlet functional 75226 Paris Cedex 05, France, or to OFFILIB, 48 rue Gay-Lussac, I. I. Danilyuk, On a variant of the two-phase Stefan problem 75240 Paris Cedex 05, France. Individual members of either AMS or SMF are entitled to the member price. (ISSN 0303-1179) 1980 Mathematics Subject Classifications: 14H45, 34B45, 35G30, 35J05, 35K05,35S10, 42A99,46F15, 47A55, 53C65, 58E15, 58F05, 82A25;31B15,33A70,47B10,47B47 ISBN 0-8218-3129-1, LC 89-17983 ORBITES UNIPOTENTES ET ISSN 0065-9290 128 pages (hardcover), November 1989 REPRESENTATIONS. VOL. I GROUPS FINIS Individual member $32, List price $54, ET ALGEBRES DE HECKE Institutional member $43 Number 168) To order, please specify TRANS2/145N (Asterisque, This volume is the first of a series of three which contain the proceedings of the ""Periode speciale: Orbites unipotentes, ASSISTANTSHIPS AND GRADUATE representations des groupes finis, reels et p-adiques et FELLOWSHIPS IN THE MATHEMATICAL representations des algebras de Heeke"" held in Paris, SCIENCES, 1990-1991 Orsay and Marseille-Luminy in June-July 1987. They include synthetic presentations and research articles. The general This publication is an indispensible source of information theme of this series is that some common ideas in geometry for students seeking support for graduate study in the play a role in all the parts of representation theory of reductive mathematical sciences. Because it provides data from a broad groups (finite groups, real or p-adic groups, adelic groups, range of academic institutions, it is also a valuable resource primitive ideals). Volume I is devoted more particularly to finite for mathematical sciences departments and faculty. groups. (Volume II is AST/171-172.) Use the order form in the back of this issue or call 800-321-4AMS to use VISA or MasterCard. 1258 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY New AMS Publications 1980 Mathematics Subject Classification: 20 ISSN 0303-1179 218 pages (softcover), 1988 ORBITES UNIPOTENTES ET Individual AMS or SMF member $18, List price $25 REPRESENTATIONS, VOLUME II: GROUPES To order, please specify AST/168N P-ADIQUES ET REELS (Asterisque, Number 171-172) The volume is the second of a series of three which contain the proceedings of the ""Periode speciale: Orbites unipotentes, representations des groupes finis, reels et p-adiques et representations des algebres de Heeke;· held in Paris, LOCAL MODULI FOR MEROMORPHIC Orsay and Marseille-Luminy in June-July 1987. They include DIFFERENTIAL EQUATIONS synthetic presentations and research articles. The general D. G. Babbitt and V. S. Varadarajan theme of this series is that some common ideas in geometry (Asterisque, Number 169-170) play a role in all the parts of representation theory of reductive groups (finite groups, real or p-adic groups, adelic groups, This paper is concerned with the local study of linear primitive ideals). Volume II is devoted more particularly to differential equations with meromorphic coefficients at an p-adic and real groups. (Volume I is AST/168.) irregular singularity. One of the most important ways in which Contents this theory differs from the theory at a regular singularity is J. Arthur, Unipotent automorphic representations: Conjectures that formal solutions are not generally convergent, and one G. Lusztig, Representations of affine Heeke algebras has to work with analytic solutions that are only asymptotic J. Adams, L -Functoriality for dual pairs to the formal solutions in sufficiently small sectors. The M. W. Baldoni-Silva and A. W. Knapp, Intertwining operators asymptotic solutions are not unique and change abruptly and unitary representations II when the sectors on which they are defined rotate; this is the A. Bouaziz, Relevement des caracteres d'un groupe Stokes Phenomenon for these equations. The main content endoscopique pour le changement de base C/IR of this paper is a systematic study of the Stokes phenomenon T. C. Hales, Shalika Germs on GSp(4) and the question of how it is affected when the differential R. Howe and A. Moy, Minimal K-types for GL(n) over a p-adic equations vary analytically but with their formal structures field fixed. D. Shelstad, A formula for regular unipotent germs Contents J. L. Waldspurger, lntegrales orbitales spheriques pour GL(N) sur un corps p-adique Part 1: Meromorphic connections and their Stokes phenomena Meromorphic connections, differential equations, and 1980 Mathematics Subject Classifications: 11 , 14, 22 differential modules ISSN 0303-1179 338 pages (softcover), 1989 Asymptotic theory of isoformal families of differential Individual AMS or SMF member $29, List price $41 modules To order, please specify AST /171-72N The Stokes sheaf of a meromorphic connection Theorems of Malgrange-Sibuya and Deligne The following publication is being reprinted with a corrected Part II: The cohomology of Stokes sheaf book description and Table of Contents. Cohomology of groups Sheaves of unipotent group schemes and the representability of their cohomology Affine structure for the cohomology of the Stokes sheaf of ACTIONS OF LINEARLY REDUCTIVE a meromorphic pair GROUPS ON AFFINE PI-ALGEBRAS Part Ill: Local moduli Nikolaus Vonessen Local moduli space for marked meromorphic pairs (Memoirs of the AMS, Number 414) Local moduli space for meromorphic pairs 1980 Mathematics Subject Classification: 34 Aimed at researchers and advanced graduate students ISSN 0303-1179 220 pages (softcover), 1989 interested in ring theory and invariant theory, this book Individual AMS or SMF member $19, List price $27 introduces readers to a new and quite beautiful area of To order, please specify AST /169-70N noncommutative invariant theory. Use the order form in the back of this issue or call 800-321-4AMS to use VISA or MasterCard. NOVEMBER 1989, VOLUME 36, NUMBER 9 1259 New AMS Publications The author examines this subject in the setting of affine Contents PI-algebras, extending both the theory of actions of finite The trace ring groups on noncommutative rings and commutative invariant theory. The work focuses on the action of a linearly reductive Affine fixed rings group G on a finitely generated PI-algebra R. One of the Borho theory book's major results is that the fixed ring RG is finitely The correspondence <1> : Spec R -o Spec RG generated, provided that R is Noetherian. Other topics Lying over explored here include localization, the behavior of prime Characterizations of linearly reductive groups through actions ideals in the ring extension RG c R, and actions by inner on affine PI-algebras automorphisms. The author also shows that many of the Actions by inner automorphisms results obtained actually characterize linearly reductive groups and are, in particular, false in prime characteristic if the acting 1980 Mathematics Subject Classifications: 16; 20 group is reductive rather than linearly reductive. This situation ISBN 0-8218-2477-5, LC 89-15148 contrasts with commutative invariant theory, where, in prime ISSN 0065-9266 106 pages (softcover), September 1989 characteristic, most results can also be proven for reductive Individual member $10, List price $17, groups. Institutional member $14 To order, please specify MEM0/414N EVERY PLANAR MAP IS FOUR COLORABLE K. Appel and W. Haken (Contemporary Mathematics. Volume 98) In this volume, the authors present their 1972 proof of the 1980 Mathematics Subject Classification: 05C15 celebrated Four Color Theorem in a detailed but self-contained ISBN 0-8218-5103-9, LC 89-15011 accessible to a general mathematical audience. ISSN 0271-4132 exposition 768 pages (softcover), October 1989 An emended version of the authors' proof of the theorem, Individual member $48, List price $80, the book contains the full text of the supplements and Institutional member $64 checklists, which originally appeared on microfiche. The To order, please specify CONM/98NA thiry-page introduction, intended for nonspecialists, provides some historical background of the theorem and details of the authors' proof. In addition, the authors have added an appendix which treats in much greater detail the argument for situations in which reducible configurations are immersed ·.,,· rather than embedded in triangulations. This result leads to a ) •••••• proof that four coloring can be accomplished in polynomial I time. ./: .... All prices subject to change. Shipment will be made by surface. For air delivery add, 1st book $5, each additional book $3, maximum $100. Prepayment required. Order from American Mathematical Society, P.O. /: Box 1571, Annex Station, Providence, RI 02901-1571, or call toll free 800-321-4AMS to charge with VISA or N MasterCard. ~~ IB______._._._._._._~ .. Use the order form in the back of this issue or call 800-321-4AMS to use VISA or MasterCard. 1260 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Reports and Communications Bylaws of the American Mathematical Society Article I bility for, or legal control of, the investments, properties, Officers and contracts of the Society. Section 1. There shall be a president, a president Article III elect (during the even-numbered years only), an ex president (during the odd-numbered years only), three Committees vice-presidents, a secretary, four associate secretaries, a Section 1. There shall be nine editorial committees treasurer, and an associate treasurer. as follows: committees for the Bulletin, for the Proceed Section 2. It shall be a duty of the president to deliver ings, for the Colloquium Publications, for the Journal, an address before the Society at the close of the term of for Mathematical Surveys and Monographs, for Mathe office or within one year thereafter. matical Reviews; a joint committee for the Transactions and the Memoirs; a committee consisting of the repre Article II sentatives of the Society on the Board of Editors of the American Journal of Mathematics; and a committee for Board of Trustees Mathematics of Computation. Section 1. There shall be a Board of Trustees consist Section 2. There shall be a Science Policy Committee. ing of eight trustees, five trustees elected by the Society in Section 3. There shall be a communications com accordance with Article VII, together with the president, mittee called the Committee to Monitor Problems in the treasurer, and the associate treasurer of the Society Communication. ex officio. The Board of Trustees shall designate its own Section 4. 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The Board may delegate to the officers communications committee and of the Science Policy of the Society duties and powers normally inhering in Committee, any former secretary for a period of two their respective corporative offices, subject to supervision years following the terms of office, and members of the by the Board. The Board of Trustees may appoint Executive Committee (Article V) who remain on the committees to facilitate the conduct of the financial Council by the operation of Article VII, Section 4. business of the Society and delegate to such committees The chairman of any committee designated as a such powers as may be necessary or convenient for the Council member may name a deputy from the committee proper exercise of those powers. Agents appointed, or as substitute. The associate secretary shall be the one members of committees designated, by the Board of charged with the scientific program of the meeting Trustees need not be members of the Board. at which the Council meets except that at a meeting Nothing herein contained shall be construed to em associated with no scientific meeting of the Society the power the Board of Trustees to divest itself of responsi- secretary may designate the associate secretary. NOVEMBER 1989, VOLUME 36, NUMBER 9 1261 Bylaws of the American Mathematical Society There is one exception. Council members by virtue as proposed or enacted federal or state legislation; condi of membership on an editorial committee or as associate tions of employment in universities, colleges, or business, secretary on January 1, 1986 shall remain members of research or industrial organizations; regulations, policies, the Council through their elected terms. This paragraph or acts of governmental agencies or instrumentalities; is no longer effective after December 31, 1989 and shall and other items which tend to affect the dignity and then be deleted. effective position of mathematics. Section 2. The Council shall formulate and adminis With the exception noted in the next paragraph, a ter the scientific policies of the Society and shall act in favorable vote of two-thirds of the entire membership of an advisory capacity to the Board of Trustees. the Council shall be necessary to authorize any statement Section 3. In the absence of the secretary from any in the name of the Society with respect to such matters. meeting of the Council, a member may be designated With the exception noted in the next paragraph, such as acting secretary for the meeting, either by written a vote may be taken only if written notice shall have authorization of the secretary, or, failing that, by the been given to the secretary by the proposer of any such presiding officer. resolution not later than one month prior to the Council Section 4. All members of the Council shall be voting meeting at which the matter is to be presented; and the members. Each member, including deputies and the vote shall be taken not earlier than one month after the designated associate secretary, shall have one vote. 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There shall be an Executive Committee of voting, action on the matter at issue shall be postponed the Council, consisting of four elected members and the until the next meeting of the Council, unless either ( 1) following ex officio members: the president, the secretary, at the discretion of the secretary, the question is made the president-elect (during even-numbered years), and the the subject of a second vote by mail, in connection with ex-president (during odd-numbered years). which brief statements of reason, for and against, are Section 2. The Executive Committee of the Council circulated; or (2) the Council places the matter at issue shall be empowered to act for the Council on matters before the Executive Committee for action. which have been delegated to the Executive Committee Section 7. The Council may delegate to the Executive by the Council. If three members of the Executive Committee certain of its duties and powers. Between Committee request that any matter be referred to the meetings of the Council, the Executive Committee shall Council, the matter shall be so referred. The Executive act for the Council on such matters and in such ways as Committee shall be responsible to the Council and shall the Council may specify. Nothing herein contained shall report its actions to the Council. It may consider the be construed as empowering the Council to divest itself agenda for meetings of the Council and may make of responsibility for formulating and administering the recommendations to the Council. scientific policies of the Society. Section 3. Each member of the Executive Committee Section 8. The Council shall also have power to speak shall have one vote. An affirmative vote on any proposal in the name of the Society with respect to matters affect before the Executive Committee shall be declared if, and ing the status of mathematics or mathematicians, such only if, at least four affirmative votes are cast for the 1262 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Bylaws of the American Mathematical Society proposal. A vote on any proposal may be determined at Section 2. The president-elect, the vice-presidents, a meeting of the Executive Committee, but it shall not the secretary, the associate secretaries, the treasurer, the be necessary to hold a meeting to determine a vote. associate treasurer, the trustees, and the members-at large of the Council shall be elected by written ballot. Article VI An official ballot shall be sent to each member of the Society by the secretary on or before October 10, and Executive Director such ballots, if returned to the secretary in envelopes Section 1. There shall be an Executive Director who bearing the name of the voter and received within thirty shall be a paid employee of the Society. The Executive days, shall be counted. Each ballot shall contain one Director shall have charge of the central office of the or more names proposed by the Council for each office Society, and shall be responsible for the general admin to be filled, with blank spaces in which the voter may istration of the affairs of the Society in accordance with substitute other names. A plurality of all votes cast shall the policies that are set by the Board of Trustees and by be necessary for election. In case of failure to secure the Council. a plurality for any office, the Council shall choose by Section 2. The Executive Director shall be appointed written ballot among the members having the highest by the Board of Trustees with the consent of the Council. number of votes. Each committee named in Article III, The terms and conditions of employment shall be fixed Section 1 or 3, shall be appointed by the Council in a by the Board of Trustees. manner designated by the Council. Each such committee Section 3. The Executive Director shall work under shall elect one of its members as chairman in a manner the immediate direction of a committee consisting of designated by the Council. the president, the secretary, and the treasurer, of which Section 3. The president becomes ex-president at the the president shall be chairman ex officio. The Executive end of the term of office and the president-elect becomes Director shall attend meetings of the Board of Trustees, president. the Council, and the Executive Committee, but shall Section 4. On or before January 15, the secretary not be a member of any of these bodies. The Executive shall send to all members of the Council for a mail Director shall be a voting member of the Committee to vote a ballot containing two names for each place to be Monitor Problems in Communication but shall not be filled on the Executive Committee. The nominees shall its chairman. be chosen by a committee appointed by the president. Members of the Council may vote for persons not Article VII nominated. Any member of the Council who is not an ex officio member of the Executive Committee (see Article Election of Officers and Terms of Office V, Section 1) shall be eligible for election to the Executive Section 1. The term of office shall be one year in the Committee. In case a member is elected to the Executive case of the president-elect and the ex-president; five years Committee for a term extending beyond the regular term in the case of the trustees; two years in the case of the on the Council, that person shall automatically continue president, the vice-presidents, the secretary, the associate as a member of the Council during the remainder of that secretaries, the treasurer, and the associate treasurer. The term on the Executive Committee. term of office in the case of members of the editorial Section 5. The president and vice-presidents shall not committees and appointed members of the communica be eligible for immediate re-election to their respective tions committees shall be four years for the Proceedings offices. A member-at-large or an ex officio member of the and the Transactions and Memoirs committees and three Council shall not be eligible for immediate election (or years for the remaining committees, except that when re-election) as a member-at-large of the Council. the size of an editorial or communications committee Section 6. If the president of the Society should die is changed, the Council may authorize the appointment or resign while a president-elect is in office, the president of a member for a shorter term. The term of office for elect shall serve as president for the remainder of the members-at-large of the Council shall be three years, five year and thereafter shall serve the regular two-year term. of the members-at-large retiring annually. The term of If the president of the Society should die or resign office for elected members of the Executive Committee when no president-elect is in office, the Council, with the shall be four years, one of the elected members retiring approval of the Board of Trustees, shall designate one of annually. All terms of office shall begin on January 1 and the vice-presidents to serve as president for the balance terminate on December 31 with the exception that the of the regular presidential term. If the president-elect officials specified in Articles I, II, III, IV, and V (except of the Society should die or resign before becoming ing the president-elect and ex-president) shall continue president, the office shall remain vacant until the next to serve until their successors have been duly elected or regular election of a president-elect, and the Society appointed and qualified. shall, at the next annual meeting, elect a president for a NOVEMBER 1989, VOLUME 36, NUMBER 9 1263 Bylaws of the American Mathematical Society two-year term. If the ex-president should die or resign Article IX before expiration of the term of office, the Council, with Dues and Privileges of Members the approval of the Board of Trustees, shall designate a former president of the Society to serve as ex-president Section 1. Any applicant shall be admitted to or during the remainder of the regular term of the ex dinary membership immediately upon election by the presidency. Such vacancies as may occur at any time in Council (Article VIII) and the discharge within sixty the group consisting of the vice-presidents, the secretary, days of election of the first annual dues. Dues may be the associate secretaries, the treasurer, and the associate discharged by payment or by remission when the provi treasurer shall be filled by the Council with the approval sion of Section 7 of this Article is applicable. The first of the Board of Trustees. If a member of an editorial or annual dues shall apply to the year of election, except communications committee should take temporary leave that any applicant elected after August 15 of any year from duties, the Council shall then appoint a substitute. may elect to have the first annual dues apply to the The Council shall fill from its own membership any following year. vacancy in the elected membership of the Executive Section 2. The annual dues of an ordinary member Committee. of the Society shall be established by the Council with the approval of the Trustees. The Council, with the approval die while in Section 7. If any elected trustee should of the Trustees, may establish special rates in exceptional shall be filled office or resign, the vacancy thus created cases and for members of an organization with which term by the Board of Trustees. for the unexpired the Society has a reciprocity agreement. Section 8. If any member-at-large of the Council Section 3. The minimum dues for a contributing should die or resign more than one year before the member shall be three-halves of the dues of an ordi expiration of the term, the vacancy for the unexpired nary member per year. Members may, upon their own term shall be filled by the Society at the next annual initiative, pay larger dues. meeting. Section 4. The minimum dues of an institutional Section 9. In case any officer should die or decline member shall depend on the scholarly activity of that to serve between the time of election and the time to member. The formula for computing these dues shall be assume office, the vacancy shall be filled in the same established from time to time by the Council, subject to manner as if that officer had served one day of the term. approval by the Board of Trustees. Institutions may pay larger dues than the computed minimum. Section 5. The privileges of an institutional member Article VIII shall depend on its dues in a manner to be determined Members and Their Election by the Council, subject to approval by the Board of Trustees. These privileges shall be in terms of Society Section 1. Election of members shall be by vote of publications to be received by the institution and of the Council or of its Executive Committee. the number of persons it may nominate for ordinary Section 2. There shall be four classes of members, membership in the Society. namely ordinary, contributing, corporate, and institu Section 6. Dues and privileges of corporate members tional. of the Society shall be established by the Council subject to approval by the Board of Trustees. Section 3. Application for admission to ordinary Section 7. The dues of an ordinary member of the membership shall be made by the applicant on a blank Society shall be remitted for any years during which that provided by the secretary. Such applications shall not be member is the nominee of an institutional member. acted upon until at least thirty days after their presen Section 8. After retirement from active service on tation to the Council (at a meeting or by mail), except account of age or on account of long term disability, any in the case of members of other societies entering under ordinary or contributing member who is not in arrears special action of the Council approved by the Board of of dues and with membership extending over at least Trustees. twenty years may, by giving proper notification to the Section 4. An ordinary member may become a con secretary, have dues remitted, on the understanding that tributing member by paying the dues for such member the member will thereafter receive the Notices but not ship. (See Article IX, Section 3.) the Bulletin. Section 5. A university or college, or a firm, cor Section 9. An ordinary or contributing member shall poration, or association interested in the support of receive the Notices and Bulletin as privileges of mem mathematics may be elected a corporate or an institu bership during each year for which dues have been tional member. discharged. 1264 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Bylaws of the American Mathematical Society Section 10. The annual dues of ordinary, contribut Such notification shall be made only when so directed ing, and corporate members shall be due by January 1 of by a previous business meeting of the Society or by the the year to which they apply. The Society shall submit Council. bills for dues. If the annual dues of any member remain Section 2. Meetings of the Executive Committee may undischarged beyond what the Board of Trustees deems be called by the president. The president shall call a to be a reasonable time, the name of that member shall meeting at any time upon the written request of two of be removed from the list of members after due notice. A its members. member wishing to discontinue membership at any time Section 3. The Council shall meet at the annual shall submit a resignation in writing to the Society. meeting of the Society. Special meetings of the Council Section 11. Any person who has attained the age of may be called by the president. The president shall call a 62 and has been a member for at least twenty years special meeting at any time upon the written request of may become a life member by making a single payment five of its members. No special meeting of the Council equal to five times the dues of an ordinary member shall be held unless written notice of it shall have been for the coming year. Insofar as there is more than sent to all members of the Council at least ten days one level of dues for ordinary membership, it is the before the day set for the meeting. highest such dues that shall be used in the calculation, Section 4. The Board of Trustees shall hold at least with the exception for members by reciprocity noted in one meeting in each calendar year. Meetings of the Board the following paragraph. A life member is subsequently of Trustees may be called by the president, the treasurer, relieved of the obligation of paying dues. The status and or the secretary of the Society upon three-days' notice privileges are those of ordinary members. (This section of such meetings mailed to the last known post office does not affect those persons who became life members address of each trustee. The secretary of the Society before October 25, 1941. They remain life members with shall call a meeting upon the receipt of a written request the status and privileges of ordinary members. When the of two of the trustees. Meetings may also be held by class of them is empty, this parenthetical remark is to be common consent of all the trustees. removed.) Section 5. Papers intended for presentation at any A member of the Society by reciprocity who has meeting of the Society shall be passed upon in advance reached the age of 62, has been a member for at least 20 by a program committee appointed by or under the years, has been a member by reciprocity for at least 15 authority of the Council; and only such papers shall of those 20 years and asserts the intention of continuing be presented as shall have been approved by such to be a member by reciprocity may purchase a life committee. Papers in form unsuitable for publication, membership by a one-time payment of a special rate if accepted for presentation, shall be referred to on the established by the Council, with the approval of the program as preliminary communications or reports. Trustees. Article XI Article X Publications Meetings Section 1. The Society shall publish an official organ Section 1. The annual meeting of the Society shall be called the Bulletin of the American Mathematical Society. held between the fifteenth of December and the tenth of It shall publish four journals, known as the Journal of February next following. Notice of the time and place the American Mathematical Society, the Transactions of of this meeting shall be mailed by the secretary or an the American Mathematical Society, the Proceedings of associate secretary to the last known post office address the American Mathematical Society, and Mathematics of of each member of the Society. The times and places Computation. It shall publish a series of mathematical of the annual and other meetings of the Society shall papers known as the Memoirs of the American Mathe be designated by the Council. There shall be a business matical Society. The object of the Journal, Transactions, meeting of the Society at the annual meeting and at the Proceedings, Memoirs, and Mathematics of Computation summer meeting. A business meeting of the Society shall is to make known important mathematical researches. It take final action only on business accepted by unanimous shall publish a periodical called Mathematical Reviews, consent, or business notified to the full membership of containing abstracts or reviews of current mathematical the Society in the call for the meeting, except that the literature. It shall publish a series of volumes called Col business meetings held at either the annual meeting or loquium Publications which shall embody in book form the summer meeting may take final action on business new mathematical developments. It shall publish a series which has been recommended for consideration by the of monographs called Mathematical Surveys and Mono Council and has been accepted by the vote of four-fifths graphs which shall furnish expositions of the principal of the Society present and voting at such a meeting. methods and results of particular fields of mathemati- NOVEMBER 1989, VOLUME 36, NUMBER 9 1265 Bylaws of the American Mathematical Society cal research. It shall also cooperate in the conduct of defense or reasonable settlement of any action, suit, legal the American Journal of Mathematics. It shall publish a or administrative proceeding, whether civil, criminal, news periodical known as the Notices of the American administrative or investigative, threatened, pending or Mathematical Society, containing programs of meetings, completed, to which that person is made a party by items of news of particular interest to mathematicians, reason of being or having been such trustee, officer and such other materials as the Council may direct. or director or Council member, except in relation to Section 2. The editorial management of the publica matters as to which the person shall be adjudged in tions of the Society listed in Section 1 of this article, with such action, suit or proceeding to be liable for negligence the exception of the Notices, and the participation of or misconduct in the performance of official duties. the Society in the editorial management of the American Such right of indemnification and reimbursement shall Journal of Mathematics shall be in the charge of the also extend to the personal representatives of any such respective editorial committees as provided in Article person, and shall be in addition to and not in substitution III, Section 1. The editorial management of the Notices for any other rights to which such person or personal shall be in the hands of a committee chosen in a manner representatives may now or hereafter be entitled by established by the Council. virtue of the provisions of applicable law or of any other agreement or vote of the Board of Trustees, or otherwise. Article XII Communications Article XIV Amendments The Committee to Monitor Problems in Communication shall perform such tasks in the field of communication These bylaws may be amended or suspended on recom of mathematics as are assigned to it by the Council. mendation of the Council and with the approval of the membership of the Society, the approval consisting of Article XIII an affirmative vote by two-thirds of the members present at a business meeting or of two-thirds of the members Indemnification voting in a mail ballot in which at least ten percent of Any person who at any time serves or has served as the members vote, whichever alternative shall have been a trustee or officer of the Society, or as a member of designated by the Council, and provided notice of the the Council, or, at the request of the Society, as a proposed action and of its general nature shall have been director or officer of another corporation, whether for given in the call for the meeting or accompanies the profit or not for profit, shall be indemnified by the ballot in full. Society and be reimbursed against and for expenses ac As amended December 1988 tually and necessarily incurred in connection with the AMS Funds, Prizes, Officers and Lecturers Endowment Fund Prize Funds In 1923 an Endowment Fund was collected to meet The Bocher Memorial Prize the greater demands on the publication program of the This prize was founded in memory of Professor Maxime Society, these demands caused by the ever-increasing Bocher with an original endowment of $1,450. It is number of important mathematical memoirs. Of this awarded every five years for a notable research mem fund, which amounted to approximately $94,000 in oir in analysis that has appeared during the past five 1960, a considerable proportion was contributed by years. Either the recipient is a member of the Society or members of the Society. In 1961, upon the death of the Memoir is published in a recognized North Amer the last legatees under the will of the late Robert ican journal; this provision, introduced in 1971, is a Henderson-for many years a Trustee of the Society-the liberalization of the terms of the award. entire principal of the estate was received by the Society, thereby bringing the total of the Endowment Fund to First (preliminary) award, 1923: To G. D. approximately $648,000. Birkhoff for his memoir, Dynamical systems with two 1266 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Funds, Prizes, Officers and Lecturers degrees offreedom. Transactions of the American Math two joint papers with Michael F. Atiyah, The index of ematical Society, volume 18 ( 1917), pp. 199-300. elliptic operators. I, III, Annals of Mathematics, Series 2, volume 87 (1968), pp. 484-530, 546-604. Second award, 1924: To E. T. Bell for his memoir, Arithmetical paraphrases. I, II, Transactions of the Amer Twelfth award, 1974: To DonaldS. Ornstein in recogni ican Mathematical Society, volume 22 (1921), pp. 1-30, tion of his paper, Bernoulli shifts with the same entropy 198-219; and to Solomon Lefschetz for his memoir, On are isomorphic, Advances in Mathematics, volume 4 certain numerical invariants with applications to Abelian ( 1970), pp. 337-352. varieties, Transactions of the American Mathematical Thirteenth award, 1979: To Alberto P. Calderon in Society, volume 22 (1921), pp. 407-482. recognition of his fundamental work on the theory of Third award, 1928: To J. W. Alexander for his mem singular integrals and partial differential equations, and oir, Combinatorial analysis situs, Transactions of the in particular for his paper Cauchy integrals on Lipschitz American Mathematical Society, volume 28 ( 1926), pp. curves and related operators, Proceedings of the National 301-329. Academy of Sciences, USA, volume 74 (1977), pp. 1324- Fourth award, 1933: To Marston Morse for his memoir, 1327. The foundations ofa theory of the calculus ofvariations in Fourteenth award, 1984: To Luis A. Caffarelli for his deep the large in m-space, Transactions of the American Math and fundamental work in nonlinear partial differential ematical Society, volume 31 (1929), pp. 379-404; and equations, in particular his work on free boundary to Norbert Wiener for his memoir, Tauberian theorems, problems, vortex theory and regularity theory. Annals of Mathematics, Series 2, volume 33 ( 1932), pp. Fifteenth award, 1984: To Richard B. Melrose for his 1-100. solution of several outstanding problems in diffraction Fifth award, 1938: To John von Neumann for his mem theory and scattering theory and for developing the oir, Almost periodic functions and groups. I, II, Transac analytical tools needed for their resolution. tions of the American Mathematical Society, volume 36 Sixteenth award, 1989: To Richard M. Schoen for his (1934), pp. 445-492, and volume 37 (1935), pp. 21-50. work on the application of partial differential equations Sixth award, 1943: To Jesse Douglas for his memoirs, to differential geometry, in particular his completion Green's function and the problem of Plateau, American of the solution to the Yamabe Problem in Conformal Journal of Mathematics, volume 61 ( 1939), pp. 545- deformation of a Riemannian metric to constant scalar 589; The most general form of the problem of Plateau, curvature, Journal of Differential Geometry, volume 20 American Journal of Mathematics, volume 61 ( 1939), (1984), pp. 479-495. pp. 590-608; and Solution of the inverse problem of the calculus of variations, Proceedings of the National The Frank Nelson Cole Prize in Algebra Academy of Sciences, volume 25 (1939), pp. 631-637. The Frank Nelson Cole Prize in Number Theory Seventh award, 1948: To A. C. Schaeffer and D. C. These prizes were founded in honor of Professor Frank Spencer for their memoir, Coefficients of schlicht func Nelson Cole on the occasion of his retirement as secretary tions. I, II, III, IV, Duke Mathematical Journal, volume of the American Mathematical Society after twenty-five 10 (1943), pp. 611-635, volume 12 (1945), pp. 107-125, years of service as editor-in-chief of the Bulletin. The and the Proceedings of the National Academy of Sci original fund was donated by Professor Cole from mon ences, volume 32 ( 1946), pp. 111-116, volume 35 ( 1949), eys presented to him on his retirement, was augmented pp. 143-150. by contributions from members of the Society, and was later doubled by his son, Charles A. Cole. The present Eighth award, 1953: To Norman Levinson for his con endowment is $2,250. The prizes are awarded at five-year tributions to the theory of linear, nonlinear, ordinary, intervals for contributions to algebra and the theory of and partial differential equations contained in his papers numbers, respectively, under restrictions similar to those of recent years. for the Bocher Prize. Ninth award, 1959: To Louis Nirenberg for his work in First award, 1928: To L. E. Dickson for his book partial differential equations. Algebren und ihre Zahlentheorie, Orell Fussli, Zurich and Tenth award, 1964: To Paul J. Cohen for his paper, Leipzig, 1927. On a conjecture of Littlewood and idempotent measures, Second award, 1931: To H. S. Vandiver for his several American Journal of Mathematics, volume 82 ( 1960), papers on Fermat's last theorem published in the Trans pp. 191-212. actions of the American Mathematical Society and in the Eleventh award, 1969: To I. M. Singer in recognition of Annals of Mathematics during the preceding five years, his work on the index problem, especially his share in with special reference to a paper entitled On Fermat's NOVEMBER 1989, VOLUME 36, NUMBER 9 1267 AMS Funds, Prizes, Officers and Lecturers last theorem, Transactions of the American Mathematical American Journal of Mathematics, volume 82 ( 1960), Society, volume 31 (1929), pp. 613-642. pp. 631-648. Third award, 1939: To A. Adrian Albert for his papers Thirteenth award, 1965: To Walter Feit and John G. on the construction of Riemann matrices published in Thompson for their joint paper, Solvability of groups of the Annals of Mathematics, Series 2, volume 35 ( 1934) odd order, Pacific Journal of Mathematics, volume 13 and volume 36 (1935). (1963), pp. 775-1029. Fourth award, 1941: To Claude Chevalley for his paper, Fourteenth award, 1967: To James B. Ax and Simon B. La theorie du corps de classes, Annals of Mathematics, Kochen for a series of three joint papers, Diophantine Series 2, volume 41 (1940), pp. 394-418. problems over local fields. I, II, III, American Journal of Fifth award, 1944: To Oscar Zariski for four papers on Mathematics, volume 87 (1965), pp. 605-630, 631-648, algebraic varieties published in the American Journal of and Annals of Mathematics, Series 2, volume 83 ( 1966), Mathematics, volumes 61 ( 1939) and 62 ( 1940), and in pp. 437-456. the Annals of Mathematics, Series 2, volumes 40 ( 1939) Fifteenth award, 1970: To John R. Stallings for his and 41 (1940). paper, On torsion-free groups with infinitely many ends, Sixth award, 1946: To H. B. Mann for his paper, A proof Annals of Mathematics, Series 2, volume 88 ( 1968), pp. of the fundamental theorem on the density of sums of 312-334; and to Richard G. Swan for his paper, Groups sets of positive integers, Annals of Mathematics, Series 2, of cohomological dimension one, Journal of Algebra, volume 43 ( 1942), pp. 523-527. volume 12 (1969), pp. 585-610. Seventh award, 1949: To Richard Brauer for his paper, Sixteenth award, 1972: To Wolfgang M. Schmidt for the On Artin 's L-series with general group characters, Annals following papers: On simultaneous approximation of two of Mathematics, Series 2, volume 48 (1947), pp. 502-514. algebraic numbers by rationals, Acta Mathematica (Upp sala), volume 119 ( 1967), pp. 27-50; T-numbers do exist, Eighth award, 1951: To Paul Erdos for his many papers Symposia Mathematica, volume IV, Academic Press, in the theory of numbers, and in particular for his paper, 1970, pp. 1-26; Simultaneous approximation to algebraic On a new method in elementary number theory which numbers by rationals, Acta Mathematica (Uppsala), vol leads to an elementary proof of the prime number theo ume 125 (1970), pp. 189-201; On Mahler's T-numbers, rem, Proceedings of the National Academy of Sciences, Proceedings of Symposia in Pure Mathematics, volume volume 35 (1949), pp. 374-385. 