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Volume 29, Number 2, February 1982

EDITORIAL COMMITTEE Ralph P. Boas, Ed Dubinsky Richard ]. Griego, Susan Montgomery Mary Ellen Rudin, Bertram Walsh Everett Pitcher {Chairman) MANAGING EDITOR Lincoln K. Durst 130 The van der Waerden Conjecture: ASSOCIATE EDITORS Two Soviet Solutions, j. C. Lagarias Hans Samelson, Queries Ronald L. Graham, Special Articles 134 1982 Cole Prizes in Number Theory SUBSCRIPTION ORDERS 136 AMS Nomination Procedure is Vulnerable to Subscription for Vol. 29 (1982): "Truncation of Preferences," Steven j. Brams $36 list, $18 member. The subscription 139 1980 CBMS Survey, Major Findings price for members is included in the annual dues. Subscriptions and orders 144 25th AMS Survey (Second Report), for AMS publications should be Employment of New Doctorates, Faculty addressed to the American Mathematical Mobility, Enrollments, Class Size Society, P. 0. Box 1571, Annex Station, Providence, Rl 02901. All orders must 150 Queries be prepaid. 151 Letters to the Editor ORDERS FOR AMS BOOKS AND 152 International Congress, Warsaw INQUIRIES ABOUT SALES, SUBSCRIP· 164 Report to Members TIONS, AND DUES may be made by calling Carol-Ann Blackwood at 166 1982 AMS Elections (Nominations by Petition) 800-556-7774 (toll free in U.S.) between 168 News and Announcements 8:00a.m. and 4:15p.m. eastern time, Monday through Friday. See page 17. 170 New AMS Publications 175 Future Meetings of the Society CHANGE OF ADDRESS. To avoid interruption in service please send Bryn Mawr, March 76, 175; Madison, April 76, address changes four to six weeks in 190; Bellingham, june 78, 193; AMS Summer advance. It is essential to include the Research Institute, 194; AMS-SIAM Summer member code which appears on the Seminar, 194; Topics: 1984 Symposium, 195; address label with all correspondence Invited Speakers, 195; Special Sessions, 195 regarding subscriptions. 196 Special Meetings INFORMATION ABOUT ADVERTISING in the Notices may be obtained from 202 Miscellaneous Virginia Biber at 401-272-9500. Personal Items, 202; Deaths, 202; CORRESPONDENCE, including changes Backlog, 202; Assistantships and Fellowships of address should be sent to American (Supplement), 204 Mathematical Society, P.O. Box 6248, 210 AMS Reports & Communications Providence, Rl 02940. Recent Appointments, 210; Reports of Meetings: Second class postage paid at Amherst, 210, Austin, 211, Santa Barbara, 212, Providence, Rl, and additional mailing 213, offices. Copyright © 1982 by the Cincinnati, 212; Election Results of 1981, American Mathematical Society. Council for 1982, 213 Printed in the United States of America. 215 Advertisements The van der Waerden Conjecture: Two Soviet Solutions by J. C. Lagarias

The problem section of the Jahresbericht der conjecture since by Stirling's formula n!/nn is Deutschen Mathematiker-Vereinigung publishes approximately v'2rn e-n. H. Mine gave a detailed both solved and unsolved problems. Several of history of work on the van der Waerden conjecture the unsolved problems have led to an extensive (14]. literature. Among these are a problem of A. At first glance it appears reasonable to suppose Scholz 1 on the minimum chain of multiplications that the van der Waerden conjecture is true, based needed, to c~culate xn, starting with x [4, 16], on the truth of the conjecture for small values Kneser s conJecture (9] (recently proved by Lovasz of n and the simple heuristic that the minimum (12]) and the van der Waerden conjecture (19]. of a symmetric function would itself likely be B. L. van der Waerden stated his problem in symmetric. The answer to a problem proposed by 1926, as follows. If A is an n X n matrix with H. S. Shapiro (17] in 1954 casts some doubt on this entries Uij (i = 1, ... , n; j = 1, ... , n) then the heuristic. Shapiro's problem is that of minimizing permanent of A, denoted per( A), is defined by the function ( ) X1 X2 per(A) = I: al,.,.(l)a2,.,.(2)" • ·an,.,.(n)> gnXl, •.. ,Xn = ---+---+··· C7ESn X2 + X3 X3 + X4 + Xn-1 +~ where Sn denotes the symmetric group on n Xn + X1 X1 + X2 symbols. Such a matrix A is said to be doubly stochastic if all its entries are nonnegative real subject to the constraints that all Xi ~ 0, numbers and all its row and column sums are 1. Xi + X;+ 1 > 0 (to avoid zero denominators). The van der Waerden conjecture asserts that for This function is invariant under the transitive any doubly stochastic matrix A, permutation group generated by the n-cycle (12 3 · · ·n). The symmetric solution (1) per(A) ~ n!/nn. X1 = X2 = ··· = Xn The doubly stochastic matrix Jn having all entries equal to 1/n has per(Jn) = n!/nn, showing (1) gives gn(Xb ..• , Xn) the value n/2, and this is the cannot be improved. A strong version of the minimum of gn for all n < 10. However for all ~onjecture asserts that equality holds in (1) only n ~ 14 the minimum is Strictly less than n/2, If A=Jn. i.e. symmetry is broken. (For a survey of these The van der Waerden conjecture attained the results, see Mitrinovic (15, pp. 132 fi].) status of a notorious unsolved problem as a The van der Waerden conjecture has been inde­ consequence of many unsuccessful attempts to pendently settled by two Soviet mathematicians, prove it. The first published results on the D. I. Falikman, at the Scientific Research Institute problem appeared in the 1959 paper of Marcus for Automated Systems of Planning and Manage­ and Newman (13]. They showed Jn was a local ment in Construction in the Ukrainian SSR and minimum of the permanent function in the set of G. P. Egorychev, at the L. V. Kirensky Institute all doubly-stochastic matrices, derived properties of Physics, Siberian Branch of the Academy of of doubly-stochastic matrices that minimize the Sciences of the USSR in Krasnoyarsk. Falikman permanent, and proved the conjecture for n = 3. apparently found his proof first, since he sub­ This was the beginning of a flood of papers by mitted his paper (6] to Mat. Zametki in May many authors, who proved the conjecture for n = 4, n = 5, and for many special subclasses of J. C. LAGARIAS received his Ph.D. in 1974 from doubly-stochastic matrices. In another direction the Massachusetts Institute of Technology; he was T. Bang (2] and, independently, S. Friedland (8] a student of Harold M. Stark. Since that time recently showed that he has been at Bell Laboratories where he is a Member of Technical Staff in the Mathematical (2) per(A) ~ e-n Studies Department. In 1978-1979 he was a visiting assistant professor at the University of Maryland. A. result for all doubly-stochastic matrices This His research interests include number theory, is not much weaker than the van der Waerden theoretical computer science, discrete mathematics 1Scholz' problem actually was first proposed in the and optimization problems. 19th century.

130 1979, while Egorychev distributed a preprint of stochastic matrices A with all aii > 0, while the his paper [5] in late 1980. Falikman proves the van boundary bd(On) consists of all doubly-stochastic der Waerden conjecture, while Egorychev obtains matrices A with some aii = 0. Marcus and in addition the stronger result that Jn is the Newman first proved there were restrictions on unique permanent-minimizing doubly stochastic the pattern of zeroes of any matrix A in bd(On) matrix. Although the two proofs differ in detail, that is a global minimum of the permanent, e.g. they both use the same new idea, which is stated that A is indecomposable. 2 Next they examined as the Main Lemma below. the necessary conditions for a minimum using Egorychev's proof was the first to become Lagrange multipliers, and for indecomposable known in the West. In late 1980 he sent pre­ matrices A they derived the conditions: prints to a number of Western mathematicians, including J. H. van Lint at Eindhoven University (3) aij ;F. 0 ::::} per A[ilj] = per A. of Technology, Ira Gessel and Richard Stanley at Next they introduced an "averaging" operation. 3 M.I.T., and later to Donald Knuth at Stanford. Write A = [at, ... , an] where ai denotes the ith At M.I.T., Ira Gessel, who reads Russian, realized row of A. Suppose A is permanent-minimizing that Egorychev's preprint announced a proof of and that all aii > 0. Then one has van der Waerden's conjecture. He prepared a translation in order that the proof could be (4) per [!(at+ a2), !(at + a2), a3, ... , an] verified by other mathematicians. At the same n time rumors rapidly spread to other universities = i L(ali + a2i)(per A[lli] +per A[2li]) that the van der Waerden conjecture had been i=l solved. Unlike most such rumors, these turned out = per(A), to be true. Egorychev's proof was self-contained and elementary, except at one point (the key using (3) and the row-stochasticity property. point!) and was easily verified. That one point Hence A{l) = [!(a1 + a2), !(at+ a2), a3, ... , an], was a reference to the Alexandrov inequalities for a matrix derived from A by averaging the mixed discriminants of quadratic forms, which was first two rows, is also a permanent-minimizing used to prove a permanent inequality called the matrix with all aii > 0. By repeating this Main Lemma below. The Main Lemma is in fact a argument, averaging over different rows, one ob­ special case of the Alexandrov inequalities, as can tains a sequence A{1),A(2),A(3), ... of permanent­ be seen after observing that the permanent of a minimizing matrices with A(n) -+ Jn. By con­ matrix A is the mixed discriminant of a certain set tinuity one concludes that of diagonal quadratic forms. Alexandrov [1, IV] proved his inequalities for mixed discriminants in per A;::=: perJn. 1938, in the process of giving his second proof of Marcus and Newman went on to prove that Jn was the better-known Alexandrov-Fenchel inequalities a strict local minimum of the permanent, and that for mixed volumes of convex bodies. His proof is if A ;F. Jn then one can arrange that all Ak ;F. Jn. not easily accessible in English. (For a statement This contradicts the local minimality of per(Jn) of the Alexandrov inequalities and a sketch of and proves that Jn is the unique permanent­ Alexandrov's proof see Busemann [3, pp. 51 fl].) minimizing matrix not on the boundary bd(On)· After reading Egorychev's preprint, J. H. van Lint Marcus and Newman could not apply their and D. Knuth both derived short direct proofs bd(On) of the Main Lemma by simplifying Alexandrov's averaging argument to matrices on because proof. They described these in detailed accounts they could not prove (4) in this case. The of Egorychev's proof [10, 20]. In July 1981 necessary conditions for a local minimum of per( A) Falikman's paper appeared in the latest issue of give some more information beyond (3), which Mat. Zametki. It came as a surprise to most Soviet however is not sufficient to directly prove (4). mathematicians as well as to those in the West. London [11] showed that these conditions imply Falikman's paper is short (7 pages) and completely that self-contained. He directly proves a special case of (5) aij = 0 ::::} per A[ilj] ;::=: per A the Main Lemma sufficient to obtain his result. We now describe the main ideas in Egorychev's provided A is a fully indecomposable matrix. and Falikman's proofs. Both proofs owe something Egorychev uses London's result in his proof. to the 1959 paper of Marcus and Newman. To The key result that Egorychev supplied is the describe their results, we introduce some notation. following. Let A[iiJ"] denote the (n -1) X (n- 1) matrix obtained by deleting row i and column J. from 2 An n X n matrix M is decomposable if there exist permutation matrices P and Q such that the matrix P MQ the n X n matrix A. The set of all doubly­ has an r X s block of zeroes in its upper right comer with stochastic matrices On is a compact, convex subset r + s ~ n. Otherwise it is indecomposable. of the (n -1)2-dimensional vector space V of all 3 The averaging argument described below differs in n X n matrices with all row and column sums detail from that used in the Marcus and Newman paper; 1. The interior int(On) is the set of all doubly the idea is the same.

131 MAIN LEMMA. Let a2, as, ... , an be 1 X n row where x, y are constants depending on E, and y vectors with nonnegative entries. Then is nonnegative. He then proves the Main Lemma per (a1, ... , an) = 0. He (6) per(a1, a1, as, ... , an) per(a2, a2, as, ... , an) in the special case that uses the Main Lemma to prove that Jn is the ~ [per(a1,a2, ... ,an)]2 • only solution to (9) as follows. Suppose (9) holds If a2, as, ... , an have only positive components, with a1 ::;6- a2. Let t = a 1 - a2, and define then equality holds in (6) if and only if a1 = >-a2 s = (s1, ... , sn) by Si = a1,ia2,i· Then the Main for some real A. Lemma gives There is another way to state the Main per(t,t,as, ... ,an)per(s,s,as, ... ,an) Lemma which may be enlightening. Observe ::; [per(t,s,as, ... ,ant· that if as, ... , an are held fixed we can regard per(x, y, as, ... , an) as a symmetric bilinear form However the conditions (9) imply after a calcula­ in the variables x and y. The Main Lemma tion that is equivalent to the assertion that whenever as, ... , an have positive entries this bilinear form per(t, s, a3, ... , an) = 0, is not degenerate and has exactly one positive n (a1,i- a2,i)2 eigenvalue, i.e. it has signature (1, n -1) [20]. per(t, t, as, ... , an) = y L ~ 0, i=l a1,ia2,i Using the Main Lemma, Egorychev shows that any doubly-stochastic matrix A that satisfies while per A[ilj] ~ per A, 1 ~ i,j ~ n, per(s, s, as, ... , an) > 0, must have since all entries in this matrix are positive. The case of equality in the Main Lemma now forces (7) per A[ilj] = per A, 1 ~ i, j ~ n. t = 0, i.e. a1 = a 2, a contradiction. This result allows one to replace (3) and (5) by What are the consequences of these two Soviet (7), and then the "averaging" argument can be proofs? The van der Waerden conjecture is legitimately applied even on the boundary bd(On)· a challenging problem, but its solution does not Egorychev uses this to show that the existence of revolutionize our state of mathematical knowledge a permanent-minimizing matrix on bd(On) implies the way a proof of the Riemann hypothesis would. that there also exists a permanent-minimizing The van der Waerden conjecture does imply ::;6- a contradiction matrix A in int(On) with A Jn, better lower bounds on the number of nonisomor­ that proves that Jn is the unique minimum of the phic Latin squares and Steiner triple systems permanent function on On. than those previously known [14, p. 135]. In Falikman's proof studies the function the long run, what may turn out to be most 1 significant is that the Alexandrov inequalities for (8) f(A) = per(A)+ E( II aij) - mixed discriminants of quadratic forms and the 1-<::;,i,j-<::;,n related Alexandrov-Fenchel inequalities [1, 9] for where E > 0, on the set int(On)· The addition mixed volumes of convex bodies imply a variety of the term E(Ili,j aij)-1 to per(A) is suggested of multilinear inequalities with interesting com­ by the difficulties in Marcus and Newman's proof. binatorial interpretations. Two such applications This term blows up as A -+ bd(On) and attains have recently been given by R. Stanley [18]. its minimum at Jn. The advantage of adding this term is that the local minima of f(A) are in REFERENCES hence satisfy a full set of Lagrangian int(On) and 1. A. D. Alexandrov, Zur Theorie der gemischten Volumina conditions. Consequently one avoids dealing von konvexen Korpem, parts I-IV. (Russian, German with boundary conditions such as (5). However, summaries) in retrospect, one can see that the addition I. Verallgemeinigerong einer Begriffe der Theorie der of the extra term E(Ili,j aij)-1 provides only a konvexen Korper, Mat. Sb. (N.S.) 2 (1937), 947-972. technical simplification of the proof; the important IT. Neue Ungleichungen zwischen den gemischten Volumina ingredient is a special case of the Main Lemma. und ihre Andwendungen, Mat. Sb. (N.S.) 2 (1937), 1205- 1238. proves that for E 0 the function Falikman > ill. Die Erweiterong zweier Lehrsatze Minkowskis uber die f(A) has a unique minimum on int(fln) at A= Jn. konvexen Polyeder auf beliebige konvexe Fliichen, Mat. He lets E -+ 0 and obtains per(A) ~ n!fnn for all Sb. (N.S.) 3 (1938), 27-46. A E int(fln)· The same result then holds for all IV. Die gemischten Diskriminanten und die gemischten A E bd(fln) by continuity, thus proving (1). To Volumina, Mat. Sb. (N.S.) 3 (1938), 227-251. show Jn is the unique minimum of f(A) when 2. T. Bang, On matrixfunctioner som med et numerisk E > 0, he derives from the conditions for a local lille deficit viser v.d. Waerdens permanenthypotse, Proc. minimum of (8) that Scand. Congr. (Turkku, 1976). 3. H. Busemann, Convex surfaces, Interscience, New York, (9) per A[ilj] = x + yfaij, 1 ~ i,j ~ n, 1958.

132 4. P. Downey, B. Leong and R. Sethi, Computing 12. L. Lovasz, Kneser's conjecture, chromatic number, and sequences with addition chains, SIAM J. Comput. 10 homotopy, J. Combin. Theory Ser. A 25 (1978), 319- (1981), 638-646. 324. 5. G. P. Egorychev, The solution of van der Waerden's 13. M. Marcus and M. Newman, On the minimum of the problem for permanents, Dokl. Akad. Sci. SSSR 258 permanent of a doubly stochastic matri.:z:, Duke Math. J. (1981), 1041-1044. (Russian); Advances in Math. 42 26 (1959), 61-72. (1981), 299-305. 14. H. Mine, Permanents, Addison-Wesley, Reading, Mass., 6. D. I. Falikman, A proof of the van der Waerden conjecture 1978. on the permanent of a doubly stochastic matrit, Mat. 15. D. S. Mitrinovic, Analytic inequalities, Springer-Verlag, Zametki 29 (1981), 931-938. (Russian) New York, 1970. 7. W. Fenchel, Inegalites quadratiques entre les volumes 16. A. Scholz, Aufgabe 253, Jahresber. Deutsch. Math.­ mi:J;tes des corps conve:z:a, Comptes Rend. Acad. Sci. Verein. 47 (1937), 41-42. Paris 203 (1936), 647-650. 17. H. S. Shapiro, Problem 4603, Amer. Math. Monthly 61 8. S. Friedland, A lower bound for the permanent of a (1954), 571. doubly stochastic matrU, Ann. of Math. (2) 110 (1979), 18. R. Stanley, Two combinatorial applications of the 167-176. Ale:z:andro11-Fenchel inequalities, J. Combin. Theory Ser. 9. M. Kneser, Aufgabe 300, Jahreaber. Deutsch. Math.­ A 31 (1981), 56-65. Verein. 58 (1955). 19. B. L. van der Waerden, Aufgabe 45, Jahresber. Deutsch. 10. D. Knuth, A permanent inequality, Amer. Math. Math.-Verein. 5 (1926), 117. Monthly 88 (1981), 731-740. 20. J. H. van Lint, Notes on Egoritsjev's proof of the van der 11. D. London, Some notes on the van der Waerden Waerden conjecture, Linear Algebra Appl. 39 (1981), conjecture, Linear Algebra Appl. 4 (1971), 155-160. 1-8.

EDITORS' NOTE. The article The van der Waerden conjecture: two Soviet solutions, by J. C. Lagarias, is the first one in the new series of Special Articles in the Notices. This series was authorized last summer: its purpose is to provide a place for articles on mathematical subjects which are of interest to the general membership of the Society. The only restrictions on such articles are that they be mathematically correct, interesting, and comprehensible to anyone with a sound mathematical education. They should not be technical in the sense that the research-expository articles in the Bulletin are. In short, these Special Articles are addressed not to experts, but to the general mathematical public. Items for this series are solicited and, if accepted, will be paid for at the rate of $250 per page to a maximum of $750. They are first refereed for accuracy, and (if approved) accepted or rejected on the basis of the breadth of their appeal to the general membership of the Society. Manuscripts to be considered for this series should be sent to Dr. Ronald L. Graham, Associate Editor for Special Articles, Notices of the American Mathematical Society, Post Office Box 6248, Providence, Rhode Island 02940.

133 1982 Cole Prizes in Number Theory Awarded at Annual Meeting in Cincinnati

Two Cole Prizes in Number Theory were awarded Modular curves provide felicitous meeting in Cincinnati on January 14. The recipients were grounds for a multitude of diverse problems in Robert P. Langlands of the Institute for Advanced Arithmetic. Rather than discuss my own paper Mazur of Harvard University. Study and Barry specifically, I should like to take this opportunity Professor Langlands received his prize for pioneer­ of these problems, to enumerate Eisenstein series and to hint at some ing work on automorphic forms, to product formulas. The selection committee noted some facets of modular curves which serve that he had proved Artin's conjecture that L(s, x) throw light on them, and finally, to suggest that is holomorphic for all characters x of 2-dimensional the adjective "diverse," which I used in the pre­ representations of tetrahedral type (Base change for vious sentence, is not terribly apt: There seems to GL(2), Annals of Mathematics Studies, volume 96, be an overarching unity to this cluster of problems, Press, 1980). Princeton University so that, surprisingly often, consideration of one of Professor Mazur received his prize for outstanding these problems reveals the secrets of another. work on elliptic curves and Abelian varieties, especially on rational points of finite order. The Rational points of modular curves are essentially committee cited his paper Modular curves and in one-to-one correspondence with elliptic curves the Eisenstein ideal, Publications Mathematiques de endowed with specific structures, 1 defined over l'Institut des Hautes Etudes Scientifiques, volume 47 the field of rational numbers. This is the simplest (1977), pages 33 to 186. instance of a fundamental theory of Shimura The prizes were awarded by the Council of (the canonical models). There is, then, a novel the American Mathematical Society on the recom­ twist to the venerable diophantine problem of mendation of a selection committee consisting of 2 time J. W. S. Cassells, Wolfgang M. Schmidt (chairman), studying these points. For, firstly, every and John T. Tate. you find a rational point you get something Frank Nelson Cole served the Society for twenty­ quite interesting; secondly, you can apply the five years as Secretary and for twenty-one years as formidable techniques of the arithmetic theory Editor-in-Chief of the Bulletin. When he retired from of elliptic curves to analyze what it is you have these positions, his friends collected a sum of money gotten. Moreover, there is the classical theory in his honor, which he in turn offered to the Society. of complex multiplication at your disposal to the gift, created the "Cole The Council, on accepting (Birch-Heegner Fund" which has been used for more than fifty years produce a further bunch of points for the award of the Cole Prizes in Algebra and points) which are defined over fields of low degree, Number Theory. The names of the recipients of these and which play an important, but still mysterious, prizes will be found in the November 1981 Notices on role. And then, of course, there are the cusps pages 650 and 651. (studied by Ogg, Manin-Drinfeld, Kubert-Lang). The original fund grew both from earnings and curve factors of the jacobians of modular a gift made in 1929 Elliptic from additional gifts, including to by Charles A. Cole, Professor Cole's son, which more curves have been conjectured (Taniyama-Well) than doubled the size of the fund. In recent years the exhaust the class of all elliptic curves defined Cole Prizes have been augmented by awards from the over the rational number field. This conjecture Leroy P. Steele Fund, and currently amount to $1500 would establish a link between modular curves each. and elliptic curves, utterly different from that At the presentation ceremony in Cincinnati, described in the previous paragraph, and indeed Professor Langlands expressed his appreciation ex much deeper. Merely to exhibit an elliptic tempore. Professor Mazur prepared a more formal response, which is reproduced below. curve as such a factor often yields number­ theoretic information otherwise unattainable, and sometimes even provides "conceptual methods" Barry Mazur for generating its Mordell-Weil group (e.g., by specific images of Birch-Heegner points). I should like to convey my warm thanks to the American Mathematical Society and the Cole 1 Precisely which specific structure depends on which Prize Committee. One of the great joys of writing modular curve you are dealing with. the paper to which the Cole Prize Committee 2For example, this diophantine problem (restricted to and a certain well known class of modular curves) is essentially referred was the continual correspondence equivalent to the determination of all possible torsion conversation with many friends, on the subject subgroups of Mordell-Weil groups of elliptic curves defined of modular curves, for which I am also thankful. over the rational number field.

134 To be sure, there is also the Langlands program which views a modular curve as a symmetric space and relates aspects of its arithmetic to the theory of automorphic representations of various reductive algebraic groups. These are some distinct views and problems, fostered by the study of modular curves, each one having deep implications for the others. We have begun to suspect that there is a unity to all this. Much work lies ahead.

Biographical Sketch Barry Mazur was born on December 19, 1937, in New York City. In 1958 and 1959 he was a Research Fellow at the Institute for Advanced Study in Princeton. He received his Ph.D. degree from Princeton University in 1959. He was a Junior Fellow in the Harvard Society of Fellows from 1959 to 1962. From 1962 to 1966 he was a fellow of the Alfred P. Sloan Foundation. In 1966 he was awarded the Society's Oswald Veblen Prize in Geometry. He is currently professor of mathematics at Harvard University and a frequent visitor to the Institut des Hautes Etudes Scientifiques in Bures-sur-Yvette. Robert P. Langlands Biographical Sketch Barry Mazur Robert P. Langlands was born in New Westminster, British Columbia, The classical geometry of modular curves on October 6, 1936. He received viewed a B.A. degree in 1957 as quotients of the Poincare and an M.A. in 1958, both plane comes to from the University of British Columbia, and a Ph.D. the service of Arithmetic insofar as a close from Yale University in 1960. He taught at Princeton study of homology classes supported on various from 1960 to 1967, and was professor at Yale from geodesics of the modular curves is an essential 1967 to 1972. He was a member of the Institute for pre-requisite to understanding special values of a Advanced Study in 1962-1963, and has been professor class of important Dirichlet series (among these of mathematics there since 1972. are the special values which appear in the Birch­ Professor Langlands has served on the AMS Swinnerton-Dyer conjecture). Organizing Committee for the Summer Institute on The function theory of modular curves has been Automorphic Forms, Representations and £­ widely Functions {1977), the Interim Editorial Committee known for over a century to have rich for Research Announcements consequences {1978), and the Bulletin for number theory: The coefficients Editorial Committee (Associate Editor, Research of Fourier expansions of functions and sections Announcements) {1979, 1980). He has given addresses of line bundles over modular curves often encap­ at the Summer Research Institute on Algebraic sulate much coveted, and otherwise inaccessible Groups and Discontinuous Subgroups (Boulder, July arithmetic information. The work of Serre, 1965), the Symposium on Mathematical Developments Swinnerton-Dyer, and Katz establish an arith­ Arising from the Hilbert Problems {DeKalb, illinois, metic theory of these Fourier coefficients. This ties May 1974), the 1977 Summer Research Institute in with the fascinating structure of the reductions on Automorphic Forms, Representations and £­ Functions, of models of modular curves in and at the International Congresses in prime characteris­ Nice {1970) and tics (as studied Helsinki {1978). by lgusa, Deligne-Rapaport, and Professor Langlands Katz). was a Miller Foundation Fellow at the University of California {Berkeley) in 1964- The fields generated by division points on the 1965, and an Alfred P. Sloan Foundation Fellow, jacobians of modular curves are usually nonabelian 1964 to 1966. His research interests include group extensions of the rational number field whose representations and automorphic forms. arithmetic can be studied in great depth by virtue He was elected a Fellow of the Royal Society of of their connections with the modular curves Canada in 1972 and a Fellow of the Royal Society in (Shimura, Serre, Ribet, Wiles). Can one generate 1981. In 1975 he received the Wilbur Cross Medal of all class fields of abelian number fields in Yale University. He is a member of the editorial boards this of Annals of Mathematics manner? We can, if we wish, and Compositio Mathematica, reverse direction and and has held visiting positions use the algebraic number at Orta Dogu Teknik theory of these fields to Universitesi in Ankara, 1967-1968, Universitii.t Bonn gain an understanding of the Selmer groups of the in 1970-1971 and 1980-1981, and at Ecole Normale modular curve jacobians via classical and modern Superieure de Jeunes Filles, 1980. methods of descent.