20, American Mathematical Society, 1971, pp. 27 5-286. Ninth award, 1954: To Harish-Chandra for his papers on representations of semisimple Lie algebras and groups, Seventeenth award, 1975: To Hyman Bass for his pa and particularly for his paper, On some applications per, Unitary algebraic K-theory, Springer Lecture Notes of the universal enveloping algebra of a semisimple Lie in Mathematics, volume 343, 1973; and to Daniel algebra, Transactions of the American Mathematical G. Quillen for his paper, Higher algebraic K-theories, Society, volume 70 ( 1951 ), pp. 28-96. Springer Lecture Notes in Mathematics, volume 341, 1973. Tenth award, 1956: To John T. Tate for his paper, The higher dimensional cohomology groups of class field Eighteenth award, 1977: To Goro Shimura for his two theory, Annals of Mathematics, Series 2, volume 56 papers, Class fields over real quadratic fields and Heche (1952), pp. 294-297. operators, Annals of Mathematics, Series 2, volume 95 (1972), pp. 130-190; and On modular forms of half Eleventh award, 1960: To Serge Lang for his paper, integral weight, Annals of Mathematics, Series 2, volume Unramified class field theory over function fields in several 97 (1973), pp. 440-481. variables, Annals of Mathematics, Series 2, volume 64 ( 1956), pp. 285-325; and to Maxwell A. Rosenlicht Nineteenth award, 1980: To Michael Aschbacher for his for his papers, Generalized Jacobian varieties, Annals paper, A characterization of Chevalley groups over fields of Mathematics, Series 2, volume 59 (1954), pp. 505- of odd order, Annals of Mathematics, Series 2, volume 530, and A universal mapping property of generalized 106 (1977), pp. 353-398; and to Melvin Hochster for his Jacobians, Annals of Mathematics, Series 2, volume 66 paper Topics in the homological theory of commutative ( 1957), pp. 80-88. rings, CBMS Regional Conference Series in Mathematics, Number 24, American Mathematical Society, 1975. Twelfth award, 1962: To Kenkichi Iwasawa for his paper, Gamma extensions of number fields, Bulletin of the Twentieth award, 1982: To Robert P. Langlands for American Mathematical Society, volume 65 (1959), pp. pioneering work on automorphic forms, Eisenstein se 183-226; and to Bernard M. Dwork for his paper, On ries and product formulas, particularly for his paper the rationality of the zeta function ofan algebraic variety, Base change for GL(2), Annals of Mathematics Studies, 1268 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Funds, Prizes, Officers and Lecturers volume 96, Princeton University Press, 1980; and to Sixth award, 1971: To Dennis P. Sullivan for his work Barry Mazur for outstanding work on elliptic curves on the Hauptvermutung summarized in the paper, On the and Abelian varieties, especially on rational points of Hauptvermutung for manifolds, Bulletin of the American finite order, and his paper Modular curves and the Eisen Mathematical Society, volume 73 ( 1967), pp. 598-600. stein ideal, Publications Mathematiques de l'Institut des Seventh award, 1976: To William P. Thurston for his Hautes Etudes Scientifiques, volume 4 7 ( 1977), pp. 33- work on foliations. 186. Eighth award, 1976: To James Simons for his work on Twenty-First award, 1985: To George Lusztig for his minimal varieties and characteristic forms. fundamental work on the representation theory of finite groups of Lie type. In particular for his contributions Ninth award, 1981: To Mikhael Gromov for his work to the classification of the irreducible representations in relating topological and geometric properties of Rieman characteristic zero of the groups of rational points of nian manifolds. reductive groups over finite fields, appearing in Charac Tenth award, 1981: To Shing-Tung Yau for his work in ters of Reductive Groups Over Finite Fields, Annals of nonlinear partial differential equations, his contributions Mathematics Studies, volume 107, Princeton University to the topology of differentiable manifolds, and for Press, 1984. his work on the complex Mange-Ampere equation on Twenty-Second award, 1987: To Dorian M. Goldfeld for compact complex manifolds. his paper, Gauss's class number problem for imaginary Eleventh award, 1986: To Michael H. Freedman for quadratic fields, Bulletin of the American Mathematical his work in differential geometry and, in particular, the Society, volume 13, ( 1985), pp. 23-3 7; and to Benedict H. solution of the four-dimensional Poincare conjecture. Gross and Don B. Zagier for their paper, Heegner points and derivatives of L-Series, Inventiones Mathematicae, The George David Birkhoff Prize volume 84 ( 1986), pp. 225-320. in Applied Mathematics The Oswald Veblen Prize in Geometry This prize was established in 1967 in honor of Professor This prize was established in 1961 in memory of Profes George David Birkhoff. The initial endowment of $2,066 sor Oswald Veblen through a fund contributed by former was contributed by the Birkhoff family and there have students and colleagues. The fund was later doubled by been subsequent additions by others. It is normally the widow of Professor Veblen, bringing the fund to awarded every five years, beginning in 1968, for an $2,000. The first two awards of the prize were made outstanding contribution to "applied mathematics in the in 1964 and the next in 1966; thereafter, an award highest and broadest sense." The award is made jointly will ordinarily be made every five years for research in by the American Mathematical Society and the Society geometry or topology under conditions similar to those for Industrial and Applied Mathematics. The recipient for the B6cher Prize. must be a member of one of these societies and a resident of the United States, Canada, or Mexico. First award, 1964: To C. D. Papakyriakopoulos for his papers, On solid tori, Annals of Mathematics, Series First award, 1968: To Jtirgen K. Moser for his contribu 2, volume 66 (1957), pp. 1-26, and On Dehn's lemma tions to the theory of Hamiltonian dynamical systems, and the asphericity of knots, Proceedings of the National especially his proof of the stability of periodic solutions Academy of Sciences, volume 43 (1957), pp. 169-172. of Hamiltonian systems having two degrees of freedom and his specific applications of the ideas in connection Second award, 1964: To Raoul Bott for his papers, The with this work. space of loops on a Lie group, Michigan Mathematical Journal, volume 5 ( 19 58), pp. 3 5-61, and The stable Second award, 1973: To Fritz John for his outstanding homotopy of the classical groups, Annals of Mathematics, work in partial differential equations, in numerical anal Series 2, volume 70 (1959), pp. 313-337. ysis, and, particularly, in nonlinear elasticity theory; the latter work has led to his study of quasi-isometric map Third award, 1966: To Stephen Smale for his contribu pings as well as functions of bounded mean oscillation, tions to various aspects of differential topology. which have had impact in other areas of analysis. Fourth award, 1966: To Morton Brown and Barry Mazur Third award, 1973: To James B. Serrin for his funda for their work on the generalized Schoenflies theorem. mental contributions to the theory of nonlinear partial Fifth award, 1971: To Robion C. Kirby for his paper, differential equations, especially his work on existence Stable homeomorphisms and the annulus conjecture, An and regularity theory for nonlinear elliptic equations, nals of Mathematics, Series 2, volume 89 ( 1969), pp. and applications of his work to the theory of minimal 575-582. surfaces in higher dimensions. NOVEMBER 1989, VOLUME 36, NUMBER 9 1269 AMS Funds, Prizes, Officers and Lecturers Fourth award, 1978: To Garrett Birkhoff for bringing methodology through which that understanding can be the methods of algebra and the highest standards of constructed. mathematics to scientific applications. Fifth award, 1985: To Clifford S. Gardner for his contri Fifth award, 1978: To Mark Kac for his important butions to applied mathematics in the areas of supersonic contributions to statistical mechanics and to probability aerodynamics, plasma physics and hydromagnetics, and theory and its applications. especially for his contributions to the truly remarkable development of inverse scattering theory for the solution award, 1978: To Clifford A. Truesdell for his Sixth of nonlinear partial differential equations. outstanding contributions to our understanding of the subjects of rational mechanics and nonlinear materials, for his efforts to give precise mathematical formulation The Leroy P. Steele Prizes to these classical subjects, for his many contributions in honor of George to applied mathematics in the fields of acoustic theory, These prizes were established in 1970 and William Cas kinetic theory, and nonlinear elastic theory, and the David Birkhoff, William Fogg Osgood, the terms of a thermodynamics of mixtures, and for his major work in par Graustein, and are endowed under Leroy P. Steele. the history of mechanics. bequest amounting to $145,000 from From 1970 to 1976 one or more prizes were awarded Seventh award, 1983: To Paul R. Garabedian for his each year for outstanding published mathematical re important contributions to partial differential equations, search; most favorable consideration was given to papers to the mathematical analysis of problems of transonic distinguished for their exposition and covering broad flow and airfoil design by the method of complexification, areas of mathematics. In 1977 the Council of the AMS and to the development and application of scientific modified the terms under which the prizes are awarded. computing to problems of fluid dynamics and plasma Since then, up to three prizes have been awarded each physics. year in the following categories: ( 1) for the cumulative Eighth award, 1988: To Elliott H. Lieb for his profound influence of the total mathematical work of the recipient, analysis of problems arising in mathematical physics. high level of research over a period of time, particular influence on the development of a field, and influence on The Norbert Wiener Prize mathematics through Ph.D. students; (2) for a book or in Applied Mathematics substantial survey or expository-research paper; (3) for This prize was established in 1967 in honor of Professor a paper, whether recent or not, that has proved to be Norbert Wiener and was endowed by a fund amounting of fundamental or lasting importance in its field, or a to $2,000 from the Department of Mathematics of model of important research. the Massachusetts Institute of Technology. The prize is normally awarded every five years, beginning in 1970, August 1970: To Solomon Lefschetz for his paper, A for an outstanding contribution to "applied mathematics page of mathematical autobiography, Bulletin of the in the highest and broadest sense." The award is made American Mathematical Society, volume 74 ( 1968), pp. jointly by the American Mathematical Society and the 854-879. The Society for Industrial and Applied Mathematics. August 1971: To James B. Carrell for his paper, written and recipient must be a member of one of these societies jointly with Jean A. Dieudonne, Invariant theory, old and a resident of the United States, Canada, or Mexico. new, Advances in Mathematics, volume 4 ( 1970), pp. First award, 1970: To Richard E. Bellman for his pio 1-80. and neering work in the area of dynamic programming, August 1971: To Jean A. Dieudonne for his paper, for his related work on control, stability, and differential Algebraic geometry, Advances in Mathematics, volume 3 delay equations. ( 1969), pp. 223-321, and for his paper, written jointly Second award, 1975: To Peter D. Lax for his broad with James B. Carrell, Invariant theory, old and new, contributions to applied mathematics, in particular, for Advances in Mathematics, volume 4 (1970), pp. 1-80. of partial his work on numerical and theoretical aspects August 1971: To Phillip A. Griffiths for his paper, differential equations and on scattering theory. Periods of integrals on algebraic manifolds, Bulletin of Third award, 1980: To Tosio Kato for his distinguished the American Mathematical Society, volume 76 ( 1970), work in the perturbation theory of quantum mechanics. pp. 228-296. Fourth award, 1980: To Gerald B. Whitham for his broad August 1972: To Edward B. Curtis for his paper, Simpli contributions to the understanding of fluid dynamical cial homotopy theory, Advances in Mathematics, volume phenomena and his innovative contributions to the 6 (1971), pp. 107-209. 1270 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Funds, Prizes, Officers and Lecturers August 1972: To William J. Ellison for his paper, War Algebraic geometry, Springer-Verlag, Berlin and New ing's problem, American Mathematical Monthly, volume York, 1977. 78 (1971), pp. 10-36. August 1979: To Joseph J. Kohn for his fundamental August 1972: To Lawrence F. Payne for his paper, paper: Harmonic integrals on strongly convex domains. I, Isoperimetric inequalities and their applications, SIAM II, Annals of Mathematics, Series 2, volume 78 (1963), Review, volume 9 ( 1967), pp. 453-488. pp. 112-248 and volume 79 (1964), pp. 450-472. August 1972: To Dana S. Scott for his paper, A proof August 1980: To Andre Weil for the total effect of of the independence of the continuum hypothesis, Mathe his work on the general course of twentieth century matical Systems Theory, volume 1 ( 1967), pp. 89-111. mathematics, especially in the many areas in which he January 1975: To Lipman Bers for his paper, Uni has made fundamental contributions. formization, moduli, and Kleinian groups, Bulletin of August 1980: To Harold M. Edwards for mathematical the London Mathematical Society, volume 4 ( 1972), pp. exposition in his books Riemann's zeta function, Pure 257-300. and Applied Mathematics, number 58, Academic Press, January 1975: To Martin D. Davis for his paper, New York and London, 1974; and Fermat's last theorem, Hilbert's tenth problem is unsolvable, American Mathe Graduate Texts in Mathematics, number 50, Springer matical Monthly, volume 80 ( 1973), pp. 233-269. Verlag, New York and Berlin, 1977. January 1975: To Joseph L. Taylor for his paper, Mea August 1980: To Gerhard P. Hochschild for his signifi sure algebras, CBMS Regional Conference Series in cant work in homological algebra and its applications. Mathematics, Number 16, American Mathematical Soci Zariski for his work in algebraic ety, 1972. August 1981: To Oscar geometry, especially his fundamental contributions to August 1975: To George W. Mackey for his paper, Er the algebraic foundations of this subject. godic theory and its significance for statistical mechanics To Eberhard Hopf for three papers of and probability theory, Advances in Mathematics, volume August 1981: importance: Abzweigung einer 12 (1974), pp. 178-286. fundamental and lasting periodischen Losung von einer stationiiren Losung eines August 1975: To H. Blaine Lawson for his paper, Foli Differential systems, Berichte tiber die Verhandlungen der ations, Bulletin of the American Mathematical Society, Sachsischen Akademie der Wissenschaften zu Leipzig. volume 80 (1974), pp. 369-418. Mathematisch-Naturwissenschaftliche Klasse, volume 95 1976, 1977, 1978: No awards were made. ( 1943), pp. 3-22; A mathematical example displaying fea tures of turbulence, Communications on Applied Math January 1979: To Salomon Bochner for his cumulative ematics, volume 1 ( 1948), pp. 303-322; and The partial influence on the fields of probability theory, Fourier differential equation u1 + UUx = J1Uxx. Communications analysis, several complex variables, and differential ge on Pure and Applied Mathematics, volume 3 ( 1950), pp. ometry. 201-230. January 1979: To Hans Levy for three fundamental August 1981: To Nelson Dunford and Jacob T. Schwartz papers: On the local character of the solutions of an for their expository book, Linear operators, Part I, atypical linear differential equation in three variables and General theory, 1958; Part II, Spectral theory, 1963; Part a related theorem for regular functions of two complex III, Spectral operators, 1971, Interscience Publishers, variables, Annals of Mathematics, Series 2, volume 64 New York. (1956), pp. 514-522; An example ofa smooth linear partial differential equation without solution, Annals of August 1982: To Lars V. Ahlfors for his expository Mathematics, Series 2, volume 66 (1957), pp. 155-158; work in Complex analysis (McGraw-Hill Book Company, On hulls of holomorphy, Communications in Pure and New York, 1953), and in Lectures on quasiconformal Applied Mathematics, volume 13 (1960), pp. 587-591. mappings (D. Van Nostrand Co., Inc., New York, 1966) August 1979: To Antoni Zygmund for his cumulative and Conformal invariants (McGraw-Hill Book Company, influence on the theory of Fourier series, real variables, New York, 1973). and related areas of analysis. August 1982: To Tsit-Yuen Lam for his expository work August 1979: To Robin Hartshorne for his expository in his book Algebraic theory of quadratic forms (1973), research article Equivalence relations on algebraic cycles and four of his papers: K0 and K 1-an introduction and subvarieties of small codimension, Proceedings of to algebraic K-theory ( 1975), Ten lectures on quadratic Symposia in Pure Mathematics, volume 29, American forms over fields ( 1977), Serre's conjecture ( 1978), and Mathematical Society, 1975, pp. 129-164; and his book The theory of ordered fields ( 19 80). NOVEMBER 1989, VOLUME 36, NUMBER 9 1271 AMS Funds, Prizes, Officers and Lecturers August 1982: To John W. Milnor for a paper of fun ( 1965), pp. 49-80; and Endomorphisms of linear alge damental and lasting importance, On manifolds homeo braic groups, Memoirs of the American Mathematical morphic to the 7-sphere, Annals of Mathematics (2) 64 Society, volume 80 (1968). (1956), pp. 399-405. August 1985: To Hassler Whitney for his fundamental August 1982: To Fritz John for the cumulative influence work on geometric problems, particularly in the general of his total mathematical work, high level of research over theory of manifolds, in the study of differentiable func a period of time, particular influence on the development tions on closed sets, in geometric integration theory, and of a field, and influence on mathematics through Ph.D. in the geometry of the tangents to a singular analytic students. space. August 1983: To Paul R. Halmos for his many graduate January 1986: To Donald E. Knuth for his expository texts in mathematics and for his articles on how to write, work, The Art of Computer Programming, 3 Volumes talk and publish mathematics. (1st Edition 1968, 2nd Edition 1973). August 1983: To Steven C. K.leene for three important January 1986: To Rudolf E. Kalman for his two fun papers which formed the basis for later developments in damental papers: A new approach to linear filtering and generalized recursion theory and descriptive set theory: prediction problems, Journal of Basic Engineering, vol Arithmetical predicates and function quantifiers, Transac ume 82, ( 1960), pp. 35-45; and Mathematical description tions of the American Mathematical Society 79 ( 1955), of linear dynamical systems, SIAM Journal on Control pp. 312-340; On the forms of the predicates in the theory and Optimization, volume 1 ( 1963), pp. 152-192; and for ofconstructive ordinals (second paper), American Journal his contribution to a third paper, (with R. S. Bucy) New of Mathematics 77 ( 1955), pp. 405-428; and Hierarchies results in linear filtering and prediction theory, Journal of of number-theoretic predicates, Bulletin of the American Basic Engineering, volume 83D (1961), pp. 95-108. Mathematical Society 61 (1955), pp. 193-213. January 1986: To Saunders Mac Lane for his many August 1983: To Shiing-Shen Chern for the cumulative contributions to algebra and algebraic topology, and in influence of his total mathematical work, high level of particular for his pioneering work in homological and research over a period of time, particular influence on categorical algebra. the development of the field of differential geometry, and August 1987: To Martin Gardner for his many books influence on mathematics through Ph.D. students. and articles on mathematics and particularly for his August 1984: To Elias M. Stein for his book, Singular column "Mathematical Games" in Scientific American. integrals and the differentiability properties of functions, August 1987: To Herbert Federer and Wendell Fleming Princeton University Press ( 1970). for their pioneering paper, Normal and integral currents, August 1984: To Lennart Carleson for his papers: An Annals of Mathematics, volume 72 ( 1960), pp. 458-520. interpolation problem for bounded analytic functions, August 1987: To Samuel Eilenberg for his fundamental American Journal of Mathematics, volume 80 ( 1958), pp. contributions to topology and algebra, in particular for 921-930; Interpolation by bounded analytic functions and his classic papers on singular homology and his work the Corona problem, Annals of Mathematics (2), volume on axiomatic homology theory which had a profound 76 (1962), pp. 547-559; and On convergence and growth influence on the development of algebraic topology. of partial sums of Fourier series, Acta Mathematica August 1988: To Sigurdur Helgason for his books Differ volume 116 (1966), pp. 135-157. ential Geometry and Symmetric Spaces (Academic Press, August 1984: To Joseph L. Doob for his fundamental 1962), Differential Geometry, Lie Groups, and Symmet work in establishing probability as a branch of mathe ric Spaces (Academic Press, 1978); and Groups and matics and for his continuing profound influence on its Geometric Analysis (Academic Press, 1984 ). development. August 1988: To Gian-Carlo Rota for his paper On the August 1985: To Michael Spivak for his five-volume set, foundations of combinatorial theory, I. Theory of Mobius A Comprehensive Introduction to Differential Geometry functions, Zeitschrift fur Wahrscheinlichkeitstheorie und (second edition, Publish or Perish, 1979). Verwandte Gebiete, volume 2 (1964), pp. 340-368. August 1985: To Robert Steinberg for three papers on August 1988: To Deane Montgomery for his lasting various aspects of the theory of algebraic groups: Rep impact on mathematics, particularly mathematics in resentations of algebraic groups, Nagoya Mathematical America. He is one of the founders of the modem theory Journal, volume 22 (1963), pp. 33-56; Regular elements of of transformation groups and is particularly known semisimple algebraic groups, Institut des Hautes Etudes for his contributions to the solution of Hilbert's fifth Scientifiques, Publications Mathematiques, volume 25 problem. 1272 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Funds, Prizes, Officers and Lecturers August 1989: To Daniel Gorenstein for his book Finite colorable, Part 1: Discharging, Illinois Journal of Mathe Simple Groups, An Introduction to their Classification matics, volume 21 ( 1977), pp. 429-490; and to Paul D. (Plenum Press, 1982); and his two survey articles The Seymour, for The matroids with the max-flow min-cut Classification of Finite Simple Groups and Classifying property, Journal of Combinatorial Theory, Series B, the Finite Simple Groups, Bulletin of the American volume 23 ( 1977), pp. 189-222. Mathematical Society, volume 1 (1979) pp. 43-199, and volume 14 (1986) pp. 1-98, respectively. Second award, 1982: To D. B. Judin and A. S. Ne mirovskii, for Informational complexity and effective August 1989: To Alberto P. Calderon for his paper methods of solution for convex extremal problems, Uniqueness in the Cauchy Problem for Partial Differential Ekonomika i Matematicheskie Metody 12 (1976), 357- Equations, American Journal of Mathematics, volume 80 369, and to L. G. Khachiyan for A polynomial algorithm ( 1958), pp. 16-36. in linear programming, Akademiia Nauk SSSR. Doklady August 1989: To Irving Kaplansky for his lasting impact 244 (1979), 1093-1096; to G. P. Egorychev, for The on mathematics, particularly mathematics in America. solution of van der Waerden 's problem for permanents, By his energetic example, his enthusiastic exposition, Akademiia Nauk SSSR. Doklady 258 (1981), 1041-1044, and his overall generosity, he has made striking changes and D. I. Falikman, for A proof of the van der Waerden in mathematics and has inspired generations of younger conjecture on the permanent of a doubly stochastic ma mathematicians. trix, Matematicheskie Zametki 29 (1981), 931-938; and to M. Grotschel, L. Lovasz and A. Schrijver, for The The Delbert Ray Fulkerson Prize ellipsoid method and its consequences in combinatorial Gifts of friends of the late Professor Fulkerson have optimization, Combinatorica 1 ( 1981 ), 169-197. provided a fund in excess of $7,000. Part or all of Third award, 1985: To J6zsef Beck, for Roth's esti the proceeds is to be used jointly by the Mathematical mate of the discrepancy of integer sequences is nearly Programming Society and the American Mathematical sharp, Combinatorica 1 (4), 319-325, (1981); and H. W. Society for the award of one or more prizes in discrete Lenstra, Jr., for Integer programming with a .fixed number mathematics at regular intervals. of variables, Mathematics of Operations Research 8 ( 4), First award, 1979: To Richard M. Karp, for On the 538-548, (1983); and Eugene M. Luks for Isomorphism computational complexity of combinatorial problems, of graphs of bounded valence can be tested in polynomial Networks, volume 5 (1975), pp. 45-68; to Kenneth time, Journal of Computer and System Sciences 25 ( 1), Appel and Wolfgang Haken, for Every planar map is four 42-65, ( 1982). Presidents G. C. Evans, 1939, 1940 Secretaries Marston Morse, 1941, 1942 J. H. Van Amringe, 1889, 1890 T. S. Fiske, 1888-1895 M. H. Stone, 1943, 1944 J. E. McClintock, 1891-1894 F. N. Cole, 1896-1920 T. H. Hildebrandt, 1945, 1946 G. W. Hill, 1895, 1896 R. G. D. Richardson, 1921-1940 Einar Hille, 1947, 1948 Simon Newcomb, 1897, 1898 J. R. Kline, 1941-1950 J. L. Walsh, 1949, 1950 R. S. Woodward, 1899, 1900 E. G. Begle, 1951-1956 John von Neumann, 1951, 1952 E. H. Moore; 1901, 1902 J. W. Green, 1957-1966 G. T. Whyburn, 1953, 1954 T. S. Fiske, 1903, 1904 Everett Pitcher, 1967-1988 R. L. Wilder, 1955, 1956 W. F. Osgood, 1905, 1906 Robert M. Fossum, 1989- Richard Brauer, 1957, 1958 H. S. White, 1907, 1908 E. J. McShane, 1959, 1960 Maxime Bacher, 1909, 1910 Treasurers Deane Montgomery, 1961, 1962 H. B. Fine, 1911, 1912 J. L. Doob, 1963, 1964 T. S. Fiske, 1890, 1891 E. B. Van Vleck, 1913, 1914 A. A. Albert, 1965, 1966 Harold Jacoby, 1892-1894 E. W. Brown, 1915, 1916 C. B. Morrey, Jr., 1967, 1968 R. S. Woodward, 1895, 1896 L. E. Dickson, 1917, 1918 Oscar Zariski, 1969, 1970 Harold Jacoby, 1897-1899 Frank Morley, 1919, 1920 Nathan Jacobson, 1971, 1972 W. S. Dennett, 1900-1907 G. A. Bliss, 1921, 1922 Saunders Mac Lane, 1973, 1974 J. H. Tanner, 1908-1920 Oswald Veblen, 1923, 1924 Lipman Bers, 1975, 1976 W. B. Fite, 1921-1929 G. D. Birkhoff, 1925, 1926 R. H. Bing, 1977, 1978 G. W. Mullins, 1930-1936 Virgil Snyder, 1927, 1928 Peter D. Lax, 1979, 1980 P. A. Smith, 1937 E. R. Hedrick, 1929, 1930 Andrew M. Gleason, 1981, 1982 B. P. Gill, 1938-1948 L. P. Eisenhart, 1931, 1932 Julia B. Robinson, 1983, 1984 A. E. Meder, Jr., 1949-1964 A. B. Coble, 1933, 1934 Irving Kaplansky, 1985, 1986 W. T. Martin, 1965-1973 Solomon Lefschetz, 1935, 1936 George Daniel Mostow, 1987, 1988 F. P. Peterson, 1973- R. L. Moore, 1937, 1938 William Browder, 1989, 1990 NOVEMBER 1989, VOLUME 36, NUMBER 9 1273 AMS Funds, Prizes, Officers and Lecturers Colloquium Lecturers Saunders Mac Lane, 1963 P. W. Bridgman, 1931 C. B. Morrey, Jr., 1964 R. C. Tolman, 1932 1896 James Pierpont, A. P. Calderon, 1965 Albert Einstein, 1934 Maxime Bocher, 1896 Samuel Eilenberg, 1967 Vannevar Bush, 1935 W. F. Osgood, 1898 D. C. Spencer, 1968 H. N. Russell, 1936 A. G. Webster, 1898 J. W. Milnor, 1968 C. A. Kraus, 1937 Oskar Bolza, I 90 I Raoul H. Bott, 1969 Theodore von Karman, 1939 E. W. Brown, 1901 Harish-Chandra, 1969 Sewall Wright, 1941 H. S. White, 1903 R. H. Bing, 1970 Harry Bateman, 1943 F. S. Woods, 1903 Lipman Bers, 1971 John von Neumann, 1944 1903 E. B. Van Vleck, Armand Borel, 1971 J. C. Slater, 1945 E. H. Moore, 1906 Stephen Smale, 1972 S. Chandrasekhar, 1946 E. J. Wilczynski, 1906 John T. Tate, 1972 P. M. Morse, 1947 Max Mason, 1906 M. F. Atiyah, 1973 Hermann Weyl, 1948 G. A. Bliss, 1909 E. A. Bishop, 1973 Norbert Wiener, 1949 Edward Kasner, I 909 F. E. Browder, 1973 G. E. Uhlenbeck, 1950 L. E. Dickson, I 913 Louis Nirenberg, 1974 Kurt Godel, 1951 W. F. Osgood, 1913 John G. Thompson, 1974 Marston Morse, 1952 G. C. Evans, 1916 H. Jerome Keisler, 1975 Wassily Leontief, 1953 Oswald Veblen, I 916 Ellis R. Kolchin, 1975 K. 0. Friedrichs, 1954 G. D. Birkhoff, 1920 Elias M. Stein, 1975 J. E. Mayer, 1955 F. R. Moulton, 1920 I. M. Singer, 1976 M. H. Stone, 1956 L. P. Eisenhart, 1925 Jiirgen K. Moser, 1976 H. J. Muller, 1958 Dunham Jackson, 1925 William Browder, 1977 J. M. Burgers, 1959 E. T. Bell, 1927 Herbert Federer, 1977 Julian Schwinger, 1960 Anna Pell-Wheeler, 1927 Hyman Bass, 1978 J. J. Stoker, 1961 A. B. Coble, 1928 Philip A. Griffiths, 1979 C. N. Yang, 1962 R. L. Moore, 1929 George D. Mostow, 1979 C. E. Shannon, 1963 Solomon Lefschetz, 1930 Julia B. Robinson, 1980 Lars Onsager, 1964 Marston Morse, I 9 31 Wolfgang M. Schmidt, 1980 D. H. Lehmer, 1965 J. F. Ritt, 1932 Mark Kac, 1981 Martin Schwarzschild, 1966 R. E. A. C. Paley, 1934 Serge Lang, 1981 Mark Kac, 1967 Norbert Wiener, 1934 Dennis Sullivan, 1982 E. P. Wigner, 1968 H. S. Vandiver, 1935 Morris W. Hirsch, 1982 R. L. Wilder, 1969 1936 E. W. Chittenden, Charles L. Fefferman, 1983 W. H. Munk, 1970 John von Neumann, 1937 Bertram Kostant, 1983 E. F. F. Hopf, 1971 A. A. Albert, 1939 Barry Mazur, 1984 F. J. Dyson, I 972 M. H. Stone, 1939 Paul H. Rabinowitz, 1984 J. K. Moser, 1973 G. T. Whyburn, 1940 Daniel Gorenstein, 1985 Paul A. Samuelson, 1974 Oystein Ore, 1941 Karen K. Uhlenbeck, 1985 Fritz John, 1975 R. L. Wilder, 1942 Shing-Tung Yau, 1986 ArthurS. Wightman, 1976 E. J. McShane, 1943 Peter D. Lax, 1987 Joseph B. Keller, 1977 Einar Hille, 1944 Edward Witten, 1987 Donald E. Knuth, 1978 Tibor Rad6, 1945 Victor W. Guillemin, 1988 Martin D. Kruskal, 1979 Hassler Whitney, 1946 Nicholas Katz, 1989 Kenneth G. Wilson, 1980 Oscar Zariski, 194 7 William P. Thurston, 1989 Cathleen S. Morawetz, 1981 Richard Brauer, 1948 Elliott W. Montroll, 1982 G. A. Hedlund, 1949 Gibbs Lecturers Samuel Karlin, 1983 Deane Montgomery, 1951 Herbert A. Simon, 1984 Alfred Tarski, 1952 M. I. Pupin, 1923 Michael 0. Rabin, 1985 Antoni Zygmund, 1953 Robert Henderson, 1924 L. E. Scriven, 1986 Nathan Jacobson, 1955 James Pierpont, 1925 Thomas C. Spencer, 1987 Salomon Bochner, 1956 H. B. Williams, 1926 David P. Ruelle, 1988 N. E. Steenrod, 1957 E. W. Brown, 1927 Elliot H. Lieb, 1989 J. L. Doob, 1959 G. H. Hardy, 1928 S. S. Chern, I 960 Irving Fisher, 1929 G. W. Mackey, 1961 E. B. Wilson, 1930 1274 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Funds, Prizes, Officers and Lecturers Fourth award, 1988: To Eva Tardos for A strongly Fifteenth award, 1988-1989: Stephen R. Bell, Don M. polynomial minimum cost circulation algorithm, Combi Blasius, and David Gabai natorica, volume 5 ( 1985), pp. 247-256; and to Narendra Sixteenth award, 1989-1990: Isaac Y. Efrat, John M. Karmarkar for A new polynomial-time algorithm for lin Lee, and Ralf J. Spatzier ear programming, Combinatorica, volume 4 ( 1984), pp. 373-395. The Levi L. Conant Fund Special Funds Levi L. Conant bequeathed a sum of $9,500 which the AMS Centennial Fellowship Fund Trustees incorporated with the permanent endowments for prize funds. This fund was established by the Society in 1973 and provides one-year Research Fellowships awarded each year in March. The number of fellowships granted The Karl Menger Fund each year depends on the contributions the Society The family of the late Karl Menger were the major receives, matched by a contribution from the Society of contributors to a fund established at Duke University between $9,000 and $20,000. Through the academic year totalling $40,000. The majority of the income from this 1983-84, this was a postdoctoral fellowship, restricted fund is to be used by the Society for annual awards at to persons only a few years past the Ph.D. In the the International Science and Engineering Fair. competition of January 1984, it was changed to an early mid-career fellowship, for persons five to ten years The Eliakim Hastings Moore Fund past the Ph.D. At the same time, the stipend was This fund was donated in 1922 in honor of Professor substantially increased. For the 1988 award, the name Eliakim Hastings Moore on the occasion of the twenty of the fellowship was changed from AMS Research fifth anniversary of the Chicago (Western) section of the Fellowship to AMS Centennial Fellowship in honor of Society. The fund is $2,575 and the income from the the Society's Centennial. fund is to be used at the discretion of the Council for and First Award, 1974-1975: Fred G. Abramson and James the publication of important mathematical books Li-Ming Wang. memoirs and for the award of prizes. Paul Second award, 1975-1976: Terence J. Gaffney, The Joseph Fels Ritt Memorial Fund Nevai, and George M. Reed. From the estate of Estelle F. Ritt, the income from a Third award, 1976-1977: Fredric D. Ancel and Joseph fund of $22,500 is available for the publication of works A. Sgro. in the field of mathematics as shall be determined by the Fourth award, 1977-1978: Steven Kalikow, Charles Pat governing bodies of the Society. ton, Duong-Hong Phong, and David Vogan. The Waldemar J. Trjitzinsky Fund Fifth award, 1978-1979: Alan Dankner, David Harbater, in 1988 from the Howard Hiller, Steven P. Kerckhoff, and Robert C. A bequest of $189,000 was received a fund in McOwen. estate of Barbara G. Trjitzinsky to establish memory of her husband, Waldemar J. Trjitzinsky. The Sixth award, 1979-1980: Scott W. Brown, Jeffrey E. income from this fund is to be used for needy students Hoffstein, Jeffry N. Kahn, James E. McClure, Rick L. studying in the field of mathematics. Smith, and Mark Steinberger. Seventh award, 1980-1981: Robert K. Lazarsfeld, Thomas Friends of Mathematics Fund H. Parker, and Robert Sachs. A Friends of Mathematics Fund has been created to Eighth award, 1981-1982: Lawrence Man-Hou Ein and incorporate monetary gifts to the Society of a general Mark Williams. nature. The principle of this fund is now $123,572. The proceeds of the fund are a part of the invested assets Ninth award, 1982-1983: Nicholas J. Kuhn. of the Society. The following gifts are components of Tenth award, 1983-1984: Russell David Lyons. this fund: $1,000 from the estate of Professor Ernest William Brown; $1,000 from the estage of Genevra B. Eleventh award, 1984-1985: Richard Timothy Durrett. Hutchinson; $3,000 from Solomon A. Joffe; $650 from Twelfth award, 1985-1986: R. Michael Beals. the estate of Professor Helen A. Merrill; $23,600 from estate Thirteenth award, 1986-1987: Dinakar Ramakrishnan the estate of Dean Marion Reilly; $1,000 from the of James K. Whittemore; and $2,700 from an anonymous Fourteenth award, 1987-1988: Richard Hain and Bill donor. Jacob NOVEMBER 1989, VOLUME 36, NUMBER 9 1275 Miscellaneous Personal Items Daniel H. Wagner, of the Naval ber 7, 1989, at the age of 82. He Postgraduate School, has accepted was a member of the Society for George D. Byrne, Research As a visiting research professorship at 53 years. sociate with Exxon Research and the U.S. Naval Academy. Allen E. Murray, of Rochester, Engineering Company, was elected New York, died on June 12, 1989, a Fellow in The Institute of Math at the age of 77. He was a member ematics and its Applications. of the Society for 32 years. Gary A. Lorden, of the Cal Deaths Institute of Technology, Sallie E. Pence, of Lexington, ifornia William P. Hanf, Professor Emer has been appointed the Institute's Kentucky, died on July 26, 1989, itus of the University of Hawaii, Vice-President for Student Affairs. at the age of 95. She was a member died on August 15, 1989, at the Michael C. Mackey, of McGill of the Society for 56 years . age of 55. He was a member of has been appointed J. Barkley Rosser, Professor University, the Society for 24 years. Director of the Centre for Nonlin Emeritus of the University of Wis ear Dynamics in Physiology and Truman L. Koehler, Professor consin, died on September 5, 1989, Medicine. Emeritus of Muhlenberg College, at the age of 81. He was a member Leopoldo Nachbin, George East died on July 17, 1989, at the age of the Society for 56 years. man Professor, University of Roch of 86. He was a member of the Robert B. Warfield, University ester, was given the title of Hon Society for 61 years. of Washington, died on September orary Professor by the State Uni Russell J. Michel, Professor 20, 1989, at the age of 49. He was versity of Campinas, Sao Paulo, Emeritus of Southeast Missouri a member of the Society for 23 Brazil. State University, died on Septem- years. 3-MANIFOLDS WHICH ARE END 1-MOVABLE Matthew G. Brin and T. L. Thickstun D (Memoirs of the AMS, Number 411) D While requiring only the basics of 3-manifold topology as The class of manifolds examined here also includes the background, this book introduces recent techniques that will ··missing boundary·· manifolds. The authors provide a new certainly find further application and brings readers to the characterization of orientable, missing boundary 3-manifolds frontiers of the topology of noncompact 3-manifolds. and contribute some information about the open question of determining which covers of compact 3··manifolds are missing Traditional techniques for analyzing noncompact 3-manifolds boundary' manifolds. involve study of its compact subsets. By contrast, this work utilizes certain open subsets called end reductions, which are .. simple·· approximations to a noncompact manifold that inherit many of the manifold's properties. In this work, the 1980 Mathematics Subject Classifications: 57N10; 57M10, 57N65 authors further their development of the concept of end ISBN 0-8218-2474-0, LC 89-15146 reduction and use it to analyze all orientable, noncompact ISSN 0065-9266 ,,t--;\IE~~77c:_., 73 pages (softcover), September 1989 3-manifolds in which loops near infinity homotop to infinity Individual member $9, List price $15, J~~""'0>~\9, while staying near infinity (this is the proper homotopy Institutional member $12 f5 ~ ~~ ) Mi ~ ::! condition ··end 1-movable.. of the title). To order, please specify MEM0/411NA .,. /db. 0llNDED \'IF All prices subject to change. Shipment will be made by surface. For air delivery add, 1st book $5, each additional book $3, maximum $100. Prepayment required. Order from American Mathematical Society, P.O. Box 1571, Annex Station, Providence, RI 02901-1571, or call toll free 800-321-4AMS to charge with VISA or MasterCard. 1276 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY New Members of the AMS ORDINARY MEMBERS Hongzhu Qiao, Univ of South Florida, Societe Mathematique de France Alfred M Barron, Metuchen, NJ Tampa Fidele Moukamba Robert T Bauer, Woodland Hills, CA John P Riley, Digital Equipment, Sociedade Portuguesa de Matemdtica William F Beck, Boulder, CO Maynard, MA Antonio Ornelas Douglas K Brotz, Adobe Systems, David B Salzman, John von Neumann Wiskundig Genootschap Mountain View, CA Center, Princeton, NJ Philippe P Clement Darlene Campbell, Tyler, TX David I Santiago, Rio Piedras, PR Charles E Chace, Columbia Univ, New Ray Schulz, Pleasantville, NJ NOMINEE MEMBERS York, NY Francisco Seeger, Univ of Washington, Auburn University Yves Cherruault, Paris, France Seattle Erin R Spicer Chi Kan Cheung, Hong Kong David M Sherer, Universal City, TX Trenton State College Jonathan Choate, Groton School, Groton, Robert A Weinstein, McGraw-Hill Constance Sue Marberry MA Publishing, New York, NY University ofArizona John W Coburn, Moore, OK Gary Weiss, Univ of Cincinnati, OH Catherine 0 McKee Balbina Garcia, San German, PR Xinlong Weng, Univ of South Florida, University of Missouri, Columbia Mandana Hashemzadeh, Van Nuys, CA Tampa Troy A Easterday R M Langer, Arlington, MA University of Nebraska at Omaha Gerson L Levin, Brooklyn, NY Wilma Trena Anderson Emmanuil Livshitz, Philadelphia, PA RECIPROCITY MEMBERS University of Pittsburgh, Pittsburgh Wallace J MacBain, Huntsville, AL Israel Mathematical Union Myong Y Lee Antony Maciocia, Mathematics lnst, Ron A Livne York College, CUNY Oxford, England Korean Mathematical Society Ebrima Nyiwg Joseph G McPhail, Univ of Windsor, Ju Young Min Ontario Canada London Mathematical Society INSTITUTIONAL MEMBER Zoltan Nagy, Kamen, Federal Republic of Bahman Tabatabaie Western Carolina University Germany Anthony W Wickstead Cullowhee, North Carolina ALGEBRAIC TOPOLOGY Mark Mahowald and Stewart Priddy D (Contemporary Mathematics. Volume 96) D This book will provide readers with an overview of some of the 1980 Mathematics Subject Classifications: 55-06; 55P42, 55P45, major developments in current research in algebraic topology. 55R45, 55T15, 18F25 Representing some of the leading researchers in the field, the ISBN 0-8218-5102-0, LC 89-15023 ISSN 0271-4132 book contains the proceedings of the International Conference 368 pages ( softcover), August 1989 on Algebraic Topology, held at Northwestern University in Individual member $25, List price $41, March, 1988. Several of the lectures at the conference were Institutional member $33 expository and will therefore appeal to topologists in a broad To order, please specify CONM/96NA range of areas. The primary emphasis of the book is on homotopy theory All prices subject to change. Shipment and its applications. The topics covered include elliptic will be made by surface. For air deliv cohomology, stable and unstable homotopy theory, classifying ery add, I st book $5, each additional spaces, and equivariant homotopy and cohomology. book $3, maximum $100. Prepayment required. Order from American Mathe Geometric topics-such as knot theory, divisors and matical Society, P.O. Box 1571, Annex configurations on surfaces, foliations, and Siegel spaces-are Station, Providence, RI 02901-15 71, or also discussed. Researchers wishing to follow current trends call toll free 800-321-4AMS to charge in algebraic topology will find this book a valuable resource. with VISA or MasterCard. NOVEMBER 1989, VOLUME 36, NUMBER 9 1277 Classified Advertisements advertising are positions available, books or lecture notes SUGGESTED USES for classified UNIVERSITY OF CALIFORNIA or rental of houses, and typing services. for sale, books being sought, exchange LOS ANGELES THE 1989 RATE IS $42.50 per inch on a single column (one-inch minimum), calculated Department of Mathematics from the top of the type; $18 for each additional 1/2 inch or fraction thereof. No discounts for multiple ads or the same ad in consecutive issues. For an additional $10 charge, TEMPORARY POSITIONS announcements can be placed anonymously. Correspondence will be forwarded. (1) Two E. R. Hedrick Assistant Pro Advertisements in the ""Positions Available·· classified section will be set with a minimum fessorships. Applicants must show very one-line headline, consisting of the institution name above body copy, unless additional strong promise in research and teaching. 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 Salary $37,000. Three year appointment. boldface at no extra charge. Classified rates are calculated from top of type in headline to Teaching load: four quarter courses per bottom of type in body copy, including lines and spaces within. Any fractional text will be year, which may include one advanced charged at the next 1/2 inch rate. Ads will appear in the language in which they are submitted. course in the candidate's field. Pref Prepayment is required of individuals but not of institutions. There are no member erence will be given to applications discounts for classified ads. Dictation over the telephone will not be accepted for classified completed by January 1 , 1990. advertising. (2) Two or three Research Assistant DEADLINES are listed on the inside front cover or may be obtained from the AMS Professorships in Computational and Advertising Department. Applied Mathematics. Applicants must U. S. LAWS PROHIBIT discrimination in employment on the basis of color, age, sex, race, show very strong promise in research religion or national origin. ""Positions Available·· advertisements from institutions outside the year U. S. cannot be published unless they are accompanied by a statement that the institution and teaching. Salary $37,000. Three does not discriminate on these grounds whether or not it is subject to U. S. laws. Details appointment. Teaching load: four quarter and specific wording may be found near the Classified Advertisements in the January and courses per year, which may include one July/August issues of the Notices. advanced course in the candidate's field. SITUATIONS WANTED ADVERTISEMENTS from involuntarily unemployed mathematicians Preference will be given to applications are accepted under certain conditions for free publication. Call toll-free 800-321-4AMS and completed by January 1, 1990. speak to Paula Montella for further information. (3) One or two Assistant Profes SEND AD AND CHECK TO: Advertising Department, Attn: Paula Montella, AMS, P. 0. Box sorships in the Program in Comput 6248, Providence, Rhode Island 02940. AMS location for express delivery packages is 201 ing (PIC). Applicants must show very Charles Street, Providence, Rhode Island 02904. Individuals are requested to pay in advance, strong promise in teaching and research, institutions are not required to do so. AMS FAX 401-331-3842. preferably in the general area of Logic, Language and Computation. Teaching load: four quarter programming courses POSITIONS AVAILABLE OREGON STATE UNIVERSITY and an advanced quarter course of the candidate's choice per year. Two year THE OHIO STATE UNIVERSITY Assistant Professor positions in Alge appointment, possibly renewable once Department of Mathematics bra/Number Theory, Numerical Analysis, or twice. Salary range: $37,000-$44,000. Geometric-Topology /Dynamical Systems, The Department of Mathematics of The Preference will be given to applications and Differential Geometry will become Ohio State University hopes to fill several completed by January 1, 1990. available September 16, 1990. Salary positions, both visiting and permanent, (4) One or two Lectureships in the depends on qualifications. Closing date effective Autumn Quarter 1990. Candi Program in Computing (PIC). Applicants December 15, 1989. Write to: in all areas of applied and pure must show very strong promise in the dates Professor Bent Petersen are invited to apply. Sig teaching of programming. Teaching load: mathematics Staff Selection Committee research accomplishments or five quarter programming courses per nificant Department of Mathematics exceptional research promise, and evi year. One year appointment, possibly Oregon State University of good teaching ability, will be renewable up to four times. Salary de dence Corvallis, Oregon 97331-4605 expected of successful applicants. pends on experience, begins at $31 ,200. Oregon State University is an Affirma Please send credentials and have (5) Subject to administrative approval, tive Action/Equal Opportunity Employer letters of recommendation sent to Pro a few adjunct assistant professorships. and complies with Section 504 of the fessor Joseph Farrar, Department of Two year appointments. Strong re Rehabilitation Act of 1973. OSU has a Mathematics, The Ohio State University, search and teaching background re policy of being responsive to the needs 231 W. 18th Avenue, Columbus, Ohio quired. Salary $32,400-$36,500 per year. of dual-career couples. 43210. Review of resumes will begin Teaching load: five quarter courses per STAFF SELECTION COMMITTEE immediately. year. B. E. Petersen, Chair Ohio State University is an Equal (6) Several positions for visitors and The B. I. Fein Opportunity 1Affirmative Action Employer. lecturers. R. Higdon To apply, write to Alfred W. Hales, R. M. Schori Chair, Department of Mathematics, Uni versity of California, Los Angeles, CA 90024-1555. Attn: Staff Search. UCLA is an equal opportunity/affirm ative action employer. 1278 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements POSITIONS AVAILABLE SUNY PLATTSBURGH UNIVERSITY OF CALIFORNIA CHAIRPERSON SANTA BARBARA DEPARTMENT OF MATHEMATICS DEPARTMENT OF MATHEMATICS WAKE FOREST UNIVERSITY The Z. Smith Reynolds Applications are invited for the KY FAN SUNY Plattsburgh invites applications Professorship in Mathematics ASSISTANT PROFESSORSHIP. The Ky for Department Chairperson in the Math Fan assistant professorship is a special ematics Department. Opportunity to pro Forest University announces the two-year non-renewable position which Wake vide leadership in undergraduate curricu of a distinguished profes carries a research stipend. Appointment establishment lum development (both for mathematics sorship made possible by the z. Smith is effective July 1, 1990. Candidates must majors and in service courses) and to Foundation. The scholar se possess a Ph.D. by September 1990. Se Reynolds help establish a supportive environment to fill this position must have an lection will be based primarily on demon lected for teaching and scholarship. record of recognized schol strated research achievement. Teaching established Qualifications: Ph.D. in Mathematics and a commitment to teaching experience is desirable. Teaching load arship or Statistics plus five years of college research in a university setting. will consist of four quarter courses per and mathematics teaching, administrative ex Duties include teaching, continuing a year. To apply send vita and publication perience at the departmental level, and program of research, contributing to list, and arrange to have 3 letters of continued involvement in mathematics the intellectual life of the Department recommendation sent to: Ky Fan Faculty research required. Experience as Chair of Mathematics and Computer Science, Search Committee, Department of Math or Vice-Chair of a Department of Mathe and fostering the mathematical growth ematics, University of California, Santa matics preferred. Rank will be Associate undergraduates. The position, Barbara, CA 93106. All applications re of gifted or full Professor, depending upon expe carries both tenure and the rank ceived by January 10, 1990 will be which rience. could be filled as early as given thorough consideration. UCSB is of professor, INDIVIDUALS WITH AN UNDER the fall semester of 1990. an Equal Opportunity1 Affirmative Action STANDING OF AND SENSITIVITY TO Forest University is a compre employer. Proof of U.S. citizenship or Wake MINORITY AND GENDER CONCERNS university with 5000 students, eligibility for U.S. employment will be re hensive ARE ENCOURAGED TO APPLY. of whom are in the undergraduate quired prior to employment (Immigration 3500 SUNY Plattsburgh is primarily an un The Department of Mathematics Reform and Control Act of 1986). college. dergraduate college with approximately Computer Science has 17 per and 5,500 students. At present, there are manent positions, 13 of which are in over 1 00 math majors. Plattsburgh is UNIVERSITY mathematics, and offers majors in math FLORIDA STATE located in Northeastern New York State and computer science and an ematics on Lake Champlain, near the Adirondack Applications are invited for an assistant in mathematics. MA Mountains and approximately sixty miles professorship with research specializa nominations, and applica Inquiries, from Montreal. tion in computational and applied mathe should be directed to: tions Deadline is December 15, 1989, how matics, geometry (especially differential Professor Richard Carmichael, ever applications will be accepted until geometry), or topology. The applica Chair the position is filled. tion deadline is January 16, 1990, and of Mathematics and Department Send nominations and applications appointment would begin August 1990. Computer Science with a list of references to: The candidate should have potential for P.O. Box 7311 Chair, Search Committee excellence in research and teaching. Wake Forest University cjo Office of Please send resume, and arrange for NC 27109 USA Winston-Salem, Personnel/ Affirmative Action three letters of recommendation to be of applicants will begin in late Evaluation SUNY Plattsburgh sent to Ralph McWilliams, Chair, De and will continue until the position winter Box 1639-401 partment of Mathematics, Florida State employer. is filled. AA/EO Plattsburgh, New York 12901 University, Tallahassee, Florida 32306. SUNY PLATISBURGH IS AN EQUAL Florida State University is an EEO/AA OPPORTUNITY EMPLOYER. employer. NOVEMBER 1989, VOLUME 36, NUMBER 9 1279 Classified Advertisements POSITIONS AVAILABLE CENTER FOR DISCRETE special consideration. All applications MATHEMATICS are due February 1. DARTMOUTH COLLEGE AND THEORETICAL Direct inquiries to: COMPUTER SCIENCE Professor Daniel Gorenstein, Senior Position in Mathematics. Asso Visiting and Post-Doctoral Positions ciate or Full Professor position avail Director able beginning in 1990-91. Candidates Applications are invited for visiting and DIMACS should have established and recognized post-doctoral positions in the Center for Hill Center for the Mathematical research program, proven ability to at Discrete Mathematics and Theoretical Sciences tract external research support, and Computer Science (DIMACS). This Cen Rutgers University interest in building and leading a strong ter is supported through the NSF Sci P.O. Box 1179 research group. Appointee will partici ence and Technology Centers Research Piscataway, NJ 08855-1179 pate in the recruitment for several junior Program. The participating institutions [email protected] positions. Proven record of excellence are Rutgers University, Princeton Uni All participating institutions are equal op in teaching at both the undergraduate versity, AT&T Bell Laboratories and Bell portunity1 affirmative action employers. and graduate levels and commitment Communications Research. Research fa to professional interaction with faculty cilities are located at the Rutgers and and Ph.D. students required. Applica Princeton campuses. DUKE UNIVERSITY tions are welcome in all fields of math Applicants are sought in all areas Department of Mathematics ematics. Department has special inter of discrete mathematics and theoreti One postdoctoral position in the Duke ests in algebra, combinatorics, geom cal computer science, including (but not Center for Non-linear Studies, working etry /topology, and probability /statistics. limited to) analysis of algorithms, com with David Schaeffer and a group of Dartmouth provides grants to new fac binatorics, complexity, computational al scientists and engineers who will be ulty members for research-related ex gebra, discrete and computational ge modelling experiments, with emphasis penses, a generous sabbatical program, ometry, discrete optimization and graph on scientific computations in granular and moderate teaching loads. The review theory. The Center will be able to of flow. This is a two-year position and of applications will begin on January 1, fer a few long-term positions (one to carries a teaching load of one course 1990. Send a letter of application, a two years) and a number of short-term per term. A SUN workstation will be curriculum vitae, the names of four peo positions (up to a few months). provided. ple who have agreed to write letters A primary activity of the Center is All candidates should send curriculum of recommendation, and a description to sponsor year-long research programs vitae, a research plan, and arrange for of research interests to: Mathematics on specific topics of current interest. three letters of recommendation to be Senior Search Committee Chair, De The topic for 1990-91 is Complexity sent. Address correspondence to: Fac partment of Mathematics and Computer Theory of Interactive Computation. Peo ulty Search Committee, Department of Science, Bradley Hall, Dartmouth Col ple with research interest in such fields Mathematics, Duke University, Durham, lege, Hanover, NH Dartmouth is 03755. as cryptography, communication com NC 27706. Duke University is an affirma firmly committed to Affirmative Action plexity, computational learning, compu tive action/equal opportunity employer. and strongly encourages applications tational number theory, and circuit com from minorities and women. plexity, are particularly encouraged to apply. DIMACS will also sponsor short term research workshops in these and ITHACA COLLEGE other areas to which a large number of The Department of Mathematics and participants will be invited. In addition, Computer Science at Ithaca College has the Center is planning a number of ed DUKE UNIVERSITY at least three tenure eligible positions Department of Mathematics ucational activities, including a summer in mathematics at the Assistant Pro workshop for high school mathematics fessor level available for the 1990-91 Applications are invited for two or more teachers and a summer workshop for academic year. All successful candi tenure track positions in Mathematics, high school students. dates will be expected to teach a wide rank and salary open, all fields. Please Postdoctoral fellows and long-term/ variety of mathematics courses at the send curriculum vitae, a research plan, short-term visitors will pursue an ac undergraduate level. A Ph.D. is required. and arrange for three ·letters of recom tive research program and participate For one of these positions, specializa mendation to be sent. Address corre in the activities of the Center. A few tion in statistics is preferred. Screening spondence to: Faculty Search Commit positions will be reserved for faculty begins December 15, 1989. Send vitae tee, Department of Mathematics, Duke members from non-research institutions to: Dr. Eric Robinson, Chair, Department University, Durham, NC 27706. Duke who might wish to spend all or part of of Mathematics and Computer Sciences, University is an affirmative action/equal their sabbatical year at DIMACS. Appli Ithaca College, Ithaca, New York 14850. opportunity employer. cations from researchers in industry are An Affirmative Action/Equal Opportunity especially encouraged and will be given Employer. 1280 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements POSITIONS AVAILABLE RUTGERS joint research with members of the fac THE STATE UNIVERSITY OF ulty. Candidates must have Ph.D., proven POMONA COLLEGE NEW JERSEY record of outstanding research accom CLAREMONT, CA 91711 Department of Mathematics plishments in pure or applied mathemat New Brunswick, NJ Pomona College invites applications for ics, and concern for teaching. These are a tenure track Assistant Professorship in anticipates the following open positions one or two year non-renewable posi the mathematical sciences beginning in beginning September, 1990. tions. the fall of 1990. The Ph.D. and demon (1) TENURE-TRACK AND TENURE (6) PART-TIME POSITIONS (all lev strated excellence in teaching and re POSITIONS. The Department anticipates els). These may be used both for can search are required. Must have a strong several openings. Depending on the .didates with primary responsibility for commitment to high quality teaching in qualifications of the applicants, appoint teaching and for candidates of outstand a variety of undergraduate courses and ments may be as tenure-track assis ing promise for research activity. contributing to the mathematical life of tant professorships or as tenured as Send resume and at least three let our department. Preference will be given sociate, full, or special professorships. ters of recommendation to SEARCH to strong candidates in statistics and Candidates must have Ph.D., outstand COMMITTEE, Department of Mathemat applied mathematics. Pomona College, ing research ability in pure or applied ics, Rutgers University, New Brunswick, the founding member of The Claremont mathematics and concern for teaching. NJ 08903 as soon as possible. Indi Colleges, offers the opportunity to teach Normal course load now averages 5 cate position desired and give # of intellectually gifted undergraduates in a hours. Preference given to applicants your area of specialty according to small liberal arts college while participat working in differential geometry, Lie the AMS Mathematics Subject Classification. ing in a mathematically active intercolle ory, logic, nonlinear analysis, topology, RUTGERS UNIVERSITY IS AN EQUAL giate community of over 30 mathemati and ring theory (ideally interacting with OPPORTUNITY/ AFFIRMATIVE ACTION cians, with clinics in applied mathemat algebraic geometry). However, excep EMPLOYER. ics and statistics. Submit applications, tionally strong candidates in all fields are including resume, transcripts and let encouraged to apply and will be given ters evaluating teaching and research careful consideration. capabilities by January 31, 1990, to The (2) HILL ASSISTANT PROFESSOR Search Committee, Department of Math non-renewable SHIP. This is a three-year UNIVERSITY OF CALIFORNIA ematics, Millikan Laboratory, Pomona position. Candidates should have re AT RIVERSIDE College, Claremont, CA 91711-6348. Ap cently received the Ph.D., show out Faculty Position in Mathematics plicants who will attend the AMS January standing promise in research ability in Meeting in Louisville should so indicate pure or applied mathematics, and have Applications and nominations are invited in their application letter prior to Jan concern for teaching. Normal course for a tenured or tenure track position uary 3. Pomona College is an affirmative load approx. 6 hours but one course in Analysis beginning July 1, 1990 or actionjequal opportunity employer and teaching reduction provided in two of later. The position is open as to rank; encourages applications from minority the three years. candidates at all levels and in all areas candidates and women. (3) LECTURESHIPS. (Assistant Pro of analysis will be considered. Demon fessor level and above). Normal course strated excellence in research and teach load approx. 6 hours. Candidates must ing is required. The eligibility pool for have Ph.D., show outstanding promise in this position will consist of those can DAEMEN COLLEGE research ability in pure or applied math didates for whom we receive a vita, a Buffalo, New York ematics and have concern for teaching. list of publications and three letters of The Department of Mathematics invites These are one or two year non-tenure recommendation by January 22, 1990. applications for a tenure-track position track positions. Established criteria of the University of in mathematics at the assistant profes (4) INSTRUCTORSHIPS. Responsible California determine salary and rank. sor level beginning September, 1990. for teaching mainly at the level of precal Candidates should send a curriculum Candidates must have a Ph.D. in math culus and below. Normal course load 12 vita, a list of publications and the names ematics and a strong commitment to hours. Candidates must have masters of at least three references to teaching. Applications will be accepted degree or equivalent related experience Professor M. M. Rao, Chair until February 15, 1990 or until the posi and provide evidence of teaching ability. Analysis Hiring Committee tion is filled. Spanish speaking desirable. These are one or two year non-tenure Department of Mathematics and Send a curriculum vitae, three letters track positions. Computer Science of recommendation, and transcripts to: (5) VISITING POSITIONS; part-time University of California Chairperson, Math. Department, Dae and full-time. Normal full-time course Riverside, California 92521 men College, 4380 Main Street, Amherst, load approx. 6 hours. These positions University of California is an Affirmative NY 14226. Daemen College is an E/0, are intended to permit individuals with Action/Equal Opportunity Employer. A/A employer. regular appointments elsewhere to visit Rutgers for the purpose of engaging in NOVEMBER 1989, VOLUME 36, NUMBER 9 1281 Classified Advertisements POSITIONS AVAILABLE UNIVERSITY OF SOUTHERN UNIVERSITY OF CALIFORNIA CALIFORNIA MATHEMATICS DEPARTMENT UNIVERSITY OF CALIFORNIA LOS ANGELES, CALIFORNIA SANTA CRUZ, CA 95064 AT RIVERSIDE 90089-1113 Faculty Position in Mathematics The Mathematics Department at the Uni The Division of Natural Sciences and versity of California, Santa Cruz expects Applications and nominations are invited Mathematics at USC has begun a five to have several visiting positions avail for a tenured or tenure track position year, $50 million Science Initiative. Sev able during the academic year 1989-90 in Geometric Analysis beginning July 1, eral tenure-track Assistant Professor and invites applications from qualified 1990 or later. The position is open as ships and possible tenured positions at mathematicians in all fields. Appoint to rank; candidates at all levels and in Associate Professor and Professor are ments will be made as Visiting Assis all areas of geometric analysis will be anticipated for 1990-91 in Mathemat tant, Associate or Full Professor, as considered. Demonstrated excellence in ics. Visiting positions (at all levels) and appropriate. Visitors will be expected research and teachng is required. The postdoctoral appointments will also be to teach, pursue their research, and eligibility pool for this position will consist available. perform some department or university of those candidates for whom we receive Any research area in pure or ap service. Such positions are available for a vita, a list of publications and three plied mathematics or statistics will be periods ranging from one quarter to letters of recommendation by January considered, including but not restricted the full academic year, with a possible 22, 1990. Established criteria of the to: Algebraic Geometry, Biomathematics, extension to a second year. There is University of California determine salary Control Theory, Differential Geometry, also a possibility that visitors will be and rank. Candidates shouuld send a Dynamical Systems, Functional Anal able to stay on to do summer school curriculum vita, a list of publications and ysis, Group Theory, Number Theory, teaching following the academic year. the names of at least three references Numerical Analysis, Ordinary or Partial Preference will be given to those who to Differential Equations, Probability, Ring can teach for the entire academic year. Professor Bun Weng, Chair Tneory, Statistic-s, aM-l'op-ology: - - ~pplicant!r must nola the Ph.D. in Math Geometric Analysis Hiring Assistant Professors teach two ematics. University teaching experience Committee courses per semester, must show strong desired. Applicants should send vitae, Department of Mathematics and research promise, and preferably should three letters of reference speaking of Computer Science work in one of the above areas. Ap the applicant's teaching _and research University of California plicants for senior positions _must have experience to: Recruiting Committee, Riverside, California 92521 an outstanding record of research and Mathematics Department, University of University of California is an Affirmative scholastic achievement. Address inquiries California, Santa Cruz, CA 95064. Clos Action/Equal Opportunity Employer. to: Chair of Appointments Commit ing Date: February 1, 1990. Please refer tee/Department of Mathematics-ORB to #T89-14 in your reply. UCSC is a 306/Los Angeles, CA 90089-1113. SAA/EOP /IRCA/EOE/ AA employer. EOE/AA. UNIVERSITY OF SOUTH FLORIDA Department of Mathematics UNIVERSITY OF MARYLAND UNIVERSITY COLLEGE At least one tenure-track position is THE OHIO STATE UNIVERSITY TEACH IN ASIA OR EUROPE available beginning August 1990. Appli Department of Mathematics cants must possess a Ph.D. degree. The University of Maryland University Research Instructorships in Applicants specializing in analysis (nu College seeks excellent teachers for Mathematics merical analysis, approximation theory, openings on U.S. military bases over special functions); differential equations; Applications are invited for the position seas. Appointments begin August, 1990. of research instructor in mathematics for probability ;mathematical statistics; the Requirements include M.A. or Ph.D., re ory of computation (algebra, combina the academic year 1990-:91. Candidates cent college teaching experience, and should hold a Ph.D. (or equivalent) in torics logic) are preferred but other out U.S. citizenship. Competence to teach standing candidates will be considered. mathematics and show strong research in another discipline desirable. Bene promise. Rank and salary will depend on creden fits include transportation and military tials. To apply, send curriculum vitae and Please send credentials and have base privileges (PX, commissary, etc.). letters of recommendation sent to Pro have three letters of recommendation Frequent travel and the cost of school sent to Kenneth L. Pothoven, Chairman, fessor Joseph Ferrar, Department of ing make these positions difficult for Mathematics, The Ohio State Univer University of South Florida, Department those with children. Send resume to Dr. of Mathematics, Tampa, Florida 33620- sity, 231 W. 18th Avenue, Columbus, Ralph E. Millis, Assistant to the Presi Ohio 4321 0. The Ohio State University is 5700. Application deadline: February 12, dent, Overseas Programs, The University 1990. The University of South Florida is an Equal Opportunity I Affirmative Action of Maryland University College, College Employer. an equal opportunity employer. Park, MD 20742-1642. AA/EEO. 1282 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements POSITIONS AVAILABLE WESTERN WASHINGTON UNIVERSITY THE UNIVERSITY OF FLORIDA Department of Mathematics UNIVERSITY OF SOUTHERN Applications are invited for tenure-track CALIFORNIA and visiting positions to begin Fall 1990. In each of the next several years, the Department of Mathematics Successful candidates will be expected Department of Mathematics intends to Chairperson to be active in research, to interact at the fill a substantial number of tenure-track faculty positions with mathematicians of The University of Southern California in research level with current department exceptional caliber. Outstanding candi vites applications and recommendations members, and to be good teachers. A dates from all academic ranks and all for the faculty position of Chairperson of Ph.D. in Mathematics is required. areas of pure and applied mathematics the Department of Mathematics (at the Candidates are especially sought in are invited to apply for these positions. rank of Professor). The Department has the following two areas, although out Applications from junior candidates with a faculty of about 45 members, repre standing candidates with other special post-doctoral experience are especially senting many areas in pure and applied ties will be considered: (1) Applied math welcome. mathematics. The Division of Natural ematics. (2) Mathematics Education. First preference will be given to can Sciences and Mathematics has begun Rank and salary are open, but a sub didates who will facilitate Department a $50 million Science Initiative, which stantial research record will be required goals of establishing strong working is expected to increment the Division's for appointment above the Assistant Pro groups in partial differential equations, annual budget by about $15 million after fessor level. The normal teaching load algebraic geometry and number theory. five years. The opportunities for growth for research faculty is two courses per Secondary preference will be given to and enhancement of the Department are quarter. candidates who will fit well into currently substantial. Western Washington University is lo functioning groups. In particular, it is The Department offers PhD and mas cated on Bellingham Bay in an area likely that one position will be filled this ter's degrees in both pure and applied of outstanding natural beauty within an year by an algebraist. mathematics, and a master's degree in hour's drive of the Seattle and Vancou Senior candidates should have dis statistics (with a PhD program planned). ver, B.C. metropolitan areas and the tinguished research records, and junior A new Center for Applied Mathematical Cascade Mountains. The department candidates are expected to have made Sciences, under the direction of H. T. has a strong undergraduate program significant research contributions. Every Banks, has been established, and of with a somewhat applied flavor and a candidate is expected to possess a fers an extensive program of visitors flourishing Master's program with more strong commitment to teaching. Candi and seminars. The Department also has than twenty students. dates should forward a resume (includ a large computer-assisted learning cen Applications should be sent to Profes ing a list of publications) and should ter for undergraduates and a statistics sor Thomas T. Read, Chairman, Depart arrange for at least four letters of rec laboratory. ment of Mathematics, Western Washing ommendation to be sent to: Candidates for the position must have ton University, Bellingham, WA 98225. David A. Drake, Chair an outstanding record of research and Interested candidates should submit Department of Mathematics scholarship and must be ready to as a letter of application, complete tran University of Florida sume the academic leadership and ad scripts, a vita, and three letters of rec 201 Walker Hall ministrative direction of a broadly-based ommendation. Deadline for applications Gainesville, Florida 32611 university department which is in the pro is February 1 , 1990; later applications