135 The AMS Nomination Procedure is Vulnerable to "Truncation of Preferences" Steven J. Brams

The "Instructions to Voters" on the ballot of the of voters in each class ranking the set of four Nominating Committee for 1982 of the American candidates { x, a, b, c} as follows: ~athematical Society (AMS) includes the follow­ I. 6: xabc mg statement: "There is no tactical advantage II. 6: xbca to be gained by marking few candidates." In III. 5: xcab this note I shall prove that this statement is false by giving two counterexamples that illustrate Thus, for example, the 6 voters in class I rank x different aspects of the problem of aggregating as their first choice, a as their second b as their fourth. ' voter preferences under the Hare system of "single third, and c as their transferable vote" used by the AMS. Specifically, Assume two of the set of four candidates are I shall show that there may be a "tactical ad­ to be elected, and a candidate must receive a vantage" to ''marking few candidates" -that is quota of 6 votes to be elected on any round. A truncat~ng one's preferences-and not followin~ ."quota" is defined as (n/(m + 1)) + 1, where n the adVIce proffered on the ballot: "It is advisable 1s the number of voters and m is the number of ca~didates to be elected. It is standard procedure, to ~ark candidates in the order of your preference unt1l you are ignorant or indifferent concerning wh1ch the AMS uses [21], to drop any fraction candidates whom you have not ranked." that results from the calculation of the quota, so the ~uota actually used is q = [(n/(m + 1)) + 1], clear how the The counterexamples will make the mteger part of the number in the brackets. Hare system works. It was first proposed by The integer q is the smallest integer ( 6 in this George Andrae Thomas Hare in England and Carl counterexample) such that it is impossible for in Denmark in the 1850s and is now widely used more than the specified number of candidates to throughout the world. For example, it is used to be elected (2 in the counterexample) to win with elect public officials in such countries as Australia first-place votes on the first round (the election of the Republic of Ireland, and South Africa' three candidates would require 18 votes, but there Massachusetts' in local. elections in Cambridge ' ' are only 17 voters). In fact, what happens is as and m numerous private organizations. John follows: ~tuart Mill placed it "among the greatest [19] First round: x receives 17 out of 17 first-place yet made in the theory and practice Improvements votes and is elected. of government." Second round: There is a "surplus" of 11 Although the Hare system has recently been votes (above q = 6) that are transferred in the that shown to violate a number of properties proportions 6:6:5 to the second choices (a b and have been proposed for voting systems [3 4 5 c, respectively) of the three classes of 'v~ters. 22], it has a number of strengths as a syste~ of Since these transfers do not result in at least proportional representation [14, 16]. However, I q = 6 for any of the remaining candidates (3.9, shall suggest at the end of this note that a new 3.9, and 3.2 for a, b, and c, respectively) then voting system, called "approval voting," deserves the candidate with the fewest (transferred) votes consideration as a simple alternative to the Hare system. STEVEN J. BRAMS is a professor of politics The Hare system was used to elect four out at New York University; his research specialties of eight candidates listed on the 1981 AMS are math~matical m<;>delling and formal political Nominating Committee ballot; those elected serve theorf, With s~?stantive interest in biblical politics, with four continuing members of the Norroinating Amencan pohtics, and international relations. He graduated from M.l. T. in 1962 and received a Ph.D. C?mmittee in 1982. My first counterexample !n political science from Northwestern University Wlll show that the Hare system is vulnerable to m .1966. He taug~t at Syracuse University before truncation of preferences when two out of four gm~~ to N.Y.U. m 19~9. He has held visiting candidates are to be elected, my second when only positrons at several umversities and worked for one candidate is to be elected and there is no government agencies; for two years he was a transfer of "surplus votes." research associate at the Institute for Defense Analys~s. He is the aut~or of f?ur books and many COUNTEREXAMPLE 1. Assume there are papers m the areas of his specialties. three classes of voters, with the indicated numbers

136 (i.e., c) is eliminated. His. supporters (class ill) Now assume the 3 class IV voters rank only d transfer their 3.2 votes to their next-highest choice first. Then d is still eliminated first, but since (i.e., a), giving him more than a quota of 7.1. the class IV voters did not indicate a second­ Thus, a is the second candidate elected. Hence, place choice, no votes are transferred. Now, the two winners are { x, a}. however, c is the (new) lowest candidate with 5 Now assume 2 of the 6 class II voters rank only votes; his elimination results in the transfer of x first: they do not indicate that they prefer b his supporters' votes to b, who is elected with 11 next, etc. The results are: votes. Because the class IV voters prefer b to a, it First round: Same as above. is in their interest not to rank candidates below d to induce a better outcome for themselves. Second round: There is a "surplus" of 11 It is true that a first choice can never be hurt votes (above q = 6) that are transferred in the by ranking a second choice, a second choice by proportions 6:4:2:5 to the second choices, if any ranking a third choice, etc., because the higher (a, b, no second choice, and c, respectively) of the choices are eliminated before the lower choices can voters. (The 2 class II voters with no second choice affect them. However, lower choices can affect the do not get their transferred votes distributed.) order of elimination, and hence transfer of votes, Since these transfers do not result in at least so that-as the counterexamples demonstrate­ q = 6 for any of the remaining candidates (3.9, a higher choice (e.g., second) can influence whether 2.6, and 3.2 for a, b, and c, respectively), then a lower choice (e.g., third or fourth) is elected. the candidate with the fewest (transferred) votes I wish to make clear that I am not suggesting (i.e., b) is eliminated. His supporters ( 4 voters that voters would routinely make the strategic in class II) transfer their 2.6 votes to their next­ calculations implicit in these counterexamples. highest choice (i.e., c), giving him 5.8, less than These calculations are not only rather complex the quota of 6. Because a has fewer (transferred) but also could, on occasion, be neutralized by votes (3.9), he is eliminated, and c is the second counterstrategic calculations of other voters in candidate elected. Hence, the two winners are gamelike maneuvers. Rather, I am suggesting {x,c}. that the advice to rank all candidates for whom Conclusion: The 2 class II voters who ranked one has preferences is not always rational under only x first induced a better, not a worse, social the Hare system. choice for themselves by truncating their ranking A nonranking system, called "approval voting," of candidates on the ballot. Thus, there may be a may be a good alternative to the Hare system. "tactical advantage" in "marking few candidates." Under approval voting, a voter can vote for, or The reason for this in the counterexample is approve of, as many candidates as he wishes. Each that 2 class II voters, by not ranking b second, candidate approved of receives one full vote, and c third, and a fourth, prevent b's being paired the candidates with the most votes, up to the against a (their last choice) on the second round, number of offices to be filled, win. by whom b would be beaten. Instead, c (their Approval voting is the most "sincere" and next-last choice) is paired against a and beats "strategyproof" of all nonranking systems and him, which is better for the class II voters. has a strong propensity to elect "Condorcet Lest the reader think that a counterexample candidates," who (if they exist) would defeat all must turn on the allocation of surplus votes, I other candidates in pairwise contests [1, 6, 8]; shall next give a counterexample in which only quantitative aspects of the system are analyzed one candidate is to be elected, so the election in [9, 10, 15, 17, 18], among other places. becomes an elimination contest that ends when A comprehensive review and synthesis of both one candidate wins at least a simple majority. theoretical and empirical material on approval COUNTEREXAMPLE 2. Assume there are voting will be available in [2]. four classes of voters, with the indicated numbers Approval voting is obviously vulnerable to of voters in each class ranking the set of four truncation of preferences, because voting, say, candidates {a, b, c, d} as follows: for a second choice may hurt one's first choice, even if a voter finds both candidates acceptable. I. 7: abed However, unlike the Hare system, approval voting II. 6: baed is "monotonic": a candidate can never do worse by ill. 5: cbad receiving more votes, whereas raising a candidate's IV. 3: dcba ranking in some voters' preference scales under Since no candidate has a simple majority of q = 11 the Hare system, without changing the ordering first-place votes (out of 21), the lowest candidate, of other candidates, may, perversely, hurt the d, with 3 votes, is eliminated on the first round, candidate who moves up in the scales [7]. These and his second-place votes go to c, giving c 8 and other problems that can afflict voting systems votes. Because none of the remaining candidates are discussed in [11, 12, 20, 23]. still has a majority, b, with the (new) lowest total Finally, it may be of interest that such of 6 votes, is eliminated next, and his second-place distinguished academic groups as the Econometric votes go to a, who is elected with a total of 13 Society, in the election of its Fellows, have votes. switched from preferential to approval voting [13].

137 References The ballot-counting method known as the Single 1. S. J. Brams and P. C. Fishburn, Approval voting, Transferable Vote was adopted several years ago American Political Science Review 72 (1978), 831- for the election of members of the AMS Nominating 847. Committee. Chandler Davis, one of the original 2. S. J. Brams and P. C. Fishburn, Approval voting, proponents of this scheme, prepared the following the forthcoming. observations on Professor Brams' article at Committee of the The Hare system is inconsistent, invitation of the Editorial 3. G. Doran, Notices. Political Studies 27 (1979), 283-286. 4. G. Doran, Is the Hare voting scheme representative?, COMMENT: The objective which the Hare Journal of Politics 41 (1979), 918-922. system aims to realize-and which Brams accepts 5. G. Doron and R. Kronick, Single transferable vote: as desirable-is "sincerity": a voter should not an example of a perverse social choice function, American feel obliged to vote for a lesser evil ahead of sake of Journal of Political Science 21 (1977), 303-311. a sincerely preferred candidate for the blocking election of a greater evil. We may Fishburn, An analysis of simple voting 6. P. C. thank Brams for showing how the system may SIAM Journal on systems for electing committees, fall short of satisfying the sincerity criterion. In Applied Mathematics 41 (1981), 499-502. his COUNTEREXAMPLE 1, two voters in class 7. P. C. Fishburn, Monotonicity paradoxes in the II can avoid their greatest evil candidate, a, by theory of elections, Discrete Applied Mathematics, truncating preferences; and evidently a single voter forthcoming. of class II can accomplish the same objective by 8. P. C. Fishburn and S. J. Brams, Approval voting, insincerely casting a class ill ballot. Condorcet's principle, and runoff elections, Public Choice I observe that Brams does not claim that the 36 (1981), 89-114. approval voting system does well by the sincerity 9. P. C. Fishburn and S. J. Brams, Efficacy, power, criterion, except in comparison with other systems and equity under approval voting, Public Choice, 37 not involving ranking of candidates. It is common (1981), 425-434. experience that under such systems people very 10. P. C. Fishburn and S. J. Brams, Expected utility often vote for the lesser evil, and it is difficult and approval voting, Behavioral Science 26 (1981), 136 to imagine how this behavior could result from -142. their having misunderstood any formal property 11. P. C. Fishburn and S. J. Brams, Paradoxes of of the system. By contrast, one would never preferential voting, mimeographed, 1981. attempt expedient "insincere" voting under the precise information about (written by L. A. Steen), Mathe­ Hare system unless given 12. M. Gardner patterns among one's games (from counting votes to making votes count: rather special preference matical electors; though it is entirely credible that of elections), Scientific American, fellow the mathematics such patterns sometimes occur, it is not to be October 1980, 16ft'. expected that any voter will have information of 13 . .f. P. Gordon, Report of the secretary, Econo­ such quality. metrica 48 (1981), 232. 14. C. G. Hoag and G. H. Hallett, Jr., Proportional No, Brams would have us prefer approval voting its representation, Macmillan, New York, 1926. to the preferential ballot on just two grounds: greater simplicity (which we certainly grant) and 15. D. T. Hoftinann, A model for strategic voting, its novelty (a claim I find puzzling). SIAM Journal on Applied Mathematics, forthcoming. 16. E. Lakeman, How democracies vote: A study Chandler Davis of electoral systems (fourth revised edition), Faber & I make no claim that the Faber, London, 197 4. REJOINDER: alone of approval voting is a virtue. But I voting: a "best buy" method novelty 17. S. Merrill ill, Approval do claim that a nonmonotonic system like Hare, in Magazine 52 for multicandidate elections?, Mathematics which more first-place votes can hurt rather than (1979), 98-102. help a candidate, is a serious vice that violates 18. S. Merrill ill, Strategic decisions under one-stage what, in my opinion, is a fundamental democratic multicandidate voting systems, Public Choice 36 (1981), ethic. By contrast, more votes can never hurt a 115-134. candidate under approval voting. Mill, Considerations on representative 19. J. S. is illustrated by New York, 1962. The monotonicity problem government, Harper and Brothers, 2. If the three class N choice of COUNTEREXAMPLE 20. R. G. Niemi and W. H. Riker, The voters raised a from fourth to first place in their voting systems, Scientific American, June 1976, 21ft'. rankings, without changing the ordering of the 21. E. Pitcher, The nominating committee and other three candidates, b would be elected rather the. preferential ballot, Notices of the American than a. Thus, candidate a would be hurt when Mathematical Society 26 (1979), 291. he moves up in the rankings of some voters and 22. H. J. Smith, Aggregation of preferences with thereby receives more first-place votes. 1027-1041. variable electorate, Econometrica 51 (1973), Steven J. Brams 23. P. D. Straffin, Jr., Topics in the theory of voting, Birkhiiuser, Boston, 1980.

138 Report of the 1980 CBMS Survey Summary of Major Findings

This article presents the Summary section of the latest Report of the Survey Committee of the Conference Board of the Mathematical Sciences (CBMS). The full report, Undergraduate mathematical sciences in unitJersities, four-year colleges, and two-year colleges, 1980-1981, by James T. Fey, Donald J. Albers and Wendell H. Fleming (with the technical assistance of Clarence B. Lindquist) was published by CBMS in December 1981, with support from the National Science Foundation. Copies of the Report may be obtained from the Conference Board of the Mathematical Sciences, 1500 Massachusetts Avenue, N.W., Washington, D.C. 20005, $6 prepaid. These excerpts are reprinted with the permission of the publisher. Copyright © 1981 by the Conference Board of the Mathematical Sciences.

In this summary we present some highlights of in institutions of higher education. The estimates the 1980 CBMS Survey results, leaving detailed are based on responses to a Survey questionnaire presentations of the data to the full text of the Report. sent to universities and colleges in a sample of 416 Some trends were found to be common among all institutions. The sampling and estimation procedure types of institutions, for instance, increased loads for are explained in an appendix to the full Report. elementary service courses and the rapid growth of [Response rates for departments of mathematics in enrollments in computer science. Nevertheless, there the sample were 95%, 86%, 73%, and 69%, for were also significant differences according to type Universities, Public Four-Year Colleges, Private Four­ of institution (university, public or private four-year year Colleges, and Two-Year Colleges, respectively. college or two-year college). The summaries of major The rate for departments of statistics in Universities findings for four-year institutions and for two-year was 70%; for departments of computer science the colleges are presented separately. rates were 68%, 54%, and 100% for Universities, The CBMS Survey Committee, in publishing Public Four-Year Colleges, and Private Four-year the results of its investigations, has always felt Colleges, respectively.] its fundamental responsibility to be the neutral The generally high response rates give us confidence presentation of a factual background for use by those in most estimates. However, for some questions the in education and government who make decisions actual reported numbers were so small that the data about the mathematical sciences, the fundamental must be used with caution. premise being that informed decisions are likely to be superior to decisions based merely on hearsay or wishful thinking. The text of the Report itself Summary for Four-Year Institutions maintains that posture, attempting to describe what the data say without assuming the more interpretive For four-year colleges and universities, high­ role of making subjective assertions about what the lights of the Survey results and prospects for the data mean. In the present Summary, we try to suggest 1980s can be summarized as follows. something of the significance of the data without, 1. Mathematical science course enrollments however, presuming to offer any recommendations for grew substantially, with a dramatic growth in specific actions which the mathematical community should take. computer science. There was a 33% increase Our findings concern mathematical science enroll­ in total mathematical science course enrollments ment trends, undergraduate majors, instructional from 1975 to 1980, compared to an increase of only formats, faculty, and administrative organization 8% in full-time-equivalent enrollments in all fields of mathematical science departments. The data during the same five-year period. In contrast, given are estimates of national totals for fall 1980 during the previous five years from 1970 to 1975, mathematical science course enrollments grew by Members of the CBMS Survey Committee only 8%, compared to an increase of 11% in all fields. DONALD J. ALBERS, Menlo College, WIL­ LIAM F. ATCHISON, University of Maryland, Most of the 33% increase in course enrollments JAMES T. FEY, executive secretary, University from 1975 to 1980 was concentrated in elementary of Maryland, WENDELL H. FLEMING, chairman, service courses and in computing courses. There Brown University, JOHN W. JEWETT (deseased), was a 30% increase in calculus enrollments and a former chairman, DON 0. LOFTSGAARDEN, 196% increase for computing and related courses. University of Montana, MARTHA K. SMITH, Enrollments in remedial (high school level) courses University of Texas, ROBERT J. THOMPSON, constitute Sandia National Laboratories, and JOSEPH were up 72%. Remedial courses now WAKSBERG, WESTAT, Inc. 16% of all mathematical science enrollments. (For public four-year colleges the figure is 25% and,

139 as noted below, it is even higher for two-year 4. Instructional formats. The 1980 survey colleges.) inquired about the instructional format used in This substantial increase in the service course selected elementary courses (finite mathematics, load from 1975 to 1980 was not indicated by calculus, computer programming, elementary trends during the years immediately preceding statistics). Overall nearly 60% of all students this period. One reason for the increase was in these courses are taught in small classes with the surge of student interest in such practically­ fewer than 40 students. Most of the rest are oriented majors as engineering and business, where taught in large classes of 40 to 80 students employment prospects have recently been excel­ or in large lectures (with or without recitation lent. The large increase in remedial mathematics sections). Fewer than 1% were taught using confirms evidence from various other sources that self-paced instruction or other modes. (This is a disappointingly large proportion of students in in contrast to two-year colleges, where alternate the U.S. come to college quite poorly trained instructional modes are used increasingly.) in mathematics. Another factor contributing The percentages of students in four-year in­ to increased elementary mathematics enrollments stitutions taught in small classes vs. large classes appears to be the growing use of quantitative or lectures varied widely according to the type of methods in the social, biological, and management institution. In universities only 36% of students in sciences. these selected courses were taught in small classes, 2. Computer science grew rapidly, measured by compared to 79% in private four-year colleges. any standard. .Ai3 mentioned above, enrollments 5. Faculty loads, part-time vs. full-time faculty. in computing courses nearly tripled from 1975 The number of mathematical science faculty to 1980. There were estimated to be about members increased by about 13% from 1975 to 8900 computer science bachelor's degrees for the 1980 measured on a full-time equivalent (FTE) academic year 1979-1980, compared with only basis. Since this was substantially less than the 3600 for 1974-1975. At the same time the 33% overall increase in course enrollments during number of bachelor's degrees in mathematics fell the same five-year period, an increase in faculty from 17,700 for 1974-1975 to 10,200 for 1979- loads resulted. Mathematical science course 1980. The number of mathematical science enrollments per FTE faculty member increased bachelor's degrees with majors in secondary from 77 in 1970 to 83 in 1975 and to 98 in 1980. teaching fell from 4800 in 1974-1975 to only Thus course enrollments per FTE faculty increased 1750 for 1979-1980. At the same time, the rapid by 27% during the decade 1970-1980, with most growth of the computer /high-technology industry of the increase during the last half. in the U.S. has created excellent employment opportunities for computer science graduates at During the ten-year period 1970-1980 there all levels (bachelor's through Ph.D.). This has has been an increase in faculty loads, measured made the recruitment and retention of computer in the number of credit hours taught per week, science faculty members difficult, particularly in though the increase was more marked from 1970 institutions without graduate programs. Only to 1975 than in the period from 1975 to 1980. about half of the computer science faculty in For example, 80% of the faculty in university four-year colleges holds doctoral degrees. Among mathematics departments taught less than 9 hours 830 private colleges only about 220 mathematical per week in 1970, but in 1980 only 62% taught science faculty members have their highest degree less than 9 hours per week. In 1970, 47% of the hi computer science, and only about 40% of those faculty in public four-year college mathematics have Ph.D.'s in computer science. departments taught less than 12 hours per week, 3. Upper division mathematics courses ex­ but in 1980 this percentage had decreased to only perienced a modest enrollment increase, 4% overall 20%. from 1975 to 1980. Enrollments were up in courses The survey data show other disturbing trends. with a more applied flavor, but down in math­ There was a 75% increase in the number of ematics courses for prospective teachers (-37%) part-time faculty members from 1975 to 1980, and in advanced ''pure mathematics" courses compared to only an 8% increase in the full-time (-19%). .Ai3 the number of mathematics majors faculty during the same five-year period. The has declined, an adequate spectrum of upper divi­ percentage of faculty members granted tenure sion mathematics courses is not available in many during 1980 was much lower than during 1975. departments. This problem is more severe in four­ These data presumably reflect the preoccupation year colleges than in universities. For example, of many institutions of higher learning with among private colleges only 13% offer a college­ holding costs down, and with avoiding additional level geometry course, and the offerings in applied longer term commitments to faculty members. On mathematics are quite meager. While logic is an the other hand, some departments in four-year important topic for computer science, only 30% colleges are unable to hire (or to retain) full­ of university mathematics departments and only time faculty members with desired credentials, about 7% of four-year college departments offer a especially for positions in computer science, course in mathematical logic. statistics, or other applied mathematical sciences.

140 In such instances, hiring a part-time person is of those in four-year colleges have doctorates sometimes the best available alternative. compared to 71% in 1975. ' 6: Faculty qualifications. A national goal The continued availability of enough qualified durmg the 1960s was to raise the educational teaching assistants is in doubt, with many depart­ qualifications of college teachers up to the doctoral ments seeking TA's from other sources in addi­ level. A great deal of progress was made tion to their own graduate students. In 1980 toward that goal between 1965 and 1975 but over 25% of all TA's employed by mathemati­ more recently there has been slippage ~ the cal science departments were not mathematical mathematical sciences. In 1980 over 90% of full­ science graduate students (graduate students in time mathematical science faculty members in other fi~ds, ~d~rgraduate TA's and others). universities. have doctorates. However, only 66% The rapid decline m the number of mathematics majors suggests that departments with traditional mathematics graduate programs may encounter The CBMS Survey Committee still more difficulty in recruiting TA's in the years ahead. I In 1963 a group of senior mathematicians thought that it was time to make a statistical 7. Faculty employment, demographic charac­ study of the state of mathematics somewhat like teristics, mobility. The estimated total number of that made by the Albert Committee about 20 full-time mathematical science faculty members years before, which even then had the quaint in four-year colleges and universities in the U.S. charm of a Victorian novel. increased from about 16,900 in 1975 to 18,300 in I was asked to take the project on. With the 1980. The addition of some 280 positions per help of a large grant from the Ford Foundation year contributed to an academic job market for we produced three volumes beginning in 1967 mathematicians better than it had been during the on undergraduate, graduate and professional bleak period immediately preceding these years. work in mathematics under the aegis of the From 1970 to 1975 there was essentially no change Conference Board of Mathematical Sciences. in the size of the full-time mathematical science Since then, there has been a CBMS Survey every faculty, and the number of new Ph.D.'s per year five years, building upon a mass of detail that reached an all time high. has proved of increasing value. . The CBMS Survey data indicate little change The surveys have been regarded by manpower m the total number of tenured mathematical experts as among the best thought out and science faculty members between 1975 and 1980. most reliable surveys of any science. In part Since the size of the full-time faculty increased that was due to the deep involvement and by 1400, the percentage with tenure declined, professional standing of the members of the from 72% in 1975 to 67% in 1980. Numbers Survey Committee over the years. In large of deaths and retirements are insufficient to part it was due to John Jewett. Jewett was account for this change. Among probable my own Ph.D. student, one I was immensely contributing factors are the growth of young proud of. He served first as executive director computer science departments (only about half of the Surveys, and then as chairman of the of the faculty members in computer science Survey Committee performing wonderfully in departments were tenured in 1980), stricter tenure both roles. His unexpected and premature death policies of some institutions, and the development last summer is a loss to us all. In particular of opportunities in industry for Ph.D.'s during it deprives us of a leader for the Surveys at a the 1970s which attracted some faculty members time when changes in CBMS raise doubts about away from academe. In 1980 greater movement the Surveys' continued existence and at a time between academic jobs in mathematical science when we urgently need reliable data on many departments and nonacademic jobs was observed topics. than. in earlier CBMS Surveys. Among doctorate­ To pick out one such topic, we have very holding faculty members newly hired for fall1980, little understanding of what our students­ ab~ut 125 came from nonacademic positions, bachelors, masters, Ph.D.'s-do in industrial or while 290 left for nonacademic positions between government work. The first Survey Committee the academic year 1979-1980 and fall 1980. had hoped to make such a study but reluctantly This resulted in a net outflow to nonacademic concluded that the task was beyond its finances. positions ?f ab~ut 1% of the ~octorate-holding Now better understanding is critically necessary mathematical science faculty durmg a single year. for our field. I could name other needs. I can The percentage of full-time mathematical only hope that the wisdom of our leadership will science faculty members who are women increased make it possible for the Surveys to continue from 10% in 1975 to 14% in 1980, with a median and to take up such problems under the 1 chairmanship of the very knowledgeable 0n the other hand, data from the Annual AMS new Survey indicate that the number of mathematics graduate Chairman, Wendell Fleming. students was nearly stable between 1978 and 1980 Gail S. Young following an earlier decline. See the February 198i Notices, page 172.

141 age for women faculty members about five years such as statistics or operations research. This less than for men. poses a dilemma for mathematics departments The AMS Survey monitors trends in faculty regarding their instructional mission in the years employment, demographic characteristics, and ahe~d. Is it to be preponderantly elementary mobility annually.2 AMS and CBMS survey results service courses, or can programs of broader appeal indicate very similar trends, but do not agree in be introduced? For example, there are successful all details. joint majors in mathematics-computer science 8. Administrative organization of mathematical ~athematics-economics, or mathematics-biolo~ science departments. In universities, mathematics m many institutions. There are reports of and computer science are usually found in shortages of high school mathematics teachers, separate departments. There are often separate ~s many teachers leave for well-paying jobs in departments of statistics, operations research or mdustry. How can student interest in teaching applied mathematics as well. However, in f~ur­ careers by rekindled? There is also the need year colleges these various subjects are more to maintain a core of future researchers and commonly taught within a single department college-level teachers, to replace an aging national which includes traditional mathematics. This is mathematics faculty. While the numbers of particularly true in the smaller private colleges. mathematics professors retiring per year are expected to remain relatively low during the of ad­ In universities rather few instances 1980s, there will be a large increase in retirements science ministrative restructuring of mathematical during the 1990s. Considering the nearly ten-year changes departments were reported. Most of these lead time from entry into graduate school until science involved the formation of a new computer crucial tenure decisions are made, there should be In colleges a department. public four-year many tenured positions in colleges and universities greater rate of administrative reorganization was for students now at the point of starting graduate included consolidations reported. Reorganizations studies.3 of mathematical science departments into larger administrative units, creation of computer science In the shorter term, there is a critical problem departments and the addition of computer science of recruiting and retaining a large enough com­ programs and titles in many mathematics depart­ puter science faculty. If the explosive growth ments. of enrollments in computing courses continues, the problem can only become more acute. More 9. Prospects for the 1980s. Student enrollments generally, departments in many four-year col­ in four-year institutions are expected to decline leges have difficulty recruiting enough doctorate­ as the size of the 18 to 21 age group decreases. holding faculty members in the applied mathe­ U.S. government sources project an overall enroll­ matical sciences to develop programs and teach ment decline by 1985 of some 7% from the 1980 courses in those areas. The numbers of new peak. The impact in the mathematical sciences Ph.D.'s in both pure and applied mathematical may be less, as long as present career-oriented fields have been declining, and there are attractive attitudes among college students persist. None­ alternatives in industry. theless, mathematical science enrollments may be problem is to expected to increase at a slower rate from 1980 to A more fundamental national in the schools. 4 1985 than from 1975 to 1980. upgrade pre-college mathematics To a considerable extent this lies outside the There is likely to be a continuing problem scope of the present Report, although college in obtaining adequate resources to cover the and university departments can help through instructional load in the mathematical sciences. their role in training teachers. It is in their While there was some increase in numbers own self-interest to help as they can. The of ~acuity members (full-time and part-time) continuing flood of entering students poorly dunng the late 1970s, the increase was by no prepared in mathematics threatens to distort the means sufficient to cover the substantially heavier normal educational goals of mathematical science instructional loads. There is presently little departments in institutions of higher education. evidence that, in the years immediately ahead higher education will command enough priority i~ the competition for scarce public funds to alleviate Summary for Two-Year Institutions matters. Duri~g the period 1975-1980, mathematics pro­ The traditional role of upper division instruction grams m two-year colleges underwent significant in college and university mathematics departments changes. Combined trends in enrollments, pro­ has been the training of future mathematics grams, student populations, and faculty popula­ teachers and researchers. These programs are tions do not bode well for the mathematical being deserted by students more interested in careers in the computing field, or to a lesser degree 3 This issue is discussed further in the February 1979 as practitioners in an applied mathematical field Notices, pages 111, 112. 4Detailed recommendations on this issue are made 2Reported in the February issue and in the October or in the 1980 NCTM report, An agenda for action: November issues of the Notices. recommendations for school mathematics of the 1980s.

142 sciences in two-year colleges. Summaries of these teaching overloads had been smaller, then it is trends follow. likely that the part-time fraction would have been 1. Enrollment trends-computer science gains. even larger. Mathematical science enrollments grew by 20%, 5. Instruction trends-self-pacing methods con­ keeping pace with overall enrollment gains of 19%. tinue to expand. Every alternative instruction This gain was much less than the 50% growth in mode that we monitored showed a gain in usage the previous five-year period, 1970-1975. Nearly from 1975 to 1980. In particular, independent all of the 20% gain was due to explosive growth of study, modules, PSI, computer-assisted instruc­ computer science courses and continued expansion tion, and several other alternative techniques of remedial courses. Computer science gains alone registered gains. The standard lecture-recitation accounted for 43% of the total gains in enroll­ format is still strongly dominant, but experimen­ ments. Remedial courses (arithmetic, elementary tation clearly is growing. It is interesting to note high-school algebra, general mathematics, and that, although computers and calculators are now high-school geometry) now account for 42% of all widespread among two-year colleges, their impact two-year college mathematics enrollments. Deal­ on the teaching of mathematics seems to be slight ing with remediation was identified by Survey at best. respondents as far and away the biggest problem facing the two-year college mathematics faculty in Reports of the CBMS Survey Committee 1980. 2. Program trends-shift away from liberal Volume I of the Report of the CBMS Survey arts. Enrollments in occupational/technical Committee (1967): Aspects of undergraduate programs grew to more than one-half of all full­ training in the mathematical sciences, by John time equivalent enrollments, outdistancing college­ Jewett and Clarence Lindquist. xvi + 164 transfer enrollments. In 1975, by way of contrast, pages. occupational/technical programs accounted for Volume II of the Report of the CBMS Survey slightly more than one-third of all full-time Committee (1969): Aspects of graduate train­ equivalent enrollments. These shifts in student ing in the mathematical sciences, by John preferences away from liberal arts were mirrored Jewett, Lowell J. Paige, Henry 0. Pollak and in enrollment gains of applied courses and sharp Gail S. Young. xxiv + 140 pages. declines in courses such as mathematics for liberal Volume III of the Report of the CBMS Survey arts. Committee (1970): Aspects of professional 3. Population trends-part-timers in the work in the mathematical sciences, by Joseph majority. Part-time enrollments increased from P. LaSalle, C. Russell Phelps and Donald E. 53% of all enrollments in 1975 to 63% in 1980. Richmond. vii+ 144 pages. This trend to an increased part-time majority may Volume IV of the Report of the CBMS Survey help to explain the program trends noted above. Committee (1972): Undergraduate education 4. Faculty trends-the full-time faculty declined in the mathematical sciences, 1970-1971, by in size. Although enrollments in mathematical John Jewett and C. Russell Phelps with the science courses grew by 20%, the full-time faculty technical assistance of Clarence B. Lindquist. decreased by 5%. For whatever reasons­ xii + 132 pages. burnout, economic exigencies, frustrations with Volume V of the Report of the CBMS Sur­ remediation, increased teaching loads-the full­ vey Committee (1976): Undergraduate math­ time faculty of 1980 was smaller than that of 1975. ematical sciences in universities, four-year Our age distributions indicate that those leaving colleges, and two-year colleges, 1975-1976, by the profession tend to be at least 45 years of age, James T. Fey, Donald J. Albers, and John which strongly suggests that experienced teachers Jewett. xii + 130 pages. are finding employment other than teaching. The Volume VI of the Report of the CBMS Sur­ financial problems of full-time faculty members vey Committee (1981): Undergraduate math­ are underscored by the fact that nearly one-half ematical sciences in universities, four-year of them are teaching overloads for extra money. colleges, and two-year colleges, 1980-1981, by The typical faculty member is now teaching 30 James T. Fey, Donald J. Albers, and Wen­ more students than he taught in 1970. dell H. Fleming, with the technical assistance During the same time frame, the part-time of Clarence B. Lindquist. xiii + 140 pages. faculty nearly doubled in size. Part-timers now outnumber full-timers. If the full-time faculty

143 25th ANNUAL AMS SURVEY 1981 Second Report A first report of the 1981 Survey appeared in the November 1981 Notices, pages 608-634. It included a report of the survey of faculty salaries, a first report of the survey of new 1980- 1981 doctorates, and a report on academic salaries aver the past two decades. This second report includes an update of the fall 1981 employment status of new doctorates, an analysis of faculty mobility, and a report on fall 1981 enrollments and class sizes. The 25th Annual AMS Survey was made under the direction of the Society's Committee on Employment and Educational Policy (CEEP), whose members in 1980 were Lida K. Barrett (chairman), Donald C. Rung, Hans Schneider, Robert J. Thompson, Barnet M. Weinstock and William P. Ziemer. A Data Subcommittee of CEEP, consisting of Lida K. Barrett, Susan J. Devlin (consultant), Lincoln K. Durst, Wendell H. Fleming, Arthur P. Mattuck and Donald C. Rung (chairman), designed the questionnaires with which the data were collected. The committee is grateful to members of the AMS staft', especially Marcia C. Almeida and Peggy Reynolds, for the diligence and efficiency with which the data were collected and compiled. Comments or suggestions regarding this program may be directed to the subcommittee. Employment of Mathematical Sciences Doctorates, Faculty Mobility, Nonacademic Employment and Enrollments, Fall1981 by Donald C. Rung

This report is one in a series of annual reports on employment patterns, enrollment and class size in In this article departments in mathematical sciences the mathematical sciences. It begins with an update in U.S. and Canadian universities and four-year colleges are classified as below. The first six groups consist of the fall 1981 employment status of new 1980-1981 of departments that have doctoral programs, of which doctorates, followed by an analysis of trends in the Groups 1-V are U.S. departments. (The numbers academic job market based upon the 1981 AMS Survey indicate how many departments were queried in the of faculty mobility. Finally it compares 1980 and 1981 Survey.) 1981 fall enrollment and class size for various levels of Group I is composed of the top 27 ACE ranked mathematics departments. courses in the mathematical sciences. Group IT is made up of the other 38 ACE rated An article in this issue of the Notices summarizes mathematics departments. the major findings of the new survey by the Conference Group m contains 87 mathematics departments not Board of the Mathematical Sciences (CBMS). This is included in the ACE study. a comprehensive analysis of the mathematical sciences Group IV includes 64 statistics, biostatistics and for 1975 to 1980 and compares the findings of the latest biometry departments. report with previous CBMS surveys. The CBMS survey Group V is made up of 137 other mathematical science departments (including 77 in computer science). agrees for the most part with the trends reported in Group VI consists of 35 Canadian departments in the the Annual AMS Survey reports, but has a much wider mathematical sciences. scope, uses more systematic statistical techniques and, Group M contains 369 departments with masters' of course, covers a span of five years. programs (of which 24 are Cimadian departments). This year's AMS Survey is noteworthy in at least Group B is made up of 1,065 departments which offer one statistic. For the first time in many years, at most bachelors' degrees (of which 34 are Canadian no 1980-1981 doctorate has been reported as still departments). Notes: Group B includes about 100 departments seeking employment. This confirms recent trends with no degree programs. Both M and B include which indicate that the demand for new doctorates, some departments in universities which have doctoral mostly in the Group M and B departments, exceeds the programs in other areas, in some cases in other areas of supply. (See the box for descriptions of the groups.) the mathematical sciences. Estimates based on AMS Survey data suggest that Response rates varied from one group to another, with the largest response rate from Groups I, IT, and over 700 full-time positions in U. S. colleges and m. Of an estimated total of about 19,262 full-time U.S. universities were filled by nondoctorates last fall and mathematical sciences faculty members, over 9,500 are that, for about half of these positions, the department members of departments which resp.onded to the survey. would have preferred someone with a doctorate. About For an account of the ACE ratings referred to above 85% of these positions were in Groups M and B schools. see A Rating of Graduate Programs by Kenneth D. Roose and Charles J. Andersen, American Council on Of course this number does not represent an annual Education, Washington, D.C., 1970, 115 pp. The demand for new doctorates but indicates that at this information on mathematics was reprinted by the time colleges cannot find enough mathematicians with Society and may be found on pages 338-340 of the doctorates to fill faculty positions. This demand is February 1971 issue of the Notices. also seen in Table 2 which shows that the number

144 of nondoctorate-holding faculty members hired {739) (Table 4). Economic conditions may account for this is substantial compared to the number of doctorate­ as well as for the decline from 168 in 1980 to 116 in holding faculty members hired {1,366). While the 1981 in the net outflow of doctorate-holding faculty estimated total increase for this year in the size of the members to nonacademic employment {Table 6). full-time faculty {612) was one of the largest in recent Fall1981 Employment Status years, the increase for Groups I, II and III was only 117 of 1980..1981 New Doetorates (Table 3). Further the net increase in the nondoctorate Table 1 contains the fall 1981 employment status faculty {208) is positive for the second consecutive year, by type of employer and field of degree for 904 new after nine consecutive years of decline. mathematical sciences doctorates who received the As they have for the last several years, enrollments degree between July 1, 1980, and June 30, 1981. and class size continue to increase in most categories The names of these 904 people, and the titles of {Tables 7 and 8), far exceeding the increase in the their doctoral theses, were published in the November number of faculty members. Part-time members of 1981 Notices, pages 619-634. Table 1 updates the the faculty continue to play a significant role in corresponding table on page 613 of the November 1981 undergraduate instruction. For example, departments Notices, using more recent information provided by in Groups M and B have four part-time members of departments and the recipients of the degrees. The total the faculty (excluding graduate assistants) for every does not include a few more recipients of doctorates ten full-time members. who were reported too late to gather employment The number of graduate students showed the first information for these reports. {A supplementary list of significant increase in years {6%) with departments recipients will appear in the April1981 Notices.) in Groqps I, II and III showing the same increase. The first five rows in Table 1 refer to those 1980- First-year graduate students increased by the same 1981 new doctorates employed by doctorate-granting percentage over the previous year. The percentage departments in the U.S. The next two rows refer of new doctorates taking nonacademic employment to those employed by U.S. mathematical sciences dropped slightly to 27% from the 1980 figure of 29% departments which grant masters and bachelors degrees

TABLE 1-1981-1982 EMPLOYMENT STATUS OF NEW DOCTORATES IN THE MATHEMATICAL SCIENCES

PURE MATHEMATICS

Type of Employer Group I 14 16 16 6 1 1 4 2 60 Group II 8 11 17 4 1 4 3 2 50 Group III 8 7 8 2 1 6 5 4 1 7 49 Group IV 2 28 1 31 Group V 1 4 24 8 7 1 45 Masters 13 21 11 3 2 14 3 3 9 1 5 85 Bachelors 24 18 11 1 8 2 5 1 2 72 Two-year College or High School 2 1 1 3 7 Other Academic Depts. 2 2 1 2 34 9 14 11 1 8 84 Research Institutes 1 3 4 6 1 2 8 1 26 Government 1 3 1 1 12 2 5 3 28 Business and Industry 7 15 7 2 7 48 28 17 30 1 7 169 Canada, Academic 2 3 1 6 6 1 5 1 3 28 Canada, Nonacademic 1 2 2 4 2 1 1 13 Foreign, Academic 17 8 9 4 18 5 2 8 1 2 74 Foreign, Nonacademic 6 10 6 10 2 11 10 2 57 Not seeking employ. 1 2 2 5 Not yet employed Unknown 2 2 2 1 5 5 1 3 21 Total 106 123 96 20 22 208 92 64 114 10 49 904

145 only. There seem to be good job prospects for new Similarly, the second row in Table 2 includes som doctorates in departments in Groups M and B. It moving to or from departments in other fields o should be noted that the survey of enrollments shows other positions in academia (e.g., in a universit: that 50% of all computer science enrollment and 60% computer or statistical laboratory). The number (+ 7 4 of all statistics enrollment reported are in M and B in parentheses represents a flow from nondoctorat departments; mathematicians prepared to teach these to doctorate status of individuals who remained a courses will find no lack of opportunity to do so at full-time faculty members in the same department. those schools. The numbers in Tables 2 and 3 were obtained b, Faculty Mobility extrapolating from AMS Survey data, and are n~ actual counts. The various totals of the responses fron This part of the Annual AMS Survey is concerned each group were adjusted according to the fractim with the number of faculty members newly hired of the total faculty reported within each group, a from various sources, as well as with the number of those individuals leaving faculty positions and with given in a previous article in this series (February 197! information on their subsequent employment status. Notices, page 108). Nevertheless, Tables 2 and : The Survey also monitors trends in the percentage are believed to give a fairly reliable overall picture o of faculty members with tenure, and the percentage current faculty mobility. of faculty members with doctoral degrees. The Table 2 shows an estimated increase, betwee1 number of departments in each of the Groups, I, fall 1980 and fall 1981, of 404 in the size of th• II, ... , B responding to the 1981 Survey of faculty doctorate-holding faculty and an increase of 208 in th• mobility are similar to those of previous years. The nondoctorate faculty, for an overall increase of 612 responding departments represent about half of all the largest in a decade. However, the increase did no mathematical sciences faculty members. More than keep pace with rising enrollments. While faculty siz1 two-thirds of the faculty members in doctorate-granting increased by 3%, the number of teaching assistant mathematics departments (Groups I-III) are included reported for fall1981 increased by 8% over the previou among responding departments. fall. But course enrollments again rose by 8% an< Table 2 shows estimated faculty flow between 1980- inevitably class sizes also increased (Tables 7 and 8). 1981 and 1981-1982 for U.S. departments. Further The pattern of faculty mobility obtained b~ analyses for Groups I-III are given in Table 3. The left comparing the two sides of Table 2 continues th• side of Table 2 shows the estimated numbers of new trend of last year. More full-time faculty members ar• full-time faculty members hired from various sources being hired before receiving the doctorate. The figul'l between fall 1980 and fall 1981. The right side of of 739 shown in Table 2 corresponds to the estimate o Table 2 shows the fall 1981 employment status of 435 four years ago (February 1978 Notices, page 101) those full-time faculty members (as of fall 1980) who Most (84%) of the new nondoctorate faculty member: permanently left their departments by fall 1981. The were hired by departments in Groups M and B. row "graduate school" on the left side includes new Attrition due to deaths and retirements continue: faculty members coming from departments outside the at the yearly rate of about 1% of the total faculty mathematical sciences, or from mathematics education. In addition, some leave tenured faculty positions t1

TABLE 2 - FACULTY FLOW 1980-1981 TO 1981-1982 Full-Time Mathematical Sciences Faculty in Four-Year Colleges and Universities in the U.S.

Sources of New Facul~ Fall1981 Em(!lo~ment Status, Facul~ Leaving FROM Doctorate-Holding Nondoctorate TO Doctorate-Holding Nondoctorate

Two-year college Graduate school 468 317 or high school 15 62 Another college or Another college or university position 638 132 university position 471 72 Nonacademic Nonacademic employment 96 106 employment 212 122 Outside U.S. 80 11 Deaths and retirements 116 72 Position outside U.S. 37 0 Graduate or professional school 32 50 Seeking employment 24 19 Other sources(1) 84 173 Other(3) 55 60 Total 1361i 739 Total 962 457 Received doctorate and Received doctorate and not moving(2) J:!:W not moving (+74) 1440 531

Estimated size of full-time U.S. mathematical sciences faculty, Fall1981 Doctorate-holding 15,123 (+404 from Fall 1980) Nondoctorate 4,144 (+208 from Fall 1980) (1)part-time to full-time in same department, from postdoctoral or two-year college position, etc. (2)Mostly in Group M and B departments. (3)No longer full-time in department, unknown employment status, etc.

146 take nonacademic positions or for other reasons. The commitment to teaching, who can fit the needs of number of faculty members who received tenure in Groups M or B departments. their institutions is about 392, down from last year's Nonacademic Employment of Doctorates total of 443. in the Mathematical Sciences Doctorate-granting departments of mathe­ Table 4 is a summary of .A:MS Survey data on the matics (Groups I, n, Ill). Table 3 gives a somewhat employment of new doctorates during the last six years different perspective of faculty mobility in and out of 1975-1976 to 1980-1981. the 152 U.S. mathematics departments with doctoral TABLE 4 programs. In Table 3 the sources of new tenured NEW MATHEMATICAL SCIENCES DOCTORATES and nontenured doctorate-holding faculty members are TAKING NONACADEMIC POSITIONS IN U.S. shown, as well as the employment status of those 1975- 1976- 1977- 1978- 1979- 1980- leaving between academic years 1980-1981 and 1981- 1976 1977 1978 1979 1980 1981 1982. In Government 74 62 44 34 37 28 In Business/Industry 112 136 166 168 165 169 This table confirms the pattern of previous years and Total 186 198 210 202 202 197 emphasizes the cap on faculty size at these universities Total new doctorates which has prevailed for almost a decade. Although employed In u.S. 787 776 734 690 691 732 enrollments in the mathematics courses soar, faculty %in Govt. /Bus. /Ind. 24% 26% 29% 29% 29% 27% size remains virtually constant. The 1974 AMS Survey Table 4 shows a levelling off in hiring of new (November 1974 Notices, page 339) estimates the size doctorates by business and industry. Many of these of faculty at 5,500, while the 1981 figures show an jobs are in companies in high technology, computer­ increase to 5,609. information processing, or communications areas. A significant number are with organizations which do Groups M and B. The number of nondoctorate consulting work in operations research, statistics or faculty members hired by Groups M and B departments applied physics, or which provide computer software has been steadily increasing, from about 350 newly or data management services; other jobs are energy hired for fall1977 to 624 for fall1981. or automotive related, or health-care related. The The M and B departments are very diverse, November 1980 issue of Employment Information ranging from medium-to-large departments in public in the Mathematical Sciences contains lists of the institutions to quite small departments in private names and addresses of nonacademic employers of the colleges of varying degrees of selectivity. Besides individuals included in Table 1 on page 608 of the mathematics instruction, mathematics departments November 1980 Notices, with an indication of the in Groups M and B often have responsibilities in thesis field of the employee. applied areas which in larger universities are taken by Table 5 shows that relatively few individuals included separate departments of statistics, operations research, in Table 4 received a Ph.D. in pure mathematics. (The or computer science. As mentioned earlier, there are somewhat arbitrary classification "Pure" mathematics opportunities for young mathematicians with a strong is the same as in Table 1. "Other'' mathematical

TABLE 3 - FACULTY FLOW 1980-1981 TO 1981-1982 Full-time Doctorate-holding Faculty in 152 Doctorate-Granting Mathematics Departments In the U.S. (Groups I, II, III)

Sources of New Facul~ Fall1981 Em(!lo~ent Status, Facult:~:: Leavin11< FROM Nontenured Tenured TO Nontenured Tenured Graduate school 160 Doctorate-granting departments 91 37 Other college or university position 43 9 Another college or Nonacademic employment 55 12 university position 149 38 Deaths and retirements 2 34 Nonacademic employment 1 Position outside U.S. 22 Outside u.s. 42 Seeking employment 7 Other sources 19 l9 ! Other 24 J6 ~ Total 371 47 Total 244 98 Received doctorate and not moving (+4) Received tenure and Received tenure and not moving (+100) not moving (+100) 380 147 336 98 Estimated size of full-time faculty, Fall 1981, Groups I-III Doctorate, Nontenured 1,288 (+44 from Fall1980) Doctorate, Tenured 3, 905 (+48 from Fall1980) Nondoctorate faculty 416 (+24 from Fall 1980) Total full-time faculty 5,609 (+117 from Fall1980)

147 Doctorates in Mathematics and Related Areas NRC Reports: July 1967-June 1980

1967- 1968- 1969- 1970- 1971- 1972- 1973- 1974- 1975- 1976- 1977- 1978- 1979- 1968 1969 1970 !l!ll. 1972 1973 1974 1975 1976 1977 1978 1979 1980

Mathematics 970 1,063 1,218 1,236 1,281 1,222 1,196 1,149 1,003 959 838 768 745 A. Algebra 145 181 190 200 167 141 124 126 115 88 87 87 78 B. Analysis 246 266 244 262 241 244 213 180 141 152 118 111 91 C. Geometry 31 25 39 35 35 32 38 26 23 26 22 25 35 D. Logic 30 28 37 31 39 33 21 38 34 17 24 21 24 E. Number Theory 20 24 27 33 36 31 23 27 26 32 18 17 28 F. Probability, Mathematical Statistics 132 49 83 91 151 156 150 174 165 159 168 165 152 G. Topology 105 108 143 120 130 111 112 94 72 70 56 60 57 H. Computing Theory and Practice 51 79 118 139 163 221 194 167 147 101 55 25 13 I. Operations Research 3 24 55 36 42 43 43 41 J. Applied Mathematics 131 127 147 122 119 119 138 101 104 113 108 111 102 K. Mathematics, General 51 86 94 108 112 90 111 115 97 89 92 81 83 L. Mathematics, Other 28 90 96 95 88 41 48 46 43 70 47 22 41

Total Pure (A, B, C, D, E, G, K) 628 718 774 789 760 682 642 606 508 474 417 402 396 Total Other (F, H, I, J, L) 342 345 444 447 521 540 554 543 495 485 421 366 349

Computer Science 121 209 218

Engineering Computer Engineering 101 119 122 76 79 62 Electrical Engineering 602 688 706 748 690 673 601 536 512 461 410 451 405 Engineering Mechanics 227 238 235 215 209 176 161 162 113 102 95 85 91 Operations Research 62 104 125 90 82 76 84 66 63 Systems Design & Systems Science 79 68 71 62 75 62

Life Sciences Biometrics and Biostatistics 23 18 37 42 30 34 35 37 46 52 45 44 42

Social Sciences Econometrics 30 20 27 27 32 31 20 27 30 29 23 22 22 Statistics 19 96 121 133 85 62 36 43 35 36 46 23 33

Education Mathematics Education 95 111 128 131 152 134 110 108 96 98 57 85 74 sciences refers to the right-hand columns: Statistics, ... , numbers for statistics, computing and operations Other in Table 1.) There is some inherent ambiguity in research are subject to variations in classification, as an the count of "Other mathematical sciences" doctorates, examination of some of the lower lines in the printed since the boundary between the applied mathematical table will reveal. The figures given are extracted from sciences and engineering is not sharp. In addition, a series of NRC reports entitled Doctorate Recipients responses to the AMS Survey of new doctorates from from United States Universities. (These reports departments in Group V (especially from those in are published annually and may be obtained from the computer science) are less complete than from Groups I Commission on Human Resources, National Research -IV. Nevertheless, the AMS data have generally fitted Council, 2101 Constitution Avenue, N.W., Washington, rather well with NRC data obtained from the doctorate D.C. 20418.) recipients themselves (cf. February 1978 Notices, page TABLE 6 108). ESTIMATED NET OUTFLOW OF TABLE 5 DOCTORATE-HOLDING FACULTY MEMBERS THESIS SUBJECTS OF THE NEW DOCTORATES TO NONACADEMIC EMPLOYMENT IN TABLE 4 1976 1977 1978 1979 W.Q. ~ 1975- 1976- 1977- 1978- 1979- 1980- Net Outflow 155 190 190 165 168 116 1976 1977 1978 1979 1980 1981 In addition to new Ph.D.'s shown in Table 5 whose Pure 46 38 41 53 59 44 job after receiving the doctorate was nonacademic, Other 140 160 121 149 143 153 a significant number of others moved to positions in 186 198 210 202 202 197 government, business or industry after a few years in The table entitled Doctorates in Mathematics and faculty positions. Table 6 shows the estimated annual Related Areas, July 1967-1980, above, extends the net outflow of doctorate-holding faculty members to table published in 1978 to cover the years 1967-1968 nonacademic positions since 1977. For instance, the through 1979-1980. It depicts the rise and fall in the number 116 for 1981 is the difference of 212 doctorates number of doctoral degrees in "mathematics" awarded shown in Table 2 leaving academia and 96 hired in each year in this interval. The reports of corresponding academia from nonacademic positions: the number

148 TABLE 7 - PERCENT CHANGE IN COURSE ENROLLMENTS By Type of Course, Fall 1980 to Fall 1981 Type of Course Groups All Groups II III IV v VI M B

Below calculus -6% 4% 1% 4% 5% 3% First year calculus 3% 7% 9% 10% 10% 9% 8% Statistics * * 7% 22% 9% 4% 8% Computer Science * * * 12% 29% 26% 35% 27% Other undergraduate mathematics courses 7% 14% 7% 14% 8% 4% 9% Graduate courses 6% -1% 6% 15% 12% 10% 10% 7% 9% All courses 2% 7% 5% 9% 18% 16% 9% 10% 8% *Enrollments in this type of course amount to less than 5% of total undergraduate enrollments for this group of departments. hired from nonacademic positions (96) exceeds last Changes in Enrollments and Class Size year's total of 88. However, almost none of these As has been the case in recent years, enrollments individuals were hired in Group I-III departments as continued to climb in nearly every category. Computer seen from Table 3. science and statistics courses showed the biggest As mentioned above, the November 1980 issue increase. A most pleasing statistic was the dramatic of Employment Information in the Mathematical increase of 15% in junior-senior mathematics majors. Sciences shows nonacademic employment of new This increase was not confined to Groups M and B. doctorates for the period 1975 to 1980, by employer The increase for Groups I, II and III was still a hefty for various and field of degree. As might be expected 46% took 13%. Table 1 gives the percentage increases positions in the Virginia to Massachusetts arc and 18% courses. compares class sizes for mathematical in California. In addition to the 1980 annual salary Finally Table 8 departments for fall 1980 and fall 1981. survey of new doctorates (November 1980 Notices, sciences Class sizes continue to increase in most courses in page 607), the AMS surveyed individual Ph.D. math­ mathematical sciences departments. (An analysis of ematicians in nonacademic jobs during 1980. This the class sizes and related parameters for fall semesters survey gave information about salaries. The results 1976 and 1977 was presented by Lida K. Barrett in the were summarized in the November 1980 Notices, pages February 1978 Notices, pages 104, 105). 610 to 614. In summary, the 1981 AMS Survey showed an in­ Graduate student enrollments. Doctorate- crease of about 400 in the number of doctorate-holding granting mathematics departments in the U.S. (Groups faculty members in U.S. colleges and universities and I, II, III) happily reported a 6% increase in the number a corresponding increase of over 200 in nondoctorate of full-time graduate students from fall 1980 to fall faculty members. Most new doctorates (65%) found 1981. Further, the number of entering full-time first­ employment in academic positions, while 22% took time graduate students in Groups I, II, III increased by positions in government or industry. There were 1%. virtually no unemployed Ph.D.'s in mathematics at any Departments in other Groups reported similar level and there seems to be a shortage of new doctorate increases. faculty members at schools in Groups M and B.

TABLE 8 - AVERAGE CLASS SIZE IN FALL 1980 AND FALL 1981 (1980 figures appear in parentheses)

Type of Course Groups

I II ill IV v VI M B Below calculus (31) (44) (45) (41) (32) 32 45 46 42 32 First year calculus (35) (42) (41) (70) (36) (27) 37 43 44 80 37 28 Statistics (38) (34) (41) (35) (28) 42 40 45 37 28 Computer Science (40) (82) (30) (26) 43 93 32 27 other undergraduate (29) (33) (32) (40) (24) (16) mathematics courses 30 36 34 44 25 17 Graduate courses (9) (9) (9) (16) (15) (8) (10) (16) 10 4 10 19 18 7 10 17 All courses (29) (37) (37) (28) (30) (47) (33) (27) 31 38 38 32 35 51 34 27 A dash indicates that these courses represent less than 5% of total undergraduate enrollment for departments in this category.

149 QUERIES Edited by Hans Samelson QUESTIONS WELCOMED from AMS members regarding mathematical matters such as details of, or references to, vaguely remembered theorems, sources of exposition of folk theorems, or the state of current knowledge concerning published or unpublished conjectures. REPLIES from readers will be edited, when appropriate, into a composite answer and published in a subsequent column. All answers received will ultimately be forwarded to the questioner. QUERIES and RESPONSES should be typewritten if at all possible and sent to Professor Hans Samelson, American Mathematical Society, P. 0. Box 6248, Providence, Rhode Island 02940. QUERIES RESPONSES 253. Philip Quartararo, Jr. (Department of 238. (vol. 28, p. 255, April 1981, John Thome) Mathematics, Southern University, Baton Rouge, Are there applications of mathematics to law? Reply: Louisiana 70813). We are all aware of the existence Rudolf Carnap presents an axiom system for legal of twin primes, and the twin prime conjecture. The kinship relations in Introduction to symbolic logic following are generalizations which I conjecture are and its applications {Dover, New York, 1958), true: pages 222-225. He contrasts this sytem with the For each even positive integer k, (a) there exists a corresponding axiom system for biological relations pair of primes that differ by k; {b) there exist infinitely (pages 220-222). (Contributed by DavidS. Hart) many pairs of primes that differ by k; (e) there exists a For another reply to this query see page 512 of the pair of consecutive primes which differ by k; (d) there October 1981 Notices. exist infinitely many pairs of consecutive primes which 247. Jvol. 28, p. 512, October 1981, Pierre Cartier) differ by k. Is anyone aware of a prior appearance of Is R bornologieal? Reply: R 1 is bornologieal iff any of these in the literature? card I is less than the first measurable cardinal (Kelley­ Namioka et al., Linear topological spaces, Van 254. Armel Mercier (Department of Mathematics, Nostrand, Princeton, N. J., 1963, page 187). Also: If Universite du Quebec, 930 est, rue Jacques-Cartier, R 1 is not bomological, then card I is not less than Chicoutimi, Quebec G7H 2B1, Canada). Let k be the first strongly inaccessible cardinal (Mackey-Ulam a positive integer and let o ~ k - 1. Then for all theorem, see G. Kothe, Topological vector spaces. I, t E [0, 1], we have Springer-Verlag, pages 385-392; also C. L. DeVito, Math. Ann. 192 {1971), 83-89, and S. Simons, J. 1 London Math. Soc. 36 {1961), 461-473). {Contributed 2: (n"'{~}lc -(n+t)"'{-x}/c)= o(x"'+ ) n_z< n n+t logz by CarlL. DeVito) 250. (vol. 28, p. 607, November 1981, Albert A. where {y} denotes the fractional part of y. Is it Mullin) Does the arithmetic progression (an+ b), with possible to improve this result? (a, b) = 1, contain infinitely many products of two distinct primes {and two related questions)? Reply: 255. Andy R. Magid {Department of Mathematics, The answer is immediate from Dirichlet's theorem: University of Oklahoma, Norman, Oklahoma 73019). Find P1 = am + b, P2 = an + 1, then P1 · P2 = Is there a subfield F of the real numbers R such that b (mod a). There are also conjectural bounds for the R has (infinite) countable dimension as an F vector number of solutions. {Contributed by D. Coppersmith, space? A. Peretti, R. Stanley)

PROCEEDINGS OF THE STEKLOV INSTITUTE

TAUBERIAN THEORY AND ITS APPLICATIONS of Tauber, Littlewood, Hardy, Fatou, Subhankulov, by A. G. Postnikov Onishi, and lkehara. This monograph is devoted to the classical version of Tauberian theory. The principal role is played by 1980, Issue 2, Number 144, v + 138 pages (soft cover) Tauberian theorems with remainder terms for power list price $29.20, institutional member $21.90, individual member $14.60 series. Some applications of the theory are presented. ISBN 0-8218·3048-1; LC 80-23821 The book is divided into 29 sections and progresses Publication date: September 1980 from the Laplaoe-Stieltjes transform through theorems To order, please specify STEKL0/144N Prepayment is required for all AMS publications. Order from AMS, P.O. Box 1571, Annex Station, Providence, Rl 02901, or call toll free 800-556-7774 to charge with Visa or MasterCard.