All applications for the academic year cess of expanding. If interested, send a will be considered if positions remain 1990-1991 should be complete by De vita and names of references to: available. Positions are subject to the cember 31, 1989. The University of Chair Search Committee continuing availability of funds. The Uni Florida is an equal opportunity employer Department of Mathematics versity is an EO/AA employer. and energetically solicits applications University of Southern California from women and minority candidates. Los Angeles, CA 90089-1113 USC is an Equal Opportunity I Affirmative Action employer. NOVEMBER 1989, VOLUME 36, NUMBER 9 1283 Classified Advertisements POSITIONS AVAILABLE may also be contacted with any ques UNIVERSITY OF UTAH tions concerning the positions. Department of Mathematics SOUTHERN METHODIST UNIVERSITY I. Gladwell's email addresses are: Department of Mathematics invites applications for the [email protected] Junior Tenure-Track Positions following positions: h5nr1 001 @smuvm1 (on bitnet) SMU is an equal opportunity/affirmative 1. At least four full time tenure track The Department of Mathematics at action/Title IX employer. appointments on any of the professorial Southern Methodist University seeks ap levels. The Department is particularly in plications for junior tenure-track posi terested in applicants who work in the tions with employment beginning Fall INDIANA STATE UNIVERSITY areas of geometry, algebra, topology, 1990. An outstanding candidate may be CHAIRPERSON group representation theory, applied considered for a more senior position. DEPARTMENT OF MATHEMATICS AND mathematics, and scientific computing. Candidates should be active researchers COMPUTER SCIENCE Selection will be based on research ex in applied or numerical mathematics and pertise and teaching ability. Applications should have a strong commitment to The Department of Mathematics and will be accepted until January 31, 1990 teaching. The department has an active Computer Science, Indiana State Univer or until the positions are filled. doctoral program. Applicants must be sity, invites applications for the position able to teach graduate level courses in of Chairperson. Applicants should have 2. Two or more nonrenewable three applied mathematics, numerical analysis a doctorate in Mathematics or Com year Instructorships. Persons of any age or scientific computation. The teaching puter Science, a record of successful receiving Ph.D. degrees in 1989 or 1990 load for each position is two courses (six teaching and research, and a commit are eligible. Applicants will be selected hours) per semester. There may also be ment to promoting research, teaching, on the basis of ability and potential in visiting positions available in academic and other scholarly activities. In addition teaching and research. Starting salary year 1990-91. applicants should have a potential for this academic year is $29,500; cost of Southern Methodist University has administering a department with both living increases are contingent on action about 8000 students. The Department Mathematics and Computer Science de by the State Legislature. Duties consist of Mathematics has a strong and on gree programs. The Computer Science of teaching five courses during the three going commitment to the development area is undergoing active development, quarter academic year. Applications will of classical and modern applied mathe so familiarity with Computer Science be accepted until December 31, 1989 or matics. Thirteen of the sixteen full-time curricular issues is desirable. until the positions are filled. faculty are applied or numerical math The Department offers BS and BA ematicians. Current areas of research degrees in Mathematics and Computer 3. One or more visiting positions of one include mathematical modeling of phys Science. It also offers MS and MA year or less. Selection criteria are teach ical and biological phenomena, nonlin degrees in Mathematics and it is de ing ability and potential contribution to ear waves, perturbation methods, fluid veloping an MS degree in Computer our research environment. Applications dyamics, numerical bifurcation, mathe Science. There are 25 faculty positions. will be accepted until January 31, 1990 matical software, numerical solution of The Department has an 8 processor or until the positions are filled. differential equations, and parallel com Sequent and a VAX minicomputer and a Applications must include curriculum putation. Candidates should be active in microcomputer laboratory. vitae,, bibliography and three letters of one of these areas or a related one. Salary and rank are commensu reference. (Instructorship applications Senior faculty and their interests include rate with qualifications and experience. must also include an abstract of the D. H. Anderson (mathematical biology), Please send a letter of application, vita thesis and either a list of graduate W. E. Ferguson (numerical partial differ and three letters of recommendation to: courses completed or a transcript of ential equations), I. Gladwell (mathemat Dr. David Hutchison, Chairperson graduate work.) ical software), R. Haberman (nonlinear Search Committee Please send your application to: waves), G. W. Reddien (bifurcation the Department of Mathematics and COMMITTEE ON STAFFING ory), D. A. Reinelt (fluid dynamics) and L. Computer Science DEPARTMENT OF F. Shampine (numerical ordinary differ Indiana State University MATHEMATICS ential equations). Among its computers, Terre Haute, IN 47809 UNIVERSITY OF UTAH the university has a Sequent Symmetry Applications received after February 1, 233 JWB for research use. 1990 cannot be guaranteed considera SALT LAKE CITY, UTAH 84112 Applications must be received by Jan tion. Proof of U.S. citizenship or eligibil The University of Utah is an equal uary 10, 1990. Please send a vita and ity for U.S. employment will be required opportunity-affirmative action employer. three letters of recommendation to: Pro prior to employment (Immigration Re fessor I. Gladwell, Chair, Department of form and Control Act of 1986). Indiana Mathematics, Southern Methodist Uni State University is an Equal Opportu versity, Dallas, Texas 75275 (Tel: (214) nity 1Affirmative Action Employer. 692-2506, FAX: (214) 692-4099) who 1284 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements POSITIONS AVAILABLE Joint Search Committee Division of Statistics UNIVERSITY OF UNIVERSITY OF CALIFORNIA University of California WISCONSIN-MADISON DAVIS Davis, CA 95616 Department of Mathematics FACULTY POSITION IN STATISTICS Employment Opportunities The University of California, in compli The Division of Statistics and the De ance with the Civil Rights Acts of 1964, partment of Mathematics, University of Title IX of the Education Amendments of The Department of Mathematics at the California, Davis, invite applications and 1972 (45 CFR 86), the Rehabilitation Act University of Wisconsin-Madison solicits nominations for a position beginning Fall of 1973, and the Age Discrimination in applications for the following positions 1990. Appointment to be made at rank Employment Act of 1967, does not dis to begin fall 1990. and salary commensurate with qualifi criminate on the basis of age, race, color, cations. Duties include teaching at all national origins, religion, sex, or hand Tenure and Tenure Track Positions. levels and research. Applicants should icap in any of its policies, procedures, Appointments will be made at the Assis have a distinguished research record or practices; nor does the University tant Professor level unless qualifications in probability theory1 applied probabil discriminate against any employees or and experience require appointment at ity /stochastic processes, strong interest applicants for employment because they higher rank. Deadline for applications is in mathematical statistics, and a record are disabled veterans or veterans of November 30, 1989. of excellence in teaching. the Vietnam era. This anti-discrimination The Division of Statistics functions policy covers admission and access to, Van Vleck Assistant Professorships. as a department with additional inter and the treatment and employment in Appointments are for a specified term of college status and scope. The Graduate University programs and activities. In three years at an academic year salary of Group in Statistics brings together the quiries regarding the University's equal at least $31,500. The usual teaching load faculty of the Division and faculty from opportunity policies may be directed to is two courses per semester. Ordinarily other disciplines who have a strong Vice Chancellor-Academic Affairs, U.C. only those applicants who have received interest in statistical applications. The Davis. their doctorate since 1987 and prior Statistical Laboratory, also a component to September 1990 will be considered. of the Division, provides campus-wide Preference will be given to candidates consultation and affords an opportunity who are likely to interact well with other for graduate students to gain practical members of the Department. Deadline for applications is December 31, 1989. experience. The Department of Mathe EASTERN ILLINOIS UNIVERSITY Candidates should provide clear evi matics includes faculty in both pure and Chairperson dence of teaching ability and excellence applied mathematics engaged in numer EASTERN ILLINOIS UNIVERSITY invites in mathematical research. Supporting ous areas of interdisciplinary research activity. In addition to the departmental applications for Chairperson of the De materials should include a vita, and graduate program, the Graduate Group partment of Mathematics. Requirements three or four recommendation letters, at in Applied Mathematics is also housed include a doctorate in a mathematical least one of which discusses, in detail, science and experience in teaching and the candidate's teaching qualification. in the department. This graduate group brings together faculty in Mathematics research; administrative experience is Van Vleck applicants are also required preferred. EIU is a residential university and faculty from other disciplines who to submit a one to three page abstract have strong interests in all areas of of 1 0,000 students located in east central of their dissertation. Illinois. The Department of Mathematics, applied Mathematics. Mathematics and Application forms are available from Statistics offer full academic programs with 28 regular faculty members, of the Hiring Committee, Department of leading to the BA, BS, MS, and Ph.D. fers Bachelors and Masters degrees in Mathematics, 223 Van Vleck Hall, 480 degrees. Mathematics and Mathematics Educa Lincoln Drive, Madison, WI, 53706. Appli The city of Davis is an energy tion, and Bachelors degrees in applied cations will be accepted for all positions Computer Science. conscious and progressive city located until they are filled; however, in order to in Northern California's Central Valley. It Send applications with transcripts, ensure full consideration, the application lies within twenty minutes of the state vita, three letters of reference, and a brief and all supporting materials should be statement of educational and adminis received by the above deadlines. The capital, Sacramento, and within ninety trative philosophy to Jon Laible, Dean, University of Wisconsin is an AA/EOE minutes of the San Francisco Bay Area. Davis residents are ideally located for College of Liberal Arts and Sciences, employer. The Immigration Reform and Control participating in the recreational opportu Eastern Illinois University, Charleston, IL 61920. The closing date is January 1, Act of 1986 requires the University to nities of Lake Tahoe, the Napa Valley, 1990 or when the position is filled. EIU is verify the identity and work authorization and the coastline of Northern California. The postmarked deadline for applica an affirmative action, equal opportunity of the successful applicant. Offer of em employer. ployment is contingent upon verification. tions is January 11, 1990. An application consists of a vitae and three letters of recommendation to be sent to: NOVEMBER 1989, VOLUME 36, NUMBER 9 1285 Classified Advertisements POSITIONS AVAILABLE KENT STATE UNIVERSITY filled or until August 18, 1990, whichever UNIVERSITY OF IOWA Department of Mathematical Sciences occurs first. Applicants should submit a Senior Position in Applied resume and arrange to have three letters The Mathematics Department of the Mathematics/Scientific Computation of recommendation sent to Chuck Gart University of Iowa invites applications land, Chair of the Applied Mathematics A:~plications are invited for a faculty po for the following positions: Search Committee, Department of Math Sition at the associate or full professor 1. Three tenure-track appointments ematical Sciences, Kent State University, level beginning Fall Semester 1990. The at the Assistant or beginning Associate Kent, OH 44242. Kent State University is ideal candidate would have a strong Professor level beginning in the 1990- an Affirmative Action/Equal Opportunity training in classical applied mathematics 91 academic year. One of these is to Employer. be in numerical analysis and two are and some experience with large-scale scientific computation. He or she would to be filled by specialists in harmonic analysis, probability theory, or topology be expected to have a solid record of manifolds. Selection will be based of research, publication, and external NORTHERN ARIZONA UNIVERSITY funding, as well as a commitment to on evidence of outstanding research ac Flagstaff, Arizona quality teaching. The appointed faculty co~plishments or potential, and teaching The Department of Mathematics an ab1hty. A Ph.D. or equivalent training is member would be expected to enhance the Department's outreach and inter nounces tenure-track openings in math required. disciplinary research efforts, supervise ematics for Fall 1990 . . 2. _one senior faculty position begin graduate students, and contribute to The first is an Associate Professor mng m 1990-91 academic year or later. ship in dynamical systems, in particular, Only applicants of extraordinary stature curricular planning and development. A competitive salary is available. qualitative theory of differential equa will be considered. A strong record of tions. A sustained, high quality research leadership in teaching and research in The Department of Mathematical Sci ence at Kent State University comprises program is required. Assistant professor one of the department's current or de appointments in the area are also antici veloping areas of strength is required. pure and applied mathematics, statistics, computer science, and the Institute for ~ated as we develop an existing strength 3. Pending availability of funds, one mto a clear focus. Related research of or more visiting positions for all or part Computational Mathematics. This new position is intended to complement ex the department concentrates mainly but of the 1990-91 academic year. Selection not exclusively on planar systems with will be based on research expertise and isti~g strengths in applied analysis (es pecially numerical analysis and approx polynomial right-hand sides. teaching ability. Preference will be given Also open is an assistant professor to applicants whose scholarly activity is imation theory) and computer science (especially symbolic computation, expert ship in algebra or combinatorics, espe of particular interest to members of the systems, and parallel computing). cially combinatorial areas of algebra or current faculty. The infrastructure of the Department geometry. Women and minority candidates are Each requires a PhD, demonstrated especially urged to apply for any of !s very good: the equipment inventory mcludes 2 VAX mini-computers plus potential for a productive, quality re the above positions. The University of search program, and substantial evi Iowa welcomes the employment of highly Encore, Sequent, Staran, and Warp parallel-processing computers and a va dence of quality teaching. qualified professional couples on its fac riety of work-stations and peripherals. Flagstaff is located in the cool pine ulty and staff, permits the appointment The University also maintains an IBM forests of Northern Arizona, near high of faculty couples within the same de mountains, the Grand Canyon and nu partment, and permits the sharing of a 3090 mainframe and a high-performance (interactive) link to the Cray Y-MP/864 merous other natural attractions. NAU single appointment by a faculty couple. has an on-campus enrollement of ap Applications will be received until Jan at the Ohio Supercomputer Center in Columbus, on which computing time is proximately 14,000. The Department of uary 31, 1990, or until the positions are 34 faculty offers bachelor's and master's filled. To apply send a complete vita and readily available. Kent State University is attractively degree programs. have three letters of recommendation Send vita and direct three letters of sent to: set in the rolling hills of northeast Ohio 40 minutes southeast of Cleveland and reference to: Screening Committee, De Professor W. A. Kirk, Chair partment of Mathematics, PO Box 5717, Department of Mathematics 20 minutes east of Akron. Some of the main research centers in the area Northern Arizona University, Flagstaff, University of Iowa include the University's internationally AZ 86011. The searches will remain Iowa City, Iowa 52242 open until the positions are filled; how kno~n Glenn H. Brown Liquid Crystal The University of Iowa is an Equal Op ever, the Screening Committee will begin portunity I Affirmative Action Employer. Institute, NASA Lewis Reseach Center in Cleveland, and Loral Systems (formerly reviewing applications on December 1, Goodyear Aerospace) in Akron. 1989. Northern Arizona University is Application deadline is February 24, an Equal Opportunity I Affirmative Action 1990. If qualified individuals do not ap Institution. Women and minorities are ply by February 24, 1990, the deadline encouraged to apply. will be extended until the position is 1286 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements POSITIONS AVAILABLE UNIVERSITY OF COLORADO AT UNIVERSITY OF COLORADO AT BOULDER BOULDER CARNEGIE MELLON UNIVERSITY FACULTY APPOINTMENTS INSTRUCTORS-VISITING A Zeev Nehari Assistant PROGRAM IN APPLIED MATHEMATICS ASSISTANT PROFESSORS Professorship in PROGRAM IN APPLIED MATHEMATICS Mathematics The University of Colorado at Boulder has made a substantial commitment to The University of Colorado at Boulder The Zeev Nehari Assistant Professor building a preeminent program in ap has made a substantial commitment to ships have been instituted in the De plied mathematics. The program fosters building a preeminent program in ap partment of Mathematics of Carnegie interdisciplinary activities and exciting plied mathematics. The program fosters Mellon University to honor the memory opportunities exist for interaction with interdisciplinary activities and exciting of Professor Zeev Nehari, a member various centers and institutes in the opportunities exist for interaction with of the Department from 1954 to his area. various centers. death in 1978. The position available A number of faculty appointments Applications are invited for instructors is for an initial period of one or two are anticipated over the next few years. or visiting assistant professor positions academic years, beginning in September Preference will be given to candidates beginning in the fall of 1990. Preference 1990, and extendable for one additional at the Assistant Professor level with will be given to candidates with a re year when mutually agreeable. It car a research emphasis in the area of search emphasis in any of the following ries a reduced academic year teaching computational mathematics. Exception three areas: computational mathematics, load of six hours per week during one ally strong candidates at other levels will physical applied mathematics, especially semester and three hours per week dur be considered. Other areas of foci in the fluids and plasmas, or nonlinear phe ing the other. Applicants are expected program are nonlinear phenomena and nomena. to show exceptional research promise, physical applied mathematics, especially The Program, an interdisciplinary ef as well as clear evidence of achieve fluids and plasmas. fort, includes faculty in computer sci ment and should have research inter Applicants are invited for tenure track ence, engineering, mathematics, astro ests which intersect those of current positions with appointments beginning physical sciences as well as other de faculty of the Department. Applicants fall, 1990. partments, institutes and centers. should send a vita, list of publications, The University of Colorado has a The University of Colorado has a and a statement describing current and strong institutional commitment to the strong institutional commitment to the planned research, and arrange to have principle of diversity in all areas. In principle of diversity in all areas. In at least three letters of recommenda that spirit we are particularly interested that spirit we are particularly interested tion sent to the committee. Applications in receiving applications from a broad in receiving applications from a broad also should include at most three two spectrum of scholars including women, spectrum of scholars including women, digit mathematics subject classification members of ethnic minorities and dis members of ethnic minorities and dis numbers (as displayed in Mathematical abled individuals. abled individuals. Reviews) corresponding to the primary Applicants should send a current cur Applicants should send a current cur area(s) of research of the applicant. All riculum vitae and selected reprints to riculum vitae, reprints, and three letters communications should be addressed Professor Mark J. Ablowitz, Director, of recommendation to Professor Mark to: Zeev Nehari Assistant Professorship Program in Applied Mathematics, Cam J. Ablowitz, Director, Program in Applied Committee, Department of Mathematics, pus Box 426, University of Colorado, Mathematics, Campus Box 426, Univer Carnegie Mellon University, Pittsburgh, Boulder, CO 80309-0426. Applications sity of Colorado, Boulder, CO 80309- PA 15213. Carnegie Mellon University is are due by February 1 , 1990. Late ap 0426. Applications are due February 1, an Affirmative Action/Equal Opportunity plications will be considered for any 1990. Applications for positions remain Employer. positions remaining unfilled on April 15, ing unfilled will be considered until April 1990. EOE/ AA. 15, 1990. EOE/ AA. NOVEMBER 1989, VOLUME 36, NUMBER 9 1287 Classified Advertisements AVAILABLE POSITIONS OKLAHOMA STATE UNIVERSITY SOUTHEASTERN MASSACHUSETTS DEPARTENT OF MATHEMATICS UNIVERSITY UNIVERSITY OF SOUTH ALABAMA VACANCY DEPARTMENT OF Several tenured, tenure-track and visit MATHEMATICS AND STATISTICS ing positions at all professorial ranks Two Full-time faculty positions in the are anticipated for Fall, 1990. All areas Department of Mathematics beginning Sep Two tenure-track positions starting are under consideration, but we espe September, 1990 will be tember 1 , 1990. Appointment cially encourage applications in Differen Earned doctorate and excellence in or made at the Assistant Professor tial Geometry, Partial Differential Equa teaching required. Research potential/ level. Ap possibly Associate Professor tions, Probability, Algebraic Geometry, experience is expected. The selected plicants must have a Ph.D. in Mathemat Topology, Several Complex Variables, candidate will join an established pro 9/1/90). ics (earned or anticipated by Harmonic Analysis, and Applied Math. gram with traditional and computer a com Strong research potential and Normal duties include research and at oriented degrees and will have the are mitment to excellence in teaching most six hours teaching per semester. opportunity to participate in the de for required. The successful candidate Minimum qualifications are a Ph.D. in velopment of mathematics courses for Professor appointment as Associate Mathematics or a related field, evidence growing undergraduate and graduate re must also demonstrate significant of research achievement or potential, programs in the Department of Mathe search accomplishments. Preference will and a commitment to teaching. Post matics and in the Department of Com exist be given to areas complementing doctoral experience is desirable, but not puter and Information Sciences. ing research specialities. Salaries will essential. For full consideration, send Application deadline: January 15, 1990. be ac be competitive. Applications will a resume and arrange to have three Applications, including resume, tran but cepted until positions are filled, confidential letters of reference sent by script, and three letters of reference should be completed by 1/31/90 to en January 15, 1990 to J. Cogdell, Appoint should be sent to: detailed sure consideration. Please send ments Committee Chairman, Department Rufus A. Winsor, Chairperson letters resume and arrange to have three of Mathematics, Oklahoma State Univer Department of Mathematics of recommendation sent to Dr. Suzanne sity, Stillwater, OK 74078-0613. O.S.U. Southeastern Massachusetts McGill, Chair; Department of Mathemat is an equal opportunity /affirmative ac University Alabama; ics/Stat; University of South tion employer. Women and minorities North Dartmouth, MA 02747 Opportu Mobile, AL 36688. An Equal are especially encouraged to apply. SMU IS AN EO/AA EMPLOYER. nity 1Affirmative Action Employer. PORTLAND STATE UNIVERSITY BRADLEY UNIVERSITY UNIVERSITY OF NORTH Department of Mathematics CAROLINA AT CHARLOTTE The Department of Mathematical Sci DEPARTMENT OF MATHEMATICS, ences invites applications for one or Applications are invited for an entry CHARLOTTE, NC 28223 more tenure track positions at the assis level tenure-track position at the rank of August, Two tenure-track and one or more Vis tant professor rank beginning Fall 1990. Assistant Professor beginning have a strong iting positions at Asst/ AssocjFull Prof. Applicants should hold a PhD degree (or 1990. Candidates should teaching. level in Mathematics and Statistics, and equivalent) in mathematics or statistics commitment to undergraduate continuing one senior Assoc/Full Prof. level in Math and have demonstrated both a strong The Ph.D. is required, and is nec Education. Rank and salary depend on research potential and a strong commit professional growth (publication) advancement. qualifications. A PH.D and a serious ment to teaching. Send a vita and have essary for tenure and all areas are invited. commitment to teaching and research at least three letters of recommendation Applicants from be given to are required. Preferred specialties are: sent to: Special consideration will mathe Algebra, Analysis, Applied Mathematics, Bruce A. Jensen those in the fields of statistics, mathematics, Math Education, Statistics, but strong Department of Mathematical matical modeling, discrete The candidates in all areas are encouraged Sciences and geometry. Salary is competitive. 1990, or until to apply. Also possible are lecturer po Portland State University closing date is January 12, positions may sitions (one or two year renewable; PO Box 751 the position is filled. Other date. Send MA/MS required). Send vitae, list of Portland, OR 97207 become available at a later vita, and three or four references, and abstracts of current Screening of applications will begin on letter of application, to: Dr. research to Prof. Hae-Soo Oh at the February 1, but applications will be more letters of recommendation Depart above address. Closing date: Feb. 2, accepted until the positions are filled. T.V. Sastry, Search Committee, Bradley University, 1990, but applications will be considered Portland State University is an equal ment of Mathematics, is an until the positions are filled. opportunity /affirmative action employer. Peoria, IL 61625. Bradley University and minorities UNCC IS AN AFFIRMATIVE ACTION/ Minorities, women and other protected AA/EO employer. Women EQUAL OPPORTUNITY EMPLOYER groups are encouraged to apply. are encouraged to apply. 1288 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements POSITIONS AVAILABLE SOUTHERN COLLEGE OAKLAND UNIVERSITY OF TECHNOLOGY Department of Mathematical Sciences Applied Statistics Position CARNEGIE MELLON UNIVERSITY Richard J. Duffin The Department of Mathematical Sci Assistant Professorship in MATHEMATICS-The Mathematics De ences at Oakland University seeks appli Mathematics partment of the Southern College of cations for a tenure-track position at the Technology seeks applicants for one or Assistant or Associate Professor level On the occasion of his 80th birthday, the more tenure-track positions at the rank in applied statistics commencing August Department of Mathematics at Carnegie of Assistant or Associate Professor. 15, 1990. Mellon University is pleased to announce The Department desires faculty who can The position involves teaching, re the inauguration of the contribute to upper division programs search and consulting in a program that RICHARD J DUFFIN in Mathematics. Ph.D. in mathematics interacts heavily with the auto-industry ASSISTANT PROFESSORSHIP or mathematical statistics required. Re in the Detroit area. Through programs The position is available for an initial search potential is desirable but is nei with Ford Motor Company and General period of one or two academic years, ther required nor heavily weighed. Motors courses are taught at industrial and is extendable for one additional The ideal candidate will show a strong sites. The position requires participa year when mutually agreeable. The first mastery of the discipline, a commitment tion in these programs. Preference will appointment is available in September to professional growth and development, be given to those applicants whose re 1990. It carries a reduced academic year an ability for and commitment to excel search interests overlap with quality and teaching load of six hours per week dur lence in teaching, and the potential and productivity issues in the auto-industry. ing one semester and three hours per desire to enhance the college's intellec Strengths especially important are re week during the other. Applicants are tual community. liability methods, warranty forecasting, expected to show exceptional research The Mathematics Department has time series methodology, robust proce promise, as well as clear evidence of fourteen tenure-track positions. There dures and design of experiments. achievement and should have research is a minor in mathematics as well as a Minimal qualifications are a Ph.D. in interests which intersect those of current substantial load of service courses. The Statistics, evidence of research achieve faculty of the Department. Applicants college is located in Marietta, Ga. ment or research potential and a com should send a vita, list of publications, A complete application consists of a mitment to effective teaching. Success and a statement describing current and letter of application, a curriculum vitae, ful applicants at the associate professor planned research, and arrange to have transcripts of all college work, and a level must demonstrate maturity as a at least three letters of recommenda minimum of two lettrs of reference. The research scholar, a record of versatile tion sent to the committee. Applications search will continue until the position and effective teaching and experience should also include at most three two is filled, but applications received by and commitment to statistical consulting. digit mathematics subject classification February 1 will be considered first. For full consideration, send a resume numbers (as displayed in Mathematical Applications and inquiries should be and arrange to have three confidential Reviews) corresponding to the primary addressed to: letters of reference sent by January 15, area(s) of research of the applicant. All Dr. James C. Kropa 1990 to communications should be addressed to: Mathematics Department Alphonse Baartmans, Chair Richard J. Duffin Assistant Professorship Southern College of Technology Department of Mathematical Committee, Department of Mathematics, Marietta, Georgia 30060-2896 Sciences Carnegie Mellon University, Pittsburgh, Southern College of Technology is an Oakland University PA 15213. Carnegie Mellon is an Affirma equal opportunity /affirmative action em Rochester, Ml 48309-4401 tive Action/Equal Opportunity Employer. ployer. Oakland University is an equal opportu nity 1affirmative action employer. Women and minorities are especially encouraged to apply. NOVEMBER 1989, VOLUME 36, NUMBER 9 1289 Classified Advertisements POSITIONS AVAILABLE UNIVERSITY OF CALIFORNIA QUEEN'S UNIVERSITY AT KINGSTON LOS ANGELES DEPARTMENT OF Department of Mathematics MATHEMATICS AND STATISTICS HEAD, DEPARTMENT OF MATHEMATICS REGULAR POSITIONS IN Applications are invited for a renewable THE UNIVERSITY OF PURE AND APPLIED MATHEMATICS (tenure track) position at the assistant TENNESSEE-KNOXVILLE Four to six regular positions in pure professor level beginning July 1990. Can and applied mathematics. Areas of spe didates are sought with demonstrated cific interest include logic; algebra, al potential in research and undergraduate Nominations and applications are in gebraic geometry, number theory and teaching. vited for the position of department combinatorics; geometry and topology; The Department is especially inter head in Mathematics. Candidates must analysis, functional analysis, mathemat ested in candidates whose area of re possess an earned doctorate, a sub ical physics and dynamical systems; search is in statistics, or applied stantial record of research achievement, numer probability, statistics and game theory; ical analysis or other applied mathemat a commitment to excellence in research linear and non-linear differential equa ics. Candidates with research interests and teaching, a demonstrated capacity tions; applied mathematics, numerical in other areas, which would make for leadership and administration, and in analysis and mathematical computer sci teraction with current members of the an understanding of and commitment ence. Very strong promise in research Department likely, may also be consid to equal employment opportunity and and teaching required. Positions ered. affirmative action. ini tially budgeted at the assistant professor A substantial portion of the Depart The University of Tennessee at Knox level. Sufficiently outstanding candidates ment's undergraduate teaching is to ville, with an enrollment of 25,000, is at higher levels will also be considered. engineering students. Candidates are the primary campus of the state uni Teaching load: Averaging 1.5 courses requested to provide evidence in their versity and a land grant institution. The per Quarter, or 4.5 Quarter courses per applications which indicates their poten department, with 46 full time faculty and year. tial or proven ability for effective teaching 65 graduate students, offers advanced To apply, write to Alfred W. Hales, in this area. degrees in many areas of pure and ap Chair, Department of Mathematics, Uni Salary is negotiable-the present as plied mathematics. Its research activities versity of California, Los Angeles, CA sistant professor base salary is $32,375 are supported by an active visitors pro 90024-1555. Attn: Staff Search. per annum. gram, center-of-excellence funds from UCLA is an equal opportunity Those interested are requested to the state of Tennessee, and interactions f affirmative action employer. send their curriculum vitae with Oak Ridge National Laboratory. and arrange for letters of recommendation from three Applications will be reviewed begin or more referees to be sent to the ning Jan. 1, 1990; the desired starting COLLEGE OF STATEN ISLAND (CUNY) address below by January 31, 1990. At date is August, 1990. Salary will be Department of Mathematics least one letter should comment on the commensurate with qualifications. Can candidate's teaching ability. didates should provide a vita and four A tenure-track position in mathematics Professor Joan M. Geramita letters of recommendation. Inquiries, ap is available for Fall 1990. Requirements: Chair, Appointments Committee plications, and letters of recommenda Ph.D., strong commitment to teaching; Mathematics & Statistics tion should be sent to Professor Ken published research beyond the Ph.D. Department neth Stephenson, Secretary, Mathemat All mathematics research areas will be Queen's University ics Search Committee, 121 Ayres Hall, considered with special preference given Kingston, Ontario K7L 3N6 The University of Tennessee, Knoxville, to probability and statistics. Rank and In accordance with Canadian Immigra TN, 37996-1300 (615) 974-4261. salary commensurate with qualifications. The College of tion requirements, this advertisement is UTK is an EEO/AA/Title IX/Section Staten Island is a se directed 504 Employer. nior college in CUNY. Send resume and to Canadian citizens and per three letters of reference to: Dr. Jane manent residents. Candidates of either Coffee, Mathematics Department, Col sex are equally encouraged to apply. lege of Staten Island, 130 Stuyvesant Queen's University is willing to help the Place, Staten Island, N.Y. 10301 by Jan spouse of a new appointee to seek uary 31, 1990. AA/EOE Employer. suitable employment. 