150 LETTERS TO THE EDITOR

Birzeit University welcomed and invited to participate in seminars and The letters from Mary Gray (April 1981 Notices) colloquia and given full use of the library. I relate and Theodore Harris (October 1981 Notices) concerned this because before I left the U.S.A. I was told that various aspects of the situation of universities and I would have lots of trouble interacting with people mathematics on the Israeli-occupied West Bank. I at both Birzeit and Hebrew University because of the would like to add some first-hand insights from the 6 huge tensions in the area. Instead I found that I was months I spent in 1981 teaching at Birzeit University. warmly welcomed and accepted by both sides in spite I believe I am the only mathematician to teach at of the fact that I was open about going back and Birzeit who holds a regular faculty position in a North forth. However, there was virtually no direct contact American university. between the two faculties, though faculty members in The mathematics department faculty consisted of both mathematics departments expressed to me the about 14 people including 4 Ph.D.'s, about 6 with desire to have more contacts. The considerable tensions Master Degrees and the rest T.A.'s with Bachelor in the area make this very difficult but not, I think, Degrees. Of these 14 only 3 were non-Palestinian. impossible. (Two Ph.D.'s and one Masters.) This year they Finally I would like to comment on a Western were scheduled to have 6 Ph.D.'s, five of whom are stereotype about the status of women in Arab society Palestinian. While I was there 5 members of the faculty -much is changing. At Birzeit two members of the (including myself) were writing research papers. mathematics faculty are women (including last year's I judged the mathematics major program to be chairperson) and in my geometry class 3 (out of 13) roughly comparable to a solid mathematics major students, including the top student in the class, were program in North America except for a slight weakness women. In addition, many women are studying science in the linear algebra offering. In addition to the usual and engineering. My informal impression is that the algebra and analysis courses there were courses in percentage of women in science, mathematics and topology, probability and statistics, computer science, engineering is higher at Birzeit than in the average non-Euclidean geometry, and transformation geometry. North American University. About 10 mathematics majors graduate each year and David Henderson some go on to graduate school in Europe or North Cornell University America. Those that do go on seem to do well. Several of the current members of the faculty are Birzeit graduates who were supported by Birzeit while they got their advanced degrees abroad. At Birzeit I taught essentially the same upper-level Poliey on Letters to Editor geometry course which I teach at Cornell. The Birzeit Readers who wish to respond to letters published students did better on the average than my students in this issue are urged to do so before May 1, 1982. at Cornell mostly because there weren't the few weak Responses received by that date may be edited to reduce students which I normally have at Cornell. In general, repetition and will be considered for publication in the I found the students at Birzeit more serious about their August 1982 issue. studies than the students at Cornell. Even during Letters submitted for publication in the Notices are periods of heightened tension and confrontations with reviewed by the Editorial Committee, whose task is the military, studying, learning and teaching went on to determine which ones are suitable for publication. The publication schedule requires from two to four whenever it was physically possible. When classes months between receipt of the letter in Providence and could not meet the students always cooperated in publication of the earliest issue of the Notices in which rescheduling extra classes during the weekends. In it could appear. addition, both the fall and spring semesters last year Publication decisions are ultimately made by majority were extended in order that missed classes could be vote of the Editorial Committee, with ample provision made up. By my observation only a small percentage for prior discussion by committee members, by mail or at meetings. Because of this discussion period, some (about 5%) of the student body took part in any violent letters may require as much as seven months before a demonstrations (such as stone-throwing). final decision is made. It was clear to me that Birzeit has been doing a The committee reserves the right to edit letters. competent job of educating Palestinians despite the The Notices does not ordinarily publish complaints oft-times adverse conditions. Currently (December about reviews of books or articles, although rebuttals 1981 ), Birzeit is closed under military order and the and correspondence concerning reviews in the Bulletin acting president and deans have been placed under of the American Mathematical Society will be considered town-arrest and have been ordered not to confer with for publication. each other. This action has been protested by many Letters should be mailed to the Editor of the academics in Israel and abroad. Notices, American Mathematical Society, Post Office Box 6248, Providence, Rhode Island 02940, and will be As another side of my stay in the area I frequently acknowledged on receipt. visited Hebrew University (Jerusalem) where I was

151 International Congress of Mathematicians, Warsaw, August 1982

The Second Announcement of the 1982 Inter­ national Congress of Mathematicians was mailed Statement by G. D. Mostow from Poland in December; almost all of it is Chairman, U. S. National Committee for Mathematics reproduced on the following pages. {The First An­ nouncement was published in the Notices August January 15, 1982 1981, page 426.) Although the second mailing of announce­ Over a year ago the AMS offered to cooperate ments pertaining to the 1982 Warsaw Congress fully with the organizers of the International of the International Mathematical Union has Congress and to publish these announcements in already gone out, anxiety that the Congress this place in order that they may be distributed will not actually take place as scheduled is to all members of the American Mathematical widespread. Society and to others around the world who have Given the current interruption of communica­ access to copies of the Notices. tion with Poland, one can only speculate about This announcement was received in the United prospects for the Congress. However, as soon as States only a few days after the imposition of travel to Poland can be resumed, the President martial law in Poland. In spite of uncertainty of the IMU, Lennart Carleson, accompanied by about the Congress, and with concern for the the Secretary of the IMU, Jacques-Louis Lions, situation of the citizens of Poland, the editorial and Olli Lehto, Chairman of the 1978 Helsinki committee of the Notices, at its meeting in Congress, will visit Poland in order to determine Cincinnati, acknowledged its obligation to publish whether the Congress can be held in Warsaw as this Announcement as originally planned. scheduled. Upon their return, they will issue a On this page readers will find (a) a statement report on their findings. prepared during the sessions in Cincinnati by According to information provided by Polish G. D. Mostow, chairman of the U. S. National officials to President Carleson, the planned trip Committee for Mathematics, and {b) lists of offices should take place around February 1. in North American cities of LOT {the Polish national airline) and of travel agencies in North "Orbis" correspondents in Canada are: American American cities which are correspondents of the Express Co. (Peel Street, Montreal 110, Quebec 1200); Polish national travel office "Orbis". Thomas Cook/Overseas Ltd. {94 Adelaide Street West, NOTES. Page numbers which appear in the Toronto, Ontario M4W1A). text of the Second Announcement are those of In Mexico they are: Wagons-Lits/Mexicana (Avenida Juarez 88, Mexico City), (Avda Vallarta 1447, Poniente, the original and may be converted to the numbers Guadalajara, Jalisco), (Calle 60, No. 466 7-D, Merida, of the pages in this reprint by adding a suitable Yucatan); Mundus Tours de Mexico (Paseo De La Reforma constant (printed at the bottom of this page). 379-40, Pisa, Mexico 5). The original contains two copies of the application In the U. S. they are: Orbis Polish Travel Bureau Inc. {500 Fifth Avenue, Apt. 1428, New York, NY 10036); form, only one of which is reprinted. The plan American Express Co. {65 Broadway, New York, NY of Warsaw followed some pages which have been 10006); PAT Polish American Tours {250 West 57th Street, omitted {the second copy of the form and several New York, NY 10019); Wegi.el Travel Service {1985 Main Street, Springfield, MA 01103); American Travel Abroad, pages containing a comprehensive list of LOT Inc. {250 West 17th Street, New York, NY 10019). offices around the world). The plan of Warsaw The addresses and telephone numbers of the offices of does not have any indication of seale, and may LOT agencies in North America are: Chicago, O'Hare not have been constructed using one of the more {LOT, 333 North Michigan Avenue, Chicago, IL 60601, 312-236-3388, 312-236-5501); New York, JFK {LOT, Sales common metries. We understand, however, that Information and Reservations, Cables: POLLOT, 212-869- the Palace of Culture is about one mile from the 1074, toll free outside New York State 800-223-0593, toll Europejski Hotel, located on the plan near Saski free New York State only 800-442-7091); (LOT Sales Office, 21 East 51st Street, New York, NY 10022, 212-371-1260); Pare. -EDITORS LOT Executive Office, 500 5th Avenue, New York, NY 10110, 212-944-8116); LOT JFK Office, 212-656-7787 /8/9); Montreal, Mirabel {LOT, International Aviation Square, 1000 Sherbrooke Street W., Suite 2107, Montreal, Quebec, Canada, 514-844-2674, teletype 0525345); Toronto (LOT, AC, 130 Bloor Street W., Toronto, Ontario, Canada, 416-364-2035, 416-925-2311).

152 INTERNATIONAL CONGRESS OF MATHEMATICIANS

WARSAW POLAND

SECOND ANNOUNCEMENT

The Organizing Committ,e.e is pleased to Science and Mechanics of the Warsaw invite you to attend the International Con­ University, gress of Mathemaon f,Oil"Ill and of payments. will be aclmowledged by the 2.1. Invited lectures Congress Bur,eau of the Polish Travel Office "Orbis". In spring 1982, the :regist.ered mem­ Plenary addresses. On the recommendation beTs wiill receive the Third Anil1lounceme'l1lt of the Consultative Committee, appointed by whkh will include names •of the 'iinvited spea­ the International Mathematical Union, the kem and the schedu1e of l·e'Ctur.es. A more Organizing Committee has invited 16 mathe­ deta~1ed schedu1e and other :informati·on w:ill maticians to give one-hour plenary addresses. be pTovided in the "ICM-82 P:r,o.guamme" These lectures are intended to be broad dis1tribut•ed ·to members upon arrival in surveys of major recent developments in w.aTISaw. mathematics meant for a wide audience. They will be given in Congress Hall at the Palace 1. Place of the Congress o.f Culture. The capacity of the hall is about The Congress, as well as most of the accom­ 3000 seats. panying events, will be held at Palace of Addresses in sections. On the recommenda­ Culture situa·ted in the center of Warsaw, tion of the Oonsultativ.e Oommi·ttee, 136 ma­ close to the central railway station, hotels, thematicians have been invited to give 45- parking lots and grean areas. Palace of -minute addresses in specified sections. These CultUI"\e houses, among othem•: lectur.es are also meant to be broadly con­ ·- Congress Hall, ceived and to present surveys not necessarily - Department of Mathematics, Computer limited to the work of the speaker.

153 The list of sections is as follows: Organizing Committee: Institute of Mathe­ 1. Mathematical Logic and Foundations of matics of the Polish Academy of Sciences, Mathematics Sniadeckich 8, P.O. Box 137, 00-950 Warsaw, 2. Algebra Poland. 3. Number Theory 4. Geometry 2.3. Seminars 5. Topology Members who want to organize spontaneous 6. Algebraic Geometry seminars are asked to make all arrangements 7. Complex Analysis ,among themselves, either in advance or during 8. Lie Groups and Representations the Congress. A room for a specified time 9. Real and Functional Analysis should be requested during the Congress 10. Probability and Mathematical Statistics through the Coogress Bureau. 11. Partial Differential Equations 12. Ordinary Differential Equations and 2.4. ICMI symposium Dynamical Systems 13. Mathematical Physics and Mechanics The International Commission on Mathema­ 14. Control Theory and Optimization tical Instruction will organize a symposium 15. Numerical Methods during four afternoons on goals and contents 16. Combinatorics and Mathematical Pro- of school education in mathematics. gramming 17. Computer and Information Sciences 3. Proceedings of the ICM-82 18. New Applications of Mathematics 19. History and Educatioo Invited addresses and a report of the Congress will be published in the Proceedings 2.2. Short communications of the ICM-82. The .Proceedings are expected to appear by the end of 1983 and each ordinary Members of the ICM-82 can present a 10- member will receive a copy. -minute oral communication, provided they have registered by April 15, 82 and have 4. A tentative schedule informed the Organizing Committee of the title of their talk and the appropriate section The Opening Ceremony will be held on by that date. They are also requested to August 11, at 9.00 in Congress Hall. The submit an abstract in English, French, German President of the International Mathematical or Russian. The abstracts, propedy prepared Union will announce the names of the Fields and received by April 15, will be reproduced medalists and the meda1ls will be awarded. and distributed to all ordinary members on After the Opening Ceremony, addresses on registration in Warsaw. The abstract must be the worik of Fields nredlaHsts rwill be given typeW!I'itten (black ribbon) within a rectangle in Congress Hall. of 16.5 em wide and 25 em high on good Invited one-hour lectures will be d&livered quality· paper. Handwritten symbols should on: Thursday, Friday, Monday,_ Tuesday, be written in indelible black ink but used Wednesday, August 12, 13, 16, 17, 18 - sparingly. Cor!'echlons

154 During the Congress, an exhibition of -82. Details and prices are given in section 15 mathematical books will be open in Palace of this announcement. of Culture. 6. Accommodation in Warsaw 5. Social events Accommodation is, handled by Congress The Organizing Committee hopes that Bureau "Orbis". Hotels are divided into fol­ scientific and social activities can be well lowing categories: Lux Intercontinental, Inter­ integrated. The staff of the Congress Bureau continental, 1st A, B and C, 2nd A, B, C, and will be pleased to provide aU poss.ible inf.o·r­ student hostels. The number of rooms with ma:tion and ass]stance to members to arrange bathrooms as well as si:ngle roams is limited informal gatherings or to explore Warsaw on in 2nd A, B and C category hotels. Suites are their own. Materials describing various acti­ available in categories Lux Intercontinental vities in Warsaw will be distributed at re­ thru 1st A, B and C. Prices of suites will be gistration. given on request. In oroer to further promote personal oont;a·ots In all hotels the block reservation for ICM between members, several social events will participants has been made. However, the be organized, such as a get-together party, distribution of the available rooms in above a concert and a picnic. categories may not conform to the wishes of The party will be organized in two groups, the ICM members. It is therefore in the in­ on Thursday 12 and Friday 13. terest of participants who reserve accommoda­ The picnic will take place at the State tion through Congress Bureau "Orbis" to Stallion Stud at Boguslawice, 125 km from return the registration form as early as Warsaw. The stud includes 160 stallion and possible. about 50 sport horses. Bestdes a picnic party, The room prices are in US dollars. Partici­ participants will be offered a horse show pants may choose between the following called "Craco·w Style Wedding". The show alternatives: has been created jointly by the management of the State Stallion Stud at Boguslawice I. Package rates especially offered for ICM-82 and a Cracow song and dance ensemble. If members: tabl9S I and II. These rates apply is a lively spectacle with fo1k songs, dances, only if a room is booked for at least five co1ourful dresses and horres in original, overnights from 9 to 21.08.82 and no refund Cra•c·ow hamesses. The "Cracow S.tyle Wed­ will be possible in case of earlier departure. ding" represents good a.rtistic level amd a high class of riding teams and equipages. It was TABLE I (for the first five nights) enthusiastically received by spectators in many Refund for countries, among others in Finland, Sweden meals per Category and F.R.G. Considering the large number of person in of hotel persons participatmg in the excursion, there Polish ::'·t =~J ::bit: Zlotys will be two groups arranged: one on August ------14 (Saturday) and the second - on August 15 Lux Int. 415 2720 (Sunday). Also, on these two days, concerts ------~1_1 Intercon. 310 430 2125 will be given, each day for the group parti­ ------cipating in the eXicursion the other day. The 1st A 251 215 405 345 1700 excursion to Boguslavice will start just after B 225 335 1700 c 210 330 1700 lunch and return is planned around midnight. ------You are requested to give your preference 2nd A 195 155 315 265 1445 an the registration form. However, it is pos­ B 155 130 250 215 1445 s;ib1e thart; your wish will mot be met as the number of places in each group is limited. The above prices are in US dollars per All the events described above are free of room. They include breakfast and two meals charge. served at the hotel of residence. Participants Orbis tours. Durilng :the Congress, "Orbis", will receive coupons for lunch and supper the Polish Tna¥el Bureau, will orga:n:ize several in the period the room is booked for. The excursions for accompanying persons in War­ coupons are not refundable if not used. How­ saw and its vicinity. Orbis will also organize ever, one can resign from taking lunches and post-congress tours for members of the ICM- suppers at the hotel of residence and in this

155 TABLE II (for every additional night above five) The occupancy in a room varies from 2 to 4 persons. The price is 15 US dollars per night . ------~ngle ;oom Double room I Refund fo~·l· and bed and part of this sum is refunded in Polish Zlotys for meals. The reservation Category ' ;:r:~np~~ I 200 of hotel can be made in the period between August w/b w/o b w/b Iw/o b Polish I 9 and August 21, only. ------__ ---···----···· _Zlot_Ys ___ You are requested to give several pre­ 1 ferences for hotel accommodation by indicating the first choice by 1, the second by 2, etc. on ~:r::. :~ 1--~-~~~-----i-- :~ the registration form. The reservation will 1st ~ ~! 143· :~- 69-----~:----. be made successively as the bookings reach c 42 66 340 Congress Bureau "Orbis" and every effort will be made to meet the requirements of each participant. After a booking has been l_~nd ~__ j_;_Ll ;! .JL_- ~~ ~ :~~:r=~- made you will be informed by Congress Bu.~;eau case a refund in Polish Zlotys will be paid, "Orbis" about the name, address and exact the amounts of which are shown in the last rate of lodging. All correspondence regarding column. Table I shows the minimal charge accommodation should be addressed to if package rates are applied. Table II shows Congress Bureau "Orbis" and not to the the charge for every additional night above Organizing Committee. Even if you do not the first five. If you wish to apply package reserve accommodation through "Orbis", you accomodation then please mark on the re­ are kindly requested to include information gistration form whether you intend to take about your reservation in the registration meals at the hotel of your residence. form. Note: the discount on room and breakfast part in the above offer is about 25G/o. 7. Congress fees II. Persons requesting accommodation for less A participant of the ICM-82 is an ordinary than 5 overnights or arriving before August 9 member or an accompanying person. The or leaving after August 21, 82 or not wishing accompanying persons will not receive copies to apply package accommodation will be of abstracts or of the Proceedings of the charged with "bed and breakfast" rate as ICM-82, but will enjoy all other privileges follows: of ordinary members. All children under 15 years of age accom­ TABLE Ill panying an ordinary member may be covered by a single accompanying person fee. No fee - -~tegory -~ Singlelro;;-~ IDouble~-;;~~1 will be charged for children if the only service requested for them is reservation of acco­ ~hotel w/b w/o b [ ~'!:_ __w~"__~ mmodation. The fees, in United States dollars, are as ::~1==1:,. follows: lstA 157 45 78 66 before May 15, 82 after B 55 64 - ordinary members US $ 90 us$ 120 c 45 64 l------accompanying persons US $ 45 us$ 60 43 31 62 50 2ndA accomodation through B 32 24 45 35 Participants reserving c 19.5 30 Congress Bureau "Orbis" have to pay the following hotel deposits: The Table Ill above gives the present - in categories Lux Intercontinental regular prices in US dollaxs for room per thru 1st A,B,C US $ 50 night. These prices include breakfast except - in other categories US $ 20 for the category 2nd C where breakfast cannot The registration fee and hotel deposit should be obtained. be paid through your travel agent {list en­ Ill. Student hostels. The rooms in student closed) or to the Account Congress Bureau hostels axe -of modest standard, there are "Orbis" 1094-3173, NBP IX OM Warrsaw neither hotel services nor private bathrooms ICM'-82. No payments should be sent to the and, in general, breakfasts cannot be obtained. Organizing Committee. It is very important

156 that the name of participant and code ICM-82 hotel deposit will be refunded. No refunds be indicated on the bank draft. Personal will be possible after May 31, 82. cheques will not he accepted. Be sure you get a receipt of your payment from the agent or 8. Registration form bank and keep a copy of it with you when Registration form should be typed or printed you arrive in Warsaw. In order to ensure the in duplicate and returned with a copy of proper remittance of fees, the members are payment enclosed to the following address: kindly requested to enclose one copy of the receipt of the payment to the registration Congress Bureau "Orbis" form. ICM-82, P.O.BOX 146 00-950 Warsaw A registration will be valid only after the Poland Congress fee has been paid. Similarly, a re­ servation of accomodation will be valid only 9. Travel after payment of hotel deposit. Warsaw can easily be reached by dkect The remaining sum for hotel accomodation planes and trains from all European countries. can be paid: There are also direct fJights from Middle and 1. through one of your local travel agencies Far East as well as from North America. (list enclosed) or to the account of Polish Airlines "LOT", the official carrier Congress Bureau "Orbis", 1094-3173 NBP of the Congress, will be pleased to provide IX OM Warsaw, ICM-82 (please keep travel information. The addresses of its offices the receipt); are attached LOT will offer a 100/o reduction on regular ticket price for every member of 2. at the Congress Desk in your hotel in the Congress having a Confirmation of Warsaw or at the Main Registration Desk Booking. Such a Confirmation is sent by the Culture. in Palace of Polish Travel Office "Orbis" to each parti­ cipant after his r·egistration form has been Deadline for registration is May 15, 1982. received. Besides using LOT agencies, connected with If a cancellation is received by Congress the ICM, members or member gr·oups are Bureau "Orbis" before May 31, 82, the free to make other arrangements for their Congress fees and other payments including travel.

POLISH AIRLINES

10. Reception in Warsaw necessary information about the date and time of arrival and flight num'ber must be included An informa1tion desk f1or ICM members will in the registration form. Participants can also operarte at Warsaw Ai!rport on August 9-11, take, at their own expenses, an Airport Bus 1982. to the Air Terminal, a city bus No. 175 to the Transportation (Airport-Hotel only) will be center of Warsaw (stopping by Forum and provided free of charge for members arriving Victoria hotels, in particular) or a taxi directly on August 9, 10 and 11, 1982. However, the to the hotel.

157 The reception desk will be functioning in to be presented to the Polish custom authori­ Pala.ce •of Cultuve. Also, on August 10 and ties on your departw-e. It is not allowed to 11, it will he possible to register directly at take Polish Zlotys ne•iither to nor out of the hotel. Congress mat,erials will be available Poland. in Balace of Culture afterr pres,e

158 houses with their late Renais~a:nce or Ba­ tery in the western patrt of the tOMTn situat·ed roqtl€ facades. on the Hill of Jasna G6ra. price: US $ 10 per person price: US $ 45 per person

2. Wilan6w 8. Kazimierz Dolny - Majdanek (full day) On the outskirts of Warsaw, the Wilanow Kazimierz - a precious arcihitectural and Pa·Lace was the summer residence of King landscape complex, town of poets and pain­ John III Sobieski - the oonquel'er att V1enna. ters, monuments of Renaissance culture and The splendo·ur of its Baroque architecture art. and exqu1sit·e interiors places Wilan6w amOillg Majdanek - Nazi concenimation camp o­ the most beautiful historical monuments in pened on Himmler's 'order in 1941. the wor1d. Its magnificent moms contain price: US $ 29 per person period furniture, collections of 16th and 19th century china, old clocll:!s and a gallery of Excursions 1-4 will be organized every Polish portraits. morning except fm the days reserv·ed for price: US $ 6.50 per person social ·events (cocktails and picnics) as well as the days museums are closed. Excursions 3. :f:..azienki 5-6 - ·every evening except for the days The private r•esidence of the la•st Polish reserved for socdal events. All 1-6 start King - Stanislaw August Poniatowski. The August 12 and continue until 19. Excursions most heatiful par

The pl1ilncip8Jl •Cente~r of religious tradi­ tions in Poland to mhich rnumeLI."ous pd,lgri­ 3. Zakopane - Tatra Mountains mages are made every yea~r (,especially in The heart of the Tatra Mountains - the August). F·ounded in 1382. Thte Baul:itne Moms- lhighestt rocky mounta'ins in Poland. Both

159 health resort and main center of winter Tours 1 and 6 start on August 20 and sports. It has preserved its regional wooden finish with an ·overnight in Warsaw and architecture, furniture and decorative art. breakfast oh August 23. price: US $ 204 Tours 2-5 sta'l't on August 20 and finish US $ 28.50 - single room with an overnight in Warsaw and break­ supplement fast on August 24. PerS\OillS requ€5!t:ilng acoomodation in Warsaw 4. Rzesz6w - Renaissance architecture in after the post-oong:ress tours · are asked to Poland indicate it ·on the 'l"egistratiQn fol'lll1. Carpathian Mountains region - capital All tours' prices include: accomodation at city with Palace of Lubomirski family, Town first category hotels (except for tour No. 1 Hall etc. l..ancut near Rzeszow has an impo­ as no single rooms are available), entrance sing residence of the Lubomirski family and fees, meals, coach transportation as well as later of Potocki family, now museum, con­ an aJSsilstance ·Of foreign language speaking taining many works of art. Bacre. Wi~th Gothic and Rena;issance gateways aoo Persons ordering different post-congress bastions. In the oldest d:ist:rict of Qd;afl.sk, the tours or excursi-ons will be given a ticket at Old Ttown, the Gothic St. Elisabe,th's Church, the registl"ation indicating time of departure. the late Golth>ic St. John's Church and the In case the numbe'l' of vegisltered members Old Town Halil. is not sufficient, the excursion/tour will be price: US $ 198 cancelled and you will be offered to partici­ US $ 52 - single room pate in another one or will get a full refund supplement of the payment made. 6. Olsztyn - Mazurian Lakes Important: We wish to inform that all The capital of the Mazurian Region, an lists will be closed on July 26, 1982. Persons industrial and cultural center and an ideal who will decide at the last moment to alttend base for toul'ling tihis region. 'llhe Mazurian ICM-82 are requested not to mail any corres­ La,kes District is o:liten called the l"egion of pondence to Congress Bureau "Orbis" - thousand lakes while in fact there are two new registrations will be accepted on the thousand. first day of the Colllgress at Main Registra­ price: US $ 172 per person tion Desk at Palaoe ,of Cu1t'lllre. However, US $ 23 - single room accomoda·tion will be provided only if hotel supplement rooms are availa:ble.

160 ICM-8! REGISTRATION FORM

1. Surname ...... First name/s ...... Title Date and place of birth ...... Citizenship ...... Sex /M or F/ ......

Accompanied by: Sex Surname First name/s /M or F/ Age if under 15 1.

2......

3......

Complete mailing address: ...... I:~::~: ·::::::::::::::::::::::::::::::::::::::::::

Number of persons attending coctail ...... picnic Aug. 14 ...... Aug. 15 ......

I wish to attend sections: ...... , to present a .communication /yes or no/ ......

2. I. request accomodation for ...... adult/s, ...... child/ren. Number of single r-ooms ...... , double rooms ...... beds. Please indicate at least two choices: first choice by 1, second choice by 2, etc.

Lux Check-in date ...... Inter. I Inter. ItA r-;;-llc I 2A ~~~

single Check-out date ...... ------_I ___ No of beds in student hostel ...... double .. I

If a single is not available, I will share a double /yes or no/ ...... I wish to be charged acc·ord:ing to Tables I and II /yes or ,nof wish to receive the refund for meals /yes or no/ ...... wish to be charged according to Table III /yes or no/ Special wishes have made my own reservation through /agent/ ...... at /hotel/ ...... am arriving on August ...... at fltght no ...... from ......

I have sent to Acc.ount Congress Bureau "Orbis" NBP IX OM Warsaw nr. 1094-3173, ICM-82 the total ...... A copy of the ·receipt of payment is enclosed. us$

The arrangements and payments have been made through /agent/ /yes or no/ ......

I have applied /I am going to apply/ for a Polish visa on/about at the Polish Embassy/Consulate in (date) (address)

Date ...... Signature ......

161 3. I wish to take paDt in the following excursions/tour-s:

Date No of US$ Total Excursion-Tour 1st 2nd persons choice choice ------'------~------··------Excursions 1. I Old Town 10 I 2. Wilan6w 6,50 ------I ---1---'---- 3. Lazienki 6,50 4. Wedding in Lowicz 26 ---1---1------5. tetazowa Wola 25 Dinner 6. ---·------>----16 ------7. Cz~tochowa 45 1---1------.--1------8. Kazimierz D.-MI\idanek 29 ----1----+---·· ------Post-congress 1. Primordial Forest 135 ------1----1----1--- tours Southem Poland 193 2. ------3. Tatra Mountains 204 -----1------1-2-00______1 4. Renaissance Architecture in Poland --1------~ ----1----1------5. Northen Poland 198 --1------11------6. Mazurian Lakes 172 Transfers date ...... time ...... flight no ...... ~--15------hotel-airport TOTAL US$: ......

Accommodation requested after the Post-Congress Tour No ...... for ...... nights (rates from table III).

4. Payments

1 ordinary member registration fee us$ ...... (US $ 90 before May 15, US $ 120 after) ...... accompanying person/s registration feels US $ ...... Hotel deposit

(US $ 50 in Lux Inter. - 1st A,B,C) us$ ...... (US $ 20 in other categories) us$ ...... Excursionis No us$ ...... Post-congress tour/s No us$ ...... Transfer us$ ...... Acoomodation after post-congress tour us$ ......

Please return this form by May 15, 1982 to: CONGRESS BUREAU "ORBIS" P.O.BOX 146 00-950 WARSAW, POLAND telex: 814728 bkorb pl, cable: ozorbis, tel: 276208

162 OLD

t.azlenkl p • r c

163 Report to the Members of the Society Where Your Dues Go

As is reported elsewhere in this issue, the Council Formally, all of the dues income from individuals has found it necessary to raise dues once again, effective is presently allocated to the accounts for the Notices, for 1983, mainly to take account of inflation. Over Bulletin and Abstracts, but this is for accounting the years I have received a good many comments from reasons having nothing to do with the substance of the members about the size of dues, and I hope that this present question. rather broad discussion of the subject might be of some Obviously not all the expenses in the list below could interest. be charged against dues. The fact is that dues income There are several classes of individual membership, does not pay (and probably has not for a number with 1982 dues ranging from zero-for student nomi­ of years paid) for all direct member services. The nees and emeritus members, principally-to $72 for balance is made up from income from other sources contributing members. We anticipate income from -publications, investment income, contributions, ~age individual dues of $475,000. Other types of dues­ charges, etc. -or it is simply not made up. The SoCie~y institutional, for example-and contributions will yield sustained a deficit during the past two years, and 1s about $250,000 more, for a total of about $725,000. budgeted for one again in. 1982, of several hundred (These and all other figures refer to t~e !982 Budget, so income and expense figures are pred1ct1ons.) thousand dollars. (It is hoped that this is not the steady state; there have been unusual expenses in connection The "major" class of dues, in a sense, is the amount paid by regular members. Here is a brief history of with computerizing the offices in Providence and Ann what this amount has been in recent times as compared Arbor and eliminating the backlog from Mathematical with the cost of living, the years listed being those in Reviews, as well as substantial investments in new which dues were raised: publications whose costs have not yet been returned.) Some members have argued that the Bulletin TABLE 1 should be removed from the list of free privileges ~ Dues Cost of Living accompanying membership in the Society, and turned 1952 $14 $ 58 into a self-supporting subscription journal. This is one 1966 20 77 1973 24-32 106 of the possibilities being considered by the Executive 1979 36-48 150 Committee in its regular triennial examination, during 1982, of the publishing program of the Society, a~d (The cutoff between low and high ~ues in 197.3 was in fact it is one that will have to be addressed qmte an annual income of $15,000, and smce 1979 1t has directly, in view of the deficit position of the. Socie~. been $20,000; approximately half the regular members But one couldn't expect much drop in dues, 1f any, 1f pay at each of the two levels. In 1981, 4400 were low the Bulletin were made a subscription journal at some and 4700 high. The cost of living is indexed ~y the future time, because of all the other needs for dues GNP Implicit Price Deflator, which was normalized at income· if the Bulletin were removed from the above 100 in 1972.) It does not appear from these figures that list, remaining expenses would still not be covered dues have risen out of proportion to other costs. th~ by dues from individuals. It has always been the Since funds are fungible, it is difficult to say exactly feeling of the Council (and its Executive Committee) what members' dues are spent for; income from many sources is mixed together in the General Fund and used that the Bulletin is important in providing intellectual to cover a wide variety of operating expenses. Dues coherence among the Society's members, since it has income from individuals should probably be thought of been the only publication containing mathematics as covering expenditures that (a) are primarily for the which is received by everyone. In the hope of making benefit of individual members, and (b) are used by, or the Bulletin a more vital force, the Council decided at least are available to, all such members. In the case of many such expenditures, the users pay a fee or a TABLE 2 price but not enough to cover the entire cost, and it .is Item Net Cost the residual expense that is covered by dues, at least m Mathematical Reviews $ 253,000 part. Some examples, from the 1982 Budget are given Bulletin 252,000 Notices 166,321 in Table 2. Abstracts 80,000 Presumably it would be reasonable to charge any of Maintenance of members' records 101,000 these items against dues income, since they are services Combined Membership List 45,000 AMS Regional Meetings 77,000 provided to-or at least available to-all members. Joint AMS/MAA Meetings 11,000 The net costs of some of them could be decreased Annual AMS Survey (salaries, etc. ) 18,000 by increasing fees or prices, but in the judgment ElMS* 16,000 of the Trustees this would put an undue burden on Employment Register 11, 000 actual users, the principle being that these services are Total $1,030,000 maintained for the common weal and should be paid for in part by all members, not just users. *Employment Information in the Mathematical Sciences.

164 about four years ago to start publishing "research­ increased by raising other prices and fees, but it is expository" articles, and to curtail the number of the policy of the Trustees to disseminate mathematics research announcements. to Society members at "rock-bottom" prices. (Anyone I might point out that the Society's dues are not out who had not known this should compare per-page of line with those of similar organizations. The Council prices of Society publications described in this issue of Engineering and Scientific Society Executives, which of the Notices, for example, with those of other represents most of the societies of these kinds in comparable publications, recalling that members get this country, partitions its members into eight classes, 50% discounts.) There appears to be no algorithm ordered according to the size of their memberships. that says that one kind of price rise is indisputably The AMS is in Group 7 (the second largest) in the better than another. In any case, a strong effort following table, which gives 1981 dues. (Of the 44 is now being made to improve the Society's financial responding societies, 19 increased their dues in 1982, position by providing new products and services, while the AMS did not.) such as MATHFILE and the new Contemporary Mathematics series, and by expanding sales of both TABLE 3 old and new products overseas, so as to be a!>le to Dues for Regular Members avoid any price rise other than that required to meet Number of inflation. Group ~ Low Average Responses Dues income is important to the Society, of course, 1 $50 $30 $37 5 but much more important is the professional support 2 62 35 46 4 3 90 14 45 9 of the community; without that, the Society could 4 60 10 36 6 not continue to exist. Not every decision made by 5 60 30 41 7 the Council, its Executive Committee, or the Board 6 50 20 34 7 7 60 28 44 5 of Trustees can meet the approval of all members of 8 31 1 the Society. If you are a member who feels that one of these bodies has made a mistake in judgment Let me conclude with some general comments about and you have a constructive suggestion, you should the financial situation of the Society. About seven­ communicate the latter to them through the Secretary, eighths of the eight million dollar annual budget of Everett Pitcher, or to me for forwarding, or you should the Society is accounted for by its publications, in raise the issue at a business meeting. both income and expense, and about 9% of the total income comes from dues; the Society anticipates William J. LeVeque a deficit in 1982 of $218,000. Income could be

growing theoretical developments in structural and mechanical design problems. L. E. Payne, On. the stabilization of Ill posed Cauchy problems In nonlinear elasticity james Moseley, A nonlinear eigenvalue problem with an exponential nonlinearity CONTEMPORARY MATHEMATICS Erich Miersemann, Eigenvalue problems for varia­ (ISSN 0271-4132) tional inequalities George H. Knightly and D. Sather, Regularity and symmetry properties of solutions of the john shell equations for a spherical shell Kyung K. Choi and Edward j. Haug, Repeated PROBLEMS OF ELASTIC STABILITY eigenvalues in mechanical optimization problems AND VIBRATIONS Vadim Komkov and Edward j. Haug, Effects of edited by Vadim Komkov some nonlinear terms on the buckling of elastic The articles collected in this volume are enlarged bodies versions of the talks presented in one of the special Raymond H. Plaut, Vibrations and stability of shal­ sessions at the spring meeting of the American Math­ low elastic arches ematical Soci11ty held in Pittsburgh in May 1981. 1980 Mathematics Subject Classifications: 73H05 73H10 All papers are directly related to problems in sta· 73030. ' , bility or eigenvalue problems arising in considera­ Volume 4, vii + 137 pages (soft cover) tions of elastic stability or elastic vibrations. A mul­ List price $8.40, Institutional member $6.30 individual member $4.20 ' titude of papers has appeared in the five years pre­ ISBN 0-8218-5005-9; LC 81-12833 ceding this meeting in various aspects of elastic sta­ Publication date: September 1981 bility and elastic vibrations because of the rapidly To order, please specify CONMI4N Prepayment is required for all AMS publications. Order from AMS, P.O. Box 1571, Annex Station, Providence, Rl 02901, or call toll free 800-556-7774 to charge with Visa or MasterCard.

165 1982 AMS ELECTIONS Nominations by Petition

Viee-President or Member-a~ Large Rules and Procedures One position of vic&-president and member of the Council ex officio for a term of two years is to be Use separate copies of the form for (a) filled in the election of 1982. The Council intends candidates for vice-president, (b) candidates to nominate two candidates, whose names may be for member-at-large, (c) candidates for the expected to appear in the June issue of the Notices, Nominating Committee. which is scheduled to be mailed by the printer on May 1. To be considered, petitions must be ad­ 21. Nominations by petition in the manner described dressed to Everett Pitcher, Secretary, Box 6248, below are acceptable. Providence, Rhode Island 02940, and must Five positions of member-at-large of the Council arrive by July 10, 1982. for a term of three years are to be filled in the 2. The name of the candidate must be given same election. The Council intends to nominate seven as it appears in the Combined Membership List. candidates, whose names may be expected to appear If the name does not appear in the list, as in the June Notices. Nominations by petition in the in the case of a new member or by error, it manner described below are acceptable. The Council must be as it appears in the mailing lists, for has stated its intent to have at least ten candidates example on the mailing label of the Notices. and will bring the number up to ten if the nominations If the name does not identify the candidate by petition do not do so. uniquely, append the member code, which may Petitions are presented to the Council, which, be obtained from the candidate's mailing label according to Section 2 of Article VII of the bylaws, or the Providence office. makes the nominations. The Council of 23 January 3. The petition for a single candidate may 1979 stated the intent of the Council of nominating all consist of several sheets each bearing the· persons on whose behalf there were valid petitions. statement of the petition, including the name Prior to presentation to the Council, petitions in aid of the position, and signatures. The name of of a candidate for the position of vic&-president or of the candidate must be exactly the same on all member-at-large of the Council must have at least 50 sheets. valid signatures and must conform to several rules and 4. On the facing page is a sample form for operational considerations, which are described in the petitions. Copies may be obtained from the box. Secretary; however, petitioners may make and The Nominating Committee for 1983 use photocopies or reasonable facsimiles. 5. A signature is valid when it is clearly that The Council has approved the continuation of of the member whose name and address is given the procedure of filling places on the Nominating in the left-hand column. Committee by election. There will be four continuing 6. The signature may be in the style chosen members of the Nominating Committee, namely by the signer. However, the printed name and David Mumford address will be checked against the Combined Ralph S. Phillips Membership List and the mailing lists. No Linda Preiss Rothschild attempt will be made to match variants of George W. Whitehead names with the form of name in the CML. A There will be four places filled by election in a name neither in the CML nor on the mailing preferential ballot. The President will name six lists is not that of a member. (Example: The candidates for these four places. The names may be name Everett Pitcher is that of a member. The expected to appear in the June issue of the Notices. name E. Pitcher appears not to be. Note that Nominations by petition, in the manner described in the mailing label of the Notices can be peeled the box, will be accepted. Should the final number of off and affixed to the petition as a convenient candidates be less than eight, the President will bring way of presenting the printed name correctly.) it up to eight. 7. When a petition meeting these various The name of a candidate for member of the requirements appears, the Secretary will ask the Nominating Committee may be placed on the ballot by candidate whether he is willing to have his name petition. The candidate's assent and petitions bearing on the ballot. Petitioners can facilitate the at least 100 valid signatures are required for a name to procedure by accompanying the petitions with a be placed on the ballot. In addition, several other rules signed statement from the candidate giving his and operational considerations which are described in the box should be followed. consent.

166 NOMINATION PETITION FOR 1982 ELECTION The undersigned members of the American Mathematical Society propose the name of

as a candidate for the position of (check one):

o Viee-President o Member-at-Large of the Couneil o Member of the Nominating Committee

of the American Mathematical Society for a term beginning January 1, 1983.

Name and Address (printed or typed, or Notices mailing label)

Signature

Signature

Signature

Signature

Signature

Signature

167 News and Announcements

Assoeiate Editors Appointed for Computing Machinery, the Association for Symbolic Bulletin (New Series) Logic, the Association for Women in Mathematics, the Institute of Mathematical Statistics, the Mathematical The new associate editors for research-expository Association of America, the National Council of papers and for research announcements in the Bulletin, Teachers of· Mathematics, the Operations Research replacing those whose terms expired on December Society of America, the Society of Actuaries, the 31, were announced too late to appear in the Society for Industrial and Applied Mathematics, and 1982 Administrative Directory of the Mathematical The Institute of Management Sciences. Sciences which went to the printer in December. The new CBMS Council consists of presidents The associate editors for research-expository papers of the member societies together with three or are Hyman Bass (1984), S. S. Chern (1984), Frederick four officers. The semi-annual meetings of the W. Gehring (1984), Irving Kaplansky (1982), Peter Council are now planned to take place invariably in D. Lax (1983), John W. Milnor (1982), Hugh L. Washington, in conjunction with the spring and fall Montgomery (1983), and Gian-Carlo Rota (1984). meetings there of the Council of Scientific Society The associate editors for research announcements Presidents (CSSP). The first meeting of the new are Spencer Bloch (1984), Charles L. Fefferman (1984), Council is scheduled for 29 April 1982. It is CSSP Ronald L. Graham (1984), Melvin Hochster (1983), that has served as a model for the reorganized Robert P. Langlands (1982), Richard K. Lashof CBMS. Organized in 1973, CSSP has exceeded most (1982), Henry McKean (1984), Richard Melrose (1984), expectations as an effective Washington voice for the Yiannis Moschovakis (1983), I. M. Singer (1982), and professional science community. Henry L. Alder is Harold M. Stark (1984). the immediate past-chairman of CSSP, and MAA Terms expire December 31 of the year indicated in president Richard D. Anderson currently chairs the parentheses. quite active CSSP Committee on Science Education. CBMS Reorganized 1981 Direetory of Women in the Mathematieal Seienees At the January meeting of its Council in Cincinnati, the Conference Board of the Mathematical Sciences A new Directory of Women in the Mathemati­ completed a reorganization that had been in progress cal Sciences has recently been published by the since last spring. Dictated by financial considerations AMB-MAA-NCTM-SIAM Committee on Women in the reorganization has had as its main objective to Mathematics. Copies of the new Directory are being preserve the most essential function of CBMS as a distributed this month by the American Mathemati­ Washington interface for the professional community in cal Society to departments listed in the Mathematical the mathematical sciences. The other major functions Sciences Administrative Directory, along with copies of CBMS, securing and carrying out grant-supported of the 1982 Administrative Directory. projects of joint concern to member societies, has The Directory of Women contains biographical become increasingly difficult in recent years and has and bibliographical information on nearly one thousand been largely eliminated. female mathematicians, essentially all of whom are at When CBMS executive director Truman Botts retires the doctoral level. at the end of May, that office will be discontinued. The members of the joint Committee on Women At that time the Washington headquarters of CBMS in Mathematics in 1981 were Pamela Cook-loannidis, will be shifted from its present location at 1500 Jessie Anne Engle, Etta Z. Falconer, Phyllis Fox, Massachusetts Avenue N.W., to the Mathematical Mary W. Gray, I. N. Herstein, Edith H. Luchins, Association of America building at 1529 18th Street Cathleen S. Morawetz, Jacqueline C. Moss, Katherine N.W. The reduced CBMS management activities are L. Pedersen, Alice T. Schafer, Joel E. Schneider, thereafter expected to be carried out on a part-time Barbara Searle, and Gail Williams. The new Directory basis by MAA associate director Marcia Sward with of Women was produced with partial support provided part-time clerical support as needed. by the AMS, MAA, SIAM, AWM and several Though its antecedents go back to World War II, commercial publishers: Addison-Wesley Publishing it was in the 1960s that CBMS was officially founded. Company, Birkhii.user Boston, Inc., Marcel Dekker, Since 1967, its member societies have been of two Inc., W. H. Freeman & Co., Harper & Row, Krieger classes: . constituent, with two Council representatives, Publishing Company, Inc., and Springer-Verlag, New and affiliate, with one Council representative. Under York. the reorganization, the thirteen member societies are Copies of the 1981 Directory of Women in the all of one class. In alphabetical order, they are: Mathematical Sciences are available at $3 per copy, the American Mathematical Association of Two-Year prepaid. Requests for copies should be addressed to Colleges, the American Mathematical Society, the Professor Alice T. Schafer, Women's Research Center, American Statistical Association, the Association for Wellesley College, Wellesley, Massachusetts 02181.

168 New version of The Joy of 'lEX It will then be possible to access MATHFILE on any computer terminal, in one's home or office, and pay A year ago (February 1981 Notices, page 176) the only for connect time by the minute. AMS announced the availability of "version -1" of The cost for using MATHFILE will be about $1 per Michael Spivak's manual entitled The Joy of TFiX minute, including the telephone call required. A typical which describes the 'lEX macro package known as search should require from 5 to 10 minutes, making A.MS-'JEX. A.MS-'IEX was designed to handle almost online information retrieval very cost-effective. all constructions that arise in typesetting, including MATHFILE contains bibliographic and subject the most complicated mathematical displays, and is classification information of entries that occurred in expected to enable mathematicians and their technical Mathematical Reviews since 1973, as well as the since July 1979. Access typists to create manuscripts in a way that will make texts of the reviews themselves points include author, reviewer, title words, any words it possible both to prepare preprints in typeset form in the review, and classification codes. Searches can be and to provide computer-readable magnetic tape which limited to specific languages, dates, document types, may be used by publishers to prepare finished "camera­ and journals. ready" copy in the style of any of the standard A User's Guide, prepared by the Society, will provide mathematical journals. all the information necessary for effective searching of A new preliminary version of the manual ("version MATHFILE. 0") is now available. It describes the present version of More details on MATHFILE can be found in a the macro package, which permits the user to do many report published in the August 1981 Notices, pages things that could not be done with the earlier version. 449 to 451. The "final" version of the macro package and of the book are expected to be available in the latter part of Fulbright Awards for 1981-1982 1982, following the release by Donald Knuth of 'JEX82. Twelve Fulbright awards were made to American 'IEX82 is a greatly enhanced version of 'JEX, written in scholars in the mathematical sciences for the 1981- Pascal. 1982 academic year. The awards for lecturing, consultation, research, or travel were announced by 'lEX was created by Knuth several years ago (see the Council for International Exchange of Scholars. the March 1979 issue of the Bulletin (New Series), The recipients of the awards, their proposed which contains Knuth's Gibbs Lecture "Mathematical activity, and the institutions which they will visit typography", pages 337 to 372), and has proved to are listed below. Wayne W. Bishop (California State be very useful for mathematical composition in AMS University, Los Angeles) will lecture on mathematics publications, and for other purposes. An increasing at Monterrey Institute of Technology, Mexico. fraction of the Notices has been set using over David E. Blair (Michigan State University, East 'lEX Lansing) will do research on !G-symmetric spaces and the past year or so, and recently 'lEX composition has other areas of differential geometry at the University been initiated in the Proceedings. of Liverpool, United Kingdom. Chris M. Burditt In order to use 'lEX one needs access to one of a (Napa College) will teach courses in mathematics growing number of computer systems. Information on and computer science at Monterrey Institute of such systems is available from the 'lEX Users Group Technology, Mexico. Bruce H. Edwards (University of (TUG), care of the AMS in Providence. Information on Florida) will lecture on numerical and computational mathematics at various universities in Colombia. how to obtain a copy of the A.MS -'lEX macro package Leslie V. Foster (San Jose State University) will on magnetic tape may also be obtained from TUG. lecture on applied mathematics at the lnstituto "Version 0" of The Joy of TEXis currently available de Investigaciones and Universidad de los Andes, to anyone interested in learning about the system and in Bogota, Colombia. Jack L. Goldberg (University participating in its further development. Until March 1, of Michigan, Ann Arbor) will lecture on applied obtained for $7.50, mathematics, complex variables, and Fourier series, 1982, copies of "version 0" may be and on mathematics for educators, economists, and prepaid, from the American Mathematical Society, social scientists at Bogazi!(i Universitesi, Istanbul, Post Office Box 1571, Annex Station, Providence, Turkey. R. Neal Hart (Sam Houston State Rhode Island 02901 (please specify code JOYT). After University, Huntsville) will lecture on abstract March 1, 1982, the price will be $9.00. algebra at the University of Liberia, Monrovia. Michael M. Krieger (University of California, Los Angeles) will assist the university in a computer-aided MATHFILE design project, participate in research and teach MATHFILE, the Society's computerized version of seminars at Universidade Federal de Minas Gerais, Belo Horizonte, Brazil. David C. Kurtz (Salem Mathematical Reviews, is expected to be available College, North Carolina) will lecture on mathematics within a few weeks. The Society has signed a contract at the University of Malawi, Lilongwe. J. Richard with BRS (Bibliographic Retrieval Services), a vendor Landis (University of Michigan, Ann Arbor) will do used by many academic libraries. A sample file was research on theoretical and computational aspects exhibited at the Society's annual meeting in Cincinnati of the analysis of multivariate categorical data at last month and generated considerable interest among the University of Newcastle, Australia. Richard those who saw the BRS system in action. Shachtman (University of North Carolina, Chapel Hill) will lecture on operations research and statistics The Society's negotiations with DIALOG, another at Hebrew University, Jerusalem, Israel. Raymond major vendor, have been completed and MATHFILE Zepp (National University of Lesotho) will lecture will be available to DIALOG's customers as soon as the on mathematics at the National University of Ivory preliminary processing of the tapes can be completed. Coast, Abidjan.

169 NEW AMS PUBLICATIONS

AMS Book Orders-Toll Free Number For Users of VISA, MASTERCARD. Individuals in the continental United States may order books published by the Society by calling 800-556-7774 and using a charge card. The number will be attended from 8:00a.m. to 4:15 p.m. Eastern Time, Monday through Friday except on holidays. When using a charge card for mail orders, please be sure to specify whether VISA or MasterCard and include the account number, expiration date, and signature.

CANADIAN MATHEMATICAL SOCIETY Jiri Dadok, The C~ Chevalley's theorem CONFERENCE PROCEEDINGS S. S. Gelbart, L-packets for SLn Paul Gerardin, On harmonic functions of sym­ metric spaces and buildings The Canadian Mathematical Society has initiated Rebecca A. Herb, Discrete series character iden­ publication of the proceedings of internationally at­ tities and Fourier inversion tended conferences on pure and applied mathematics Jonathan Rosenberg, L 2-cohomology and Lie (including probability and statistics), and has arranged algebra cohomology for them to be published by the American Mathemat· W. Rossman, R-groups and orbits ical Society. The Editorial Committee for this new F. Shahidi, On non-vanishing of L-functions for book series consists of F. V. Atkinson, University of GL(n) Toronto; B. Banaschewski, McMaster University; C. Clark, University of British Columbia; Erwin Krey­ DIFFERENTIAL AND szig, University of Windsor, chairman; and J. B. PSEUDO-DIFFERENTIAL OPERATORS Walsh, University of British Columbia. The committee Roe Goodman, Horospherical functions on sym­ will maintain the highest professional standards. metric spaces Volume 1, 1980 Seminar on Harmonic Analysis, Tosinobu Muramatu and Michihiro Nagase, L 2- has been published. This volume is the proceedings boundedness of pseudo-differential operators of the 1980 Annual Seminar of the Canadian Mathe­ with non-regular symbols matical Society, held at McGill University August P. G. Rooney, Conjugates connected with the gen­ 4-22. It was devoted to Harmonic Analysis with eralized axially symmetric potential equation special emphasis on connections with Number The­ J. C. Taylor, An elementary proof of the theorem ory. A substantial part of the book is taken up by of Fatou-Naim-Doob the notes for James Arthur's minicourse on Auto­ Harold Widom, Szego's theorem and pseudo-differ­ morphic Representations and Number Theory. The ential operators rest consists of papers by speakers who submitted HARMONIC ANALYSIS sufficiently detailed expositions of their talks to con­ J. Aczel, Some good and bad characters I have form to the requirements of this series. known and where they led Volume 2 in the series, Current Trends in Alge­ John J. F. Fournier, Multilinear Grothendieck in­ braic Topology, edited by Stanley 0. Kochman of equalities via the Schur algorithm the University of Western Ontario, will be the pro­ David Gurarie, Burnside type theorems for Banach ceedings of a conference held at Vancouver in representations of motion groups and algebras December 1980. Hans P. Heinig, Interpolation of quasi-normed Conferences planned for 1982 are in Numerical spaces Involving weights Analysis and Approximation Theory. Paul Koosis, Entire functions of exponential type Anyone interested in recent developments in the as multipliers for weight functions mathematical sciences and their applications should Michael A. Rains, A function which does not be aware of this new series. As a matter of editorial operate policy, good authoritative survey articles will be en­ Eric T. Sawyer, Weighted norm inequalities for couraged, particularly in areas that presently are in fractional maximal operators rapid development. 1980 Mathematics Subject Classifications: 43-02, 22-02, 22E55, 42A50, 43A65. 1980 SEMINAR ON HARMONIC ANAlYSIS Volume 1, vi + 313 pages (soft cover) edited by Carl Herz and R. Rigelhof List price $15.20, institutional member $11.40, CONTENTS individual member $7.60 ISBN 0-8218-6000-3; LC 81-19116 LECTURE COURSE Publication date: January 1982 James Arthur, Automorphic representations and To order, please specify CMSAMS/1 N number theory REPRESENTATION THEORY OF SEMI-SIMPLE liE GROUPS Brian E. Blank, Embedding limits of discrete series of semi-simple Lie groups

170 COMPLEX CONTOUR CONTEMPORARY MATHEMATICS INTEGRAL REPRESENTATION (ISSN 0271-4132) OF CARDINAL SPLINE FUNCTIONS UMBRAL CALCULUS AND HOPF ALGEBRAS by Wolter Schempt edited by Robert Morris This monograph with a Foreword by Professor CONTENTS: I. J. Schoenberg is not a treatise on the theory of cardinal spline functions. It is a set of lecture notes S. A. Joni and G.-C. Rota, Coolgebros and biolge­ bros In combinotorics aimed at acquainting the student with the complex contour integral representation approach to cardinal Warren Nichols and Moss Sweedler, Hopf algebras and combinotorics spline functions. The basic idea is to use a suitable inverse integral transform instead of the direct This book represents a unique blending of two transform itself and then to have recourse to the fields only recently recognized as related. On one methods of complex analysis. Special emphasis is hand lies the field of combinatorics with roots (at placed on the cardinal exponential splines, which are least immediately traceable via generating functions represented by an application of the inverse bilateral to umbra! calculus, the speciality at hand) in the Laplace transform, and on the cardinal logarithmic 19th century writings of Booie on operator calculus. splines, the complex contour integral representation Both the foundations and much of the history of of which is obtained by the inverse unilateral Mellin the ~mbral calculus are explored in great clarity in transform. Although the convergence behavior of prev10us papers by Rota and others. On the other these two kinds of cardinal spline functions is hand is the field of Hopf algebras, which is usually totally different, the method of complex contour traced to a paper of Milnor and Moore but whose integral representation yields a unified treatment of first general exposition by Sweedler is little more both cases and gives powerful insight into what than a decade old. actually happens. In particular, the Newman-Schoen­ Both Rota and Sweedler were pleased when the berg divergence phenomenon loses some of its University of Oklahoma was able to support their mystery. The book will be useful to a broad audi­ joint appearance at a conference funded by the ence, interested in present trends of univariate J. C. Karcher Foundation in May, 1978. The confer­ approximation theory. In particular, it might prove ence centered on lectures they gave, with S. A. joni helpful for the development of seminars since most assisting Rota. Sweedler lectured first on elementary of the material covered is of recent origin. It is coalgebra theory aimed at combinatorists, Rota on however, primarily intended to serve as a elementary combinatorics aimed at the algebraists. textb~ok and guide to spline approximation theory for a Both lectures converged toward those who were or student with some familiarity in real and complex would work at the intersection. Sweedler and Warren analysis in one variable. No specific prior knowledge Nichols prepared notes of Sweedler's talks and joni of spline functions is necessary. and Rota of Rota's and a mimeographed version was The complex contour integral representation of circulated by the Oklahoma Mathematics Department. cardinal splines by means of linear integral trans­ The present volume makes these more accessible. form methods is a very effective technique for The Sweedler notes here are essentially unchanged dealing with these functions. In particular, their from those distributed by Oklahoma. They aim, in a asymptotic behavior as the degree tends to infinity direct and elementary way, to give the reader suffi­ can be analyzed conveniently and handled ade­ cient knowledge of coalgebra theory to understand quately by integral transform methods. The approach the coalgebra formulation of special sequences of to cardinal spline functions as described in the polynomials. monograph provides a very instructive illustration The Rota notes are reproduced from Studies in of the applications of inverse integral transform Applied Mathematics, volume 61, and represent a techniques combined with complex variables meth­ reworking of the original, with corrections and a ods to recent problems in approximation theory. few additions. They contain detailed applications not only to umbra) calculus, but to partition stud­ Even mathematicians specialized in the field of ies, incidence algebras, lattice theory, and other spline approximation are sometimes unfamiliar with traditional spheres of combinatoric interest. The the methods of integral transform analysis and the notes form a broad survey for anyone who would efficiency of this technique. For this reason the like detailed and concrete examples of the areas monograph gives full details of the necessary tools already known to be amenable to a coalgebraic ap­ from this important branch of applied mathematics proach. with the intention of presenting the material in a ' self-contained and fairly complete manner. 1980 Mathematics Subject Classifications: 16A24 05820 05-02, 16A20 ' ' Besides presenting an outline of inverse integral Volume 6, viii + 84 pages (soft cover) transform technique, the author studies several List price $7.60, institutional member $5.70 closely related topics. These include individual member $3.80 ' ISBN 0-8218·5003-2; LC 81-22756 - various complex integral representations of the Publication date: February 1982 basis spline functions, To order, please specify CONMI6N

171 - a useful complex contour integral representa­ developed here permit the author to consider, from tion of the Euler-Frobenius polynomials and a single point of view, the main concepts and laws its consequences, of mathematical statistics, methods of constructing - the classical Meray-Runge phenomenon as optimal statistical estimates, etc. The book is in­ preparation for Newman-Schoenberg. tended for those working in mathematical statistics, The author has published seven papers in this information theory, game theory, and also applica­ field recently, four of them in 1981 issues of the tions of probabilistic and statistical methods. Indi­ journal of Approximation Theory. vidual sections may be of interest to specialists in Based primarily on the author's own investiga­ measure theory, differential geometry and nonlinear tions and results in the field, the monograph deals functional analysis. with cardinal spline functions in a new way by a CONTENTS: systematic application of the method of complex 1. The formal decision problem contour integral representation. There exists no 2. Equivariant differential geometry of a collection treatment of the Newman-Schoenberg divergence of probability distributions phenomenon comparable with the presented one. 3. Smooth families of probability distributions and Most of the material covered is of recent origin and the information inequality appears for the first time in book form. The book 4. Geometry of exponent families of probability can be viewed in a certain sense as a complement distributions to I. j. Schoenberg's well-known monograph Cardi­ 5. Optimal decision rules in the equivariant problem nal Spline interpolation, SIAM, Philadelphia, PA, of point estimation 1973. Appendix, Notes and Comments, Bibliography, Index. 1980 Mathematics Subject Classifications: 41 A15; 44A 10, 1980 Mathematics Subject Classifications: 62COS, 62E1 0. 30E20, 41A10. 44A1S, Volume 53, viii + 499 pages Number/Volume 7, xiii + ·1 OS pages (soft cover) List price $76.00, institutional member $57.00 List price $8.80, institutional member $6.60, individual member $38.00 individual member $4.40 ISBN 0-8218-4502·0; LC 81-15039 ISBN 0-8218-5006-7; LC 81-22771 Publication date: january 1982 Publication date: February 1982 To order, please specify MMON0/53N To order, please specify CONMI7N

REFERENCE WORK SELECTED TRANSLATIONS MATHEMATICAL SCIENCES IN MATHEMATICAL STATISTICS ADMINISTRATIVE Dl RECTORY AND PROBABILITY This directory, published annually, lists key per­ (ISSN 0065-9274) sonnel-officers and committee members-of 31 pro­ fessional mathematical organizations and of a VOLUME15 selected group of government agencies, editors of edited by Lev}. Leifman over 100 journals, over 3,000 heads of academic The books in this series are published for the departments in the mathematical sciences, and heads Institute of Mathematical Statistics. The papers are of mathematical units in nonacademic organizations. selected by a joint committee of the IMS and AMS. Information includes current addresses (including CONTENTS: telephone numbers in many cases), terms of office, I. V. Ostrovskii, Description of the class 10 in a and other pertinent information for the organiza­ special semigroup of probability measures. tions represented. L. D. Me~alkin and B. A. Rogozin, An estimate of 1982 Volume, iv + 108 pages (soft cover) the distance between distribution functions In Price $12.60 terms of the proximity of their characteristic ISBN 0-8218-0074-4 functions and its application to the central limit Publication date: February 1982 To order, please specify ADMDI R/82N theorem. V. M. Zolotarev, The analytic structure of infinitely TRANSLATIONS OF divisible laws of class L. G. P. Cistjakov, On the stability of the decomposi­ MATHEMATICAL MONOGRAPHS tion for a class of Infinitely divisible laws. (ISSN 0065-9282) A. E. Fryntov, On a-components of infinitely divis­ ible laws. STATISTICAL DECISION RULES L. S. Kudina, On the closure of the set of indecom­ AND OPTIMAL INFERENCE posable distributions with given spectrum. by N. N. tencov L. Z. Liv~ic, On some conditions for the absence of Translation by Israel Program for Scientific indecomposable components in infinitely divisible Translations laws. I, II. Edited by Lev j. Leifman L. Z. Liv~ic, On some conditions for the absence of ABSTRACT. This monograph is devoted to the indecomposable components in Infinitely divisible general theory of statistical inference. The approaches laws.