1290 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements POSITIONS AVAILABLE OAKLAND UNIVERSITY DARTMOUTH COLLEGE Department of Mathematical Sciences John Wesley Young OAKLAND UNIVERSITY Applied Discrete Mathematics Position Research Instructorship Department of Mathematical Sciences Continuous Applied The Department of Mathematical Sci The John Wesley Young Research In Mathematics Position ences at Oakland University seeks appli structorship is a two year post-doctoral cations for a tenure-track position at the appointment for promising new or re The Department of Mathematical Sci Assistant or Associate Professor level in cent PhD's whose research interests ences at Oakland University seeks appli applied discrete mathematics commenc overlap a department member's. Current cations for a tenure-track position at the ing August 15, 1990. departmental interests include areas in Assistant or Associate Professor level All fields of discrete mathematics will algebra, analysis, algebraic geometry, in applied mathematics commencing Au be considered. Preference will be given combinatorics, computer science, differ gust 15, 1990. to candidates who have interest andjor ential geometry, logic and set theory, All fields of applied mathematics will experience in directing students to solve number theory, probability and topol be considered, but preference will be industrial problems through mathemati ogy. Teaching duties of four ten-week given to candidates in P.D.E., control cal modeling with applied discrete math courses spread over two or three quar theory, optimization, numerical analysis, ematics. ters typically include at least one course and mathematical modeling. Minimal qualifications are a Ph.D. in the instructor's specialty and include Minimal qualifications are a Ph.D. in Mathematics, evidence of research elementary, advanced and (at instruc in Mathematics, evidence of research achievement or research potential and tor's opinion) graduate courses. Nine achievement or research potential and a commitment to effective teaching. Ap month salary of $31 ,000 supplemented a commitment to effective teaching. Ap pointments at the Associate Professor by summer (resident) research stipend pointments at the Associate level require level require a proven record of research of $6,889 (two-ninths). Send letter of a proven record of research achieve achievements, and a record of versatile application, resume, graduate transcript, ments, and a record of versatile and and effective teaching. thesis abstract, description of other re effective teaching. For full consideration, send a resume search activities and interests if ap For full consideration, send a resume and arrange to have three confidential propriate, and 3 or preferably 4 let and arrange to have three confidential letters of reference sent by January 15, ters of recommendation (at least one letters of reference sent by January 15, 1990 to should discuss teaching) to Richard E. 1990 to Alphonse Baartmans, Chair Williamson (Recruiting), Department of Alphonse Baartmans, Chair Department of Mathematical Math and CS, Bradley Hall, Hanover, NH, Department of Mathematical Sciences 03755. Applications received by Jan. 15 Sciences Oakland University receive first consideration; applications Oakland University Rochester, Ml 48309-4401 will be accepted until position is filled. Rochester, Ml 48309-4401 Oakland University is an equal opportu- Dartmouth College is committed to affir Oakland University is an equal opportu- nity1 affirmative action employer. Women mative action and strongly encourages nity /affirmative action employer. Women and minorities are especially encouraged applications from minorities and women. and minorities are especially encouraged to apply. EOE/AA. to apply. GEORGIA INSTITUTE NORTH CAROLINA STATE UNIVERSITY UNIVERSITY OF ARIZONA OF TECHNOLOGY Department of Mathematics DEPARTMENT OF MATHEMATICS TUCSON, ARIZONA 85721 The School of Mathematics expects to A junior-level tenure-track position in have some visiting and tenure-track po probability and stochastic processes will The Mathematics Department at the sitions at various levels beginning in Fall become available July 1 , 1990. Require University of Arizona will have several 1990. Candidates with strong research ments include records in or strong po visiting positions for next year. Applica and teaching records or potential should tential for research and instruction. To tions received by February 1 , 1990 will send a resume, at least three letters apply, send resume, any reprints or pre be considered first, if suitable candidates of reference, and a summary of future prints, and thesis abstract, and arrange are not found then late applications will research plans to The Hiring Commit to have three letters of reference sent to: be reviewed. Send applications (please tee, School of Mathematics, Georgia J. W. Bishir, Department of Mathematics, include Social Security number if pos Institute of Technology, Atlanta, Georgia Box 8205, North Carolina State Univer sible) to Department Head, Department 30332-0160. Georgia Tech, a member sity, Raleigh, NC 27695-8205. AA/EOE. of Mathematics. The University of Ari of the University System of Georgia, is Applications from women and minorities zona is an Equal Opportunity1 Affirmative an Equal Opportunity I Affirmative Action are especially encouraged. Action Employer. Employer. NOVEMBER 1989, VOLUME 36, NUMBER 9 1291 Classified Advertisements AVAILABLE POSITIONS TRINITY UNIVERSITY GMI ENGINEERING & Position Announcement MANAGEMENT INSTITUTE HOBART AND WILLIAM FACULTY POSITION IN MATHEMATICS SMITH COLLEGES Trinity University invites applications and Department of Mathematics nominations for a tenure-track position The Science and Mathematics Depart and Computer Science in mathematics, appointment beginning ment of GMI Engineering & Management August, 1990. The appointment will be Institute is seeking to fill a tenure-track Assistant Professor, tenure track posi made at the rank of Assistant Professor. position in mathematics at the level of tion starting in September 1990. Salary Responsibilities include teaching nine Assistant Professor. Outstanding candi is competitive. Applicants should have a credit hours per semester, continuing dates may be considered for appoint Ph.D. in computer science or a Ph.D. scholarly activity, assisting in curriculum ment at the rank of Associate Professor in mathematics and experience in com development, advising, and committee or the rank of tenured, Full Professor. puter science. Duties include teaching service. Minimum qualifications are the GMI is a highly competitive private undergraduate computer science, teach Ph.D. in Mathematics with excellence in college whose academic year starts July ing some mathematics (depending on and strong commitment to teaching. 1. The Mathematics faculty consists of interests and qualifications), and partic Founded in 1869, Trinity University 14 full-time members, who offer a wide ipating in the Colleges' Interdisciplinary occupies a modern campus overlook range of undergraduate courses. The General Curriculum. A strong commit ing the San Antonio skyline. Purposely feasibility of initiating a degree program ment to teaching and promise of contin small and selective, with about 2500 in mathematics or computer science is ued scholarly activity required. Teaching students, Trinity stresses a high quality, currently under investigation. load: two courses per trimester. Hobart undergraduate liberal arts and science The minimum requirements for this and William Smith are coordinate, four program; in particular, the Mathemat position include an earned Ph.D. in math year, liberal arts colleges, committed to ics Department does not offer graduate ematics or a related field and evidence teaching and interdisciplinary study with courses. San Antonio is a city of ap of strong research and undergraduate a combined enrollment of 1900 students. proximately 850,000 people situated in a teaching abilities. Areas of expertise of Within an hour's drive are three ma metropolitan area of 1.2 million. special interest include mathematics ap jor universities: Cornell, Rochester, and Closing date for applications is De plied to engineering disciplines, mathe Syracuse. cember 29, 1989. Send vita, graduate matics education, actuarial mathematics, Send detailed resume, three letters of transcripts and three letters of reference and computer applications. recommendation (at least one including to: Please send resume, statement con comments on teaching), and undergrad Professor William F. Trench cerning current research interests, and uate and graduate transcripts (photo Department of Mathematics three letters of reference to: Dr. J. copies acceptable) to: Prof. David Eck, Trinity University J. Salacuse, Search Committee Chair, of Mathematics and Com Department 715 Stadium Drive Science and Mathematics Department, puter Science, Hobart and William Smith San Antonio, Texas 78212 GMI Engineering & Management Insti Colleges, Geneva, NY 14456. Evaluation Trinity University is an equal opportunity tute, 1700 West Third Avenue, Flint, of applications will begin January 15, affirmative action employer. Michigan 48504-4898. Applications will 1990 and will continue until the posi be accepted until February 1, 1990 or tion is filled. Women and minorities are until the position has been filled. encouraged to apply. An Equal Opportu GMI is an Affirmative Action/Equal OF GEORGIA nity I Affirmative Action Employer. UNIVERSITY Opportunity Employer. Department of Mathematics Athens, GA 30602 BOSTON UNIVERSITY The department may have some tenure THE JOHNS HOPKINS UNIVERSITY DEPARTMENT OF MATHEMATICS track positions available for the 1990-91 po The Department anticipates two posi academic year at the assistant and as Applications are invited for a junior to begin in Fall 1990. tions in pure mathematics for Fall 1990. sociate professor levels. The rank and sition in statistics, and One at the Full or Associate Profes salary will be commensurate with the Selection is based on demonstration teach sor level. The other level depending applicant's abilities and experience. The promise of excellence in research, on candidates. Record of distinguished principle requirement is excellence in ing, and innovative application. AA/EOE. furnish a vita, achievements in research and commit teaching and research. Some prefer Applicants are asked to profes ment to excellence in teaching required. ence will be given to areas in which transcripts, a letter describing and Preference will be given to candidates the department is already well repre sional interests and aspirations, in Number Theory and/or Algebraic Ge sented. Send curriculum vitae and four arrange for three letters of recommen John C. ometry. Send applications to: Search letters of recommendation to Richard dation to be sent to Prof. Sci Committee, Department of Mathematics, A. Bouldin Head (address above) by Wierman, Chairman, Mathematical Hopkins 111 Cummington St., Boston, MA 02215. January 15, 1990. UGA is an Equal Op ences Department, The Johns AA/EOE. portunity I Affirmative Action Employer. University, Baltimore, MD 21218. 1292 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements POSITIONS AVAILABLE MILLS COLLEGE UNIVERSITY OF ILLINOIS Oakland, California AT URBANA-CHAMPAIGN CALIFORNIA STATE DEPARTMENT OF MATHEMATICS UNIVERSITY, NORTHRIDGE The Department of Mathematics and Computer Science invites applications Applications are invited for one or more Applications are invited for four tenure for a tenure track position as an As permanent faculty positions, rank open track positions for the Fall of 1990. Three sistant Professor of Mathematics, to (subject to administrative approval). positions at the assistant professor level commence in the fall of 1990 (subject Some visiting appointments are also in areas of interest to the faculty and to final budgetary approval). Applicants anticipated. Appointments are to com possibly one at the associate profes must have a Ph.D. in mathematics and mence August 1990. Competitive salary sor level, will be available. A Ph.D. by should submit evidence of exceptional and teaching load. Candidates must have the Fall of 1990 is required. Candidates teaching ability and strong research po completed Ph.D. by time appointment in Mathematics Education and Applied tential. Mills is a small liberal arts college begins. Candidates should send letter mathematics (especially with experience for women, located in the San Francisco of application, vita and publication list in industry) are encouraged to apply, but Bay Area, and is known for its innovative and arrange to have three letters of candidates in all areas of mathematics mathematics and computer science pro reference sent directly to with a commitment to both teaching and grams. Applications should include a vita C. Ward Henson, Chair research will be considered. Responsi and three letters of reference (address Department of Mathematics bilities include teaching 9-12 hours, de ing both teaching ability and research University of Illinois at pending on research and/or other con potential). Please have all materials sent Urbana-Champaign tributions. Send vita and three letters of to: 1409 W. Green St. recommendation to Jerry Rosen, Hiring Head of the Mathematics Search Urbana, IL 61801 Committee Chair, Dept. of Mathematics, Committee tel. {217)333-3352 California State University, Northridge, Department of Mathematics and In order to ensure full consideration, CA 91330 by Feb. 15 for full con Computer Science application materials should be received sideration. Women and minorities are Mills College by December 1, 1989. Interviews may especially encouraged to apply. CSUN 5000 MacArthur Blvd. be conducted prior to December 1, but is located in a Northwestern suburb of Oakland, California 94613 all applications received by that date will Los Angeles and is in close proximity The deadline for completed applications receive full consideration. Candidates to Cal. Tech., U.S.C., and U.C.L.A. {15 is January 20, 1990. Mills College is are expected to present evidence of mins. away). an affirmative action/equal opportunity excellence, or potential for excellence, AFFIRMATIVE ACTION/EQUAL OP employer. in research and teaching. Applications PORTUNITY EMPLOYER from women and minority candidates are especially encouraged. The University of Illinois is an Affirmative Action/Equal Opportunity Employer. UNIVERSITY OF NORTH CAROLINA MACALESTER COLLEGE AT CHAPEL HILL Mathematics/Computer Science Dept. of Mathematics 1600 Grand Ave. Chapel Hill, N.C. 27599-3250 St. Paul, MN 55105 UNIVERSITY OF TOLEDO Department of Mathematics Tenure-track and visiting faculty posi Applications are invited for two approved tions anticipated, pending Dean's ap tenure-track positions in Mathematics, Applications are invited for anticipated proval, effective Fall 1990. Rank and and one position, subject to adminis tenure track positions beginning in Sep salary dependent on qualifications and trative approval, in Computer Science, tember 1990. Applicants should have a budget considerations. Ph.D., exception beginning in September, 1990. Candi Ph.D. by September 1990 and be com ally strong research program and com dates should have a Ph.D. and an mitted to teaching and research. While mitment to excellent teaching required. interest in a career of teaching and re we are particularly interested in alge Send 4 letters of recommendation, vi search in a four-year liberal arts college. braic topology, combinatorics, probabil tae, and abstract of current research Teaching load is 6-9 hours a week. ity, algebraic geometry and dynamical program to: Search Committee Chair Competitive salary scale, good benefits, systems, applicants in all areas will be man, Mathematics Dept., UNC at Chapel pleasant urban residential location. Ap considered. Rank open (subject to fund Hill, CB #3250 Phillips Hall, Chapel plicants should supply resume and three ing). Applicants should send a vita and Hill, N.C. 27599-3250. Equal Opportu references to Professor Wayne Roberts, arrange for three letters of reference nity/Affirmative Action Employer. Women address above. Applications received un to be sent to Harvey Wolff, Chairman, and minorities are encouraged to identify til positions filled. Macalester is an equal Department of Mathematics, University themselves voluntarily. Completed appli opportunity, affirmative action employer. of Toledo, Toledo, Ohio 43606. The Uni cations received by January 10, 1990 are Women and minorities are especially versity of Toledo is an equal opportunity, assured of full consideration. encouraged to apply. affirmative action employer. NOVEMBER 1989, VOLUME 36, NUMBER 9 1293 Classified Advertisements POSITIONS AVAILABLE BARNARD COLLEGE UNIVERSITY OF CENTRAL FLORIDA of Columbia University Department of Mathematics CASE WESTERN RESERVE Department of Mathematics UNIVERSITY Applications are invited for at least two DEPARTMENT OF Senior position in Mathematics. Barnard tenured track and visiting positions at MATHEMATICS AND STATISTICS College of Columbia University invites Associate, Assistant Professor or in applications for a tenure or tenure-track structor level beginning in August 1990. Tenure-track, possibly senior, positions position in its Department of Mathemat Ph.D. degree with strong research po anticipated to beging August 15, 1990. ics. Applicants must have research ac tential or experience and dedication to Outstanding research record and/or complishments appropriate to a perma teaching required for appointment at proven research potential and teach nent appointment at a major research Associate or Assistant Professor level. ing excellence required. Preferred areas: oriented university, and in addition be Candidate with substantial completion of Statistics and Probability. The recently interested in an ready to assume a Ph.D. requirements will be considered established CWRU Center for Stochastic leadership role in Barnard's undergrad for the instructor level. The positions and Chaotic Processes in Science and uate mathematics program. The ideal are unrestricted as to area of spe Technology will provide an especially applicant will be ready for immediate cialization within mathematical sciences. friendly environment for probabilists do tenure, although tenure-track candidates For one of the tenured track positions ing theoretical research motivated by will also be considered by the search preference will be given to those with serious applications. Interacting particle committee. The successful applicant will research interests in numerical analysis, systems, stochastic control, population be welcome to participate in all aspects computational mathematics or related genetics, random media and infinite di of the Columbia University graduate pro applied fields. Candidate should send a mensional stochastic processes (Malli gram. Normal teaching duties will be two detailed resume and arrange to have avin calculus and stochastic P.D.E.) are courses 1semester. at least three letters of recommendation good examples here. The statisticians Qualified candidates are invited to and a transcript sent to: Dr. Lokenath are expected to work within an au send a letter of application and a Cur Debnath, Department of Mathematics, tonomous Applied Statistics unit. Women riculum Vita, and to arrange for three University of Central Florida, Orlando, and minority groups candidates are es letters of recommendation. Application Florida 32816, postmarked by February pecially encouraged to apply. Visiting materials should be sent to: 2, 1990. Some Search Committee mem positions also possible. Send vita plus Professor Joan Birman, bers will be available at the Louisville three letters of recommendation to Pro Chairperson meeting in January 1990 for an interview. fessor W. A. Woyczynski, Chairman, Department of Mathematics The University is an equal opportunity af Department of Mathematics' and Statis Barnard College firmative action employer. As an agency tics. Case Western Reserve University, 3009 Broadway of the State of Florida, UCF makes Cleveland, OH 44106. New York, New York 10027 all application materials and selection An affirmative action equal opportu EOE/AA. procedures available for public review. nity employers. OHIO UNIVERSITY TEMPLE UNIVERSITY Department of Mathematics SAINT LOUIS UNIVERSITY Department of Mathematics Department of Mathematics and The Department of Mathematics antic Computer Science The Department of Mathematics expects ipates the appointment of one tenure Saint Louis, MO 63103 to have at least two tenure track posi track assistant professor in the area of tions at the junior level for Fall, 1990. algebra or analysis beginning September A tenure track position is available at Preferred specialties: Applied Math., Dy 1, 1990. Salary will be competitive. Du the Assistant Professor level beginning namical Systems, Geometry, Probability. ties include research and teaching at the fall 1990. The department offers the Outstanding research potential and se undergraduate and graduate level. Appli B.A., M.A., and Ph.D in Mathematics and rious commitment to teaching required. cants must have a Ph.D. in Mathematics the B.A. in Computer Science. Persons are At least two years experience preferred. and have research interests compatible holding a Ph.D. in Mathematics who Vita and three letters of reference should with the current faculty in algebra or committed to teaching and research are be sent by December 31, 1989 to D. Re analysis. Send resume and have three invited to apply. Preferred specialties ich, Head, Search Committee, Box Q, letters of recommendation sent to Shih include geometric topology, differential Department of Mathematics, Temple Uni liang Wen, Chairman, Department of geometry, Lie groups and functional versity, Philadelphia, PA 19122. Mathematics, Ohio University, Athens, analysis, group theory and representa Women and minorities are especially Ohio 45701. The deadline for applica tion theory. Have a vita and three letters encouraged to apply. Temple Univer tions is January 1 , 1990. of recommendation sent to Professor sity is an Affirmative Action and Equal Ohio University is an Equal Opportu Charles Ford at the above address. An Opportunity employer. nity and Affirmative Action Employer. AA/EOE. 1294 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements POSITIONS AVAILABLE STETSON UNIVERSITY QUEEN'S UNIVERSITY AT KINGSTON Department of Mathematics DEPARTMENT OF UNIVERSITY OF CALIFORNIA and Computer Science MATHEMATICS AND STATISTICS AT RIVERSIDE Faculty Position in Mathematics Applications are invited for a tenure track Applications are invited for a renewable position in mathematics at the Assistant (tenure track) position at the rank of as Applications and nominations are invited Professor level beginning Fall, 1990. A sistant professor in arithmetic algebraic for a tenured or tenure track position in Ph.D. in mathematics is required. Appli geometry to begin July 1991. The suc Algebraic Geometry or Commutative Al cants should have a strong commitment cessful applicant will have an excellent gebra beginning July 1, 1990 or later. The to undergraduate teaching in a liberal research record and be able to interact position is open as to rank; candidates arts environment. Teaching load: 9-10 with the members of the Department at all levels and in all areas of algebraic hrsjwk. Responsibilities include teach working in this area. geometry and commutative algebra will ing mathematics courses at all levels Salary will be negoitiable-the current be considered. Demonstrated excellence of the undergraduate curriculum, and assistant professor floor is $32,375.00 in research and teaching is required. The continuing scholarly activity. The depart Those interested are requested to eligibility pool for this position will con ment currently has 10 full-time faculty send their curriculum vitae and arrange sist of those candidates for whom we members. Stetson University, located in for letters of recommendation from three receive a vita, a list of publications and Central Florida, is a small, private, com or more referees to be sent to the three letters of recommendation by Jan prehensive university of 2500 students. address below by November 1, 1989. At uary 22, 1990. Established criteria of the Its three schools-the College of Arts and least one letter should comment on the University of California determine salary Sciences, the School of Business, and candidate's teaching ability. and rank. Candidates should send a cur the School of Music-are dedicated to Professor Joan M. Geramita riculum vita, a list of publications and the excellence in teaching and are united Chair, Appointments Committee names of at least three references to by a commitment to the liberal arts. Mathematics & Statistics Professor Richard Block, Chair Send vitae and three letters of recom Department Algebraic Geometry /Commutative mendation to: Professor Dennis Klet Queen's University Algebra zing, Department of Mathematics and Kingston, Ontario K7L 3N6 Hiring Committee Computer Science, Stetson University, In accordance with Canadian Immigra Department of Mathematics and Deland, Florida 32720. Deadline for ap tion requirements, this advertisement is Computer Science plications is January 31, 1990, or until directed to Canadian citizens and per University of California position is filled. Stetson University is manent residents. Candidates of either Riverside, California 92521 an equal opportunity employer and en sex are equally encouraged to apply. University of California is an Affirmative thusiastically solicits applications from Queen's University is willing to help the Action/Equal Opportunity Employer. women and minorities candidates. spouse of a new appointee to seek suitable employment. TEXAS TECH UNIVERSITY SUNY-COLLEGE AT NEW PALTZ THE CITY UNIVERSITY OF NEW YORK Texas Tech University seeks applica Professorship John Jay College of Criminal Justice A tenure track Assistant tions for a position in the Department doing Department of Mathematics is available for a mathematician of Mathematics opening in the Fall of branch of analysis research in some 1990. To qualify applicants must 1) have Assistant Professor, tenure-track posi offers or probability theory. Department a Ph.D. from a recognized university, 2) tion, January 1990. Requirements: Ph.D.; in mathematics, bachelor's and master's have a strong dedication to both teach demonstrated potential for research; education and computer mathematics ing and research, 3) exhibit research strong commitment to teaching. Com located in the science. The College is interests that are compatible with ongo puter science, numerical analysis or op /Catskill region of New Hudson Valley ing programs in the department and 4) erations research background preferred. its natural beauty and York, known for be willing and able to work with students John Jay College of Criminal Justice, Send applica easy access to NYC. at both the undergraduate and graduate located in Manhattan, is a senior col attesting tion and 3 recommendations level. To apply send resume and have lege in CUNY. Send resume, graduate excellence and scholarly to teaching three letters of recommendation sent transcript, relevant reprints, dissertation Clark, Chairman, Dept. potential to D. to Harold Bennett, Chairman of Hiring abstract and three letters of reference to & Computer Science, of Mathematics Committee, Department of Mathematics, Samuel Graff, Chairperson, Department at New Paltz Box 10, SUNY, College Texas Tech University, Lubbock, Texas of Mathematics, John Jay College of of applications will be 12561. Review 79409. Applications are to be received Criminal Justice, 445 West 59 Street, approval. gin 12/1/89, pending funding no later than December 15, 1989. Texas New York, NY 10019 by December 1, minorities are An AA-EOE. Women and Tech University is an equal opportunity 1989. Minorities and women are encour urged to apply. employer. EOE/ AA. aged to apply. AA/EOE Employer. NOVEMBER 1989, VOLUME 36, NUMBER 9 1295 Classified Advertisements POSITIONS AVAILABLE UNIVERSITY OF ARIZONA STETSON UNIVERSTIY DEPARTMENT OF MATHEMATICS Department of Mathematics WESTERN KENTUCKY UNIVERSITY TUCSON, ARIZONA 85721 and Computer Science Headship, Department of Mathematics MATHEMATICS EDUCATION: The Uni Applications are invited tor a non-tenure Applications are invited for the Head versity of Arizona Department of Math track position in computer science tor ship of the Department of Mathemat ematics is seeking nominations and ap 1990-1991, beginning Fall 1990. The ics with appointment date as early as plications for a tenure-track Assistant position is on a year-to-year basis, re July 1, 1990. WKU has an enrollment Professorship in mathematics educa newable tor at most three years. The of more than 14,500 students and is tion. Responsibilities include teaching Department has a Micro VAX II running located in Bowling Green, KY (popula mathematics and mathematics educa ULTRIX 2.2 and assorted microcom tion approximately 56,000), two hours tion courses, developing programs for puters. University facilities reside in an south of Louisville and one hour north mathematics teachers, initiating research Academic Computer Center which has a of Nashville, TN. The department con and development projects, and involve VAX 6210 running VMS, and numerous sists of 28 full-time faculty and otters ment with state and national projects to microcomputers and graphics peripher masters and baccalaureate degree pro improve mathematics education. A can als, including IBM PS/2's, model 50, and grams with undergraduate enrollment of didate should be an excellent teacher Mac SE's and Mac ll's. Stetson Uni approximately 170 majors and 100 mi and should show promise of making versity, located in Central Florida, is a nors. Applicants must hold a doctorate substantial contributions to the improve private liberal arts university of 2500 stu in mathematics and have at least five ment of the teaching of mathematics dents with a commitment to excellence years of college mathematics teaching through research or its creative equiva in undergraduate education. Applicants experience. Applications should provide lent and through service to the profes should have an MS degree in computer evidence of administrative leadership, sion. This is a tenure-track position that science. Send vitae and three letters effective teaching, public service and will begin in the fall of 1990. Closing of recommendation to: Professor Den research/scholarly activities. To insure date tor applications is 15 January 1990. nis Kletzing, Department of Mathematics consideration, respond by January 15, Candidates should send a resume and and Computer Science, Stetson Univer 1990. The position will remain open until a list of at least three references to sity, Deland, Florida 32720. Deadline tor filled. Send letter of application, vita and Alan Newell, Head, Department of Math applications is January 31, 1990, or until names of at least three references to ematics, University of Arizona, Tucson, position is tilled. Stetson University is Office of Academic Affairs, Mathemat AZ 85721. The University of Arizona is an equal opportunity employer and en ics Headship Search, Western Kentucky an Equal Opportunity I Affirmative Action thusiastically solicits applications from University, Bowling Green, KY 42101. Employer. women and minority candidates. Women and minorities are encouraged to apply. An Affirmative Action, Equal Opportunity Employer. CALIFORNIA STATE UNIVERSITY LONG BEACH BOSTON UNIVERSITY Department of Mathematics UNIVERSITY OF ARIZONA DEPARTMENT OF MATHEMATICS DEPARTMENT OF MATHEMATICS Two tenure-track positions beginning The Department of Mathematics at TUCSON, ARIZONA 85721 Fall, 1990: one in statistics and one in Boston University invites applications Math Education. Both positions require The Mathematics Department of the tor two anticipated positions in the area completed Ph.D., evidence of excellent University of Arizona is happy to an of Dynamical Systems. One position teaching, strong research record or po nounce several postdoctoral fellowships is a permanent position at the Assistant tential. Asst. or Assoc. Prot. preferred; (Research Associate) which will be avail Professor level or higher. The successful applicants with distinguished records in able beginning August '90. Applicants applicant should be a recognized scholar teaching and research may be consid with science and nonlinear optics may in the field of dynamics and should have ered tor Professor. Must be U.S. citizen quality tor special Center of Excellence research interests which complement or permanent resident. Further details of Awards. Only candidates with outstand those of current members of the Dynam duties, salary range, specialty and de ing research records or potential should ics group at Boston University. Salary gree requirements provided on request. apply. Applications received by Febru and academic rank are negotiable. The Positions open until filled, but selection ary 1 , 1990 will be considered first, if Department also seeks applications tor begins from applicants with complete suitable candidates are not found then a two year visiting Assistant Professor tiles (resume, transcript, 3 reference late applications will be reviewed. Send ship in this field. Applications should letters) 12/1/89. Apply to Roberto A. applications (please include Social Se be sent to: Search Committee, Depart Mena, Chair, Mathematics Department, curity number if possible) to Department ment of Mathematics, Boston University, CSULB, Long Beach, CA 90840. CSULB Head, Department of Mathematics. The 111 Cummington St., Boston, MA 02215. is an Affirmative Action/Equal Opportu Ur.iversity of Arizona is an Equal Oppor AA/EOE. nity Employer. tunity I Affirmative Action Employer. 1296 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements POSITIONS AVAILABLE WEST VIRGINIA UNIVERSITY UNIVERSITY OF CALIFORNIA Department of Mathematics AT BERKELEY UNIVERSITY OF CALIFORNIA Department of Mathematics SANTA BARBARA The Department of Mathematics intends Berkeley, CA 94720 Department of Mathematics to make several faculty appointments that will commence August 1990. Ap TEMPORARY POSTDOCTORAL Applications are invited for a ladder pointments are expected to be made at POSITIONS position at the Assistant Professor level the Assistant or Associate rank. Can Several temporary positions begin in the area of nonlinear partial differential didates are expected to have a PhD ning in Fall 1990 are anticipated for equations, including the numerical and in mathematics or equivalent with a new and recent Ph.D.'s of any age, in applied aspects thereof. Salary will de strong record or demonstrated potential the areas of algebra, analysis, applied pend upon qualifications. Appointment in both research and teaching. Prefer mathematics, foundations, or geome will be effective July 1 , 1990. Candidates ence will be given to applicants whose try and topology. The terms of these must possess the Ph.D. degree or equiv research interests complement those appointments may range from one to alent. Strong evidence of commitment to currently in the Department in algebra, three years. Applicants for NSF or other teaching and outstanding promise in re analysis, applied or numerical analysis, postdoctoral fellowships are encouraged search is required. To apply send vita discrete mathematics. Normal responsi to apply for these positions; combined and publication list, and arrange to have bilities include research and a two course teaching/research appointments may be 3 letters of recommendation sent to: POE teaching assignment per semester at made for up to three years. Mathe Search Committee, Department of Math the graduate or undergraduate level. maticians whose research interests are ematics, University of California, Santa Applications and inquiries should be close to those of regular department Barbara, CA 931 06. Deadline to apply is directed to James Lightbourne, Depart members will be given some preference. January 15, 1990. ment of Mathematics, West Virginia Uni Applicants should send a resume, and UCSB is an Equal Opportunity Affirm I versity, Morgantown, WV 26506. Appli reprints, preprints, andjor dissertation ative Action Employer. Proof of U.S. citi cants should submit a vita and have abstract, and ask three people to send zenship or eligibility for U.S. employment three letters of reference sent (senior letters of recommendation to Andrew J. will be required prior to employment (Im applicants may choose to submit names Casson, Vice Chair for Faculty Affairs, migration Reform and Control Act of of references). Applications will be re at the above address. We should re 1986). viewed beginning January 15, 1990. WVU ceive this material no later than January is an affirmative actionjequal opportunity 15, 1990. The University of California is employer. Qualified women and minori an Equal Opportunity, Affirmative Action ties are especially encouraged to apply. Employer. WESTERN ILLINOIS UNIVERSITY DEPARTMENT OF MATHEMATICS Applications and nominations for the RUTGERS UNIVERSITY-NEWARK position of chairperson with associate UNIVERSITY OF ARIZONA Professor of Mathematics DEPARTMENT OF MATHEMATICS or full professor faculty rank are in TUCSON, ARIZONA 85721 The Department of Mathematics and vited. The doctorate in mathematics, Computer Science anticipates an open statistics, or mathematics education is Tenure track positions. Ph.D., excel ing at the Rank of Professor I or Profes required. Evidence of excellence in un lent research record or potential, strong sor II beginning Fall 1990. Candidates dergraduate and graduate teaching, a commitment to teaching required. Field should exhibit outstanding research ac record of substantial research/scholarly is less important than ability but should complishments. Salary and teaching load achievement, and the demonstration of complement existing strengths in al are negotiable. Applicants from all fields appropriate administrative ability is ex gebra, computational science, differen are invited. Areas of research inter pected. The selection process will begin tial equations, dynamical systems, ge est in the department include number November 1 , 1989 and continue until the ometry, mathematical physics, nonlin theory, representation theory and auto position is filled. Send application, vita, ear analysis, number theory, probability morphic forms, Lie algebras, transfor photocopies of transcripts, and at least and statistics. Applications received by mation groups, low dimensional topol three letters of reference to: Chairperson February 1, 1989 will be considered first, ogy and Teichmuller theory. Nominations Search Committee; Department of Math if suitable candidates are not found then and applications should be sent to: Jane ematics; Macomb, II 61455. WIU IS AN late applications will be reviewed. Send Gilman, Chair, Department of Mathemat EQUAL OPPORTUNITY AFFIRMATIVE applications (please include Social Se ics, Rutgers University, Newark, New ACTION EMPLOYER. WOMEN, MINORI curity number if possible) to Department Jersey 07102. The closing date for appli TIES, AND HANDICAPPED PERSONS Head, Department of Mathematics. The cations is 1/15/90 but applications will ARE ESPECIALLY ENCOURAGED TO University of Arizona is an Equal Oppor be considered until the position is filled. APPLY. tunity I Affirmative Action Employer. AA/EOE. NOVEMBER 1989, VOLUME 36, NUMBER 9 1297 Classified Advertisements AVAILABLE POSITIONS STANFORD UNIVERSITY SOUTHERN ILLINIOS UNIVERSITY DEPARTMENT OF MATHEMATICS AT CARBONDALE UNITED STATES NAVAL ACADEMY DEPARMENT OF MATHEMATICS Department of Mathematics Assistant Professorships in honor of CARBONDALE, IL 62901 Gabor Szego. The department expects The Naval Academy anticipates having to make one or more appointments in POSITION DESCRIPTION one or two tenure-track and several one 1990-91 for a term of two years, possibly Applications are invited from qualified year visiting positions available, all at the renewable for a third year. Applicants are candidates for a tenure track position assistant professor level, commencing expected to show outstanding promise in beginning on August 16, 1990. Ph.D. in in August of 1990. The initial salary will research and clear evidence of achieve mathematics with a strong background be competitive and commensurate with ment. They should have received the in pure or