172 G. P. Cistjakov, On the precision of the estimates MEMOIRS OF THE AMERICAN in theorems on stability of decompositions of MATHEMATICAL SOCIETY normal and Poisson distributions. (ISSN 0065-9266) A. I. ll'inskii, The indecomposable components of some infinitely divisible laws. THE BRANCHED CYCLIC COVERINGS A. D. Milka, lndecomposabl/ity of a convex surface. OF 2 BRIDGE KNOTS AND LINKS I. V. Ostrovskii and P. M. Flekser, Remark on the argument of a characteristic function. by jerome B. Minkus A. A. Gol'dberg and I. V. Ostrovskii, On the There is a need for concrete examples in 3-dimen­ growth of entire ridge functions with real zeros. sional topology. The manifolds Mn(k, h) are a 3 B. N. Ginzburg, On the growth of entire character­ parameter family of such examples-a family of istic functions of multidimensional probability "lenslike" spaces. They are obtained by pasting laws. together pairs of regions on the boundary of a B. I. Grigelionis, On stochastic equations for non­ 3-ball. Because of the explicit nature of the con­ linear filtering of random processes. struction it is easy to describe the fundamental I. I. E~ov and V. S. Koroljuk, Limit theorems for a groups and 1-dimensional homology groups of class of conditional Markov processes. these manifolds. It is hoped that much of this work I. N. Volodin, On discriminating between types con­ will be accessible to a reader who has a knowledge nected with the generalized gamma distribution. of very little more than the basics of combinatorial Endre Csaki, Investigations concerning the empirical topology and group theory. The manifold Mn(k, h) distribution function. is closely related to the 2 bridge knot or link of 1980 Mathematics Subject Classification: 60, 62 type (k, h). This approach also leads to a formula Volume 15, vi + 317 pages for the Alexander polynomials of 2 bridge knots. List price $50.00, institutional member $37 .SO, 1980 Mathematics Subject Classifications: 57M25, 57M12, individual member $25.00 57MOS, 20FOS. ISBN 0-8218-1465-6; LC 61-9803 Number 255, iv + 69 pages (soft cover) Publication date: December 1981 List price $4.80, institutional member $3.60 To order, please specify STAPR0/1 SN individual member $2.40 ' ISBN 0-8218-2255-1; LC 81-19099 Publication date: january 1982 PROCEEDINGS OF THE To order, please specify MEM0/255N STEKLOV INSTITUTE (ISSN 0081-5438)

LIMITS OF INDETERMINACY IN MEASURE OF THE EXPONENTIAL MAP T-MEANS OF SUBSERIES OF A AT AN ISOLATED SINGULAR POINT TRIGONOMETRIC SERIES by David A. Stone This work is a study in the local geometry of by D. E. Men'~ov translated by R. P. Boas geodesics in a metric space M which has an "iso­ lated conical singularity" at a point P; this means ABSTRACT. This monograph is devoted to the that M - {P} is a Riemannian n-manifold and that problem of the representation of functions by trigo­ near P the metric is approximately that of a cone nometric series. In the very general situation when from P on a closed, compact (n -1)-manifold. The the functions under consideration may even take main results are that M has at P a "tangent metric infinite values on sets of positive measure, the space" TpM, which is a cone, and an "exponential author establishes the existence, for a given regular map": a distinguished homeomorphism expp: summation method, of a universal trigonometric TpM --+ M defined near P, which carries each ray series, with coefficients tending to zero, which repre­ from P in TpM into a geodesic from P in M whose sents, in the sense of summability in measure of "tangent direction" at Pis the given ray. Affine appropriate subseries, all measurable functions. complex analytic hypersurfaces provide examples. The monograph will be of interest to specialists P is an "unbranched" isolated singularity of M if it in the theory of functions and related parts of is an isolated singularity (in the sense of Milnor) of analysis, and to graduate and postgraduate students the Whitney tangent cone T of M at P. In this case in mathematics. TpM exists and is homeomorphic toT. When n = 1, 1980 Mathematics Subject Classification: 42A24 any singular point P is an isolated conical singularity, Volume 149, iv + 56 pages (soft cover) so TpM and expp exist; there is a natural map List price $20.00, institutional member $1 S.OO, TpM--+ T which illustrates the algebraic multipli­ individual member $10.00 ISBN 0-8218-3043-0; LC 81-14992 city of P. An example is given, with n = 2, of an Publication date: November 1981 isolated singularity P which fails to be unbranched To order, please specify STEKL0/149N such that there can be no exponential map at P. '

173 AMS {MOS) Subject Classification (1970): 53B20. APPROXIMATION WITH RATIONAL FUNCTIONS Number 256, vi + 185 pages (soft cover) by D. ]. Newman List price $10.40, institutional member $7.80, CBMS Regional Conference Series in Mathematics individual member $5.20 Number 41,52 pages {ISBN 0-8218-1691-8) ISBN 0-8218-2256-X; LC 81-19100 1979; reprinted 1981 (soft cover) Publication date: January 1982 List price $11.00, individual $5.50 To order, please specify MEM0/256N To order, please specify CBMS/41 N FINITE GROUP ACTIONS ON SIMPLY­ CONNECTED MANIFOLDS AND CW COMPLEXES SPECIAL FUNCTIONS AND LINEAR by Amir H. Assadi REPRESENTATIONS OF LIE GROUPS Many problems in transformation groups are con­ by jean Dieudonne cerned with existence of actions of certain types. It CBMS Regional Conference Series in Mathematics is possible to formulate such problems as special Number 42,59 pages {ISBN 0-8218-1692-6) cases of the question of extending a prescribed 1980, reprinted 1981 {soft cover) action on a submanifold to the given ambient mani­ List price $9.40, individual $4.70 fold with control over the isotropy subgroups of To order, please specify CBMS/42N the action. This extension problem has been studied when the ambient space is simply-connected. The FOUNDATIONS OF POINT SET THEORY necessary homological and differential topological by R. L. Moore tools to solve the problem are developed. Colloquium Publications, Volume 13 Among the applications are: existence of PL and {ISBN 0-8218-1013-8), 419 pages (soft cover) topological actions on spheres leaving any finite 1932; revised 1962; reprinted 1981 List price $27.20, institutional member $20.40, simplicial complex fixed; classification of concor­ individual member $13.60 dance classes; construction of special actions on To order, please specify COLL/13N Euclidean spaces, disks, and spheres; solutions to some problems of P. A. Smith, Bredon, and Ray­ FUNCTIONAL ANALYSIS AND SEMI GROUPS mond. A final chapter surveys some of the recent developments of related problems. by Einar Hille and Ralph S. Phillips Colloquium Publications, Volume 31 1980 Mathematics Subject Classifications: 57S15, 57S25, {ISBN 0-8218-1031-6), 808 pages (soft cover) 57R65. 1948; enlarged and revised 1957; reprinted 1981 List price $30.40, institutional member $22.80, Number 257, x + 117 pages (soft cover) individual member $15.20 List price $7 .20, institutional member $5.40, To order, please specify COLL/31 N individual member $3.60 ISBN 0-8218-2257-8; LC 81-19104 Publication date: January 1982 To order, please specify MEM0/257N MODERN MODELING OF CONTINUUM PHENOMENA RECENT REPRINTS edited by R. C. DiPrima MATHEMATICS INTO TYPE Lectures in Applied Mathematics Volume 16,251 pages {ISBN 0-8218-1116-9) by Ellen Swanson 1977, reprinted 1981 {soft cover) 90 pages (soft cover) {ISBN 0-8218-0053-1) List price $44.40, institutional member $33.30, 1971; revised edition 1979; reprinted 1981 individual member $22.20 List price $12.40, institutional member $9.30, To order, please specify LAM/16N individual member $6.20 To order, please specify MIT/N GEOMETRY OF THE LAPLACE OPERATOR ON AXIOM A DIFFEOMORPHISMS edited by Robert Osserman and Alan Weinstein by Rufus Bowen Proceedings of Symposia in Pure Mathematics CBMS Regional Conference Series in Mathematics Volume 36, 323 pages {ISBN 0-8218-1439-7) Number 35,45 pages {ISBN 0-8218-1685-3) 1980, reprinted 1981 (soft cover) 1978; reprinted 1981 {soft cover) List price $20.40, institutional member $15.30, List price $8.20, individual $4.10 individual member $10.20 To order, please specify CBMS/35N To order, please specify PSPUM/36N

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174 Bryn Mawr, March 16-17, Bryn Mawr College Program for the 793rd Meeting

The seven hundred ninety-third meeting of the Jerrold R. Griggs, Daniel J. Kleitman, Frank Thomson American Mathematical Society will be held at Leighton, Andrew M. Odlyzko, Torrence D. Parsons, Bryn Mawr College, Bryn Mawr, Pennsylvania, on J. Scott Provan, David P. Robbins, Fred S. Roberts, Tuesday and Wednesday, March 16-17, 1982. The Thomas W. Tucker, Douglas B. West, and Thomas meeting will be followed by a symposium sponsored Zaslavsky. by the Association for Women in Mathematics to Operator theory, RHONDA J. HUGHES, Bryn commemorate the 100th anniversary of the birth of the Mawr College. Speakers will be Allen Devinatz, celebrated mathematician Emmy Noether. I. Erdelyi, Seymour Goldberg, Rhonda J. Hughes, Abel Invited Addresses Klein, Mark A. Kon, A. Edward Nussbaum, and Judith A. Packer. By invitation of the Committee to Select Hour Speakers for Eastern Sectional Meetings, there will be Applied mathematics, FERN HUNT, Howard four invited one-hour addresses, all of which will be University. The speakers are Gail A. Carpenter, presented in Goodhart Hall. The speakers, and the G. Bard Ermentrout, Nicholas Kazarinoff, Annett Nold, titles of their talks follow: and Jane Cronin Scanlon. ALBRECHT FROHLICH, University of London, Differential and differential-delay equations, England, and the University of Illinois, Urbana­ MARIO MARTELLI, Bryn Mawr College, and Champaign, Rings of algebraic integers as Galois ROGER D. NUSSBAUM, Rutgers University. The modules. speakers will be Kathleen T. Alligood, Jack K. Hale, STEPHEN S. SHATZ, University of Pennsylvania, John Mallet-Paret, Walter V. Petryshyn, William F. Philadelphia, What does it mean to classify algebraic Trench, and James Yorke. varieties and how does one do it? Mathematics of voting and bargaining, SAMUEL NANCY K. STANTON, University of Notre Dame, MERRILL, Wilkes College. The speakers will be The heat equation in several complex variables. Francine F. Abeles, Douglas H. Blair, Peter C. Fishburn, Arthur Q. Frank, William V. Gehrlein, LEONID N. VASERSTEIN, Pennsylvania State Dale T. Hoffman, William Lucas, Samuel Merrill, University, University Park, Classical groups over III, Christopher H. Nevison, Edward W. Packel, and rings. Donald G. Saari. Special Sessions Applications of algebra, VERA PLESS, University By invitation of the same committee, there will of Illinois at Chicago Circle. The speakers are N.J.A. be twelve special sessions of selected twenty-minute Sloane, and Richard P. Stanley. papers, some of which will be related to the Noether Algebraic geometry and cognate areas: Al­ Symposium. The sessions will be held in the Physical gebraic number theory, and commutative algebra, Sciences Complex. The topics of these special sessions, STEPHEN S. SHATZ. The speakers will be Greg names of the organizers, and lists of speakers follow: W. Anderson, J. Eric Brosius, Bruce Crauder, Sankar Constructive methods in algebra, CHRISTINE P. Dutta, Lawrence Ein, David Harbater, Melvin AYOUB, Pennsylvania State University, University Hochster, Marc N. Levine, Rick Miranda, Yevsey A. Park. The speakers will be Michael M. Anshel, Gilbert Nisnevich, Ulf A. Persson, and V. Srinivas. Baumslag, J. T. B. Beard, Jr., Dennis Estes, Anthony Representation theory of finite groups and Lie M. Gaglione, Robert Gilmer, Christoph M. Hoffmann, groups, BHAMA SRINIVASAN, University of Illinois Erich Kaltofen, Ray Mines, Ani! Nerode, M. Pobst, at Chicago Circle. The speakers will be Dean Boris Raykshteyn, Fred Richman, James Solderitsch, Alvis, Kristina Hansen, Rebecca A. Herb, Philip C. Hale F. Trotter, David Y. Y. Yun, and Hans J. Kutzko, Kathy McGovern, Ch. Riedtmann, Linda Zassenhaus. Portions of the lectures by Nerode and Preiss Rothschild, Diana Shelstad, Peter L. Slodowy, Zassenhaus will refer to the work of Emmy Noether. Birgit Speh, and A. Turull. Galois module structure of algebraic integers, Several complex variables, NANCY K. STAN­ ALBRECHT FROHLICH. The speakers will be TON. The speakers are Eric Bedford, Stephen R. Stephen U. Chase, Lindsay N. Childs, Ted Chinburg, Bell, Harold P. Boas, AI Boggess, Daniel M. Burns, Maryse Desrochers, Kurt C. Foster, Donald E. Maurer, Jr., Alexander Dynin, Leon Ehrenpreis, James J. Faran, Leon R. McCulloh, Jacques Queyrut, Jack Sonn, C. Robin Graham, C. Denson Hill, J. J. Kohn, Steven Stephen V. Ullom, and David L. Webb. G. Krantz, John C. Polking, R. Michael Range, Bernard Combinatorics and graph theory, C. M. Shiffman, Geraldine Taiani, David S. Tartakoff, and GRINSTEAD, Virginia Polytechnic Institute and State Pit-Mann Wong. University, and STEPHEN B. MAURER, Swarthmore Algebraic K- and L-theory, LEONID N. College. The speakers will be Robert G. Bland, Ethan VASERSTEIN. The speakers will be Hyman Bass, S. D. Bolker, Robert Calderbank, Fan R. K. Chung, Don Bloch, Ruth Charney, James F. Davis, Keith Dennis, Coppersmith, Ira M. Gessel, Charles H. Goldberg, Eric M. Friedlander, Susan C. Geller, Charles H. Giffen,

175 Henri Gillet, Daniel R. Grayson, Bruce A. Magurn, American Mathematical Society's meeting and should Andrew A. Ranicki, Michael R. Stein, Richard G. make their own reservations. Although the cut-off date Swann, R. W. Thomason, Karen Vogtmann, and was February 15, rooms might still be available. Rates Charles Weibel. listed are subject to possible change and do not include the 6 percent Pennsylvania state tax. Contributed Papers St. Davids Inn (3 miles from Bryn Mawr College) There will also be sessions for contributed ten-minute Lancaster Avenue, (Route 30), St. Davids 19087 papers on Wednesday. Telephone: 215-688-5800 Single $52 Double $59 Council Meeting Arrangements have been made to run bus service The Council of the Society will meet at 7:00 p.m. between the St. Davids Inn and Bryn Mawr College on Tuesday, March 16, in Delaware Room 1 at the three times a day from Tuesday through Friday, March Philadelphia Marriott Hotel, City Line Avenue and 16---19. St. Davids and Bryn Mawr are also connected Monument Road. by ConRail (Penn Central) Railroad, which provides frequent Registration service. Philadelphia Sheraton Hotel (10 miles) The AMS meeting registration desk will be located 1725 J. F. Kennedy Boulevard, Philadelphia 19103 outside Room 245 on the second floor of the Physical Telephone: 215-568-3300 or 800-325-3535 Sciences Building, and will be open from 8:30 a.m. Single $49 Double $59 until 4:00 p.m. on Tuesday and Wednesday, March 16- The Sheraton is located directly above the Penn Center 17. The registration fees for the AMS meeting will Station; see the TRAVEL section for directions to Bryn be $10 for members of the AMS or the AWM, $16 Mawr College by train. for nonmembers, and $5 for students or unemployed mathematicians. Valley Forge Hilton (8 miles) 251 West DeKalb Pike (Route 202) King of Prussia 19406 AWM Noether Symposium Telephone 215-337-1200 Single $55 Double $70 The Association for Women in Mathematics has A limited number of dormitory rooms might be organized a symposium to commemorate the lOOth available on campus, mostly for single occupancy. anniversary of the birth of Emmy Noether. The Anyone interested in obtaining these inexpensive symposium will start on Wednesday evening, March accommodations should write to Ms. Dedi Feldman, 17, and continue Thursday and Friday, March 18- c/o Department of Mathematics, Bryn Mawr College, 19, following the AMS meeting. It is anticipated Bryn Mawr, Pennsylvania 19010, to determine whether that the symposium will be supported in part by a or not accommodations might still be available. grant from the National Science Foundation. Although rooms have not been bloeked at the On Tuesday and Wednesday the registration desk following, they are included here for information for the symposium will be located near the AMS purposes. registration desk outside Room 245 on the second Budget Lodge at Valley Forge (8 miles) floor of the Physical Sciences Building, and will Route 202 and Schuylkill Expressway (I-76) be open from 8:30 a.m. until 4:00 p.m. On King of Prussia 19406 Thursday and Friday the symposium registration Telephone: 215-265-7200 desk will be located in Goodhart Hall and will be Single $25 Double $30 and $35 open from 8:30 a.m. until 3:00 p.m. Registration Howard Johnson's Motor Lodge (8 miles) fees for the symposium will be $3 for members of Route 202 and Gulph Road the Association for Women in Mathematics or the King of Prussia 19406 Telephone: 215-265-4500 American Mathematical Society, $5 for nonmembers, and $1 for students or unemployed mathematicians. Single $37 Double $40 (1 bed) $44 (2 beds) Philadelphia Mamott Hotel (6 miles) The Organizing Committee includes Michael City Line Avenue and Monument Road (Route 1) Artin, Israel N. Herstein, Rhonda Hughes (chair), Philadelphia 19131 Alice Schafer, Martha K. Smith, and Bhama Telephone: 215-667-0200 Srinivasan. The Organizing Committee thought Single $66 -72 Double $76 - 82 it was appropriate to hold the symposium at Bryn Food Service Mawr in conjunction with the Society's meeting, as a fitting tribute to Emmy Noether. The symposium Participants may obtain meals at restaurants in the Bryn Mawr program is included following the AMS meeting area; a list will be available at the program in this issue of the Notices. registration desks. Meals on campus will only be provided in Haffner Hall on a prepaid reservation basis. The form which must be used for subscribing Accommodations to the campus meal service is included on the next Rooms have been blocked for participants at the page; it must be returned to Ms. Peggy Linus, following hotels or motels in the area. Individuals Department of Mathematics, Bryn Mawr College, Bryn should identify themselves as participants in the Mawr, Pennsylvania 19010, by Marcil 10, along with

176 AMERICAN MATHEMATICAL SOCIETY ASSOCIATION FOR WOMEN IN MATHEMATICS

BRYN MAWR MEETING- MEAL SERVICE RESERVATION FORM

Meals on campus will be provided ONLY in Haffner Hall, on a prepaid reservation basis. Place a check mark in appropriate column(s) for each meal to be reserved; indicate total number of meals ordered and total cost for each. Mail this form to Ms. Peggy Linus, Department of Mathematics, Bryn Mawr College, Bryn Mawr, Pennsylvania 19010 so as to arrive by MARCH 10, along with a check or money order payable to Bryn Mawr College to cover the cost of all meals reserved. Participants will be sent a receipt, and meal tickets may be picked up at the registration desks.

NAME OF PARTICIPANT------ADDRESS------

ZIP CODE

Monday Tuesday Wednesday No. of MARCH 16-19, 1982 Thursday Friday Saturday Total Cost Dinner only) (Brkfst. only) Meals of Meals

Breakfast-$3/day xxxx $

Lunch-$4. 50/day xxxx xxxx $

Dinner-$7. 50/day xxxx $

Meal Plan- $11. 50/da xxxx xxxx $

Thursday evening Banquet-add $2.25 if paying for Thursday dinner above $ Thursday evening Banquet-add $9.75 if not paying for Thursday dinner above $

Participants are advised to retain a copy of this form for their records. Total amount enclosed: $

"""''"""""~----"'

\ - 1 ~N MAWR COLLEGE \_ -~~~N MAWR, PENNSYLVANIA MONTGOMERY ®=PARKING -free AVENUE

177 payment for the total number of meals reserved. baggage claim areas to assist passengers. Participants Participants will be sent a receipt, and meal tickets arriving at the airport can also take the SEPTA bus may be picked up at the registration desks. from the baggage areas at the airline terminals to the The daily rate for three meals is $11.50, which 30th Street train station in downtown Philadelphia, includes breakfast, lunch, and dinner. Meals may also and follow the directions below for train service to be reserved on an individual basis, the prices for which Bryn Mawr. These buses run every half hour from 6:50 would then be: breakfast $3, lunch $4.50, dinner $7.50. a.m. untilll:lO p.m. daily. Vegetarian choices are available at all meals. Breakfast Trains arrive at either the Penn Center Station will be served from 7:00 to 9:00a.m., Tuesday through (sometimes called the Suburban Station) at 16th Street Saturday; lunch from 11:45 a.m. to 1:15 p.m., Tuesday and J. F. Kennedy Boulevard, or the 30th Street Station through Friday; and dinner from 6:00 to 7:00 p.m., at 30th and Market Streets in downtown Philadelphia. Monday through Friday. Take either the Paoli or the Bryn Mawr local trains to reach Bryn Mawr. The walk from the station to Soeial Event the college takes approximately 8 minutes; walk across A banquet will be held in Thomas Great Hall at 6:15 Montgomery Avenue by the Baldwin School to Yarrow p.m. on Thursday evening for participants attending Road and turn left on Yarrow Road to Rockefeller Arch the Noether Symposium. The cost is an additional at the college. Taxis also operate from Bryn Mawr $2.25 for those already paying for Thursday dinner station daily, and a direct-line telephone is located on under the meal plan, and $9.75 for others. Individuals the wall of the taxi booth on the west-bound train may purchase tickets for the banquet at the registration platform. The estimated train time to Bryn Mawr desk until noon on Tuesday, or in advance by sending station is 18 minutes from 30th Street and 21 minutes in the meal service form referred to above. from Penn Center. Book Store Participants coming by car via the Pennsylvania Turnpike should take Exit 24 (Valley Forge Inter­ The Bryn Mawr College Book Shop will be open change), and follow signs to Route 76 East (Expressway daily Monday through Friday from 9:00 a.m. until 4:30 to Philadelphia). Drive approximately 3 miles and leave p.m. Route 76 at Gulph Mills Exit, taking Route 320 South Child Care (Gulph Road becomes Montgomery Avenue). Continue Arrangements for babysitting on campus may be 4 miles on Montgomery to Morris Avenue; turn left made for both the AMS meeting and the Noether (north) on Morris and, after one block, turn left Symposium. Participants are advised to make arrange­ again onto Yarrow Street. The distance from the ments in advance by contacting Ms. Nancy Solderitsch, Pennsylvania Turnpike to the campus is 8 miles, and Department of Mathematics, Villanova University, Vil­ estimated driving time is 25 minutes. lanova, Pennsylvania 19085; the telephone number is Those coming from north of Philadelphia on 215-645-7336. Information will also be available at the the New Jersey Turnpike should take Exit 6 registration desk. (Pennsylvania Turnpike Entry) and drive west to Exit 24 (Valley Forge Interchange) then follow the above Library and Noether Exhibit directions. Canaday Library will be open from 8:00 a.m. to Drivers coming from south of Philadelphia should 10:00 p.m. Monday through Friday. There will be leave the New Jersey Turnpike at Exit 3 (Camden­ a display of Noether memorabilia from the College Woodbury) and follow the green "Walt Whitman archives in the library foyer. Bridge" signs to Route 168 North; drive approximately Athletic Facilities 1 mile and follow signs to Route 295 South. Take Route 295 South for about 1 mile and bear left to join Route The College's athletic facilities will be available to 76 North, still following the Walt Whitman Bridge participants on a limited basis. Details will be available signs; after crossing the bridge this becomes Route at the registration desk. 676. Continue on Route 676 following the blue signs Parking indicating "Schuylkill Expressway-West Philadelphia" A limited number of parking spaces will be available and join the Expressway (which is still Route 676). to participants on campus at no charge in either the As the Expressway reaches center-city Philadelphia, Wyndham or Erdman lots, both off Morris Avenue. follow signs indicating "through traffic" and "Route 76 West, Valley Forge". From this area continue to follow Travel the ''Valley Forge" signs, until about 4 miles west Bryn Mawr is a 35-40 minute drive from Philadelphia of center-city take Exit 41, which is a ramp marked International Airport, which is served by most major "U.S. 1 South-City Avenue"; continue on U.S. 1 to airlines. Bennett Airport Limousine Service provides Lancaster Pike (Route 30) and turn right on Route transportation to and from the airport, Bryn Mawr 30 to Bryn Mawr. When reaching Bryn Mawr, turn College, and St. Davids Inn between 7:00 a.m. and right at the Bryn Mawr Trust Company and follow the 11:30 p.m. daily, at a one-way cost of $7 for each traffic pattern under the railroad to a traffic light at person. Liberty Limousine travels to and from the Montgomery and Morris Avenues. Continue one block airport and the Valley Forge Hilton between 8:00 a.m. on Morris Avenue to Yarrow Street. The distance from and midnight, and the one-way fare is $8.20 per person. the New Jersey Turnpike to center-city Philadelphia is Both services have dispatchers on duty at the airport 9 miles; estimated driving time is 20-30 minutes.

178 PRESENTERS OF PAPERS

Following each name is the number corresponding to the speaker's position on the program • Invited one-hour lecturers * Special session speakers

*Abeles, F. F. 114 * Ermentrout, G. B. 37 *Kon, M. A. 16 *Rothschild, L. P. 82 *Alligood, K. T. 97 *Estes, D. 48 Kramer, K. 162 *Saari, D. G. 34 *Alvis, D. 123 *Faran, ]. ]. 68 *Krantz, S. G. 2 *Scanlon, ]. C. 39 *Anderson, G. W. 126 *Fishburn, P. C. 117 * Kutzko, P. C. 80 •Shatz, S. S. 19 *Anshel, M. M. 74 *Foster, K. C. 148 *Leighton, F. T. 26 *Shelstad, D. 120 Balogun, B. 0. 95 *Frank, A. Q. 31 *Levine, M. N. 42 Shengwang, W. 94 *Bass, H. 1 04 *Friedlander, E. M. 59 Longyear, J. Q. 87 *Shiffman, B. 1 07 Bauer, D. 83 •Frohlich, A. 112 *Lucas, W. 115 *Sloane, N. J. A. 152 *Baumslag, G. 51 *Gaglione, A. M. 72 *Magurn, B. A. 133 *Siodowy, P. 119 *Beard, J. T. B., Jr. 50 *Gehrlein, W. V. 32 Makar-Limanov, L. 85 *Solderitsch, ]. 49 *Bedford, E. 3 *Geller, S. C. 58 *Mallet-Paret, J. 96 *Sonn, ]. 150 *Bell, S. R. 4 Gerth, F. E., Ill 161 *Maurer, D. E. ·146 *Speh, B. 121 *Blair, D. H. 35 Gerver, ]. L. 153 *McCulloh, L. R. 149 Spigler, R. 91 *Bland, R. G. 6 *Gessel, I. M. 1 0 *McGovern, K. 81 *Srinivas, V. 127 *Boas, H. P. 5 *Giffin, C. H. 103 *Merrill, S., Ill 118 *Stanley, R. P. 151 *Boggess, A. 66 *Gillet, H. 132 Mihram, G. A. 90 •Stanton, N. K. 18 *Bolker, E. D. 144 *Gil mer, R. 1 36 *Mines, R. 137 Stehney, T. 165 Brewer, ]. W. 157 *Goldberg, C. H. 29 *Miranda, R. 45 *Stein, M. R. 56 *Brosius, J. E. 130 *Goldberg, S. 15 * Nerode, A. 1 38 Sugar, A. C. 89 *Burns, D. M., Jr. 1 Gordon, C. 93 *Nevison, C. H. 30 *Swan, R. G. 1 00 *Calderbank, R. 7 *Graham, C. R. 69 *Nisnevich, Y. A. 41 Taft, E. ]. 155 *Carpenter, G. A. 36 *Grayson, D. R. 1 31 *Nold, A. 38 *Taiani, G. 1 08 *Charney, R. 1 35 *Griggs, ]. R. 24 *Nussbaum, A. E. 21 *Tartakoff, D. S. 1 09 *Chase, S. U. 65 *Hale, ]. K. 13 *Odlyzko, A. M. 27 *Thomason, R. W. 101 *Childs, L. N. 147 Hamilton, E. P. 92 *Packel, E. W. 33 *Trench, W. F. 99 *Chinburg, T. 62 *Hansen, K. 79 *Packer, ]. A. 17 *Trotter, H. F. 47 *Chung, F. R. K. 8 * Harbater, D. 129 *Parsons, T. D. 28 *Tucker, T. W. 145 *Coppersmith, D. 9 Healey, P. 88 *Persson, U. A. 43 *Turull, A. 122 Costa, D. L. 156 *Herb, R. A. 78 *Petryshyn, W. V. 12 *Ullom, S. V. 64 *Crauder, B. 46 *Hill, C. D. 70 Pittel, B. 86 •Vaserstein, L. N. 113 *Davis, ]. F. 134 *Hochster, M. 128 *Pohst, M. 77 *Vogtmann, K. 1 02 Deckhart, R. W. 158 *Hoffman, D. T. 116 *Pol king, ]. C. 105 von Rimscha, M. 84 *Dennis, K. 54 *Hoffmann, C. M. 75 *Provan, ]. S. 140 *Webb, D. L. 61 *Desrochers, M. 63 Hoi mes, C. S. 163 *Queyrut, ]. 60 *Weibel, C. 57 *Devinatz, A. 14 *Hughes, R. ]. 23 *Range, R. M. 1 06 *West, D. 11 * Dutta, S. P. 125 *Kaltofen, E. 53 *Ranicki, A. A. 55 *Wong, P.-M. 110 *Dynin, A. 111 Kappe, L-C. 1 60 * Raykshteyn, B. 76 Wong, R. W. 164 *Ehrenpreis, L. 67 *Kazarinoff, N. 40 *Richman, F. 73 *Yorke, J. A. 98 *Ein, L. 44 *Klein, A. 22 * Riedtmann, C. 124 *Yun, D. Y. Y. 52 Eisenberg, S. M. 154 *Kieitman, D. J. 25 *Robbins, D.P. 141 *Zaslavsky, T. 143 *Erdelyi, I. 20 *Kohn, ]. ]. 71 *Roberts, F. S. 142 *Zassenhaus, H. ]. 139

179 PROGRAM OF THE SESSIONS

The time limit for each contributed paper in the AMS general sessions is ten minutes. In the special sessions the time varies from session to session and within sessions. To maintain the schedule, the time limits will be strictly enforced. Abstracts for papers presented in AMS sessions at this meeting will be found in the February 1982 issue of Abstracts of papers presented to the American Mathematical Society, ordered accord· ing 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. TUESDAY, 9:00 A. M. Special Session on Several Complex Variables. I, Physical Sciences Complex, Room 166, Chemistry Lecture Room 9:00- 9:20 (1) An eigenvalue problem for the complex-Mange-Ampere operator. Preliminary report. DANIEL M. BURNS, JR., University of Michigan, Ann Arbor (793-32-160) 9:25- 9:45 (2) Boundary behavior of holomorphic and meromorphic functions. Professor STEVEN G. KRANTZ, Pennsylvania State University (793-32-2) 9:50-10:10 (3) An Invariant norm on complex manifolds with application to holomorphic map­ pings. Professor ERIC BEDFORD, Princeton University (793-32-27) 10:15-10:35 (4) Boundary regularity of proper holomorphic mappings. STEVEN R. BELL* and DAVID W. CATLIN, Princeton University (793-32-20) 10:40-11:00 (5) Regularity of the Bergman projection in weakly pseudoconvex domains. STEVEN R. BELL, Princeton University, and HAROLD P. BOAS*, Columbia University (793-32-83) TUESDAY, 9:00 A. M. Special Session on Combinatorics and Graph Theory. I, Physical Sciences Complex, Room 243, Physics Lecture Room 9:00- 9:20 (6) Linear programming duality, Minty's Lemma, oriented matrolds, and signed-set systems. Professor ROBERT G. BLAND, Cornell University (793-05-123) 9:25- 9:45 (7) The Haemers partial geometry and the Steiner System S(5, 8, 24). ROBERT CALDERBANK*, Bell Laboratories, Murray Hill, and DAVID B. WALES, California Institute of Technology (793-05-80) 9:50-10:10 (8) Unavoidable stars in 3-graphs. Preliminary report. Dr. F. R. K. CHUNG, Bell Laboratories, Murray Hill (793-05-136) 10:15-10:35 (9) Rapid multiplication of rectangular matrices. Dr. DON COPPERSMITH, IBM Thomas j. Watson Research Center (793-15-5) 10:40-11:00 (10) Hash coding, depth-first search, and the Tutte polynomial. Preliminary report. Professor IRA M. GESSEL, Massachusetts Institute of Technology (793-05-45) 11:05-11:25 (11) The Interval number of a planer graph: three intervals suffice. Preliminary report. EDWARD SCHEINERMAN and Professor DOUGLAS WEST*, Princeton University (793-05-65)

TUESDAY, 9:00 A. M. Special Session on Differential and Differential-Delay Equations, Physical Sciences Complex, Room 100, Geology Classroom 9:00- 9:20 (12) Existence theorems for higher order nonlinear periodic BV problems at resonance. W. V. PETRYSHYN*, Rutgers University, New Brunswick, and Z. S. YU, jilin University, People's Republic of China (793-34-127) 9:25- 9:45 (13) On a gradient like integra-differential equation. Professor jACK K. HALE* and Dr. K. P. RYBAKOWSKI, Brown University (793-34-148) 9:50-10:10 Informal Session