applied combinatorics, graph experience and qualifications. Research Ph.D. prior to the start of the appoint theory or combinatorial designs required. opportunities exist for augmenting salary ment but not before 1988. Stanford is Candidates must have demonstrated ex during the summer intersessional period. committed to excellence in teaching, and cellence in research or potential for Specialization in applied mathematics or applicants should count this as one such. Evidence of teaching effectiveness operations research is of particular inter of their goals. The teaching load con is required. Rank will be at the assistant est. Applicants must possess an earned sists of five 3-hour quarterly courses, or associate level; substantial record of Ph.D. by the date of appointment, have and may include graduate courses. The published research required for appoint a commitment to excellence in teaching, nine-month salary for 1990-91 will be at ment at a non-entry level. Send letter of and be capable of pursuing an inde least $32,750. Candidates should send application, resume and three letters of pendent program of research. Inquiries a letter of application with a curriculum recommendation to: and applications should be sent to J. vitae, a list of publications and infor Combinatorics Position M. D'Archangelo, Mathematics Depart mation concerning teaching experience, cjo Ronald B. Kirk, Chair ment, U.S. Naval Academy, Annapolis, and should arrange to have three let Department of Mathematics Maryland 21402-5002. Required of each ters of recommendation sent to Prof. Southern Illinois University applicant are a resume, transcripts of Gregory Brumfiel, Acting Chairman, De Carbondale, IL 62901 academic records, and three letters of partment of Mathematics, Stanford Uni The closing date is December 15, 1989, recommendation from persons familiar versity, Stanford, CA 94305-2125, by or until the position is filled. with the applicant's teaching and re January 1, 1990. Stanford is an Affirma SIUC IS AN EQUAL OPPORTUNITY/ search. Interviews will be conducted tive Action, Equal Opportunity Employer, AFFIRMATIVE ACTION EMPLOYER. at the annual AMS/MAA meeting in and welcomes applications from women Women and minorities are particularly Louisville in January. The Naval Academy and minorities. encouraged to apply. is an EO/AA employer. COLLEGE OF CHARLESTON CALIFORNIA STATE UNIVERSITY UNIVERSITY OF COLORADO AT DEPARTMENT OF MATHEMATICS SACRAMENTO COLORADO SPRINGS DEPARTMENT OF MATHEMATICS Applications are invited for at least 2 Three tenure track positions for Fall COLORADO SPRINGS, CO 80933-7150 tenure-track positions at the Assistant 1990, at a step appropriate to the ap Applications are invited for 1 or 2 possi Professor level beginning August 1990. plicant's experience. Must have PhD ble tenure track Assistant Professor po Candidates must have a Ph.D. in one in Math or Statistics by Sept. 1990. sitions for Fall 1990. Prefer areas consis of the mathematical sciences, a com Salary range begins at $31 ,668. Appli tent w /present research interests: alge mitment to undergraduate teaching, and cants should be committed to excellence bra, diff. eq., computer vision, harmonic potential for continuing research. The in teaching (12 units/semester). The analysis, probability and math physics. normal teaching load is 9 hrsjwk for dept. has a diverse curriculum currently Applicants should have significant re those engaged in research. The salary experiencing growth in undergrad. and search accomplishments or exceptional is competitive. Applicants should send grad. degree and teacher preparation research promise and evidence of good a vita and have three letters of recom programs. Send vita, transcripts, and teaching. Ph.D. is required. The average mendation sent to William L. Golightly, three letters of recommendation (at least weekly teaching load is 7 1 /2 hours. Chairman, Department of Mathematics, one commenting on teaching ability), by Generous support for faculty develop College of Charleston, Charleston, SC 2/1/90, to Hiring Committee, Math and ment such as travel, teaching off-loads 29424. The process of evaluating appli Stat Dept., Sacramento, CA 95819-2694. and summer research. Send resume and cations will begin on January 22, 1990, The dept. is committed to improving the 3 letters of reference to James E. Daly, but applications will be considered until diversity of its faculty and encourages Chairman. Screening will begin on Feb. the positions are filled. The College of qualified women, underrepresented eth 1 , 1990 and continue until all positions Charleston is an Affirmative Action/Equal nic minorities, disabled individuals, and are filled. AA/EEO. Opportunity Employer. Vietnam-era veterans to apply. AA/EOE. 1298 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements POSITIONS AVAILABLE UNIVERSITY OF SOUTH CAROLINA STANFORD UNIVERSITY Department of Mathematics DEPARTMENT OF MATHEMATICS THE UNIVERSITY OF ALABAMA MATH FACULTY POSITIONS Applications are invited for anticipated The department expects to make one tenure-track faculty positions at all ranks. or more tenure-track or tenured ap The department expects to fill from two Applications in all areas of mathemat pointments beginning September 1990, to five tenure track positions at the ics will be considered. The Depart among the following fields: (1) analysis, rank of Assistant Professor or possibly ment is building on existing research (2) geometry or topology, (3) algebra, at a higher rank beginning August 16, strengths and is increasing the scope number theory, or logic, (4) applied 1990. Areas of special interest are: al of its program in applied and compu mathematics or probability; in the last gebra, analysis, fluid mechanics, compu tational mathematics. Faculty research case there are also possibilities for joint tational mathematics, differential equa is supported by excellent departmental appointments with other departments. tions, differential geometry, optimization, library and high-performance computing At the tenured level, preference will go stochastic modeling, and topology. Ap facilities. The Ph.D. degree or its equiv to individuals in the early years of their plicants for Assistant Professor should alent is required, and all appointments ranks, though a more senior appoint have or reasonably expect to have by Au will be consistent with the Department's ment may be possible for an extremely gust 16, 1990 a Ph.D. or the equivalent. commitment to excellence in research well-qualified individual. Excellence in both teaching and research and teaching at the undergraduate and Candidates should send a letter of is required. An established record of re graduate levels. A resume, containing a application and a curriculum vitae with search and leadership in one of the summary of research accomplishments a list of publications, and arrange to areas described above is expected of and goals, and four letters of recom have three letters of recommendation applicants for a senior position. We also mendation should be sent to: and some evidence of commitment to invite applications for visiting positions. Dr. Colin Bennett, Chairman excellence in teaching sent to Prof. Women and minorities are particularly Department of Mathematics Gregory Brumfiel, Acting Chairman, De encouraged to apply. Send a curriculum University of South Carolina partment of Mathematics, Stanford Uni vitae, reprints andjor preprints, and at Columbia, South Carolina 29208 versity, Stanford, CA 94305-2125, by least three letters of recommendation to: The closing date for applications is Jan January 1, 1990. Search Committee, Department of Math uary 31, 1990. The University of South Stanford is an Equal Opportunity, Af ematics, The University of Alabama, Box Carolina is an Affirmative Action/Equal firmative Action Employer, and welcomes 870350, Tuscaloosa, AL 35487-0350. UA Opportunity Employer. applications from women and minorities. is an AA/EOE. MICHIGAN TECHNOLOGICAL THE UNIVERSITY OF MICHIGAN TECHNOLOGICAL UNIVERSITY TEXAS AT AUSTIN UNIVERSITY DEPARTMENT OF MATHEMATICS Department of Mathematical Sciences The Department of Mathematical Sci AUSTIN, TEXAS 78712 ences is seeking a director for the Fluids Subject to final administrative approval, Research Oriented Group (F.R.O.G.). A number of openings are expected we expect to fill the following positions. F.R.O.G. is an interdisciplinary group, for Fall 1990 at all levels, including In Starting date is Sept. 1990. involving Departments of Mathematical structor (customarily appointees are new 1. One tenure-track Assistant Profes Sciences, Mechanical Engineering, and PhDs), Assistant Professor (customar sorship. Strong research and teaching Chemical Engineering, engaged in an ily appointees have at least two years' background required. Teaching load: five active program of research in Fluid experience beyond the PhD), Associate quarter courses per year. Mechanics. This position will carry an Professor, and Professor. Candidates 2. At least two Visiting Assistant appointment as Associate Professor or should have outstanding research abil Professorships. These are one year po Professor. Candidates should have an ity and concern for teaching. Salaries sitions with a teaching load of six quarter active research record in Fluid Mechan are competitive. Please send vita, de courses per year. ics or Computational Mathematics. A tailed summary of research interests, 3. One instructorship. An M.S. and good funding record and experience and three recommendation letters to strong teaching background is required. with Ph.D. students is required. The po address above, directed as follows: Teaching load: nine quarter courses per sition starts in September 1990. Send Instructor and Assistant Professor: cjo year. a curriculum vitae and three letters of Recruiting Committee To apply, submit vitae and three let recommendation to Recruitment Com Associate Professor and Professor: cfo ters of recommendation to Recruitment mittee, Dept. of Math. Sciences, MTU, John Dollard, Chairman · Committee, Dept. of Math. Sciences, Houghton, Ml 49931. MTU is an equal The University of Texas at Austin is an MTU, Houghton, Ml 49931. MTU is opportunity educational institution/equal equal opportunity employer. Minorities an equal opportunity educational institu opportnity employer. and women are encouraged to apply. tion/equal opportunity employer. NOVEMBER 1989, VOLUME 36. NUMBER 9 1299 Classified Advertisements POSITIONS AVAILABLE SOUTHERN ILLINIOS UNIVERSITY MIAMI UNIVERSITY AT CARBONDALE Middletown, Ohio WEST VIRGINIA UNIVERSITY DEPARMENT OF MATHEMATICS Department of Mathematics and EBERLY PROFESSORSHIP CARBONDALE, IL 62901 Statistics IN MATHEMATICS POSITION DESCRIPTION anticipates an assistant professorship The Department of Mathematics invites Applications are invited from qualified (tenure track) or an instructorship be applications and nominations for the candidates for a tenure track position ginning August, 1990. Miami University EBERLY PROFESSORSHIP IN MATH at the Assistant Professor level be Middletown is a two-year regional cam EMATICS. Candidates are sought who ginning on August 16, 1990. Ph.D. in pus. Duties include teaching 12 hours have outstanding scholarly accomplish mathematics and a strong background per semester, service and scholarship. ments, research interests which comple in analysis required. Preference will be Applicants for the assistant professor ment current areas of concentration in given to the areas of complex, functional ship should have a doctorate in one of applied analysis or discrete mathemat or stochastic analysis, but other areas the mathematical sciences or in mathe ics, a record of funded research, and a of analysis will be considered. Selec matics education by 8/90. Applicants for commitment to instruction. The individ tion will be based on the potential and an instructorship should have a master's ual selected will be expected to provide demonstration of excellence in research degree in one of the mathematical sci academic leadership with continued ex and teaching. Applicants are asked to ences or in mathematics education by cellence in these areas. The position send letter of application, vita, and three 8/90. A strong interest in teaching alge will commence August 1990. Applica letters of recommendation to: bra and pre-calculus is desired. Please tions, nominations and inquiries should Analysis Position send vita, graduate transcript and three be directed to James Lightbourne, De cjo Ronald B. Kirk, Chair reference letters to John Skillings, Mid partment of Mathematics, West Virginia Department of Mathematics dletown Search, Department of Mathe University, Morgantown WV 26506. Can Southern Illinois University matics and Statistics, Miami University, didates should submit a letter of appli Carbondale, IL 62901 Oxford, Ohio 45056. Review of appli cation, vita, and names and addresses The closing date for applications is cations will commence on January 15, of five references. Applications will be December 15, 1989, or until the po 1990. Women and minorities are encour reviewed as received and accepted until sition is filled. SIUC IS AN EQUAL aged to apply. Miami provides equal the position is filled. WVU is an affirma OPPORTUNTY/AFFIRMATIVE ACTION opportunity in employment and educa tive action/equal opportunity employer. EMPLOYER. Women and minorities are tion. EOE/ AA. Qualified women and minorities are es particularly encouraged to apply. pecially encouraged to apply. ILLINOIS WESLEYAN UNIVERSITY DEPARTMENT OF MATHEMATICS UNIVERSITY OF HAWAII BLOOMINGTON, IL 61702 UNIVERSITY OF KANSAS DEPARTMENT OF MATHEMATICS Department of Mathematics Applications are invited for a tenure Applications are invited for some antici track position at the rank of Assis Applications are invited for tenure-track pated positions beginning Fall 1990, one tant Professor starting the fall semester and temporary positions at all levels, tenure-track and some temporary (one 1990. Candidates must possess a Ph.D. commencing August 16, 1990 or as year). Rank open. Duties include math in mathematics, a dedication to excel negotiated. Field is unrestricted but pref ematical research and teaching 6 credit lent teaching in an independent, liberal erence will be given to numerical analysis hours per semester. Minimum qualifica arts university, and active research in then to probability /statistics, then to ar tions include a Ph.D., commitment to terests. Preference will be given to in eas meshing well with the department's research and teaching, and achievement dividuals with active interests in applied needs. Require Ph.D. or Ph.D. disserta appropriate to rank. Research interests . mathematics. The initial closing date for tion accepted with only formalities to be complementing those of the Department applications is January 10, 1990 (prior completed. are desirable. Normal salary range as of to the AMS/MAA Louisville meeting). Application, detailed resume with de 7/90 is from $30,240 (minimum for assis Thereafter until the position is filled, the scription of research, and three recom tant professor) to $68,928 (maximum for closing dates are February 10, March mendation letters should be sent to C. full professor). To apply, write to Pro 10, and April 10. Women and minorities J. Himmelberg, Chairman, Department fessor L. Thomas Ramsey, Chairman, are strongly encouraged to apply. Can of Mathematics, University of Kansas, Department of Mathematics, 2565 The didates should submit a curriculum vitae Lawrence, KS 66045-2142. Mall, Keller 401A, Honolulu, HI 96822. and three letters of recommendation Deadlines: December 1, 1989 for first Have 3 references send confidential let to Melvyn W. Jeter, Head, Department consideration, then monthly until August ters directly to the chairman. DEADLINE of Mathematics, Illinois Wesleyan Uni 1, 1990. FOR APPLICATION: 1/22/90. The Uni versity, Bloomington, IL 61702. Equal The University of Kansas is an AA/EOE. versity of Hawaii is an AA/EO employer. Opportunity Employer. 1300 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements POSITIONS AVAILABLE CLARKSON UNIVERSITY PORTLAND STATE UNIVERSITY AUBURN UNIVERSITY The Department of Mathematics and The Department of Mathematical Sci DEPARTMENT OF ALGEBRA, Computer Science at Clarkson Univer ences invites applications for one or COMBINATORICS AND ANALYSIS sity invites applications for tenure track more tenure track positions at the assis positions in mathematics. PhD in math tant professor rank beginning Fall 1990. The department expects to make two ematics or a closely related discipline Applicants should hold a PhD degree (or tenure-track appointments at the rank of is required. Rank and salary are ne equivalent) in mathematics or mathemat assistant professor beginning Septem gotiable. Strong candidates in all areas ics education with a strong mathematics ber 1990. One position is in any area are encouraged to apply. We are espe emphasis, have demonstrated a strong of probability theory. One position is in cially interested in new colleagues with commitment to teaching and to work combinatorics with preference given to interests in differential and algebraic ge ing with secondary teachers, and have candidates in coding theory or cryptog ometry, probability and statistics, and demonstrated an ability to conduct re raphy. computational mathematics. search. Applicants should send a vita Some temporary one-year appoint The university is located in upstate and have at least three letters of recom ments at the rank of assistant professor New York close to the scenic Adirondack mendation sent to are also expected for September 1990. and Thousand Island regions. The con Bruce A. Jensen For these, research interests compatible centration of college campuses in the Department of Mathematical with current faculty in algebra, analysis, vicinity creates a rich cultural environ Sciences combinatorics, differential equations, lin ment with a high quality of life without Portland State University ear algebra or probability desired. the problems of major cities. PO Box 751 Excellence required in both teaching Applications including vita and names Portland, OR 97207 and research for all positions. Send of three references should be submit Screening of applications will begin on resume and arrange for at least three ted to Professor A. Fokas, Department February 1 , but applications will be letters of recommendation to be sent to of Mathematics and Computer Science, accepted until the positions are filled. James Wall, 120 Math Annex, Auburn Clarkson University, Potsdam, NY 13676. Portland State University is an equal University, AL 36849-5307. Minorities Clarkson University is an equal oppor opportunity /affirmative action employer. and women are encouraged to apply. tunity /affirmative action employer and Minorities, women and other protected AUBURN UNIVERSITY IS AN EQUAL encourages applications from women groups are encouraged to apply. OPPORTUNITY AFFIRMATIVE ACTION and minorities. EMPLOYER. GOUCHER COLLEGE THE UNIVERSITY OF MISSISSIPPI UNIVERSITY OF TORONTO MATHEMATICS AND COMPUTER Professor and Chair of Mathematics Department of Mathematics SCIENCE DEPARTMENT The Department of Mathematics seeks Applications are invited from recent Applications are invited for two tenure applications and nominations for the po Ph.D.'s for a tenure-stream position track positions at the Assistant Profes sition of Professor and Chair of the at Erindale Campus beginnng July 1, sor level beginning August, 1990. Quali Department of Mathematics. The de 1990. This position which is subject to fications include a Ph.D. in mathematics partment consists of 16 full-time faculty, final budgetary approval is open to all or computer science and a strong com and offers the Ph.D. degree. Applicants branches of pure and applied mathemat mitment to and demonstrated excellence must possess a Ph.D. in Mathematics ics. in undergraduate teaching. Responsibil or a Mathematical Science, a research Duties will consist of research and ities include a teaching load of 9-1 0 record appropriate for leadership in a teaching and candidates must demon hrsjwk and continuing scholarly activity. research institution, evidence of admin strate clear strength in both. Goucher is a select, private, coeduca istrative ability, and a commitment to Applicants should send their complete tional, liberal arts college located eight quality teaching. Salary is open. Initial C.V. together with a list of publications miles north of Baltimore and is conve applicant screening will begin Decem and arrange to have at least three letters nient to Washington, D.C. The selection ber 8, 1989 with applications accepted of reference sent directly to Professor process will begin Jan., 1990. Goucher until the position is filled. Desired ap D. Masson, Associate Chairman, De is an EOE. Send vita and three letters of pointment date is July 1, 1990. Send partment of Mathematics, University of recommendation to: application, curriculum vitae, and three Toronto, Toronto, Canada, M5S 1 A1. Dr. Joan S. Morrison letters of recommendation to: Dr. El To insure full consideration, this in Chair of the Mathematics and don Miller, Department of Mathematics, formation should be recieved by January Computer Science Department University of Mississippi, University, MS 15, 1990. Goucher College 38677. The University of Mississippi is The University of Toronto encourages Towson, MD 21204 an Affirmative Action/Equal Opportunity both women and men to apply. Employer. NOVEMBER 1989, VOLUME 36, NUMBER 9 1301 Classified Advertisements POSITIONS AVAILABLE UNIVERSITY OF LOUISVILLE UNIVERSITY OF PITTSBURGH DEPARTMENT OF MATHEMATICS Department of Mathematics and SOUTHERN ILLINIOS UNIVERSITY Statistics AT CARBONDALE The Department of Mathematics in the DEPARMENT OF MATHEMATICS College of Arts and Sciences at the The following positions are expected, CARBONDALE, IL 62901 University of Louisville, is seeking 2 As subject to funding approval: sistant Professors for tenure-track po 1. Specialist in applied mathematics POSITION DESCRIPTION sitions. Candidates must have active with emphasis on scientific computing. Applications are invited from qualified research program in applicable math 2. A position in pure mathematics. We candidates for a tenure track position ematics, probability or statistics. Pri are interested particularly in algebraic at the Assistant Professor level be mary teaching responsibilities will in topology, algebra, and analysis, but out ginning on August 16, 1990. Ph.D. in clude courses in applicable mathemat standing applicants in any field will be mathematics and a strong background ics or probability/statistics as well as considered. in algebra or topology required. Selec introductory undergraduate courses. A The rank is open on each posi tion will be based on the potential and Doctorate in the Mathematical Sciences tion. Requirements include outstanding demonstration of excellence in research is required, as is evidence of schol research accomplishment or potential. and teaching. Applicants are asked to arly achievement. Teaching experience is Excellence in teaching is also essential. send letter of application, vita, and three desirable. Interested candidates should Junior applicants should send a re letters of recommendation to: send a letter of application, curriculum sume and arrange to have at least th.ree Algebra Position vitae and at least 3 letters of recommen letters of recommendation sent to: Stu cjo Ronald B. Kirk, Chair dation by January 29, 1990 to: art Hastings, Department of Mathematics Department of Mathematics Dr. Robert B. Mcfadden and Statistics, University of Pittsburgh, Southern Illinois University Chair, Department of Pittsburgh, PA 15260. Senior applicants Carbondale, IL 62901 Mathematics should write directly to the same ad The closing date for applications is College of Arts and Sciences dress. December 15, 1989, or until the po UNIVERSITY OF LOUISVILLE The University of Pittsburgh is an sition is filled. SIUC IS AN EQUAL Louisville, Ky 40292 equal opportunity I affirmative action em OPPORTUNITY/ AFFIRMATIVE ACTION The University of Louisville is an Affirma ployer. Women and minorities are espe EMPLOYER. Women and minorities are tive Action/Equal Opportunity Employer. cially encouraged to apply. particularly encouraged to apply. UNIVERSITY OF CALIFORNIA UNIVERSITY OF CALIFORNIA UNIVERSITY OF CALIFORNIA AT BERKELEY AT BERKELEY IRVINE Department of Mathematics Department of Mathematics DEPARTMENT OF MATHEMATICS Berkeley, CA 94720 Berkeley, CA 94720 IRVINE, CALIFORNIA 92717 ASSISTANT PROFESSORSHIPS TENURED POSITION Applications for an Assistant Profes applications for one or We invite applications for one or We invite sorship opening in the academic year more positions effective July 1, 1990, more positions effective July 1, 1990, at 1990-91 are invited: at the tenure-track Assistant Professor tenure level (Associate or full Profes Candidates for the position must have budgetary approval, in sor), subject to budgetary approval, in level, subject to a Ph.D. and a research record in either algebra, analysis, applied the areas of algebra, analysis, applied the areas of Mathematical Physics or Differential Ge mathematics, foundations, or geometry mathematics, foundations, or geometry ometry. Duties include research, under Applicants are expected and topology. Demonstrated leadership and topology. graduate and graduate teaching. Send to have demonstrated outstanding re in research is expected of applicants. applications, curriculum vitae, work in search potential, normally including ma Applicants should send a curriculum vi print or in preparation, and three let jor contributions beyond the doctoral tae, list of publications, a few selected ters of recommendation to: Professor Applicants should send a reprints or preprints, and the names of dissertation. Abel Klein, Chairman of the Recruitment reprints, preprints, and/or three references to Andrew J. Casson resume, and Committee, Department of Mathematics, abstract, and ask three peo Vice Chair for Faculty Affairs at the abov~ dissertation University of California, Irvine, CA 92717. of recommendation address. We should receive this material ple to send letters Appointment begins on July 1, 1990. Casson, Vice Chair for no later than January 15, 1990. (Appli to Andrew J. UC Irvine is an Affirmative Action/Equal at the above address. cations received for our earlier October Faculty Affairs, Opportunity Employer. this material no later 1, 1989 deadline will automatically be We should receive If no qualified candidates apply, there The University considered for this deadline also.) The than January 15, 1990. is a possibility that the position may be is an Equal Opportunity, University of California is an Equal Op . of California upgraded. Affirmative Action Employer. portunity, Affirmative Action Employer. 1302 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements POSITIONS AVAILABLE DEPARTMENT OF STATISTICS UNIVERSITY OF CALIFORNIA UNIVERSITY OF CALIFORNIA SANTACRUZ VIRGINIA POLYTECHNIC INSTITUTE AT BERKELEY AND STATE UNIVERSITY The Mathematics Department at the DEPARTMENT OF MATHEMATICS Pending final budgetary approval, we in University of California, Santa Cruz is vite applications for a faculty position at recruiting for a position in algebra or We anticipate making several tenure any tenured or tenure-track rank, to be number theory. The teaching load is track appointments at the assistant pro gin July 1, 1990. We will consider strong 4 one-quarter courses per year. Rank: fessor level or above beginning with the candidates in any area of theoretical and Assistant Professor 1-111. Minimum Quali academic year 1990-1991. Very strong applied statistics, probability and applied fications: Ph.D. in Mathematics. Demon research potential is required for junior probability theory. strated achievements in, or potential level appointments and a demonstrated Interdisciplinary interests are encour for, research, teaching and professional outstanding record for senior-level ap aged and joint appointments are a pos service, commensurate with experience. pointments. A Ph.D. is required. Primary sibility. The department is particularly Salary: $32,400-$34,900. Effective: July areas of interest are algebraic and differ interested in hearing from suitably qual 1, 1990. Applicants should send vitae, ential geometry, discrete mathematics, ified women or members of minorities information about their research and dynamical systems, and computation currently under-represented in faculty teaching experience and four letters of ally oriented mathematics. Exceptional positions. Send inquiries and applica recommendation commenting on their candidates in other areas will be consid tions including a resume and three ref teaching and research, to-Recruitment ered. Applications will be accepted until erences by November 30, 1989 to: Committee, Mathematics Department, March 15, 1990, or until the positions David R. Brillinger University of California, Santa Cruz, are filled. Applicants should send vita Personnel Committee CA 95064. Closing Date: December 31, and three letters of reference to: Chair Department of Statistics 1989. Please refer to #190-890 in your man, Search Committee, Department of University of California reply. UCSC IS AN EEO/AA/IRCA EM Mathematics, Virginia Tech, Blacksburg, Berkeley, CA. 94720 PLOYER VA 24016-0123. Women and minorities The University of California is an Equal are encouraged to apply. Virginia Tech is Opportunity-Affirmative Action Employer. an Equal Opportunity I Affirmative Action Employer. UNIVERSITY OF CALIFORNIA AT BERKELEY VANDERBILT UNIVERSITY Department of Mathematics SAN JOSE STATE UNIVERSITY DEPARTMENT OF MATHEMATICS Berkeley, CA 94720 Department of Mathematics and NASHVILLE, TN 37235 Computer Science CHARLES B. MORREY JR. San Jose, California 95192-0103 ASSISTANT PROFESSOR (Ph.D. re ASSISTANT PROFESSORSHIPS quired) two positions with two year ap Assistant or Asso We invite applications for these spe Four openings for pointments beginning Fall, 1990. These (Professor in exceptional cial two-year (non-tenure-track) posi ciate Professor are not tenure track appointments but Ph.D. in any tions effective July 1, 1990. Applicants case) to start Fall 1990. are intended for individuals with demon science, we are especially should have a recent Ph.D. in the ar mathematical strated research potential who would partial differential equations, eas of algebra, analysis, applied math looking for like to spend time in a department with a applied mathematics ematics, foundations, or geometry and numerical analysis, vigorous research atmosphere. We are or computer science. Must topology, and should have demonstrated education, especially interested in individuals who high ability and in superior research potential. Applicants have demonstrated work in one of the areas of deparmental undergraduate teaching at all should send a resume, and reprints, terest in strengths which include universal alge to take an active role preprints and/or dissertation abstract, levels and be able bra, differential equations, approximation affairs. Rank and salary and ask three people to send letters in departmental theory, operator theory, applied mathe with experience. Signif of recommendation to Andrew J. Cas commensurate matics, graph theory, and topology. Have activity required for son, Vice Chair for Faculty Affairs, at icant professional vita and four letters of recommendation Applica the above address. We should receive eventual tenure consideration. (including one about teaching) sent to January 1, 1990. Send vita, this material no later than January 15, tion deadline Professor Glenn Webb, Chairman. of reference, and transcripts The University of California is three letters VANDERBILT UNIVERSITY IS AN 1990. Chairman, SJSU is an Equal Opportunity, Affirmative Action to Dr. Veril L. Phillips, EQUAL OPPORTUNITY/ AFFIRMATIVE Affirmative Action Employer. an Equal Opportunity 1 ACTION EMPLOYER. Employer. NOVEMBER 1989, VOLUME 36, NUMBER 9 1303 Classified Advertisements POSITIONS AVAILABLE OREGON STATE UNIVERSITY THE UNIVERSITY OF NEW MEXICO VIRGINIA POLYTECHNIC INSTITUTE The Andreotti Assistant Professor posi Albuquerque, New Mexico AND STATE UNIVERSITY tion in mathematics will become available Department of Mathematics and DEPARTMENT OF MATHEMATICS September 16, 1990. Salary depends on Statistics qualifications. Closing date is December We are seeking a distinguished scholar The Department expects to have four 15, 1989. Write to: as our nominee for the College of Arts tenure track positions available, begin Professor Bent Petersen, Chair and Sciences C. C. Garvin Visiting En ning in the Fall Semester, 1990. We are Andreotti Professorship Selection dowed Professorship for the 1991-92 particularly interested in candidates at Committee academic year. The position will be the assistant professor level with post Department of Mathematics awarded to one of the three depart doctoral experience, but we will consider Oregon State University ments in the Mathematical Sciences outstanding applicants at all levels. Can Corvallis, Oregon 97331-4605 Division of the college. The Visiting En didates must have a strong research Oregon State University is an Affirma dowed Professor will be expected to record or outstanding potential and a tive Action/Equal Opportunity Employer stimulate faculty research and to give commitment to excellence in teaching. and complies with Section 504 of the one public lecture in the fall semester The Department of Mathematics and Rehabilitation Act of 1973. OSU has a on a subject of interest to the general Statistics currently has 40 faculty mem policy of being responsive to the needs university community. Applicants should bers and an active and expanding gradu of dual-career couples. submit a curriculum vita by February 1 , ate program. The Department has close STAFF SELECTION COMMITTEE 1990 to: Chairman, Endowed Professor research ties with Los Alamos and San B. E. Petersen, Chair ship Search Committee, Department of dia National Laboratories, and access B. I. Fein Mathematics, Virginia Tech, Blacksburg, major computing facilities. Joint ap R. Higdon to VA 24061-0123. Women and minorities with other departments are R. M. Schori pointments are encouraged to apply. Virginia Tech possible. is an Equal Opportunity j Affirmative Em Review of applications will begin Jan ployer. uary 15, 1990, and will continue until UNIVERSITY OF CALIFORNIA the positions are filled. All exception DEPARTMENT OF MATHEMATICS ally strong candidates, especially women CA 95616 DAVIS, and minority group members, are urged Applications are invited for two or more to apply. Please have vitae and three anticipated tenure track positions in the letters of reference sent to: Department of Mathematics, University Professor Robert Cogburn, Chair of California, Davis, effective July 1, Hiring Committee MIAMI UNIVERSITY 1990. Appointments will be made at rank Dept. of Mathematics & Statistics Oxford, Ohio The University of New Mexico Department of Mathematics and and salary commensurate with qualifica Albuquerque, NM 87131 Statistics tions. Qualifications include a Ph.D. and an outstanding record or great promise THE UNIVERSITY OF NEW MEXICO IS anticipates a tenure track assistant pro in teaching and research. Duties include AN AA/EOE. fessorship beginning August, 1990 in the undergraduate and graduate teaching area of mathematics education. Duties and mathematical research. We are in include teaching 8-9 hours per semester, terested in applicants in one or more of continuing scholarship and service. Ap the following areas. Applicants should plicants should have (by 8/90) a doc indicate in which area(s) they are ap torate in mathematics education or a plying: 1) Geometric Partial Differential doctorate in mathematics with expertise Equations; 2) Mathematical Biology; 3) in mathematics education. Please send Algebra, particularly Algebraic Geometry vita, transcripts and three reference let and Lie Groups/Representation Theory; ters to John Skillings, Math Education 4) Applied Analysis. The postmarked Search, Department of Mathematics and deadline for applications is December Statistics, Miami University, Oxford, Ohio 18, 1989. An application consists of 45056. Review of applications will com a curriculum vitae, list of publications, mence on January 15, 1990. Women and at least three letters of reference and minorities are encouraged to ap sent to: Chair of Search Committee, ply. Miami provides equal opportunity in Department of Mathematics, University employment and education. EOE/ AA. of California, Davis, CA 95616. The University of California is an Equal Op portunity j Affirmative Action Employer. 