TUESDAY, 9:00 A. M. Special Session on Operator Theory. I, Physical Sciences Complex, Room 339, Physics Classroom 9:00- 9:20 (14) Some remarks on oscillating potential scattering. Professor ALLEN DEVINATZ, Northwestern University (793-4 7-42) 9:25- 9:45 (15) Finite-dimensional Wiener-Hop( equations and factorizations of matrices. ISRAEL GOHBERG, Tel-Aviv University, Israel, and SEYMOUR GOLDBERG*, University of Maryland, College Park (793-47-69) 180 9:50-10:10 (16) Regularity properties of generalized Schrodinger operators. Professor DAVID GURARIE, Texas A&M University, College Station, and Professor MARK A. KON* Boston University (793-46-141) 10:15-10:35 (17) von Neumann algebras corresponding to ergodic actions of discrete groups. Preliminary report. JUDITH A. PACKER, Harvard University (793-47-91) TUESDAY, 11:10 A.M. Invited Address, Goodhart Hall (18) The heat equation in several complex variables. Professor NANCY K. STANTON, University of Notre Dame (793-32-18) TUESDAY, 1:10 P.M. Invited Address, Goodhart Hall (19) What does it mean to classify algebraic varieties and how does one do it? Professor STEPHEN S. SHATZ, University of Pennsylvania (793-14·139) TUESDAY, 2:20P.M. Special Session on Operator Theory. II, Physical Sciences Complex, Room 339, Physics Classroom 2:20- 2:40 (20) Monotonic spectral resolvents. Dr. I. ERDELYI*, Temple University, and Dr. WANG SHENGWANG, Nanjing University, China (793-47-12) 2:45- 3:05 (21} Multi parameter local semi-groups of Hermitian operators. Professor A. EDWARD NUSSBAUM, Washington University (793-47-21) 3:10- 3:30 (22) Construction of a unique self-adjoint generator for a symmetric local semigroup. Professor ABEL KLEIN*, University of California, Irvine, and Professor LAWRENCE j. LANDAU, Bedford College, University of London, England (793-4 7·9 5) 3:35- 3:55 (23} Singular perturbations in the interaction representation, II. Professor RHONDA j. HUGHES, Bryn Mawr College (793-47-161} TUESDAY, 2:20 P. M. Special Session on Combinatorics and Graph Theory. II, Physical Sciences Complex, Room 243, Physics Lecture Room 2:20- 2:40 (24) Lower bounds on the independence number of a graph. Preliminary report. Professor JERROLD R. GRIGGS, University of South Carolina, Columbia (793-05-125) 2:45- 3:05 (25) Longest chains of part partitions ordered by majorization. Professor DANIEL). KLEITMAN* and Professor CURTIS GREENE, Massachusetts Institute of Technology (793-05-78) 3:10- 3:30 (26) Applications of combinatorics to very large scale integration ( VLSI). Preliminary report. Dr. FRANK THOMSON LEIGHTON, Massachusetts Institute of Technol­ ogy (793-05-30) (Introduced by Professor Stephen B. Maurer) 3:35- 3:55 (27) The average height of monotonically labeled binary trees. ANDREW M. ODL YZKO, Bell Laboratories, Murray Hill (793-05-70} 4:00- 4:20 (28) Hamiltonian paths in vertex-symmetric graphs. Dr. DRAGAN MARUSIC, Koper, Yugoslavia, and Professor T. D. PARSONS*, Pennsylvania State University, University Park (793-05-46} 4:25- 4:45 (29) Even splittings of circle colorings. Professor CHARLES H. GOLDBERG* and Professor DOUGLAS B. WEST, Princeton University (793-05-44) TUESDAY, 2:20 P. M. Special Session on Mathematics of Voting and Bargaining_ I, Physical Sciences Complex, Room 330, Mathematics Classroom 2:20- 2:40 (30) Structural satisfaction in simple games. CHRISTOPHER H. NEVISON, Colgate University (793-90-49) 2:45- 3:05 (31) The distribution of power in the U.S. Supreme Court. Professor ARTHUR Q. FRANK*, University of Rochester, and Professor LLOYD SHAPLEY, University of California, Los Angeles (793-90-143) (Introduced by Professor Samuel Merrill Ill} 3:10- 3:30 (32) Powers of subgroups in voting bodies. Dr. PETER C. FISHBURN, Bell Labora­ tories, Murray Hill, and Professor WILLIAM V. GEHRLEIN*, University of Delaware (793-60-1 03) 181 3:35- 3:55 (33) Strategic equilibria and decisive set structures for social choice mechanisms. Professor EDWARD W. PACKEL *, Lake Forest College, and Professor DONALD G. SAARI, Northwestern University (793-90-39) (Introduced by Professor Samuel Merrill Ill) 4:00- 4:20 (34) The geometry which is associated with voting paradoxes. Professor DONALD G. SAARI, Northwestern University (793-90-16) 4:25- 4:45 (35) Subjective evaluations of n-person games. Professor DOUGLAS H. BLAIR*, Rutgers University, New Brunswick, and Professor RICHARD P. McLEAN, University of Pennsylvania (793-90-1 02) (Introduced by Professor Samuel Merrill Ill)

TUESDAY, 2:20P.M. Special Session in Applied Mathematics, Physical Sciences Complex, Room 100, Geology Classroom 2:20- 2:40 (36) The intracellular dynamics of a vertebrate cone. Dr. GAIL A. CARPENTER*, Northeastern University, and STEPHEN GROSSBERG, Boston University (793-92-154) 2:45- 3:05 (37) Frequency plateau in intestinal oscillations. Preliminary report. Dr. G. B. ERMENTROUT*, NIAMDD, National Institutes of Health, Bethesda, and Professor N. KOPELL, Northeastern University (793-58-126) 3:10- 3:30 (38) Modeling saturation and replacement for a population with age-structure. Preliminary report. Dr. ANNETT NOLD, U.S. Environmental Protection Agency, Washington, D. C. (793-92-98) 3:35- 3:55 (39) Noble's model of the cardiac Purkinje fiber. Preliminary report. Professor JANE CRONIN SCANLON, Rutgers University, New Brunswick (793-92-55) 4:00- 4:20 (40) Starfish predation of a growing coral reef. Professor PETER ANTONELLI, University of Alberta, and Professor NICHOLAS KAZARINOFF*, State University of New York, Buffalo (793-99-165)

TUESDAY, 2:20 P. M. Special Session in Algebraic Geometry and Cognate Areas: Algebraic Number Theory, and Commutative Algebra. I, Physical Sciences Complex, Room 349, Mathematics Classroom 2:20- 2:40 (41) Rationally trivial G-torsors of reductive group schemes. Preliminary report. YEVSEY A. NISNEVICH, Harvard University (793-14-43) 2:45- 3:05 (42) Deformations of irregular threefolds. Preliminary report. Dr. MARC N. LEVINE, University of Pennsylvania (793-14-61) (Introduced by Professor Paul Edelman) 3:10- 3:30 (43) Double planes with maximal Picard numbers. Dr. ULF A. PERSSON, Institute for Advanced Study (793-14-72) 3:35- 3:55 (44) The ramification divisor of a finite cover of Pc is ample. Preliminary report. Dr. LAWRENCE EIN, Institute for Advanced Study (793-14-133) 4:00- 4:20 (45) Explicit resolutions of terminal compound AN singularities. Preliminary report. RICK MIRANDA, Colorado State University and Institute for Advanced Study (793-14-135) 4:25- 4:45 (46) Canonical forms for degeneration and applications to surface theory. Professor BRUCE CRAUDE R, Institute for Advanced Study (793-14-152)

TUESDAY, 2:20 P. M. Special Session on Constructive Methods in Algebra. I, Physical Sciences Complex, Room 354, Mathematics Classroom 2:20- 2:40 (47) Statistical aspects of factoring polynomials p-adically and mod p. Professor HALE F. TROTTER, Princeton University (793-12-82) 2:45- 3:05 (48) Remarks on spinor genera for lattices of rank<; 4. Professor DENNIS ESTES, University of Southern California (793-10-113) (Introduced by Professor Robert M. Guralnick) 3:10- 3:30 (49) An algebraic system for class group computations for quadratic number fields. Preliminary report. Dr. JAMES SOLDERITSCH* and ANNE COSTA SOLDER­ ITSCH, Villanova University (793-12-31) 3:35- 3:55 (50) On matrix fields over GF(q, x). Preliminary report. Professor J. T. B. BEARD, JR., Tennessee Technological University (793-12-57)

182 4:00- 4:20 (51) Constructive commutative algebra. GILBERT BAUMSLAG, City College, City University of New York (793-20-34) 4:25- 4:45 (52) On the support of algebraic computations. Preliminary report. Dr. DAVID Y. Y. YUN, IBM Thomas j. Watson Research Center (793-99-162) 4:50- 5:10 (53) An alternate construction of succinct certificates for normal univariate irreducible polynomials with integer coefficients. Preliminary report. ERICH KAL TOFEN, University of Delaware (793-12-138) (Introduced by Professor Christine W. Ayoub}

TUESDAY, 2:20P.M. Special Session on Algebraic K- and L-Theory. I, Physical Sciences Complex, Room 025, Biology Lecture Room 2:20- 2:40 (54) K3 of fields and lgusa's pictures. Preliminary report. Professor KEITH DENNIS, Texas Tech University (793-18-53) 2:45- 3:05 (55) Algebraic and geometric sp/ittings of K- and L-groups. Professor ANDREW A. RANICKI, Institute for Advanced Study (793-18-8)

3:10- 3:30 (56) Stickelberger ideals and K2 of elementary abelian p-groups. Preliminary report. Professor MICHAEL R. STEIN, Northwestern University (793-18-52) 3:35- 3:55 (57} K3 of the real and complex numbers. CHARLES WEIBEL, Rutgers University, New Brunswick (793-18-7} 4:00- 4:20 (58) Double relative K-theory. Preliminary report. Professor SUSAN C. GELLER*, Texas A&M University, and Professor CHARLES A. WEIBEL, Rutgers University, New Brunswick (793-16-19) 4:25- 4:45 (59} Cohomology of algebraic groups. Professor ERIC M. FRIEDLANDER*, North­ western University, and Professor BRIAN PARSHALL, University of Virginia (793-20-51}

TUESDAY, 2:20 P. M. Special Session on Galois Module Structure of Algebraic Integers. I, Physical Sciences Complex, Room 387, Physics Classroom 2:20- 2:40 (60} Gaussian sums and Galois module structure of algebraic integers. jACQUES QUEYRUT, University of Bordeaux I, France (793-12-3) (Introduced by Professor Albrecht Frohlich} 2:45- 3:05 (61) A sufficient condition for GO(ZG) to be GO of the maximal order. Preliminary report. DAVID L. WEBB, Cornell University (793-20-15) (Introduced by Professor Albrecht Frohlich) 3:10- 3:30 (62} On the Galois structure of algebraic integers and units. Dr. TED CHINBURG, University of Washington (793-12-23) 3:35- 3:55 (63) Self-duality in wildly ramified extensions of algebraic number fields. MARYSE DESROCHERS, Cornell University (793-12-35} 4:00- 4:20 (64) Congruences for class numbers of quadratic fields. Preliminary report. Professor STEPHEN V. ULLOM, University of Illinois, Urbana-Champaign (793-12-56} 4:25- 4:45 (65} A"ramification invariant and the Galois Gauss sum. Preliminary report. Professor STEPHEN U. CHASE, Cornell University (793-12-67} (Introduced by Professor Albrecht Frohlich)

TUESDAY, 2:20 P. M. Special Session on Several Complex Variables. II, Physical Sciences Complex, Room 166, Chemistry Lecture Room 2:20- 2:40 (66) CR extension near a point where the first Leviform vanishes. Dr. AL BOGGESS, University of Michigan, Ann Arbor (793-32-119} 2:45- 3:05 (67} Geometry and topological algebra related to several complex variables. Professor LEON EHRENPREIS, Yeshiva University (793-32-132} 3:10- 3:30 (68) An embedding theorem for real hypersurfaces. JAMES). FARAN V, Institute for Advanced Study (793-32-118} 3:35- 3:55 (69} The Dirichlet problem for the Bergman Laplacian. C. ROBIN GRAHAM, Courant Institute of Mathematical Sciences, New York University (793-32-117)

183 4:00- 4:20 (70) What is the notion of a complex manifold with a smooth boundary? C. DENSOf\: HILL, State University of New York, Stony Brook (793-32-146) 4:25- 4:45 (71) Microlocal estimates for Db. Preliminary report. Professor J. J. KOHN, Princet< University (793-32-59)

WEDNESDAY, 8:35 A. M. Special Session on Constructive Methods in Algebra. II, Physical Sciences Complex, Room 354, Mathematic Classroom 8:35- 8:55 (72) The lower central series of ( x, y; x 25 = y 25 = 1). Preliminary report. Profes! ANTHONY M. GAGLIONE, U.S. Naval Academy (793-20-149) 9:00- 9:20 (73) Constructive abelian group theory. FRED RICHMAN, New Mexico State Univer­ sity, Las Cruces (793-20-58) 9:25- 9:45 (74) HNN groups, Petri nets, complexity theory. Professor MICHAEL M. ANSHEL, City College of New York (793-99-164) 9:50-10:10 (75) The imprimitivity problem for 2-groups and its relevance to trivalent graph isomorphism. Dr. CHRISTOPH M. HOFFMANN, Purdue University, West Lafayette (793-20-114) (Introduced by Professor Christine W. Ayoub) 10:15-10:35 (76) Cross-ratio in 2n-space. Dr. BORIS RA YKSHTEYN, Susquehanna University (793-51-81) 10:40-11:00 (77) On integra/lattice constructions. Preliminary report. Professor M. POHST, Universitat Dusseldorf, Federal Republic of Germany (793-12-14) (Introduced by Professor Christine W. Ayoub)

WEDNESDAY, 9:00 A. M. Special Session on Representation Theory of Finite Groups and Lie Groups. I, Physical Sciences Complex, Room 349, Mathematics Classroom 9:00- 9:20 (78) Characters of induced representations and weighted orbital integrals. Dr. REBECCA A. HERB, University of Maryland, College Park (793-22-10) 9:25- 9:45 (79) Decomposition of ramified supercuspida/ representations of GL(2, F) to GL(2, 0 Professor KRISTINA HANSEN, University of Michigan, Ann Arbor (793-20-13) 9:50-10:10 (80) A method for computing characters of supercuspidal representations of p-adic groups. Professor PHILIP C. KUTZKO, University of Iowa (793-22-121) 10:15-10:35 (81) On the lifting theory of finite groups of Lie type. Preliminary report. K. McGOVERN, Ohio State University, Columbus (793-20-131) 10:40-11:00 (82) Applications of representation theory in linear partial differential equations. LINDA PREISS ROTHSCHILD, Institute for Advanced Study (793-58-41)

WEDNESDAY, 9:00 A. M. Session on Graph Theory, Physical Sciences Complex, Room 330, Mathematics Classroom 9:00- 9:10 (83) A Turan type theorem for regular K4 free graphs. Professor DOUGLAS BAUER Stevens Institute of Technology (793-05-105) 9:15- 9:25 (84) The reconstruction-problem for certain infinite graphs. Dr. MICHAEL VON RIMSCHA, Universitat Stuttgart, Federal Republic of Germany (793-05-63) 9:30- 9:40 (85) On Grassmann algebras of graphs. Professor LEONID MAKAR-LIMANOV, Wayne State University (793-05-74) 9:45- 9:55 (86) On distributions related to transitive closures of the random finite mappings. Preliminary report. BORIS PITTEL, Ohio State University, Columbus (793-05-7- (lntroduced by Professor Louis Sucheston) 10:00-10:10 (87) Moore-Hanani type constructions for nested designs. Professor JUDITH Q. LONGYEAR, Wayne State University (793-05-75) 10:15-10:25 (88) Repeatedly nested balanced incomplete block designs with block sizes 2k. Dr. PAUL HEALEY, American University (793-05-155)

WEDNESDAY, 9:00A.M. General Session, Physical Sciences Complex, Room 387, Physics Classroom 9:00- 9:10 (89) On the demise of mathematical continuity. ALVIN C. SUGAR, Los Angeles, California (793-26-1 00)

184 9:15- 9:25 {90) Why it matters that computer programming is not mathematics. Preliminary report. Dr. G. ARTHUR MIHRAM, Princeton, New Jersey (793-03-110) 9:30- 9:40 {91) The linear differential equation whose solutions ore the products of solutions of two given differential equations. RENA TO SPIGLER, Courant Institute of Mathematical Sciences, New York University (793-34-151) 9:45- 9:55 {92) Global and local approaches to variational derivatives and integral representations of Gateaux differentials. Professor E. P. HAMILTON*, Washington College, and Professor M. Z. NASHED, University of Delaware (793-46-112) 10:00-10:10 {93) Isometry groups of solvmonifolds. Preliminary report. Dr. CAROLYN GORDON*, Lehigh University, and Dr. EDWARD N. WILSON, Washington University {792-53-422) 10:15-10:25 {94) On the duality theorem of S-decomposable operators. Dr. WANG SHENGWANG* and Dr. LIU GUANGYU, Nanjing University, China {793-47-22) {Introduced by Professor I. Erdelyi) 10:30-10:40 {95) C*-algebras associated with amalgamated products of groups. Dr. BOLA 0. BALOGUN, University of lfe, Nigeria (793-46-96) WEDNESDAY, 9:00 A. M. Special Session on Differential and Differential-Delay Equations. II, Physical Sciences Complex, Room 100, Geology Classroom 9:00- 9:20 {96) Homotopy methods for finding zeros of entire functions. Preliminary report. Professor JACK CARR, Heriot-Watt University, Edinburgh, Scotland, and Professor JOHN MALLET-PARET*, Michigan State University {793-65-157) 9:25- 9:45 {97) Virtual periods and global Hopf bifurcation. Preliminary report. KATHLEEN T. ALLIGOOD*, College of Charleston, and JAMES A. YORKE, University of Maryland, College Park {793-34-88) 9:50-10:10 {98) Examples of strange ottroctors. Preliminary report. JAMES A. YORKE, University of Maryland, College Park {793-34-144) 10:15-10:35 {99) Systems of differential equations subject to mild integral conditions. Professor WILLIAM F. TRENCH, Drexel University {793-34-25) 10:40-11:20 Informal Session WEDNESDAY, 9:00 A. M. Special Session on Algebraic K- and L-Theory. II, Physical Sciences Complex, Room 025, Biology Lecture Room 9:00- 9:20 {100) Projective modules over binary polyhedral groups. Professor RICHARD G. SWAN, University of Chicago {793-16-159) 9:25- 9:45 {1 01) The splitting principle in higher algebraic K-theory. Preliminary report. R. W. THOMASON, Massachusetts Institute of Technology (793-18-128) 9:50-10:10 {102) Automorphisms of SL 20_d· KAREN VOGTMANN*, Columbia University, and JOHN SMILLIE, University of California, Berkeley (793-20-129) 10:15-10:35 {103) K-theory of norms for group algebras and Kummer extensions. Preliminary report. Professor CHARLES H. GIFFIN, University of Virginia {793-55-130) 10:40-11:00 {104) The general nonlinear group. Preliminary report. HYMAN BASS, Columbia University {793-13-158) WEDNESDAY, 9:00 A. M. Special Session on Several Complex Variables. Ill, Physical Sciences Complex, Room 166, Chemistry Lecture Room 9:00- 9:20 {105) The a-Neumann problem on the boll in en. Professor JOHN C. POLKING, Rice University {793-32-37) 9:25- 9:45 {106) An elementary integral solution operator for a on pseudoconvex domains in en. Professor R. MICHAEL RANGE, State University of New York, Albany {793-32-60) 9:50-10:10 {107) Capacity and transfinite hyperdiameter on complex projective space. Professor ROBERT E. MOLZON, University of Kentucky, and Professor BERNARD SHIFFMAN*, johns Hopkins University {793-32-116)

185 10:15-10:35 (108) On the Hans Lewy extension phenomenon in higher cod/mens/on. Professor C. DENSON HILL, State University of New York, Stony Brook, and Professor GERALDINE TAIANI*, Pace University (793-32-36) 10:40-11:00 (109) Nonhypoe/lipt/c operators on Heisenberg groups. LINDA P. ROTHSCHILD, Institute for Advanced Study, and DAVIDS. TARTAKOFF*, University of Illinois, Chicago Circle (793-32-84) 11:05-11:25 (110) On complete proper circular domains In cn+1. Preliminary report. Professor PIT-MANN WONG* and GIORGIO PATRIZIO, University of Notre Dame (793-32-32) (Introduced by Professor Nancy K. Stanton} 11:30-11:50 (111) Toeplitz operator algebras on Siegal domains. Preliminary report. Dr. ALEXANDER DYNIN, Ohio State University, Columbus (793-32-29)

WEDNESDAY, 11:10 A.M. Invited Address, Goodhart Hall (112) Rings of algebraic integers as Galois modules. Professor ALBRECHT FROHLICH, University of Illinois, Urbana-Champaign (793-124}

WEDNESDAY, 1:10 P.M. Invited Address, Goodhart Hall (113) Classical groups over rings. Professor L. N. VASERSTEIN, Pennsylvania State University, University Park (793-20-79)

WEDNESDAY, 2:20P.M. Special Session on the Mathematics of Voting and Bargaining. II, Physical Sciences Complex, Room 330, Mathematics Classroom 2:20- 2:40 (114} A unified system of proportional representation. Professor FRANCINE F. ABELES, Kean College of New jersey {793-90-145} 2:45- 3:05 (115} Weighted voting for county boards in New York State. Professor WILLIAM LUCAS*, MICHAEL HILLIARD and DAVID HOUSMAN, Cornell University, and Professor JOHN MACELI, Ithaca College {793-90-64} 3:10- 3:30 {116} Relative efficiency of voting systems. Professor DALE T. HOFFMAN, College of the Virgin Islands (793-90-137} 3:35- 3:55 (117} Probabilities of dominant candidates based on first-place votes. Dr. PETER C. FISHBURN, Bell Laboratories, Murray Hill {793-60-104} 4:00- 4:20 (118} Equilibrium strategies for final-offer arbitration. Professor STEVEN J. BRAMS, New York University, and Professor SAMUEL MERRIL Ill*, Wilkes College {793-90-85)

WEDNESDAY, 2:20P.M. Special Session on Representation Theory of Finite Groups and Lie Groups. II, Physical Sciences Complex, Room 349, Mathematics Classroom 2:20- 2:40 (119} Adjoint quotients for Kac-Moody Lie groups and deformations of singularities. Dr. PETER SLODOWY, Yale University {793-20-90) {Introduced by Professor Bhama Srinivasan} 2:45- 3:05 (120} Twisted endoscopic groups In the obelion case. D. SHELSTAD, Rutgers University, Newark {793-22-120} 3:10- 3:30 (121) Moving parameters of unitary representations. Preliminary report. Professor A. W. KNAPP and Professor B. SPEH*, Cornell University (793-22-11) 3:35- 3:55 (122) Supersolvoble regular orbits and modules and fixed-point-free action. Preliminary report. A. TURULL, University of Chicago {793-20-89) 4:00- 4:20 (123} Ratios of dual degrees. Dr. DEAN ALVIS, Massachusetts Institute of Technology (793-20-150} (Introduced by Professor Bhama Srinivasan) 4:25- 4:45 (124} Skew group algebras. I. REITEN, Universitetet i Trondheim, Norway, and CH. RIEDTMANN*, Mathematisches lnstitut, Basel, Switzerland (793-20-97}

186 WEDNESDAY, 2:20 P. M. Special Session on Algebraic Geometry and Cognate Areas: Algebraic Number Theory, and Commutative Algebra. II, Physical Sciences Complex, Room 166, Chemistry Lecture Room 2:20- 2:40 (125) Weak linking of modules. Preliminary report. SANKAR P. DUTTA, University of Pennsylvania (793-13-62) 2:45- 3:05 (126) Arithmetic applications of some results on ordinary differential equations. Dr. GREG W. ANDERSON, Harvard University (793-34-134) 3:10- 3:30 (127) K-theory on affine cones. V. SRINIVAS, University of Pennsylvania (793-14-153) 3:35- 3:55 (128) Euler characteristics over unramified regular local rings. Professor MELVIN HOCHSTER, University of Michigan, Ann Arbor (793-13-93) 4:00- 4:20 (129) Convergent power series over the integers. Preliminary report. Professor DAVID HARBATER, University of Pennsylvania (793-13-94) 4:25- 4:45 (130) Rank-2 vector bundles on ruled surfaces. Preliminary report. J. ERIC BROSIUS, University of Pennsylvania (793-14-140)

WEDNESDAY, 2:20 P. M. Special Session on Algebraic K- and L-Theory. Ill, Physical Sciences Complex, Room 025, Biology Lecture Room 2:20- 2:40 (131) Dilogarithm computations for K2 of elliptic curves. DANIEL R. GRAYSON, In- stitute for Advanced Study (793-12-156) 2:45- 3:05 (132) K-theory of twisted complexes. Preliminary report. HENRI Gl LLET, Princeton University (793-20-54) 3:10- 3:30 (133) A survey of Krtheory of finite groups. Preliminary report. Professor BRUCE A. MAGURN, University of Oklahoma, Norman (793-18-87) 3:35- 3:55 (134) Evaluation of the Swan finiteness obstruction. Preliminary report. Dr. JAMES F. DAVIS, Princeton University (793-57-17) 4:00- 4:20 (135) Cohomology of the Satake compactification. Professor RUTH CHARNEY* and Professor RONNIE LEE, Yale University (793-55-40)

WEDNESDAY, 2:20P.M. Special Session on Constructive Methods in Algebra. Ill, Physical Sciences Complex, Room 354, Mathematics Classroom 2:20- 2:40 (136) Finitely generated ideals of the ring of Integer-valued polynomials. Preliminary re- port. Professor ROBERT GILMER*, Florida State University, and Professor WIL­ LIAM W. SMITH, University of North Carolina, Chapel Hill (793-13-107) 2:45- 3:05 (137) Valuation theory. Professor RAY MINES, New Mexico State University (793-12-9) 3:10- 3:50 (138) Recent developments in recursive analysis and algebra. ANIL NERODE, Cornell University (793-05-86) 3:55- 4:35 (139) Computation of Hasse symbols of a simple hypercomplex system over a global field. Professor HERBERT BENZ, University of Cologne, Federal Republic of Germany, and Professor HANS J. ZASSENHAUS*, Ohio State University, Colum­ bus (793-99-163)

WEDNESDAY, 2:20P.M. Special Session on Combinatorics and Graph Theory. Ill, Physical Sciences Complex, Room 243, Physics Lec­ ture Room 2:20- 2:40 (140) Calculating bounds on reachability and connectedness in stochastic networks. Dr. MICHAEL 0. BALL, University of Maryland, College Park, and Dr. J. SCOTT PROVAN*, National Bureau of Standards, Washington, D. C. (793-05-71) (Intro­ duced by Professor Stephen B. Maurer) 2:45- 3:05 (141) Alternating sign matrices and descending plane partitions. W. H. MILLS, DAVID P. ROBBINS* and HOWARD RUMSEY, JR., Institute for Defense Analyses (793-05-122) 3:10- 3:30 (142) A characterization of competition graphs. Preliminary report. Professor FRED S. ROBERTS* and JEFFREY E. STEIF, Rutgers University, New Brunswick (793-05-124) 3:35- 3:55 (143) Matchings and Chebyshev polynomials. THOMAS ZASLAVSKY, Ohio State Uni­ versity, Columbus (793-05-77)

187 4:00- 4:20 (144) The finite Radon transform, geometry over finite fields, and Kirkman's schoolgirl problem. Professor ETHAN D. BOLKER, University of Massachusetts, Boston (793-05-33) 4:25- 4:45 (145) The genus of a quotient group. Preliminary report. Professor THOMAS W. TUCKER, Colgate University (793-05-38)

WEDNESDAY, 2:20P.M. Special Session on Galois Module Structure of Algebraic Integers. II, Physical Sciences Complex, Room 387, Physics Classroom 2:20--- 2:40 (146) Constructing normal integral bases. Dr. DONALD E. MAURER, Center for Naval Analyses, (793-12-92) 2:45- 3:05 (147) Sticke/berger conditions on tame Kummer extensions. Professor LINDSAY N. CHILDS, State University of New York, Albany (793-12-99) 3:10- 3:30 (148) An equal-distribution result for Galois module structure. KURT C. FOSTER, Uni- versity of Illinois, Urbana-Champaign (793-12-101) 3:35- 3:55 (149) Galois modules and Stickelbergerrelations: Abelian extensions of type (Ln, .. . , Ln). Preliminary report. Professor LEON R. McCULLOH, University of Illinois, Urbana­ Champaign (793-12-142) 4:00- 4:20 (150) Direct summands of class groups. JACK SONN, Technion-Institute of Technology, Israel, and Brown University (793-12-24)

WEDNESDAY, 2:20P.M. Special Session on Applications of Algebra, Physical Sciences Complex, Room 339, Physics Classroom 2:20--- 2:40 (151) Linear diophantine equations, combinatorial reciprocity theorems, and local co­ homology. Professor RICHARD P. STANLEY, Massachusetts Institute of Tech­ nology (793-13-48) 2:45- 3:05 (152) The polynomial invariants of finite groups. Dr. N. J. A. SLOANE, Bell Labora­ tories, Murray Hill (793-99-166) 3:10- 3:30 Informal Session

WEDNESDAY, 2:20P.M. Session on Algebra and Number Theory, Physical Sciences Complex, Room 100, Geology Laboratory 2:20- 2:30 (153) Factoring large numbers with a quadratic sieve. Preliminary report. Dr. JOSEPH L. GERVER, Rutgers University, Camden (793-10-73) 2:35- 2:45 (154) An algorithm for Pel/-type puzzle problems. Professor SHELDON M. EISENBERG* and Professor STEPHEN SNOVER, University of Hartford (793-10-68) 2:50- 3:00 (155) The left antipodes of a left Hopf algebra. Professor WARREN D. NICHOLS, Florida State University, and Professor EARL J. TAFT*, Rutgers University, New Brunswick (793-16-1) 3:05- 3:15 (156) Torsion-freeness of symmetric powers. Preliminary report. Professor DOUGLAS L. COST A, University of Virginia (793-13-6) 3:20--- 3:30 (157) Seminormality in power series rings. Preliminary report. Professor jAMES W. BREWER, University of Kansas (793-13-108) 3:35- 3:45 (158) Lie algebras over Z and applications. Preliminary report. Professor ROBERT W. DECKHART, Miami University, Oxford (793-17-106) 3:50- 4:00 (159) Withdrawn 4:05- 4:15 (160) Engle margins in metabel/an groups. Preliminary report. Professor LUISE­ CHARLOTTE KAPPE, State University of New York, Binghamton (793-20-109) 4:20- 4:30 (161) Counting certain number fields with prescribed /-class numbers. Professor FRANK E. GERTH Ill, University of Texas, Austin (793-12-50) 4:35- 4:45 (162) Large Tate-Shafarevitch groups. Preliminary report. KENNETH KRAMER, Queens College, City University of New York (793-12-111) 4:50--- 5:00 (163) Split extensions of Abelian groups with identical subgroup structures. Professor CHARLES S. HOLMES, Miami University, Oxford (793-20-115)

188 5:05- 5:15 (164) On hereditary monoid rings. Professor CHARLES CHING-AN CHENG, Oakland University, and Professor ROMAN W. WONG*, Washington and jefferson College (793-16-147) 5:20- 5:30 (165) The Pythagorean theorem-just o special case after o/1. Preliminary report. Pro­ fessor TOM STEHNEY, Pennsylvania State University, New Kensington (793-51-26) (Introduced by Professor DAVID M. WELLS) Raymond G. Ayoub University Park, Pennsylvania Associate Secretary

PROGRAM FOR THE AWM NOETHER SYMPOSIUM

All lectures will be presented in Goodhart Hall

WEDNESDAY 8:00p.m. Brauer factor sets, Noether foetor sets, and crossed products. NATHAN jACOBSON

THURSDAY 9:00a.m. Noether's work in Galois theory. RICHARD SWAN 10:30 a.m. Noether normalization. jUDITH SALLY 1:15 p.m. The explicit description of moduli spaces since Noether's work on ternary quortics. DAVID MUMFORD 2:30p.m. Poisson-Pioncherel formula for Lie groups. MICHELE VERGNE 8:15p.m. PANEL DISCUSSION: Emmy Noether at Erlongen, Gottingen, and Bryn Mawr. Members of the panel are Marguerite Lehr, Ruth McKee, Gottfried Noether, Grace Quinn, and Olga Taussky-Todd.