1304 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements POSITIONS AVAILABLE MICHIGAN TECHNOLOGICAL FAIRFIELD UNIVERSITY UNIVERSITY Tenure-track Position in Mathematics GEORGIA INSTITUTE Department of Mathematical Sciences OF TECHNOLOGY An entry level Assistant Professor is We invite applications and nominations sought to start in September 1990 The Center for Dynamical Systems and for the position of Department Head. The who must have a Ph.D. in Mathematics Nonlinear Studies expects to have some department offers B.S. and M.S. degrees and evidence of teaching ability. Normal long and short-term visiting positions and is developing a Ph.D. program. We teaching load is 3 courses per semester beginning Fall 1990. These positions have a strong commitment to research, plus research. Salary is competitive and are in nonlinear differential equations, especially in Applied Mathematics, and full consideration is given to dossiers dynamical systems, computational meth to excellence in undergraduate educa completed by February 1 , 1990. Please ods and related areas. In addition to tion. We are seeking a distinguished send a resume and three letters of a resume and at least three letters senior mathematician to further develop reference to Joseph B. Dennin, Chair, of reference, candidates should send a and enchance our programs. To apply, Dept. of Math and Computer Science, summary of future research plans to send a curriculum vitae and at least Fairfield University, Fairfield, CT 06430- Professor Jack Hale, Director, CDSNS, three letters of recommendation to Head 7524. Fairfield is a Jesuit University Georgia Institute of Technology, Atlanta, Search Committee, Dept. of Math. Sci located 60 minutes from New York City. Georgia 30332. Georgia Tech, a member ences, MTU, Houghton, Ml 49931. MTU It is an Equal Opportunity I Affirmative of the University System of Georgia, is is an equal opportunity educational insti Action Employer. an Equal Opportunity1 Affirmative Action tution/equal opportunity employer. Employer. THE PENNSYLVANIA STATE UNIVERSITY COLLEGE BELOIT DEPARTMENT OF MATHEMATICS (N) RUTGERS UNIVERSITY, CAMDEN Tenure track Assistant or Associate Pro 228 MC ALLISTER BUILDING UNIVERSITY PARK, PA 16802 The Mathematical Sciences Department fessor beginning 8/90 to teach computer seeks highly qualified applicants for science and mathematics in a liberal arts Applications are invited for tenure track an anticipated assistant professorship. setting. Qualifications: Ph.D. in a mathe faculty positions at all levels. Candidates Tenure track, very low teaching for matical science, excellence in teaching, from all areas of mathematics are wel the first two years, competitive salary. potential for growth. Computer Science come to apply (Ph.D. required). Inquiries Strong research credentials a necessity. and/or Statistics must be area(s) of should be accompanied by a vitae, publi Send resume, at least three letters of professional interest. Apply by letter and cations record and a list of references to recommendation, and reprintsjpreprints full vita to R. Roy, Acting Chairman, Professor Richard Herman, Chairman at as soon as possible to: Mathematics & Computer Science, Be the above address. Applications will be Search Committee loit College, 700 College St., Beloit, WI reviewed beginning October 15th, 1989 Mathematical Sciences 53511; arrange for letters of reference and continue until positions are filled. Department and graduate and undergraduate tran AN EQUAL OPPORTUNITY/ AFFIRM Rutgers University scripts to be sent. Deadline: 1 Feb ATIVE ACTION EMPLOYER. WOMEN Camden, NJ 08102 1990. Beloit College is an Affirmative AND MINORITIES ENCOURAGED TO AA/EOE. Action/Equal Opportunity Employer. APPLY. NOVEMBER 1989, VOLUME 36, NUMBER 9 1305 Classified Advertisements POSITIONS AVAILABLE SAINT OLAF COLLEGE LOYOLA UNIVERSITY OF CHICAGO NORTHFIELD, MINNESOTA 55057 RICE UNIVERSITY The Department of Mathematical Sci Department of Mathematics One two-year postdoctoral position, par ences anticipates at least one tenure tially funded by the Fund for the Im track position and some visiting positions Applications are invited for a tenure track provement of Post-Secondary Educa beginning in August, 1990. Requirements assistant professorship. There is a pos tion. This position is half time teaching are the Ph.D., an active research pro sibility of an upgrade to associate or full (three courses/year) and half time re gram in any area, and a commitment to professorship for an exceptional senior search. Unlike most postdoctoral posi quality teaching. The department offers candidate. Candidates must have an ex tions, there will be a strong emphasis courses in mathematics, computer sci tremely strong research background and upon developing the teaching aspect of ence, and statistics at the undergraduate good teaching skills. Preference will be an academic career through a mentored and masters level. Interviews will begin given to applicants in low-dimensional internship. This position is allotted gen in January and continue until all positions topology, although outstanding candi erous research and professional travel are filled. Send detailed C.V. and three dates in analysis, geometry, and topol budgets. Salary: $31 ,500. For new or letters of recommendation to Professor ogy will also be considered. recent Ph.D.'s only. Write to Professor R. J. Lucas, Department of Mathematical Please send a curriculum vitae and Paul D. Humke, Mathematics Depart Sciences, Loyola University, Chicago, IL at least 3 letters of recommendation to: ment, St. Olaf College, Northfield, MN 60626. Loyola University of Chicago is Appointments Committee, Department of 55057. St. Olaf is an Equal Opportunity an Equal Opportunity1 Affirmative Action Mathematics, Rice University, P.O. Box Affirmative Action Employer. Employer. 1892, Houston, Texas 77251. Rice University is an Equal Opportu nity I Affirmative Action Employer. MIAMI UNIVERSITY Oxford, Ohio VIRGINIA POLYTECHNIC INSTITUTE Department of Mathematics and AND STATE UNIVERSITY Statistics DEPARTMENT OF MATHEMATICS We are seeking applications for one RICE UNIVERSITY anticipates a tenure track assistant pro fessorship beginning August, 1990. Du senior visiting appointment (Associate Griffith Conrad Evans Instructorships. ties include teaching 8-9 hours per or Full Professor) for the academic Postdoctoral appointments for two to semester, continuing scholarship and year 1990-1991. Duties are expected to three years for promising research math service. Applicants should have a Ph.D. include teaching a topics course and ematicians with research interests in in pure or applied mathematics by 8/90. interacting with faculty and graduate stu common with the active research ar Please send vita, graduate transcript dents. The review of applications will be eas at Rice. Applications should be in and three reference letters to John gin on November 15, 1989 and continue by 15 January 1990. Rice University Skillings, Mathematics Search, Depart until the position is filled. To apply submit is an Equal Opportunity 1Affirmative Ac ment of Mathematics and Statistics, Mi a curriculum vita to: Chairman, Senior tion Employer. Inquiries and applications ami University, Oxford, Ohio 45056. Re Visitor Search Committee, Department of should be addressed to Chairman, Evans view of applications will commence on Mathematics, Virginia Tech, Blacksburg, Committee, Department of Mathematics, January 15, 1990. Women and minorities VA 24061-0123. Women and minorities Rice University, Box 1892, Houston, are encouraged to apply. Miami pro are encouraged to apply. Virginia Tech is Texas 77251. vides equal opportunity in employment an Equal Opportunity 1Affirmative Action and education. Employer. 1306 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements POSITIONS AVAILABLE POSITION WANTED BOSTON UNIVERSITY DEPARTMENT OF MATHEMATICS EMBRY-RIDDLE AERONAUTICAL UNIVERSITY The Department of Mathematics at 1 earned a Ph.D. from Harvard in 1973, DEPARTMENT OF MATHEMATICS Boston University anticipates an opening an M.D. from the Univ. of Miami in 1978, & PHYSICAL SCIENCE for an Assistant Professor in Probability and have done both number theory and for Fall 1990. Outstanding candidates Mathematics: Tenure-track entry level family practice. I am now interested in should be able to teach courses in Op positions beginning Spring and Fall1990. mathematical biology and modelling in erations Research. Preference given to A commitment to teaching excellence medicine. Will consider both academic applicants with a strong theoretical back and scholarly activities is essential. Ph.D. and private sector, association with med ground and a commitment to teaching. in Applied Mathematics required. The ical school ideal. If interested contact Send vita and 3 letters of reference to: department offers a B.S. degree in En Joseph E. Carroll, 1355 Fickle Hill Road, Murad Taqqu, Department of Mathemat gineering, Physics and provides support Arcata, Ca. 95521. 707-822-7371. ics, Boston University, 111 Cummington courses for other Programs throughout St., Boston, MA 02215. AA/EOE. the campus. We offer a comprehensive compensation/benefits package. Send a letter of interest, resume and three letters of reference to: Chair, MA/PS WILLIAMS COLLEGE Department of Mathematics FOR SALE Department (NOTICES/NOV), cjo Of Williamstown, Massachusetts 01267 fice of Human Resources, Embry-Riddle Aeronautical University, Daytona Beach, Three anticipated positions, probably at FL 32114-3900. EOE the rank of assistant professor, for Symbolism: Sculptures and Tapestries, Fall 1990. Strong Commitment to both by John Robinson. Catalogue produced teaching and scholarship is essential. for the POP Maths Roadshow, Leeds, Please have a vita and three letters Sept., 1989. Colour photographs of 4 of recommendation on teaching and tapestries: 14 symbolic and 5 represen research sent to Frank Morgan, Chair. tational sculptures. Beautifully crafted, ROSE-HULMAN INSTITUTE Evaluation of applications will continue mainly in bronze. Includes trefoil, (8, OF TECHNOLOGY until positions are filled. 3) and (15, 4) torus knots. Comments DEPARTMENT OF MATHEMATICS AA/EOE by John Robinson and Ronnie Brown. Order from: Mathematics and Knots, A tenure-track assistant or associate University of Wales, Bangor, Gwynedd professorship will be available Septem LL57 1UT, U.K. Fax: (248)361429:email: ber 1, 1990. Applicants should have a CANISIUS COLLEGE R.Brown&UK.AC.Bangor.VAXA Ph.D. in mathematics or statistics and DEPARTMENT OF MATHEMATICS (£6 sterling, P/P £1.20 Surface, £2.60 a strong commitment to teaching and Applications are invited for a tenure Air: Mastercard/VISA to home address). scholarship. Ability and interest to teach track position in mathematics to begin in statistics, operations research andjor late August 1990. Applicants must have applied mathematics is desirable. Send the Ph.D. in mathematics and a strong letter of application, resume, three let commitment to quality teaching. Salary ters of recommendation and graduate and fringe benefits are competitive com transcripts to George Berzsenyi, Chair mensurate with credentials and experi American Math Monthly and Bulletin of man, Department of Mathematics, Rose ence. Applicants should send resume, AMS from 1961. Bound volumes. Am Hulman Institute of Technology, Terre transcripts and three letters of recom retiring and am willing to negotiate at Haute, IN 47803. mendation to Dr. Richard Escobales, bargain prices for the entire collection. Rose-Hulman Institute of Technology Chairman, Department of Mathematics, For details write to Prof. Bert Ross, Math is an equal opportunity employer. Canisius College, Buffalo, NY 14208. Dept. Univ. of New Haven, West Haven, AA/EOE. Conn. 06516 NOVEMBER 1989, VOLUME 36, NUMBER 9 1307 INSTITUTE FOR MATHEMATICS AND ITS APPLCATIONS ANNOUNCES A NEW PROGRAM PHASE TRANSITIONS AND FREE BOUNDARIES ADVISORY COMMITTEE: H. Brezis, L.A. Caffarelli, D. Kinderlehrer, J. Serrin ORGANIZING COMMI'ITEE: R. Fosdick, M. E. Gurtin, W.-M. Ni, L. A. Peletier A one-year program with two components: September 1990- January 1991: Phase Transitions Evolution of Phase Boundaries Modern Calculus ofVariations in Materials Science Shock Induced Transitions and Phase Structures in General Media Statistical Thermodynamics and Differential Geometry ofMicrostructured Material January - June 1991: Free Boundaries Degenerate Diffusions Variational Problems and Applications Free Boundaries in Viscous Flows POSTDOCTORAL MEMBERSHIPS All requirements for a doctorate should be completed by September 15, 1990. Applicants must show evidence of mathematical excellence, but they do not need to be specialists in the field. The following materials must be submitted (all material should arrive by January 15, 1990): (1) Personal statement of scientific interests, research plans, and reasons for wishing to participate in this program. (This is an essential part of the application.) (2) Curriculum vitae and a list of publications. (3) Three letters of recommendation, to be sent directly to the IMA. SENIOR MEMBERSHIPS Preference will be given to supplementary support for persons with sabbatical leaves, fellowships, or other stipends. All correspondence should be sent to VISITING MEMBERSHIP COMMITTEE INSTITUTE FOR MATHEMATICS AND ITS APPLICATIONS UNIVERSITY OF MINNESOTA 514 VINCENT HALL 206 CHURCH ST. S.E. MINNEAPOLIS, MN 55455-0436 The University of Minnesota is an equal opportunity educator and employer, and specifically invites and encourages applications from women and minorities. IMAPARTICIPATING INSTITUTIONS: Georgia Institute of Technology, Indiana University, Iowa State University, Michigan State University, Northern Illinois University, Northwestern University, Ohio State University, Purdue University, University of Chicago, University of Cincinnati, University of Houston, University of lllinois (Chicago), University of lllinois (Urbana), U niver sity oflowa, University of Michigan, University of Minnesota, University ofNotre Dame, University of Pittsburgh, Wayne State University. IMA PARTICIPATING CORPORATIONS: Bellcore, Cray Research, Eastman Kodak, Honeywell, 3M, UNISYS INSTITUTE FOR MATHEMATICS AND ITS APPLICATIONS ANNOUNCES A NEW PROGRAM POSTDOCTORATES IN INDUSTRIAL MATHEMATICS IMA announces 4 one-to-two year positions in Industrial Mathematics, beginning September 1, 1990. These appointments are in addition to the regular IMA postdoctoral program and are funded jointly by the NSF and by Honeywell, Inc. and 3M. They are designed to prepare mathematicians for research careers involving industrial interaction. Applicants should have received their Ph.D. in Mathematics or Applied Mathematics by September 1, 1990. Familiarity with pde and/or numerical analysis is desired, but no knowledge in engineering is required. Postdoctorates will spend 50% effort working with scien tists from Honeywell or 3M on one of the followi:qg topics: (1) Signal processing and computational ocean acoustics (Honeywell) (2) Diffractive optics; Maxwell equations in periodic structure (Honeywell) (3) Computational fluid mechanics - viscous free-surface flows (3M) (4) Scattering of electromagnetic waves from complex objects (3M) (5) Magneto-optic recording media; the writing process (3M) and 50% effort in the regular IMA program. The following materials must be submitted (all material should arrive by January 15, 1990): (1) Personal statement of scientific interests, research plans, and reasons for wishing to participate in this program. (This is an essential part of the application.) (2) Curriculum vitae and a list of publications. (3) Three letters of recommendation, to be sent directly to the IMA. All correspondence should be sent to INDUSTRIAL MATHEMATICS POSTDOCTORATE MEMBERSIDP COMMITIEE INSTITUTE FOR MATHEMATICS AND ITS APPLICATIONS UNIVERSITY OF MINNESOTA 514 VINCENT HALL 206 CHURCH ST. S.E. MINNEAPOLIS, MN 55455-0436 The University of Minnesota is an equal opportunity educator and employer, and specifically invites and encourages applications from women and minorities. IMA PARTICIPATING INSTITUTIONS: Georgia Institute of Technology, Indiana University, Iowa State University, Michigan State University, Northern Illinois University, Northwestern University, Ohio State University, Purdue University, University of Chicago, Universityh of Cincinnati, University of Houston, University of Illinois (Chicago), University of lllinois (Urbana), Univer sity oflowa, University of Michigan, University of Minnesota, University of Notre Dame, University of Pittsburgh, Wayne State University. IMA PARTICIPATING CORPORATIONS: Bellcore, Cray Research, Eastman Kodak, Honeywell, 3M, UNISYS INTRODUCTION TO FRACTAL GEOMETRY: ELLIPTIC SYSTEMS THE THEORY OF ERROR· Mathematical Foundations and AND QUASICONFORMAL CORRECTING CODES, 2nd Ed. Applications MAPPINGS K.J. Falconer, University of Bristol, U.K. Vera Pless, University of Illinois - Chicago H. Renelt, Martin Luther University, GDR 1-92287-0 224pp Dec. 1989 $33.95 1-61884-5 224pp Sept. 1989 $34.95 1-91731-1 146pp June 1989 $33.95 PARTIAL DIFFERENTIAL INTRODUCTION TO MATHEMATICAL BIOECON· EQUATIONS OF APPLIED MODERN SET THEORY OMICS: THE OPTIMAL MAN· MATHEMATICS, 2nd Ed. Judith Roitman, University of Kansas AGEMENT OF RENEWABLE Erich Zauderer, Polytechnic University 1-63519-7 250pp Aug. 1989 $39.95 RESOURCES, 2nd Ed. 1-61298-7 891pp June 1989 $64.95 Colin Clark, University of British Columbia 1-50883-7 400pp Mar. 1990 $44.95* ALGEBRA PRIMES OF THE FORM x2 + ny2 2nd Ed., Volume II Fermat, Class Field Theory, and P.M. Cohn, University College, U.K. NONNEGATIVE MATRICES Complex Multiplication 1-92234-X 428pp June 1989 $54.95 IN DYNAMIC SYSTEMS David A Cox, Amherst College A Berman, Technion, Israel, 1-50654-0 368pp Sept. 1989 $42.95 M. Neumann, University of Connecticut & ABS PRO..JECTION R.J. Stern, Concordia University, Canada ALGORITHMS: 1-62074-2 225pp Sept. 1989 $36.95 FIBONACCI AND LUCAS Mathematical Techniques for NUMBERS AND THE GOLDEN Linear and Nonlinear Equations J. Abaffy, Karl Marx University of Economics, CHAOTIC DYNAMICS OF SECTION: Budapest NONLINEAR SYSTEMS Theory and Applications E. Spedicato, University of Bergamo, Italy S. Neil Rasband, Brigham Young University S. Vajda, University of Sussex, U.K. 0-21507-0 220pp Aug. 1989 $59.95 1-63418-2 256pp Nov. 1989 $39.95 0-21508-9 189pp July 1989 $64.95 MATHEMATICAL METHODS FOR ABSTRACT AND CONCRETE SCIENTISTS AND ENGINEERS CATEGORIES LINEAR OPERATORS IN Linear and Nonlinear Systems SPACES WITH AN INDEFINITE Jiri Adamek, Technical University Prague, Peter B. Kahn, SUNY at Stony Brook Czechoslovakia METRIC 1-62305-9 656pp Oct. 1989 $54.95 1-60922-6 520pp Feb. 1990 $49.95* T. Y. Azizov and I.S. lokhvidov, Voronezh State University, USSR 1-92129-7 304pp Mar. 1990 $82.95* To order, write: .JOHN WILEY & SONS, INC. 1m 605 Third Avenue, Box 0-0115, CHEBYSHEV POLYNOMIALS: WILEY New York, NY 10158. Attn: Peter Drogin, 10th Floor. From Approximation Theory to Algebra and Number Theory, To order by phone, calli toll-free: 1·800·526·5368 2nd Ed. All other inquiries, call: 212-850-6418 Theodore J. Rivlin, IBM - Thomas J. Watson Research Center ( * ) denotes a tentative, pre-publication price 1-62896-4 208pp Mar. 1990 $49.95* Prices subiectto change without notice & higher in Canada Centre de Recherches Mathematiques A focal period for special topics in N(Q)NILllNlEA~ JP>liJ)lE 0§ atliDtdl AJP>JP>ILITCA 1rll(Q)N§ MAY 14 -JULY 13, 1990 MAY 14 - JUNE 8: Informal rencontre involving extended, in-depth interaction on partially formulated and unsolved problems. Partial list of invitees E. Di Benedetto (Northwestern) L. Caffarelli (lAS, Princeton), S. Davis (Northwestern) C. Evans (Maryland) P. Fife (Utah) A. Friedman (Minnesota) J. Glim (Courant) S. Howison(Oxford) J. Keller (Stanford) P. Ortoleva (Indiana) Postdoctoral fellows and advanced graduate students are encouraged to apply for financial support. Organizers: J. Chadam and H. Rasmussen JUNE 13 - JUNE 22: The fifth of a series of triennial International Colloquia on Free Boundary Problems: Theory and Applications. Invited participants H.-W. Alt (Bonn) P. Fife (Utah) P. Knabner (Augsburg) E. DIBenedetto (Northwestern) A. Friedman (Minnesota) S. Luckhaus (Heidelberg) C.Baiocchi (Pavia) M. Glicksman (RPI, Troy) E. Magenes (Pavia) Ph. Benilan (Besanc:;on) J. Glimm (Courant) G. Meyer (Georgia Tech.) H. Brezis (Paris VI & Rutgers) s. Howison (Oxford) P. Ortoleva (Indiana) L. Caffarelli (lAS, Princeton) L.S. Jiang (Suzhou) R. Pego (Michigan) M. Chipot (Metz) s. Kamin (Tel Aviv) R. Ricci (Firenze) A. Damian ian (Ecole Poly., France) J. Keller (Stanford) G. Sivashlnsky (Tel Aviv) S. Davis (Northwestern) D. Kinderlehrer (Minnesota) I. Stakgold (Newark) Those interested in applying for the limited number of spaces should contact the organizers a.s.a.p. Organizers: J. Chadam and H. Rasmussen JIINE 25- JIII.Y 13: Seminaire de Mathematiques Superieures (29th session) on "Shape Optimization and Free Boundary Problems". This related event is a NATO-ASI organized by the Departement de Mathematiques et de Statistique of the Universite de Montreal. Partial list of lecturers H. Brezls (Paris VI & Rutgers) M. Fortin (Laval) R. Temam (Orsay & Bloomington) J. Chadam (McMaster) 0. Pironneau (Paris VI & INRIA) J. Vazquez (Madrid) M. Delfour (Montrllal) J. Sokolowski (Warsaw) J.P. Zolesio (Montpellier) A. Fasano (Firenze) I. Stakgold (Newark) It Is expected that partial financial assistance will be available for a certain number of participants. Priority will be givento graduate students. For Information and registration forms, please contact Ms. Ghislaine David (Secretaire I Semlnaire de Mathematiques Superieures, Unlverslte de Montreal, C.P. 6128-A, Montreal, Quebec, Canada, H3C 3J7, Tel.:(514) 343-6710). Organizers: M. De/four (Scientific Organizer) and A. Daigneault (Permanent Director) To request detailed Information about any of the above activities, please contact organizers directly at: Memphis State University POSITIONS IN THE MATHEMATICAL SCIENCES Department of Mathematical Sciences The Department of Mathematical Sciences invites applications for anticipated tenure track positions for 1990. The Department offers degrees at all levels through the Ph.D. in Computer Science, Mathematics, and Applied Statistics. Our library and computing facilities (including an Intel Hypercube), teaching load, and travel opportunities contribute to a very favorable research environment. Preferred re search areas in computer science include software engineering, algorithms, parallel and distributive processing, artificial intelligence/ cognitive science, network design and analysis, data communications, and theory. Preferred research areas in statis tics include applied statistics, biostatistics, stochastic models, and time series. Pre ferred research areas in mathematics include approximation theory & numerical analysis, differential equations & nonlinear analysis, dynamical systems & ergodic theory, graph theory & combinatorics, functional analysis & operator theory, math ematics education, and number theory. Applicants must have a Ph.D. by September 1, 1990, and a strong potential for excellence in teaching and research. Selection will begin on January 31, 1990. Applications will continue to be ac cepted until all positions are filled. Women and Minorities are strongly urged to apply. Successful candidates must meet Immigration Reform Act criteria of 1986. Applicants should submit a resume and direct three letters of ~eference to: Ralph Faudree, Chair Department of Mathematical Sciences Memphis State University Memphis, TN 38152 An Equal Opportunity/ Affirmative Action Employer. MATHEMATICAL REVIEWS ASSOCIATE EDITOR Applications and recommendations are invited for a two-year appointment as an Associate Editor of Mathematical Reviews (MR), to commence no later than the summer of 1990. Appli cations will be welcomed from persons taking leave from other positions, and in particular from tenured faculty members who can take leave to come to MR for two years. The MR office of the American Mathematical Society is located in Ann Arbor, Michigan, not far from the campus of the University of Michigan, and the editors (although employees of the AMS) enjoy many privileges at the university. At present MR employs fourteen mathemati cal editors, about ten consultants, and over sixty nonmathematicians. It produces Mathematical Reviews, Current Mathematical Publications, various indexes, the online service MathSci, and MathSci Disc. The responsibilities of an Associate Editor fall primarily in the day-to-day opera tions of selecting articles and books suitable for review, classifying these items, assigning them to reviewers, editing the reviews when they are returned, and correcting galley proof. At this time an individual with considerable breadth in applied mathematics is sought (such as in differential equations, optimization, operations research, systems theory, control theory, information theory, etc.). The ability to write good English is essential, and the ability to read mathematics in major foreign languages is important. (The ability to read mathematical articles in Russian or Chinese is especially desirable.) Persons interested in combining a sabbatical or other leave with a part-time appointment as an Associate Editor should write (or telephone) for further details. The twelve-month salary is negotiable, and will be commensurate with the experience the applicant brings to the position. Salary and fringe benefits are similar to those in universities. Of special importance is a policy providing termination pay of three months full pay for an editor serving full time for two years. Applications (including curriculum vitae, bibliography, and names and addresses of at least three references) and recommendations should be sent to Dr. R. G. Bartle, Executive Editor, Mathematical Reviews, P. 0. Box 8604, Ann Arbor, MI 48107-8604. (Telephone: 313-996-5255; FAX: 313-996-2916; INTERNET: [email protected].) Persons who may be interested in applying for this position are urged to inquire without delay. The American Mathematical Society is an equal opportunity employer. Assistantships and Graduate Fellowships in the Mathematical Sciences, 1990-1991 Assistantships and Graduate Fellow listed in the Mathematical Sciences ships in the Mathematical Sciences, Professional Directory receive 1990-1991, continues to provide vital complimentary copies of the issue. information about university graduate AMS individual and institutional mathematics programs. In addition, it members are also eligible to purchase includes information on thesis and additional copies at a reduced price. foreign language requirements within each listing. Due in December 1989, 144 pages updated annually Up-To-Date ______ISBN 0-8218-0141-4 The up-to-date information contained List price $15, AMS member $9 To order, please specify ASST/90NA within the pages of A&GF is compiled from data supplied by university depart ments. The list of assistantships and graduate fellowships includes approxi mately 409 departments of mathematics, applied mathematics, statistics, com puter science, and related mathematical disciplines; these represent about 337 colleges and universities. A section on STANDING ORDERS are accepted for this publication and any series published by the stipends for study and travel and Society. Proforma invoices are sent to addresses of sources of graduate fellow standing order customers prior to the ship information is also included. publication of each new volume. Shipment is made upon receipt of payment and Wide Distribution ______pubUcation. To begin a standing order, contact the Customer Services Depart The A&GF has a wide distribution - ment of the AMS. academic departments who are institu tional members of the AMS or who are PREPAYMENT REQUIRED. Order from the American Mathematical Society, P. 0. Box 1571, Annex Station, Providence, RI 02901-1571 USA or call800-321-4AMS from within the continental U.S. (401-272-9500 else where) to use VISA or MasterCard. Prices subject to change without notice. • PHYSICISTS • OCEANOGRAPHERS XonTech, Inc. is expanding its ongoing efforts involving state of-the-art signal processing, data modeling and phenom MATHEMATICS enology studies. We need bright, energetic and flexible mathematicians and physicists for these challenging as signments. We have positions available for all levels of STATE UNIVERSITY OF NEW YORK experience. Background in one or more of these tollowing AT BUFFALO areas is highly desirable: physical interpretation of sensor data, characterization and understanding of noise and signal phenomenology, advanced signal processing algorithm The Department of Mathematics anticipates the appointment of several tenured or tenure-track faculty members beginning September 1, development, algorithm design experience for parallel 1990. Salary will be competitive. Outstanding applicants in all fields of architectures, mathematical modeling of physical phenomena mathematics are encouraged to apply. We seek applicants with excellent and sensor data. research accomplishments/potential and a strong corrunitment to teaching. U.S. CITIZENSHIP REQUIRED Applicants should send any supporting information and have four letters of recorrunendation sent to: We offer challenging assignments, competitive salaries, an outstanding benefits package, and a pleasant working Dr. Nicolas Goodman environment. The openings for the above positions are at our Search Committee Chairman Van Nuys, CA headquarters facility. Qualified professionals Department of Mathematics SUNY /Buffalo are invited to submit resumes and salary history to: Human 106 Diefendorf Hall Resources, XonTec:h, Inc., 6862 Hayvenhurst Ave., Buffalo, New York 14214 Van Nays, CA 91406. The deadline for applications is December 1, 1989. Late applications will be considered until ~ XonTech, Inc. positions are filled. SUNY /Buffalo is ao Equal Opportunity/ Affirmative Action Employer. We are interested in identifying prospective minority and women candidates. "People, Science and 'lechnolop'' No person, in whatever relationship with the State University of New York Los Anples Area • Oranp County • Northern California at Buffalo shall be subject to discrintination on the basis of age, creed, color, Colorado Sprlnp • Washlncton, D.C. • Huntsville, Alabama handicap, national origin, race, religion, sex, marital or veteran status. Kluwer Academic Publishers are Pleased to Announce a 25% Discount on All of Their Books for Individual Members of the American Mathematical Society Members Wishing to Take Advantage of this Concession Should Send Their Orders Directly to the Publisher at the Addresses Given Below. Orders Should be Prepaid, and Should be Accompanied by the Signed Statement: "/ am a member of the American Mathematic a[ Society and I am ordering these books for my own personal use" •••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• • Orders inside the U.S. and Canada: Orders outside tM U.S. and Canada: • • Kluwer Academic Publishers Kluwer Academic Publishers • • Order Department -M, P.O. Box 358 Distribution Center, P.O. Box 322 • • Accord Station, Hingham, MA 02018-0358 3300 AH Dordrecht, The Netherlands • •••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• TITLES OF PARTICULAR INTEREST ... G. Szekely /Paradoxes in Probability Theory and Mathematical Statistics 1986 ISBN 90-277-1899-7 252pp. Cloth $67.50 ($51.00)* V.D. Goppa/ Geometry and Codes 1988 ISBN 90-277-2776-7 176pp. Cloth $64.00 ($48.00)* P.J.M. van Laarhoven/Simulated Annealing: Theory and Applications 1987 ISBN 90-277-2513-6 198pp. Cloth $49.00 ($37.00)* Yu. L. Rodin/The Riemann Boundary Problem on Riemann Surfaces 1988 ISBN 90-277-2653-1 200pp. Cloth $64.00 ($49.00)* • AMS Individual Member Price ARIZONA STATE UNIVERSITY Department of Mathematics The Department of Mathematics invites applications for tenure-track and visiting faculty positions at all ranks and in all areas of mathematics beginning in August 1990. The Department is in the third year of a major development program intended to build Functions Matliematics nationally recognized research groups of four to seven faculty members in Computational Bowdoin 1987 Mathematics, Differential Equations Department (including POE's). Discrete Mathematics, Dynamical Systems, Operator Theory. Robert C. Gunning and Colby College invites applications for two Algebraic Geometry and Number Theory, Leon Ehrenpreis, Editors tenure-track and one visiting position (at any Systems and Control and Probability and level) in mathematics/computer science. While Statistics. During the past two years. 12 we welcome applications from well-qualified tenure-track or tenured appointments have and highly motivated candidates in all been made and we anticipate making at least Theta functions have a long and distin branches of mathematics, our principal aim is 5 appointments during each of the next three guished history and play a many-faceted and to fill one vacancy in each of the general areas: academic years. central role in a number of areas of mathe algebra, analysis, and a branch of mathematics matics. Interest in these functions has re strong For 1990. the majority of the tenure-track closely related to computer science. A kindled in recent years as a result of the wide research program plus a firm commitment appointments will be made at the Assistant variety of areas in which they have made to undergraduate teaching are essential for Professor level. To be considered for such an major contributions. these positions. appointment. the candidate must demonstrate potential for outstanding research while providing effective teaching at both the under Crossing the lines of semi-simple Lie group Well-qualified female applicants at the level of and graduate levels in a public theory and nilpotent Lie group theory, theta assistant or associate professor will, in addition, graduate university environment. For candidates at functions are relevant to the arithmetic of be considered for one of the College's Clare Professor level, additional quadratic forms and to partition theory, Boothe Luce Chairs for women scientists. the Associate requirements include a proven record of through which they relate to statistical outstanding research accomplishments and mechanics and quantum field theory. In private, liberal arts Colby is a highly selective, versatile and effective teaching. At the Full addition, they are used to study Riemann college with an enrollment of 1700 students. Professor level. applicants should be surfaces, abelian varieties, and solutions of It is located in mid-Maine, on the edge of the recognized nationally forthcquality and scope differential equations from physics. In this Belgrade Lakes recreation area, just over 3 of their research and leadership activities. way, they relate to partial differential hours' drive north of Boston, and one hour Salaries are competitive and commensurate equations and algebraic from the Maine coast. The nearby towns of with experience and qualifications. Waterville, Oakland, and Winslow offer geometry. excellent public schools and a variety of In support of its research and graduate affordable housing. education programs. the Department has This two-volume collection contains the pro installed an Advanced Computing Facility ceedings of an AMS Summer Research Insti The present faculty search is part of a signifi centered around a network of Titan Mini tute on Theta Functions, held in July 1987 at With papers from some of cant mathematics development at Colby follow Super Graphics computers plus a cluster of Bowdoin College. ing the recent appointment of Keith Devlin Work Stations. Research efforts were the top experts in this area, these volumes from Stanford to the Carter Professorship and enhanced by direct access to the University's will provide readers with an excellent Chair of the Mathematics Department. CRA Y XMP-14/se and IBM 3090-SOOENF overview of the current research in and super computers. applications of theta functions. The College offers a rich computing environ Arizona State University has more than 43,000 ment based on VAX mainframes and Apple students and is located in the rapidly growing Macintosh workstations. Faculty offices are Phoenix Metropolitan area-a center of 00 provided with networked Macintosh llcx or business. finance and high technology. The 1980 Mathematics Subject Classification: (set) 0-8218-1485-0; (Part I) 0-8218-1483-4; SE30 computers, in addition to which there are valley offers a wide range of educational, ISBN (Part 2) 0-8218-1484-2, LC 89-6723, ISSN 0082- a number of networked Macintosh clusters cultural and recreational opportunities. 0717 spread around the campus. The Mathematics Pleasant and convenient housing is widely 728 pages (Part 1), 376 pages (Part 2) hardcover 1989 Department recently upgraded its inhouse campus. available near the university Set: List $149, Inst mem $119, Indiv mem $89 teaching/research laboratory to comprise 18 Part I only: List $99, Inst mem $79, Indiv mem $59 Macintosh ll/llcx computers, a central file Applications should be received by Part 2 only: List $58, lnst mem $46, Indiv mem $35 visual display apparatus. December 1, 1989, and the Department server; and associated To order, please use PSPUM/49NA (Set) will begin to review applications as of this Colby is an acknowledged national leader in PSPUM/49.1NA(Part I) will be extended on a the development of computer-aided instruction date. The deadline PSPUM/49.2NA (Part 2) in mathematics. month-to-month basis until all available positions are filled. Please send a letter of application and a resume Applicants should send their resumes and and the names of three referees to Professor arrange for at least three letters of Keith Devlin, Chair, Department of recommendation to be sent to: William T. Mathematics, Colby College, Waterville, Trotter, Chair, Department of ME 04901. Mathematics, Arizona State University, The deadline for applications is 12 December Tempe, AZ 85287-1804. AA/EOE we shall 1989 in the first instance; thereafter; Prepayment required. Order from American continue to review applications until the posi Mathematical Society, P. 0. Box 1571, Annex tions are filled. Colby is an AA/EO Employer Station, Providence, Rl 02901-1571 or call toll free and encourages applications from women ARIZONA STATE UNIVERSITY 800-321-4AMS to charge with VISA or MasterCard. and minorities. All prices subject to change. Shipment will be made by surface. For air delivery add, 1st book $5, each additional $3, maximum Florida Atlantic University and IJCAI announce the First INTERNATIONAL SYMPOSIUM on There is a vacancy at the MATHEMATICS ARTIFICIAL INTELLIGENCE INSTITUTE of the UNIVERSITY of ZUERICH and MATHEMATICS for a January 3-5, 1990 at Pier 66 Ocean Resort Fort Lauderdale, Florida PROFESSOR IN GEOMETRY Keynote Speaker: David Mumford Invited Speakers: Martin Davis to complement the existing areas of teaching Zohar Manna Drew McDermott and research. Applicants should be expert in a field such as Geometry, Topology, Global Alan Robinson Leslie Valiant or Harmonic Analysis. Selected papers from the Symposium will appear in a Applications, with curriculum vitae and list of special volume of the journal, publications, should reach the Dekanat der ANNALS of MATHEMATICS and Philosophischen Fakultat II, Universitat Zurich, ARTIFICIAL INTELLIGENCE Winterthurerstrasse 190, CH-8057 Zurich, Switzerland, before .30.11.1989. Details of the Symposium are Applications from overseas may be accepted available from F Hoffman, until the end of December 1989. Mathematics Dept, Florida Atlantic University, Boca Raton, FL 33431 (407)367-3345. email: [email protected] RINGS OF DIFFERENTIAL OPERATORS ON CLASSICAL RINGS OF INVARIANTS T. Levasseur and J. T. Stafford UNIVERSITY OF HONG KONG (Memoirs. of the AMS, Number 412) Lecturer in Mathematics This book will provide readers with an understanding of Applications are invited for a Lectureship in Math the interrelationship between differential operators, invariant theory, and the primitive ideal theory of semisimple Lie ematics, tenable from September 1, 1990. Appli algebras. The main topic concerns a study of rings of cants specializing in any main branch of Mathemat differential operators on classical rings of invariants, in the ics will be considered. sense of Weyl's book, The Classical Groups. The authors consider three different classes of rings of invariants and Annual salary (superannuable} is on an 11-point show that, for each of these cases, the ring of differential scale: HK$233,700-390,600 (approx. £19, 160-32,020; operators is a simple factor ring of a certain enveloping algebra. In particular, the ring of differential operators is a sterling equivalent as at September 20, 1989}. Start simple Noetherian ring. They also demonstrate that, if SO(k) ing salary will depend on qualifications and expe acts in the natural way on the ring of complex polynomials in rience. At current rates, salaries tax will not ex kn variables, then, for k ::; n, the ring of differential operators ceed 15% of gross income. Children's educational on C[X]50{klis finitely generated as a module of a certain enveloping algebra. lowances, leave, and medical benefits are provided; housing or tenancy allowances are also provided in 1980 Mathematics Subject ClassiWcations: 17835, 13N05, 14L30, 14M12, 17820, 16A19, 16A33 most cases at a charge of 7!% of salary. ISBN 0-8218-2475-9, LC 89-15147 ISSN 0065-9266 particulars and application forms may be 117 pages (soltcover), September 1989 Further Individual member $11, List price $19, obtained from Appointments (36949}, Association Institutional member $15 To order, please specify MEM0/412NA of Commonwealth Universities, 36 Gordon Square, London WC1 H OPF, UK, or from the Appointments All prices subject to change. Shipment will be made by surface. University of Hong Kong, Hong Kong For air delivery add, I st book $5, each additional book $3, Unit, Registry, maximum $100. Prepayment required. Order from American (Fax (852} 5-8582549}, Closes 30 November 1989. 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Additional details may be found on the Advertising Rate Second class postage is paid at Providence, Rhode Island Card. Any questions should be directed to Paula Montella in Volume 36, Number 9, November 1989, Pages 1145 - 1332 the AMS Advertising Department, P.O. Box 6248, Provi Copyright @ 1989 by the American Mathematical Society dence, RI 02940; telephone 401-272-9500 or 800-321-4AMS US ISSN 0002-9920 in the continental U.S.; FAX 401-331-3842. UEDA THEORY: THEOREMS AND PROBLEMS THE METAPLECTIC REPRESENTATION, MPc Amnon Neeman STRUCTURES AND GEOMETRIC (Memoirs of the AMS. Number 415) QUANTIZATION P. L. Robinson and J. H. Rawnsley Ueda explored the question of which algebraic varieties over (Memoirs of the AMS, Number 410) the complex numbers give rise to Stein manifolds. Affines are one obvious example, but there are others. In 1983, Ueda defined an invariant that "measures" the Steinness of a Zariski open subset of a compact complex surface. The purpose of this book is to study this fascinating and mysterious homological invariant by exploring its functoriality properties, variational properties, and higher dimensional generalizations. The author sets Ueda's invariant in the right pairing of vacuum states for positive polarizations. They r·':.. ,:':i...... _:: ..,'_ :l_ ...... ·'... formal framework, permitting formulation of many problems §.!~f~~ff.~~~~~~~:,develop a scheme for the geometric quantization of symplectic ·'·~_ and conjectures indicating that further study might reveal truly surprising and interesting phenomena. Aimed at researchers in several complex variables and in algebraic geometry, the book requires familiarity with coherent analytic sheaves and the solution of the Levi problem, as well as some basic knowledge of algebraic geometry. 1980 Mathematics Subject ClassiWcations: 32E10, 14J15, 32J15, 32C35 I I ISBN 0-8218-2478-3, LC 89-15176 ~~~~~~~~~~ ISSN 0065-9266 123 pages (softcover), September 1989 Individual member $11, List price $19, Institutional member $15 '.'1.,'1,:..':. To order, please specify MEM0/415NA '1.,:.. =~=];~~:-~·::: ~ ~ All prices subject to change. Shipment will be made by surface. . ;;;;~~;;:;;,;~.:~~;~: I For air delivery add, I st book $5, each additional book $3, maximum $100. Prepayment required. Order from American Mathematical Society, P.O. Box 1571, Annex Station, Provi dence, RI 02901-1571, or call toll free 800-321-4AMS to charge with VISA or MasterCard. Application for Membership 7990 AMERICAN MATHEMATICAL SOCIETY Date ...... 19 ...... 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Name: ______Customercode: ______ Changeeffectiveasof ______ Old mailing address: ------ NEW mailing address: ------ New position: ------ If mailing address is not that of your employer, please supply the following information: New employer: ______ Location of employer: ------City State/Province Country Zip Code Telephone number(s): ------ Electronic address(es): ------ Recenthonorsandawards:------ Personal items for publication in Notices: ------ Mail completed form to: Customer Service, AMS, P.O. Box 6248, Providence, RI 02940 Staple here Fold here NO POSTAGE NECESSARY IF MAILED IN THE UNITED STATES BUSINESS REPLY MAIL FIRST-CLASS MAIL PERMIT NO. 554B PROVIDENCE, RI POSTAGE WILL BE PAID BY ADDRESSEE Customer Service Department AMERICAN MATHEMATICAL SOCIETY P. 0. Box 6248 Providence, RI 02940 Fold here Fasten PAYMENT securely MAA Minicourse Preregistration Form, Louisville, Kentucky January 17-20, 1990 NOTE: This Is NOT an AMS Short Course Form. Please use the Joint Meetings Pregistration/Houslng Form to preregister for the AMS Short Course. To register for MAA Mlnlcourse(s), please complete THIS FORM or a PHOTOCOPY OF THIS FORM and return it with your payment to: Susan Wilderson Mathematical Association of America 1529 Eighteenth Street, N. W. Washington, DC 20036 Telephone: 202-387-5200 Telephone: ------(Please print) Surname First Middle Street address City State Zip • Deadline for MAA Minicourse preregistration: November 17, 1989 (After this date, potential participants are encouraged to call the MAA headquarters at 800-331-1622.) • Deadline for cancellation in order to receive a 50% refund: January 3, 1990 • Each participant must fill out a separate Minicourse Preregistration form. • Enrollment is limited to two Minicourses, subject to availability. • Please complete the following and send both form and payment to Susan Wilderson at the above address: I would like to attend D 1 Minicourse D 2 Minicourses Please enroll me in MAA Minicourse(s): #--and#- In order of preference, my alternatives are: #-- and #- • PAYMENT Check enclosed: $ __ Credit card type: D MasterCard D Visa Credit card#------Expiration date:------ Your Employing Institution Signature (as it appears on credit card) Minicourse Number and Name Organized by 1. Computer based discrete mathematics Nancy Hood Baxter, Ed Dubinsky & Donald Muench $50 2. Finite-Pak - Software for Linear Programming Marvin L. Bittinger & J. Conrad Crown $50 3. Random mappings Bernard Harris $30 4. Lagrange first year calculus Francesca Schremmer & Alain Schremmer $30 5. Teaching mathematical modeling Frank R. Giordano & Maurice D. Weir $30 6. Coaching a team for the modeling contest B. A. Fusaro $30 7. Derive workshop Wade Ellis, Jr. $50 8. Using history in teaching calculus V. Frederick Rickey $30 9. How to use inexpensive graphing calculators to enhance Bert K. Waits & Franklin Demana $30 teaching and learning of precalculus mathematics and calculus 10. A seminar on women in mathematics Miriam P. Cooney $30 11. Writing in mathematics courses George D. Gopen & David A. Smith $30 12. An introduction to the mathematical elements of computer graphics Joan Wyzkoski Weiss $50 13. A survey of educational software Virginia E. Knight & Vivian Yoh Kraines $50 14. Creating order out of chaos in freshman mathematics: Linda H. Boyd $30 instituting a mathematics placement program 15. Mathematica and college teaching Stan Wagon $30 16. Starting, funding and sustaining mathematics laboratories Stavros N. Busenberg $50 17. The informed consumer's instructional guide to graphing calculators John W. Kenelly & Iris B. Fetta $30 n I plan on preregistering for the Louisville, Kentucky meetings ONLY in order to attend the MAA Minicourse(s) indicated above. It is my understanding tnat, should the course(s) of my choice be filled, full refund of the Louisville meetings preregistration fee will be made. MathSciSM Instructions for Applicant's Form on facing page WHEN MathSci IS ONLINE The form. Applicants' forms submitted for the Em ployment Register will be photographically reproduced MATHEMATICS IS in the December 1989 issue of Employment Informa ON THE SCREEN tion in the Mathematical Sciences {ElMS). Resumes of those attending will be posted at the meeting. One MilHon Entries Searched The forms must be carefully typed using a fresh in Seconds black ribbon. The best results are obtained with a carbon-coated polyethylene film ribbon, but satisfac MathSci is the online database that fmds, in a tory results may be obtained using a ribbon made of matter of seconds, any information published in Mathematical Reviews (MR), Current Mathemati nylon or other woven fabric if suitable care is exer cal Publications (CMP), Current Index to Statistics cised. It is important that the keys be clean and make (CIS), the Index to Statistics and Probability a sharp, clear impression. Do not erase-it causes (Tukey), Computing Reviews (CR) and the Guide smudges which reproduce when photographed. Use a to Computing Literature (GC.l.J. These combined correcting typewriter or correction tape or fluid if nec sources give you over one million entries in all essary. Submit the original typed version only. Copies areas of the mathematical sciences. will not reproduce properly and are not acceptable. Hand lettered forms will be returned. Monthly Updates Applicants' forms must be received by the Society MathSci is updated monthly, with over 4,000 by November 17, 1989 in order to appear in the spe new entries from MR and 4,300 from CMP; also cial issue of ElMS and must be accompanied by the quarterly updates of 2,250 new entries from CIS. Preregistration/Housing Form printed in this issue, if attending the meeting. Forms received past the dead Easy Fingertip Access line or not completed will be returned. When can you use MathSci? Anytime ... 24 hours @ Specialties a day. Now you can search for all the informa AL = Algebra AN = Analysis tion from MR. CMP, CIS, the Tukey Index, CR. BI = Biomathematics BS = Biostatistics and GCL when you want it and need it. From CB = Combinatorics CM = Communication your office. From your home. Anywhere you can CN = Control CS = Computer Science connect a modem to a microcomputer (or CT = Circuits DE = Differential Equations terminal) and dial a local number. EC = Economics ED = Mathematical Education FA= Functional Analysis FI =Financial Mathematics Where to Get OnHne with MathSci FL = Fluid Mechanics GE = Geometry MathSci is produced by the American Mathe HM = History of Math LO = Logic matical Society, a source of information for the MB = Mathematical Biology ME = Mechanics mathematical community. MathSci can be MO = Modelling MP = Mathematical Physics accessed on BRS, DIALOG, CompuServe, MS =Management Science NA =Numerical Analysis EasyNet, and the European Space Agency (ESA). NT= Number Theory OR= Operations Research PR = Probability SA = Systems Analysis To learn more about MathSci, contact Taissa ST = Statistics TO = Topology Kusma at the AMS by calling 800-321-4AMS in the continental United States. @ Career Objectives AR =Academic Research AT= Academic Teaching New Addition in 1989 NR = Nonacademic R&D NC = Nonacad. Consulting Computing Reviews (CR) and the annual ACM NS = Nonacademic Supervision Guide to Computing Literature (GCL) from the @@Duties Association of Computing Machinery are being T =Teaching U = Undergraduate added to MathSci in 1989. These ACM publica G =Graduate R =Research tions provide comprehensive coverage of the C = Consulting A = Administration international research literature in computing S = Supervision IND = Industry and computer science. GOV = Government DP = Data Processing Location American Mathematical Society E =East S =South M =Mountain P. 0. Box 6248 C =Central I = Indifferent Providence, RI 02940 W =West 0 =Outside U.S. (401) 272-9500 Telex 797192 • FAX (401) 331-3842 SM - MalhSctls a service mark or the American Mathematical Society MATHEMATICAL SCIENCES EMPLOYMENT REGISTER APPLICANT FORM JANUARY 17-19, 1990 LOUISVILLE, KENTUCKY The form must be typed. (Please see instructions on facing page) APPLICANT: Nrune ______ Mailing address (include zip code) ------ @ Specialtie"------ @ Career objectives and accomplishments ACADEMIC: 0 Research, 0 Teaching NON-ACADEMIC: 0 Research and Development, 0 Consulting, 0 Supervision Near-term career goals, ______ Significant achievements or projects, including rol"------ Honorsandoffice'"------ Other (e.g., paper to be presented at THIS meeting)------ Selected titles of papers, reports, books, patent"------ @ Degree Year Institution @No. of abstracts, internal report~~------® No. of papers accepte:u______------® No. of books and patent"------EMPLOYMENT HISTORY: Present Previous Previous @Employe"------ Position @Duties Years ______;to, ______to ______to ____ _ DESIRED POSITION:'------(!) Dutie~~------0 Available mo. __ fyr.__ Location ______Salary______®References (Nrune and Institution) © Citizenship: (check one) 0 U.S. Citizen 0 Non-U.S. Citizen, Permanent Resident 0 Non-U.S. Citizen, Temporary Resident g, AVAILABLE FOR INTERVIEWS: (Interviews for Session 4 scheduled on the basis of employer's request only.) Session 1 0 Session 2 0 Session 3 0 Session 4 0 Thurs. AM 9:30-11:45 Thurs. PM 1:15-5:00 Fri. AM 9:30-11:45 Fri. PM 1:15-5:00 I do not plan to attend the Louisville meetings 0 one one be be yr. yr. printed printed 1990 1990 Please Please will will only only I I Sessions Sessions scheduled. scheduled. above. above. code code below. below. the the 17-19, 17-19, mo. mo. @ @ computer computer be be Equations=DE, Equations=DE, @start @start a a on on 0J1[TI 0J1[TI positions, positions, @ @ Statistics=ST, Statistics=ST, notes notes FORM FORM of of may may Unknown Unknown Government=GOV, Government=GOV, employer employer the the 01190; 01190; * * set set the the seclion seclion prepare prepare in in Interviewers Interviewers ®No. ®No. which which one one e.g. e.g. to to see see Differential Differential I,[IJ I,[IJ @ @ Biology=MB, Biology=MB, the the CD,DDDD CD,DDDD same same Supervised Supervised JANUARY JANUARY ( ( ) 1:15-5:00 1:15-5:00 4, 4, to to 4 4 ( ) I I than than Position Position used used the the Analysis=SA, Analysis=SA, No No provided provided I I be be PM, PM, for for and/or and/or refer refer @)Date @)Date People People More More interviews interviews Industry=IND, Industry=IND, are are I I or or 3, 3, Track Track will will Restriction Restriction of of position position of of Session Session Fri. Fri. Circuits=CI', Circuits=CI', ( ( ) 2, 2, Mathematical Mathematical Systems Systems 1,1 1,1 of of used used I, I, (Please (Please be be Ye; Ye; number.) number.) I I Tenure Tenure position, position, number number 1,11111, 1,11111, to to Title Title Scientist); Scientist); Number Number complete) complete) Check Check I I the the table table to to Citizenship Citizenship Supervision=S, Supervision=S, Logic=LO, Logic=LO, Science=CS, Science=CS, assigned. assigned. I I Experience Experience II II @ @ sure sure same same the be be Probability=PR, Probability=PR, ® ® (Research (Research increase increase for for (be (be separate separate CD CD will will interviews: interviews: abbreviations abbreviations to to Computer Computer and and for for Interviewers Interviewers RESC RESC State State Possible Possible Impossible Impossible ( ( ) codes codes STRJP STRJP order order ) ) ) ) KENTUCKY KENTUCKY 9:30-11:45 9:30-11:45 2. 2. I,CD,I I,CD,I Dept. Dept. 4. 4. STRIP; STRIP; in in Administration=A, Administration=A, Mathematics=HM, Mathematics=HM, Research=OR, Research=OR, interviewing interviewing schedule schedule I I so, so, available available AM, AM, of of be be Engineer), Engineer), do do employer employer Control=CN, Control=CN, I I to to Session3 Session3 Fri. Fri. will will SUMMARY SUMMARY two two I I Periods Periods History History SUMMARY SUMMARY computer computer able able Operations Operations Duties Duties (Project (Project The The I I and and the the Consulting=C, Consulting=C, Positions Positions LOUISVILLE, LOUISVILLE, I I ®Renewal ®Renewal of of Experience Experience and and CD CD PREN PREN separate separate are are they interviewers interviewers I I a a required required submitted. submitted. all all Q) Q) Theory=NT, Theory=NT, I I are are FORM FORM Geometry=GE, Geometry=GE, when when as as (If (If Communication=CM, Communication=CM, Number Number Research=R, Research=R, _ _ I I receive receive Analyst), Analyst), the the City City FL. FL. forms forms in in restriction=NR; restriction=NR; I I yrs. yrs. @ @ @ @ Number Number then then exactly exactly __ __ No No two two Interviewers Interviewers 1:15-5:00 1:15-5:00 I I scheduled. scheduled. items items interviewer interviewer @ @ would would be be I I (Operations (Operations 2 2 ( ) Graduates=G, Graduates=G, one one Mechanics= Mechanics= PM, PM, Register Register Duties Duties I I may may the the positions, positions, than than Combinatorics=CB, Combinatorics=CB, Fluid Fluid Analysis=NA, Analysis=NA, OPAN OPAN I I at at of of resident=CP, resident=CP, Q) Q) REGISTER REGISTER Session Session Thurs. Thurs. interviewer interviewer corresponding corresponding I I more more sets sets Staff), Staff), Appointment Appointment interviews interviews display display I I each each of of Numerical Numerical on on permanent permanent I I provide provide identify identify disjoint disjoint Undergraduates=U, Undergraduates=U, or or to to Biostatistics=BS, Biostatistics=BS, Mathematics=Fl, Mathematics=Fl, Term Term two two Technical Technical 1,1 1,1 placed placed letters letters therefore, therefore, HI, HI, are are be be simultaneous simultaneous I I Citizen Citizen @ @ EMPLOYMENT EMPLOYMENT ouly. ouly. Science=MS, Science=MS, will will I I there there Teaching=T, Teaching=T, Financial Financial (Member (Member encouraged encouraged U.S. U.S. Circled Circled whom whom if if assigned; assigned; Sought Sought I I are are itself itself (f) (f) request request for for be be 9:30-11:45 9:30-11:45 MTS MTS Interviewers Interviewers Accepted Accepted I I Thus, Thus, below. below. Q) Q) 1. 1. will will 3. 3. sought sought Biomathematics= Biomathematics= 1 1 ( ) Management Management I I AM, AM, Citizen~ Citizen~ SCIENCES SCIENCES FORM FORM Open, Open, form form Analysis=FA, Analysis=FA, announ~ement.) announ~ement.) Employers Employers Degree Degree Specialties Specialties I I employers employers The The U.S. U.S. number number intetviewers intetviewers positions. positions. of of Dean, Dean, I I Thurs. Thurs. of of Session Session Doctor=D; Doctor=D; all all @ @ ® ® @ @ code code meeting meeting I I baSIS baSIS Specialities Specialities sessions. sessions. Salary Salary for for Physics=MP, Physics=MP, completing completing Functional Functional Analysis=AN, Analysis=AN, suggested. suggested. the the I I number number ® ® on on are are before before Zip Zip the the I I Master=M, Master=M, employer employer Register Register Louisville Louisville interview interview oflnterviewer(s) oflnterviewer(s) Prof, Prof, Asso Prof, required=N; required=N; I I the the one one MATHEMATICAL MATHEMATICAL Form Form not not the the session session State, State, capitals capitals Mathematical Mathematical at at Algebra=AL, Algebra=AL, ---yr:-- I I Prof, Prof, carefully carefully Education=ED, Education=ED, I I the the Institution Institution Name Name ouly ouly will will this this ® ® I I on on City, City, in in Block Block Bachelor=B, Bachelor=B, Asst Asst read read and and experience experience Institution Institution mo. mo. following following I I Interviews Interviews ink. ink. no no distribution distribution Lect, Lect, I I for for Please Please ffidicate ffidicate hrs./wk hrs./wk oflntervlewers oflntervlewers for for FORM FORM Modeling=MO, Modeling=MO, @@ @@ interviewers interviewers Mathematical Mathematical scheduled scheduled to to ofPosition(s) ofPosition(s) black black Preferred Preferred Inst, Inst, submitted submitted CODE CODE I I Register Register in in are are be be Impassible=!; Impassible=!; care care some some I I TO; TO; @ @ if if type type Date Date Degree Degree Teaching Teaching Title(s) Title(s) Available Available Number Number take take I I summaries summaries or or should should Processing=DP, Processing=DP, ® ® of of I I Interviews Interviews @ @ ©Starting ©Starting @ @ @ @ © © • • Employment Employment required required Please Please print print Data Data Economics=EC, Economics=EC, NOTES: NOTES: Possible=P, Possible=P, form form list list EMPLOYER EMPLOYER INSTRUCTIONS: INSTRUCTIONS: Mechanics=ME, Mechanics=ME, Topology= Topology= EMPLOYER EMPLOYER @ @ D,D,CDDJCDCDCD,CDCDCDITJCD,D,D,IIIII,IIIII,II D,D,CDDJCDCDCD,CDCDCDITJCD,D,D,IIIII,IIIII,II I I Preregistration/Housing Form, Louisville, Kentucky January 17-20, 1990 Please complete this form and return it with your payment to Mathematics Meetings Housing Bureau P.O. Box 6887, Providence, Rhode Island 02940- Telephone: (401) 272-9500, Ext. 290-Telex: 797192 DEADLINES: Room Lottery Qualification October 31, 1989 Preregistration/Employment Register /Hotel Reservations November 17, 1989 Final Preregistration ONLY December 18, 1989 Housing Changes/Cancellations December 15, 1989 50% Refund on Preregistration/Employment Register /Banquets January 3, 1990 (no refunds after this date) REGISTRATION FEES Preregistration by At Meeting December 18, 1989 JOINT MATHEMATICS MEETINGS $ $ Member of AMS, CMS, MAA 68 88 Nonmember 105 136 * Student, Unemployed, or Emeritus 21 27 AMS SHORT COURSE Member/Nonmember 40 50 * Student or Unemployed 15 20 EMPLOYMENT REGISTER -Employer fee (1st Interviewer) 75 100 -Employer fee (2nd / 3rd Interviewer) 35 50 - Applicant fee 15 20 - Posting fee for job descriptions for noninterviewing employers 10 15 (N.B.: A separate form appears in this issue for preregistration for MAA Minicourses) * All full-time students currently working toward a degree or diploma qualify for the student registration fees, regardless of income. The unemployed status refers to any person currently unemployed, actively seeking employment, and who is not a student; it is not intended to include persons who have voluntarily resigned from their latest position. The emeritus status refers to any person who has been a member of the AMS or MAA for twenty years or more and is retired on account of age or on account of long term disability from his or her latest position. PREREGISTRATION SECTION: Please check the function(s) for which you are preregistering: Joint Meetings D AMS Short Course (January 1&-17, 1990) D Employer D Co-Interviewer D Applicant D Posting D 1) ~~----~~~------~~------~~~------Telephone: ------(Please print) Surname First Middle 2) (Mailing address for acknowledgement, badge, and program) I do not wish my badge and program to be mailed D 3) Badge information: a) Nickname (optional): ______b) Affiliation------c) City&State ------4) I am a student at 5) Emeritus member D Unemployed D MR Classification # ------MR Reviewer D 6) Accompanied by spouse------Number of children ------(Enumerate only if accompanying to meeting) (name) 7) Member of AMS D CMS D MAA D Nonmember D Member of other organizations: AWM D NAM D 8) Joint Meetings fee $ 9) AMS Short Course fee $ 10) Employer fee(s) $ 11) Co-Interviewer fee(s) $ ______12) Applicant fee$ 13) Posting fee$ 14) Hotel deposit $ (necessary ONLY if paying deposit by check) 15) AMS 25-Year Banquet ticket(s)@ $20 each=$ 16) NAM Banquet ticket(s)@ $20 each=$ ______17) TOTAL AMOUNT ENCLOSED FOR 8 through 16 $ NOTE: May be paid by check payable to AMS (Canadian checks must be marked "U.S. Funds") or VISA or MasterCard credit cards. Credit card type: ; Card number: ; Expiration date: ------If this is your credit card, please print your name as it appears on the credit card on the line below as well as sign your name. If this is not your credit card, please print card holder's name as it appears on the credit card on the line below, and have the card holder sign: (Printed name) (Signature) Please complete the appropriate sections on the reverse. For office use only: Codes: Options: Hotel: Room type: Dates: Hotel Deposit Total Amt. Paid: Special Remarks: you 1990 room made for be a.m./p.m. 17-20, available, will accepted January longer I I be no is will assignment cards 225 400 200 the Suites requested 195-325 20(}-300 credit $ rate hotels, DATE at other the If wfcot No BELOW. 95 85 ranked N/A N/A N/A rate. beds the 2 and DEPARTURE at DATES reservation. 70 85 68 64 58 type beds housing only). Quad Quad filled 2 $ $ room (for room of been Kentucky wfcot 85 80 Express have N/A N/A N/A Triple requested beds tax. 2 (date) the confirmation Louisville, rooms on for American 75 64 65 all beds ARRIVAL/DEPARTURE or circling Triple handicapped. 2 $ $ FORM, BELOW depart by and address the and GIVE sales/occupancy and 58 63 63 for 60 beds DATE LISTED 2 Double mailing 9.2% ranked, MasterCard, form, to on NOT with are equipped a.m./p.m., PLEASE 58 65 65 63 53 53 53 60 bed VISA, 1 ARRIVAL left Double also subject the hotels with are together are at all 59 58 55 60 49 $ $ $ Single and NEEDED, below not spaces HOTEL/MOTEL guarantee If ROOM PREREGISTRATION/HOUSING NOT A the REVERSE, A listed Hotel) in IS card rate. AT availability, THE children. etc. Rates of 3, credit ON space Suites) a 2, REQUIRE available at on rate. 1, ages STAYING (All OR HOUSING (Headquarters next NOT BE IF based East the writing check available NAME at by WILL WILL by Regency indicating House House rooms, Brown INFORMATION EVEN $50 next hotel YOU YOU FULL Galt Hyatt The Galt Seelbach L_ THIS IF IF the preference of of another nonsmoking occupants; with at HERE HERE ___ Order choice SUPPLY order ... have L room in hotel room a requests: REQUIREMENTS: (date) CHECK CHECK hotels SECTION: hotels PLEASE other on list housing assigned rank unranked arrive PLEASE PLEASE following be an will HOUSING Please at The GUARANTEE guarantees. will 0 0 Special I Please MathDocsM Your Best Access to Inaccessible Items in the Mathematical Literature What is MathDoc? How to Use MathDoc MathDoc is the document delivery service offered This labor-intensive service is a very low-cost by the AMS, designed for users of CMP, MR, and method of locating documents. The AMS makes MathSci who wish to obtain copies of original MathDoc available essentially at cost as a service to articles. the mathematical community. MathDoc is particularly useful for obtaining "inacces The current price for each item is sible" items that cannot easily be obtained through $12 for the first ten pages interlibrary loan. For example, you might want one $2 for each succeeding ten pages or less of these: copyright royalties * (if applicable) Acta Sci. Natur. Univ. Sunyatseni (1986), No. 1, plus postage. pages 90-93 Many Chinese journals are available only in a An invoice is sent with the requested item. There is a very small number of U.S. libraries. 5% discount for VISA and MasterCard prepayments. Documents are mailed first class within North Amer Methods and Algorithms in Numerical Analysis (1984), ica and airmail elsewhere. Moskov. Gos. Univ., pages 154-162 ------Russian collections are often printed in limited *MathDoc complies with copyright laws and adds copyright quantities and MathDoc may be the only U.S. royalties, when applicable. MathDoc is affiliated with the source. Copyright Clearance Center (CCC), Salem, MA. Surikaisekikenkyusho Kokyuroku (1986), No. 581, SM MathDoc is a service mark of the American pages 85-100 Mathematical Society This Japanese journal is available only through a limited number of sources in the U.S. Ordering Information 600,000+ Item Access For further information or to place an order through MathDoc, write to MathDoc has access to over 600,000 items at present MathDoc Document Delivery in mathematics and related subjects, including 70,000 Mathematical Reviews articles from Soviet journals. 416 Fourth Street P. 0. Box 8604 95% Success Rate in Two Ann Arbor, MI 48107-8604 USA W()rking Days _ OR telephone (313) 996-5268 and ask for MathDoc. And MathDoc has over a 95% success rate in quickly 0 R send your order via FAX (313) 996-2916 locating and supplying the articles in journals, collec OR send electronic mail (Internet) to tions, and conference proceedings listed in CMP, MR, [email protected] and MathSci...usually within two working days. All electronic mail will be acknowledged. Although MathDoc cannot ordinarily supply an entire OR order through the DIALOG DIALORDER or book, it often can give you information about the the BRS systems. book's availability through other sources. Available from JPBM: MA1'HEMA 1'XCAL lPOS1'EJRS AND JP>OS'fCARDS On the occasion of Mathematics Awareness Week, the Joint Policy Board for Mathematics commissioned the printing of the posters and postcards that were designed to acquaint the public with this year's theme, "Mathematics: Discovering Patterns". Copies are still available of these well-designed objects: A. Five-color poster, size 16x20 inches, suitable for framing and ideal as a gift. The poster shows a photograph of silicon bronze sculpture by Helaman Ferguson, Umbilic Torus. $5 B. Black and white poster with the Mathematics Awareness Week theme, from Tilings and Patterns, by Branko Griinbaum and G. C. Shephard. $3 C. Set of 20 color postcards, 10 each of two different bronze works by Helaman Ferguson, Torus with Cross Cap, and Alexander's Horned Wild Sphere, Five Bifurcations. $10 D. Set of 20 color postcards, 5 each of four different fractal images. Limited supply from the 1988 Mathematics Awareness Week. $10 Proceeds will be used to start a fund to underwrite the JPBM Communications Award, given the first time in 1988 to James Gleick for his bestseller CHAOS. Your purchase of these postcards and the poster will help promote a better public understanding of mathematics. Please specify your order, indicating the quantity desired, by using the appropriate letter for that item. Send a check, payable to American Mathematical Society, to: JPBM Visuals 818 Connecticut Ave., NW Suite 515 Washington, DC 20006 "The importance of the program cannot be overlooked .. "Mathematica has quickly become a valuable tool in my daily "Mathematica has a real chance of replacing pencil and paper it so fundamentally alters the mechanics of mathematics." work." as the standard desktop environment for scientists and engineers New York Times William Thurston William Press Professor of Mathematics, Professor of Astrophysics. Princeton University Harvard University Mathematic a. Macintosh User Interface: Notebook interac A System for tive documents mixing text, graphics, anima tions, Mathematica input, output. Macintosh Doing Mathematics front end can be used with kernels on other computers. Macintosh graphics standards by Computer used. Documentation: "Mathematica: A System for Some facts: Doing Mathematics by Computer" by Stephen Function: Numerical, symbolic, graphical com Wolfram (Addison-Wesley, 1988) available at putation, interactive programming. Integrated bookstores. Additional documentation sup technical computing environment. plied with specific versions. Mathematica Jour nal to be published in 1990. Numerical Computation: Arbitrary precision arithmetic, complex numbers, special functions Versions Now Available: Apple Macintosh: (hypergeometric, elliptic, etc.), combinatorial $495 (Plus, SE, etc.); $795 (II, IIx, IIcx, SE/30, and integer functions. Matrix operations, root etc.) • 386-based MS-DOS systems: $695 (no finding, function fitting, Fourier transforms, nu coprocessor); $995 (287 /387); $1295 (Weitek) • merical integration, minimization, linear pro Apollo DN 3000, 4000: $2400 • DEC VAX VMS, gramming. ULTRIX, DECstation: from $2400 • Hewlett Packard 9000/300, 800: from $2400 • IBM AIX/ RT: $2400 • MIPS: from $2800 • NeXT: bundled as standard system software • Silicon Graphics IRIS-4D: from $2800 • Sony NEWS: from $2400 • Sun 3, 4, 386i: from $2250 • Supercomputer and other versions also available. • Educa tional, volume, reseller, and other discounts available • Now shipping Version 1.2. Symbolic Computation: Equation solving, symbolic integration, differentiation, power se ries, limits. Algebraic operations, polynomial expansion, factorization, simplification. Opera tions on matrices, tensors, lists. Graphics: 2D, 3D plots of functions, data, geo metrical objects. Contour, density plots. 3D rendering with intersecting surfaces, lighting models, symbolic descriptions. Color PosT ScRIPT output, publication quality graphics, ani mation (most versions). Implementation: 770 pre-defined Mathematica functions (C source 180,000 lines). Design, de velopment led by Stephen Wolfram. Version 1.0 released June 1988. Typical Applications: Research, engineering, education, mathematical modeling, publication graphics, data analysis, visualization, systems analysis, algorithm development. Awards: Best 10 New Products, Business Week 1988 • Editor's Choice Award, Mac User 1989 • Award of Distinction, BYTE 1988. Programming: High-level, interactive, sym bolic system. Full procedural language, func tional programming constructs. General trans Wolfram Research, Inc. formation rule paradigm based on pattern P.O. Box 6059, Champaign. IL 61826-6059, USA. matching. Information: 217-398-0700. Orders: 800-441-MATH. Or visit your local software dealer. External Interface: Input from external files, programs. Output in TeX, C, FORTRAN, PosT © 1989 Wolfram Research, Inc. Mathematica is a registered trademark of Wolfram Research, Inc. All other trademarks are trademarks of their respective companies. ScRIPT. Interactive external process control Prices and specifications are subject to change without notice. Graphic is a part of a (most versions). Graphics and Visualization tubular neighborhood of a six-strand braid generated by Mathematica. Excellent Titles for Mathematicians • From Springer-Verlag • A Classic- Mathematical Problems from Combustion Theory Introduction to Calculus and J. Bebernes, University of Colorado, Boulder, CO, and Analysis D. Eberly, University of Texas, San Antonio, TX Volume I Systematically develops models of a spatially-varying transient R. Courant and F. John, Courant Institute of process describing thermal events. Such events should be entirely Mathematical Sciences, New York University, NY predictable for a given set of physical properties, system geometry, and initial-boundary conditions. Primary emphasis is placed on Primarily concerned with functions of a single variable, explosive thermal events; the authors refer to three aspects of such this volume's purpose is to exhibit the interaction between events as Blowup- When, Where, and How. mathematical analysis and its various applications, and to • Features a unified development of mathematical models, emphasize the role of intuition. It does not pretend to make mathematical analysis of various models and blowup the subject easy by glossing over difficulties, but rather phenomena for the ignition models. tries to help the genuinely interested reader by throwing Contents: Introduction. Steady-State Models. The Rigid Ignition light on the interconnections and purposes of the whole. Model. The Complete Model for Solid Fuel. Gaseous Ignition Instead of obstructing access to the wealth of facts by Models. Conservation Systems for Reactive Gases. References. lengthy discussions of a fundamental nature, appendices Index. are provided. In addition, numerous examples and 1989/177 pp., 14 illus./Hardcover $34.00 problems are given at the end of the various chapters. ISBN 0-387-97104-1 Introduction to Calculus and Analysis is addressed to Applied Mathematical Sciences, students on various levels, and to mathematicians, Volume 83 scientists, and engineers. 1989/661 pp., 204 illus./Hardcover $45.00 Analysis I ISBN 0-387-97151-3 Integral Representations and Asymptotic Methods (originally published as a Wiley-lnterscience M.A. Evgrafov, Publication, a division ofJohn Wiley & Sons, Inc., Institute for Oceanology of the Academy inl974) of Sciences of the U.S.S.R., Moscow, U.S.S.R.; and M. V. Fedoryuk, Moscow Institute of Physics and Introduction to Calculus and Technology, Moscow, U.S.S.R. Analysis Translated from the Russian by D. Newton Presents the major achievements of mathematical analysis from Volume II Newton and Euler to modem applications of mathematics in the R. Courant and F. John, Courant Institute of physical sciences, engineering and other areas. Its three parts cover Mathematical Sciences, New York University, NY the methods of analysis: representation methods, asymptotic With the assistance ofA.A. Blank and A. Solomon methods and transform methods. The authors have not simply This second volume discusses the more ramified theories presented a compendium of techniques but have stressed of calculus for functions of several variables. As in volume throughout the underlying unity of the various methods. The one, it demonstrates that meaningful mathematics is fundamental ideas are clearly presented and illustrated with created from a union of intuitive imagination and interesting and non-trivial examples. deductive reasoning. References, together with guides to the literature, are provided for The exercises have been incorporated into the text and those readers who wish to explore further. their solutions can be found at the end of the volume. The 1989/238 pp., 3 illus./Hardcover $59.50 ISBN 0-387-17008-1 intended audience consists of students on various levels, as well as mathematicians, scientists and engineers. Encyclopaedia of Mathematical Sciences, Volume 13 Contents: Functions of Several Variables and Their Derivatives. Vectors, Matrices, Linear Transformations. A Course in Modern Geometries Developments and Applications of the Differential J. Cederberg, St. Olaf College, Northfield, Calculus. Multiple Integrals. Relations Between Surface MN and Volume Integrals. Differential Equations. Calculus of The major emphasis of this text is on the geometries developed Variations. Functions of a Complex Variable. List of after Euclid's Elements (circa 300 B.C.). In addition to the primary Biographical Dates. Index. goal of studying these "newer" geometries, this study provides an 1989/954 pp., 120 illus.!Hardcover $59.00 excellent opportunity to explore aspects of the history of mathe ISBN 0-387-97152-1 matics. Also, since algebraic techniques are frequently used, this (originally published by lnterscience Publishers, a study demonstrates the interaction of several areas of mathematics division of John Wiley & Sons, Inc., in 1965) and serves to develop geometrical insights into mathematical results which previously appeared to be completely abstract in nature. A course based on this text provides excellent preparation for the Order Today! standard undergraduate course in abstract algebra. Call Toll-Free: 1-800-SPRINGER. In NJ, call (20 I )348-4033. Contents: Axiomatic Systems and Finite Geometries. Non Or send FAX: (201)348-4505. Euclidean Geometry. Geometric Transformations of the Euclidean For mail orders, send payment plus $2.50 for postage to: Plane. Projective Geometry. Appendices. Bibliography. Index. Springer-Verlag New York, Inc., Attn: S. Klamkin- Dept. S362, 1989/ 232 pp., 133 illus./ Hardcover $42.00 175 Fifth Avenue, New York, NY 10010. We accept Visa, ISBN 0-387-96922-5 MasterCard and American Express charges (please include exp. Undergraduate Texts in Mathematics date and signature), as well as personal checks and money orders. NY, NJ and CA residents please add state sales tax. Or visit your local technical bookstore! Springer-Verlag New York Berlin Heidelberg Vienna London Paris Tokyo Hong Kong