FRIDAY 9:30a.m. Conservation lows and their application in global differential geometry. KAREN UHLENBECK 11:00 a.m. Some non-commutative methods in number theory. OLGA TAUSSKY-TODD 1:30 p.m. The classification of finite simple groups and some consequences. WALTER FElT 3:00p.m. L 2-cohomology and intersection homology of some arithmetic varieties. ARMAND BOREL

PROCEEDINGS OF SYMPOSIA range of topics discussed there. It should be of in­ IN PURE MATHEMATICS terest to mathematicians or advanced students in geometry and analysis; physicists and chemists inter­ GEOMETRY OF THE LAPLACE OPERATOR ested in spectral theory of the Laplace operator and the Schroedinger equation. The fundamentals of edited by Robert Osserman and Alan Weinstein Riemann geometry and some knowledge of analysis This book contains a series of papers covering on manifolds is indispensible for the enjoyment and most of the topics that would be subsumed under understanding of the papers included. One will be the heading of "geometry of the Laplace operator." rewarded with an overview of the type of problems In particular, one has the most recent results on in this field under active investigation, and an up-to­ bounds for low eigenvalues of the Laplace operator date report on many of the latest results. in terms of geometric quantities, total distribution of the spectrum in relation to closed geodesics and This symposium received support from the other geometric entities, harmonic mappings, and National Science Foundation. geometric scattering theory. Volume 36, vii + 323 pages (hard cover) The book contains expanded versions of most of List price $20.40, institutional member $15.30, individual member $10.20 the invited lectures and a few contributed papers ISBN 0·8218·1439·7; LC 79-26934 from a symposium held at the University of Hawaii Publication date: February 1980 i'n March 1979 and represents quite faithfully the To order, please specify PSPUM/36 N Prepayment is required for all AMS publications. Order from AMS, P.O. Box 1571, Annex Station, Providence, Rl 02901, or call toll free 80Q-556-7774 to charge with Visa or MasterCard.

189 Madison, Aprill6-17, 1982, University of Wisconsin Second Announcement of the 794th Meeting

The seven hundred ninety-fourth meeting of the Circle and University of Notre Dame. The tentative American Mathematical Society will be held at the list of speakers includes Walter L. Bailey, Jr., Robert University of Wisconsin, Madison, on Friday and J. Bond, H. Kiselevsky, William Messing, Dinakar Saturday, April 16-17, 1982. The Association for Ramakrishnan, Michael J. Razor, Michael E. Rosen, Symbolic Logic will also meet on Friday and Saturday. William Sinnott, and Steven I. Sperber. Sessions will be held in the Wisconsin Center, located Partial differential equations, PAUL H. at the comer of Langdon and Lake Streets. RABINOWITZ, University of Wisconsin, Madison. Invited Addresses The tentative list of speakers includes Felix E. Browder, Emanuele DiBenedetto, C. Evans, Ronald F. Gariepy, By invitation of the 1981 Committee to Select Hour Robert Jensen, Carlos E. Kenig, Alan C. Lazer, P. Speakers for Central Sectional Meetings, there will be Sacks, Joel A. Smoller, Bruce E. Turkington, and four invited one-hour addresses. The speakers, their William P. Zemer. titles, and the scheduled times of presentation are as follows: Classical real analysis, DANIEL WATERMAN, MICHAEL G. CRANDALL, University of Wis­ Syracuse University. The tentative list of speakers includes Peter Bullen, Richard B. Darst, James Foran, consin, Madison, Degenerate nonlinear diffusion Krishna M. Garg, Paul D. Humke, Cheng-Ming Lee, equations, 11:00 a.m. Friday. David A. Legg, Jan S. Marik, Christoph J. Neugebauer, CASPER GOFFMAN, Purdue University, Some Richard J. O'Malley, Brian S. Thomson, and Clifford uses of Sobolev spaces and of Cesari spaces, 1:45 E. Weil. p.m. Friday. Topics in the theory of functions of a single JAMES S. MILNE, University of Michigan, Ann complex variable, JACK WILLIAMSON, University Arbor, Arithmetic varieties, 11:00 a.m. Saturday. of Hawaii, Honolulu, and University of Wisconsin, YASUTAKA SIBUYA, University of Minnesota, Madison. The tentative list of speakers includes Albert Minneapolis, Gevrey expansions and cohomological Baernstein III, Johnny E. Brown, David Drasin, Albert methods in the theory of asymptotic solutions, 1:45 Edree, Stephen D. Fisher, Robert Gethner, Bruce p.m. Saturday. Hansen, Joseph B. Miles, Rao V. Negisetty, Richard All four talks will be given in the auditorium on the H. Rochberg, John F. Rossi, Li-Chien Shen, Charles first floor of the Wisconsin Center. Stanton, David A. Stegenga, Allen W. Weitsman, Special SeBB.ions Thomas Wolff, and Jang-Mei Gloria Wu. By invitation of the same committee, there will be Contributed Papen seven sessions of selected twenty-minute papers. The There will also be sessions for contributed ten­ topics of these special sessions, names of the organizers, minute papers. Abstracts should have been sent to and partial lists of speakers are as follows: the American Mathematical Society, P. 0. Box 6248, Minimal manifolds, RICHARD L. BISHOP, Providence, Rhode Island 02940, so as to arrive prior University of Illinois, Urbana-Champaign. The tenta­ to the deadline of February 22. Abstracts should be tive list of speakers includes Robert D. Gulliver III, prepared on the standard AMS form available from Nicholas J. Korevaar, Johannes C. C. Nitsche, and the AMS office in Providence, or in departments of Karen Uhlenbeck. mathematics. The legacy of Srinivasa Ramanujan, DAVID M. BRESSOUD, Pennsylvania State University, Uni­ Symposium on Several Complex Variables versity Park. The tentative list of speakers includes With the anticipated support of the National Richard A. Askey, George E. Andrews, R. Balasub­ Science Foundation, a symposium on Several Complex ramanian, Bruce C. Berndt, W. Burge, Sarvadaman Variables is scheduled to take place Monday through Chowla, P.D.T.A. Elliott, Marvin I. Knopf, Carlos Thursday, April12-15. This topic was selected by the J. Moreno, K. G. Ramanathan, Robert A. Rankin, 1980 Committee to Select Hour Speakers for Western Dennis W. Stanton, and SamuelS. Wagstaff, Jr. Sectional Meetings, whose members were Paul T. Asymptotic solutions of ordinary differential Bateman, William H. Jaco (chairman), Albert Marden, equations, Po-FANG HSIEH, Western Michigan Mary E. Rudin, and Paul J. Sally, Jr. [See page 210.] University. The tentative list of speakers includes Since the 1975 AMS Summer Institute on Several Donatus U. Anyanwu, Harry Gingold, Leon M. Hall, Complex Variables, there have been a number B. J. Harris, Ching-her Lin, Donald A. Lutz, Richard of important developments in the field. These E. Meyer, Robert E. O'Malley, Jr., Seymour V. Parter, developments infringe upon several related fields of T. K. Puttaswamy, William H. Reid, Maxwell A. mathematics such as partial differential equations, Rosenlicht, Reinhard Schafke, and Charles Tier. differential geometry, and algebraic geometry. The Applications of cohomology in number theory, purpose of the symposium is to bring together active JOHN M. MASLEY, University of Illinois at Chicago researchers and major contributors to the recent

190 Central Madison

1. The Concourse 6. Madison Inn 2. Edgewater Hotel 7. Memorial Union 3. Howard Johnson's 8. Town and Campus Motel Motor Lodge 9. Wisconsin Center 4. Inn on the Park 10. Van Vleck Hall 5. Lowell Hall (Dept. of Math.)

~ = Public Parking

LAKE mononA

191 developments to present a coherent and comprehensive own reservations prior to the cut-oft' date of March review of the recent important results and to discuss 15, and should identify themselves as participants in the future directions of research in the field of several the American Mathematical Society's meeting. Rates complex variables. listed do not include the 4 percent Wisconsin State or The Organizing Committee for the symposium the 6 percent City of Madison taxes, and are subject includes Robert C. Gunning, Princeton University; F. to possible change. Reese Harvey, Rice University; Raghavan Narasimhan, Howard Johnson's Motor Lodge University of Chicago; Walter Rudin, University 525 W. Johnson Street, Madison, WI 53703 of Wisconsin, Madison; Yum-Tong Siu (chairman) Telephone: 608-251-5511 or 800-654-2000 Stanford University; Wilhelm F. Stoll, University Single $34 (1 queen bed, 1 person) of Notre Dame; and Shing-Tung Yau, Institute for Double $39 (1 queen bed, 2 people) Advanced Study. Double $43 (2 double beds, 2 people) There will six onil-hour survey talks and a number Lowell Hall (Wisconsin Center Guest House) of more specialized half-hour lectures. The on~hour 610 Langdon Street, Madison, WI 53706 speakers who have thus far accepted invitations, and Telephone: 608-256-2621 the titles of their talks, are: HANS GRAUERT, Single $22 Double $26 University of GOttingen, West Germany, Complex Madison Inn Morse theory; JOSEPH J. KOHN, Princeton Univer­ 601 Langdon Street, Madison, WI 53703 sity, Microlocalization of TJ and TJb; MICHAEL Telephone: 608-257-4391 SCHNEIDER, University of Bayreuth, West Germany, Single $30-40 Double $40 How many equations are needed to describe a Town & Campus Best Western Motel variety in projective or affine space?; HENRI State at Frances Street, Madison, WI 53703 SKODA, Universite de Paris VI, Extension of closed Telephone: 608-257-4881 or 800-528-1234 positive currents; and SHING-TUNG YAU, The Single $36 Double $44 Institute for Advanced Study, A survey on recent development in differential geometry of Kahler Food Service manifolds. A cafeteria located in the basement of the Wisconsin A partial list of the half-hour speakers, which Center is open Monday through Friday from 7:30 to includes only those who have accepted invitations, is: 11:00 a.m. for continental breakfast, and from 11:30 Eric D. Bedford, Steven R. Bell, Thomas Bloom, Daniel a.m. to 12:30 p.m. for lunch; it is not open Saturday M. Bums, Jr., David Catlin, John P. D'Angelo, John or Sunday. A wider variety of food can be purchased E. Fornaess, Michael B. Freeman, Gary A. Harris, at the Lakeside Cafeteria on the first floor (northeast Norberta Kerzman, Shoshichi Kobayashi, Steven G. comer) of the Memorial Union. The Lakeside cafeteria Krantz, Laszl6 Lempert, Ngaiming Mok, Alexander is open Monday through Friday from 7:00a.m. to 3:00 Nagel, John Polking, R. Michael Range, Hugo Rossi, p.m. and 4:45 to 6:30 p.m., and Sunday from 9:00 a.m. Halsey L. Royden, Andrew Sommese, Nancy K. to 1:30 p.m. It is closed on Saturday. The Tripp Stanton, B. A. Taylor, Andrei N. Todorov, Sidney M. Commons, which is on the floor above the Lakeside Webster, R. 0. Wells, Jr., Pit-Mann Wong, and Hung Cafeteria, specializes in a salad bar where salad is paid HsiWu. for by the ounce. Tripp Commons is open only Monday A complete list of speakers and the symposium through Friday from 11:45 a.m. to 1:00 p.m. Also program will appear in the April issue of the Notices. in the Memorial Union is the Ratskeller which serves Registration beer, hamburgers, and sandwiches; it is open Monday through Friday from 7:30a.m. until 9:30p.m. The registration desk will be open from 8:30 a.m. until 4:00 p.m. Monday through Friday, and from Many restaurants are to be found within walking 8:30 a.m. until noon on Saturday in the lobby of the distance of the Wisconsin Center, and a list will be Wisconsin Center. Registration fees for the symposium available at the registration desk. and meeting are: Parking Symposium Only All of the hotels or motels listed above offer parking Nonmember $15 for their guests. There is a public parking ramp only Members of AMS or ASL $10 a block and a half from the Wisconsin Center on Lake Student/Unemployed $ 5 Street, between State Street and University Avenue. Meeting Only Travel Nonmember S16 Members of AMS or ASL $10 Madison is located 150 miles northwest of Chicago (via Route I-90) and 80 miles west of Milwaukee (via Student/Unemployed $ 5 Route I-94). The Dane County Regional Airport is Symposium and Meeting located five miles northeast of Madison and is served Nonmember $31 by Frontier, Northwest, Ozark, and Republic Airlines. Members of AMS or ASL S20 Transportation between the airport and all points in Student/Unemployed $10 Madison is provided by Bender's Limousine Service and Accommodations Union Cab Company. The trip from the airport takes Blocks of rooms are being held for participants at the approximately 20 minutes and the cost per person for following area motels. Individuals should make their the limousine is $2.75, while the taxi service costs

192 about $6.50 regardless of the number of passengers. In Madison the Alco buses arrive at and depart from Flights between Madison and distant points have not the front entrance of the Memorial Union. Up-to-date been affected too much by the air controller's strike, information may be obtained by calling Alco Bus in but the former frequent flights between Madison and Madison at 608-257-5593. Chicago have become more sporadic. This gap has Madison is also served by Greyhound and Trailways been partially filled by the Alco Bus Company, which bus lines, and by the major rental car companies. operates buses between O'Hare Airport and Madison. The closest Amtrak service is to or from Columbus, Buses are scheduled to depart from O'Hare daily at Wisconsin, located 30 miles northeast of Madison. 9:30 and 11:00 a.m., 2:00, 5:00, 7:00 and 10:00 p.m., and return daily from Madison at 7:00 and 10:00 a.m., Paul T. Bateman 1:00, 2:30, and 5:30 p.m. The trip in either direction Urbana, Illinois Associate Secretary takes approximately 3 hours and costs $10 per person.

Bellingham, June 18-19, 1982, Western Washington University First Announcement of the 795th Meeting

The seven hundred ninety-fifth meeting of the the deadline of April19. Abstracts should be prepared American Mathematical Society will be held at Western on the standard form available from the AMS office in Washington University, Bellingham, Washington, on Providence or in departments of mathematics. Friday and Saturday, June 18-19, 1982. This meeting Other Organizations will be held in conjunction with a meeting of the Mathematical Association of America (MAA). The MAA program will include an invited address by JAMES A. COCHRAN of Washington State Invited Addresses University. There will be an MAA special session By invitation of the Committee to Select Hour on Different methods of teaching mathematics, and Speakers for Far Western Sectional Meetings, there will a panel discussion on Mathematics and computer be two invited omrhour addresses. The speakers, and science. The featured lecture at the Friday evening the titles of their talks, are as follows: banquet will be delivered by EDWIN HEWITT MICHAEL FREEDMAN, University of California, of the University of Washington, entitled Even San Diego, Bing topology, infinite procedures, and mathematicians are odd. At the Saturday afternoon the Poincare conjecture in dimension four. luncheon the featured speaker will be MARCIA P. MARINA RATNER, University of California, SWARD, Associate Director of the MAA; the title of Berkeley, Some interactions between ergodic theory her talk is Like 55, mathematics saves lives. and topological geometry. Registration Special Sessions The registration desk will be located outside of By invitation of the same committee, there will be Room 105 in Bond Hall. It will be open from 10:00 one special session of selected twenty-minute papers. a.m. to 5:00 p.m. on Friday and from 8:30 a.m. to 12:30 The topic of this special session and the name of the p.m. on Saturday. The registration fees will be $6 for organizer is: members of the AMS or MAA, $8 for nonmembers, Continuum theory, LEWIS E. WARD, JR., and $2 for students or unemployed mathematicians. University of Oregon. Accommodations Most of the papers to be presented at this special Persons interested in obtaining information about session will be by invitation. However, anyone sub­ dormitory accommodations, on-campus meals, and mitting an abstract for the meeting who feels that other information about the area should write directly his or her paper would be particularly appropriate for to Dorothy Tellis, Department of Continuing Educa­ the special session should indicate this clearly on the tion, Western Washington University, Bellingham, abstract form and submit it by March 29, 1982, three Washington 98225. weeks before the deadline for contributed papers. Additional information about accommodations and Contributed Papers travel will appear in the April issue of the Notices. There will also be sessions for contributed ten­ minute papers. Abstracts should be sent to the Hugo Rossi American Mathematical Society, P. 0. Box 6248, Salt Lake City, Utah Associate Secretary Providence, Rhode Island 02940, so as to arrive prior to

193 1982 SUMMER SEMINAR 1982 SUMMER IN APPLIED MATHEMATICS RESEARCH INSTITUTE

Applications of Group Theory Recursion Theory in Physics and Mathematieal Physics June 28-July 16, 1982 July 6-16, 1982 Cornell University, Ithaca, New York University of Chicago, Chicago, Rlinois The thirtieth Summer Research Institute sponsored The fourteenth AMS-SIAM Summer Seminar in by the American Mathematical Society will be devoted Applied Mathematics will be held July 6-16, 1982, to recursion theory. The Institute which will take place and will take place at the University of Chicago, at Cornell University in Ithaca, New York, from June Chicago, Illinois. The seminar will be sponsored 28 to July 16, will be cosponsored by the Association for jointly by the American Mathematical Society and Symbolic Logie. Members of the Organizing Committee the Society for Industrial and Applied Mathematics, include Solomon Feferman, Yiannis Mosehovakis, Anil and it is anticipated that it will be supported by a Nerode (eo-chairman), Hilary Putnam, Gerald Sacks, grant from a federal agency. The topic Applications Joseph Shoenfield, Richard A. Shore (eo-chairman), of Group Theory in Physics and Mathematical and Robert I. Soare. It is anticipated that the institute Physics was selected by the AM8-SIAM Committee will be supported by a grant from the National Science on Applied Mathematics whose members at the time Foundation. were Roger Brockett, Lily E. Christ, John Dennis, The main objective of the institute is to explain Norman Lebovitz, Sanjoy K. Mitter, John A. Morrison, recent developments of new techniques and approaches Alan Newell (chairman), and George C. Papanicolaou. to major problems in recursion theory to a wider The members of the organizing committee are M. Flato audience, and to encourage interaction between workers (Mathematical Physics), University of Dijon, France; in various areas of recursion theory with researchers C. Fronsdal (Physics), University of California, Los in related branches of set theory, model theory, Angeles; I. Kaplansky (Mathematics), University of constructive mathematics, and computer science, with Chicago; Y. Nambu (Physics), University of Chicago; an eye toward the dissemination of problems and P. J. Sally (Mathematics), chairman, University of techniques. No such major meeting on recursion theory Chicago; I. M. Singer (Mathematics), University has taken place since the institute held at Cornell of California, Berkeley; J. Wolf (Mathematics), in 1957 and, needless to say, the field has developed University of California, Berkeley; and G. Zuckerman enormously since that time. (Mathematics), Yale University. Housing accommodations will be available on campus This conference will provide a means for the for those attending the institute, and daily meals will exchange of ideas, methods, and recent results among be served in a dining hall near the dormitOries. In mathematicians who work in Lie superalgebras, Kac­ the early spring a brochure will be available, which Moody Lie algebras, and group representations, and will include information about the scientific program, mathematical physicists and physicists who use these firm room and board rates, the residence and dining theories in their study of physical phenomena. hall facilities, local information, and a reservation form Formal talks will be presented by members of all to be used for accommodations on campus. Each groups, and considerable time will be provided for participant will pay a social fee to cover the cost of informal discussions. refreshments served at breaks and for social events. Individuals may apply for admission to the sem­ There will also be a meeting registration fee of $45 ($15 inar. Application blanks for admission and/or for students). financial assistance can be obtained from the Meeting Funds for support will be limited, and it is hoped Arrangements Department, American Mathematical that a number of participants who wish to attend Society, P. 0. Box 6248, Providence, Rhode Island will obtain their own support. Those interested in 02940. The application deadline has been extended taking part in the institute and/or being considered for to April 15, 1982. An applicant will be asked to financial assistance should send their requests to the Co­ indicate his or her scientific background and interest, chairmen of the Organizing Committee, c/o Meeting and should have completed at least one year of Arrangements Department, American Mathematical graduate school. A graduate student's application Society, P. 0. Box 6248, Providence, Rhode Island must be accompanied by a letter from his or her faculty 02940, prior to April 9, 1982. The Committee will advisor concerning the applicant's ability and promise. consider such requests, and applicants will be informed Those who wish to apply for a grant-in-aid should so later if funds are available. indicate; however, funds available for the seminar are limited and so individuals who can obtain support from other sources should do so.

194 INVITED SPEAKERS Call For Topics AND SPECIAL SESSIONS

Invited Speakers 1984 AMS-SIAM SYMPOSIUM at AMS Meetings Some Mathematieal Questions in Biology The individuals listed below have accepted invita­ Suggestions for topics for the May 1984 Symposium tions to address the Society at the times and places Some Mathematical Questions in Biology should indicated. For some meetings, the list of speakers is be submitted to the AMS-SIAM Committee on incomplete. Mathematics in the Life Sciences before the end Madison, April1982 of May 1982. Michael G. Crandall James S. Milne The Symposium is held in conjunction with the Casper Goft'man Yasutaka Sibuya Annual Meeting of the AAAS in May. The Chairman of the committee is Robert M. Miura, Bellingham, June 1982 Department of Mathematics, University of British Michael Freedman Marina Ratner Columbia, Vancouver, British Columbia, Canada V6T 1 Y4; other members of the committee are H. Thomas Organizers and Topies Banks, Brown University; Joel E. Cohen, Rockefeller of Speeial University; Frank C. Hoppensteadt, University of Sessions Utah; Joseph B. Keller, Stanford University; Donald Names of organizers of special sessions to be held A. Ludwig, University of British Columbia; Garrett M. at meetings of the Society are listed below, along with Odell, Rensselaer Polytechnic Institute; and Charles S. the topic of the session. Most of the papers presented Peskin, New York University. at special sessions are by invitation. Other papers will Some recent topics in these annual symposia be considered at the request of the author provided have been Theoretical and experimental studies in that this is indicated clearly on the abstract form and cellular, developmental and population biology {1980), the abstract is submitted by the deadlines given below. Biomechanics and models in developmental biology These deadlines are usually three weeks earlier than {1981), and Neurobiology, the study of the nervous the normal abstract deadlines for meetings. Papers systems of organisms (1982). The 1983 Symposium will not selected for special sessions will automatically be be on Muscle Physiology. considered for regular sessions unless the author gives specific instructions to the contrary. MEMOIRS OF THE AMERICAN April1982 Meeting in Madison MATHEMATICAL SOCIETY Deadline for consideration: E:r:pired Richard L. Bishop, Minimal manifolds THE DEGENERATE PRINCIPAL SERIES David M. Bressoud, The legacy of Srinivasa FOR Sp(2n) Ramanujan by Robert Gustafson Po-Fang Hsieh, Asymptotic solutions of ordinary A series of induced representations of the sym­ differential equations plectic group of 2n x 2n matrices over a p-adic field k is decomposed. John M. Masley, Applications of cohomology A maximal parabolic sub­ in group P and a family {xs Is E C} of unramified char­ number theory acters of P are considered. The techniques developed Paul H. Rabinowitz, Partial differential equations may be useful for decomposing degenerate principal Daniel Waterman, Classical real analysis series of p-adic Chevalley groups. Jack Williamson, Topics in the theory of functions 1980 Mathematics Subject Classifications: 22E50, 22E35, 20G05, of a single complex variable 20G25. Memoir Number 248, vi + 88 pages (soft cover) June 1982 Meeting in Bellingham List price $4.80, Institutional member $3.60, individual member $2.40 Deadline for consideration: March. 29 ISBN 0-8218-2248-9; LC 81-13033 Lewis E. Ward, Jr., Continuum theory Publication date: September 1981 To order, please specify MEM0/248N

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

195 SPECIAL MEETINGS

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

1981-1982. Distinguished Leeture Series in Applied 25-27. Statisties on Spheres: Sixth Annual Leeture Series Mathematies, Chicago, lllinois. in the Mathematieal Scienees, University of Arkansas, Sponsor: The Chicago Area Applied Mathematics Con­ Fayetteville, Arkansas. (January 1982, p. 77) sortium, consisting of the Department of Engineering 29-31. Conference on Principles of Database Systems, Los Sciences and Applied Mathematics at Northwestern Angeles, California. University, the Departments of Mathematics at the Sponsors: ACM/SIGMOD and ACM/SIGACT. University of Chicago, University of lllinois {Chicago Topics: Concurrency control, distributed database Circle), and lllinois Institute of Technology, and the systems, design and semantics of relational database Applied Mathematics Division of Argonne National systems, and physical data storage and structuring. Laboratory. Information: Seymour Ginsburg and Dennis McLeod, Speakers: L. E. Fraenkel (Sussex University), R. S. Department of Computer Science, University of Rivlin (Lehigh University) and J. S. Langer (Institute Southern California, Los Angeles, California 90007. for Theoretical Physics). 29-April 2. Symposium on Funetional Analysis and Matkowsky, Department of Engineer­ Information: B. J. Differential Equations, Lisbon, Portugal. ing Sciences and Applied Mathematics, Northwestern Information: Comissao Organizadora do Symp. en Anal. lllinois 60201. University, Evanston, fonc. e Equac. dif., 37 av. da Republica, P-1000 Lisbon, 1981-1982. Special Program in Algebraie Number Theory Portugal. and Algebra, University of lllinois at Urbana-Champaign, 29-April 2. Conference on Ordinary and Partial Differential Urbana, lllinois. (October 1981, p. 546) Equations, University of Dundee, Scotland. (August 1981, 1981-1982. Aeademie Year Devoted to Mathematieal p. 438; January 1982, p. 75) Problems in Theoretieal Physies, The Mittag-Leffler '30-April 3. Thirty-Fourth British Mathematieal Collo­ Institute, Djursholm, Sweden. (February 1981, p. 177) quium, University College of North Wales, Bangor, January 3-0ctober 2, 1982. Mathematisehes Forsehungs­ ~wynedd, United Kingdom. (October 1981, p. 547) institut Oberwolfaeh, (Weekly Conferences), Federal Republic of Germany. (January 1982, p. 74) APRIL 1982 September 1, 1982-August 31, 1983. Statistical and 2-3. Diserete Geometry and Convexity Days, New Continuum Approaehes to Phase Transition, Institute York Academy of Sciences and Courant Institute of for Mathematics and its Applications, University of Mathematical Sciences, New York, New York. (January Minnesota, Minneapolis, Minnesota. (January 1982, p. 74) 1982, p. 75) Invited Speakers: F. R. K. Chung (Bell Laboratories), MARCH 1982 J. E. Goodman (City College, CUNY), R. L. Graham (Bell Laboratories), W. 0. J. Moser {McGill University), 11-13. Spring Topology Conference, U.S. Naval Academy, P. F. Pickel (Polytechnic Institute of New York), R. Annapolis, Maryland. {November 1981, p. 643) Pollack (Courant Institute, NYU), G. B. Purdy (Texas (Carnegie-Mellon 15-19. Seventh International Time Series Meeting, Dublin, A & M University), M. I. Shamos University), R. P. Stanley (Massachusetts Institute of Ireland. (October 1981, p. 547) Technology), P. Ungar (Courant Institute, NYU), J. E. 22-26. Workshop on Algebraie Topology, Universidad Wetzel (University of lllinois), and T. Zaslavsky (Ohio AutOnoma de Barcelona, Spain. State University). Invited Speakers: P. Hilton, G. Mislin, L. Smith, C. 3. Illinois Number Theory Conference, lllinois State Wilkerson, A. Zabrodsky. University, Normal, lllinois. Information: J. Aguade, Secci6 de Matematiques, Univer­ Call for Papers: Send title and short abstract of 15-minute sidad AutOnoma de Barcelona, Bellaterra, Barcelona, papers to the address below by March 22, 1982. Spain. Information: Charles Vanden Eynden, Department of 22-26. Homotopy Theory, Northwestern University, Mathematics, lllinois State University, Normal, lllinois Evanston, lllinois. (January 1982, p. 75) 61761.

196 :HI. Eleventh Midwest Partial Dift'erential Equations 26-28. Society for Industrial and Applied Mathematies Conference, University of illinois, Chicago Circle. Special Conferenee on Linear Algebra and Applieations, Program: There will be four invited one-hour talks each Raleigh, North Carolina. (October 1981, p. 547) day. 26-29. Society for Industrial and Applied Mathematiea Support: Limited (up to $85) travel support for faculty Special Conferenee on Applied Linear Algebra, Raleigh, members and especially graduate students may be North Carolina. (October 1981, p. 547; January 1982, p. available. 76) Information: Melvin Heard or David S. Tartakoff, 26-30. NSF-CBMS Conference on Automorphism Groups Department of Mathematics, University of illinois, of von Neumann Algebras and the Strueture of Faetors, Chicago Circle, P. 0. Box 4348, Chicago, illinois 60680, University of Iowa, Iowa City, Iowa. (October 1981, p. 547) (312)996-2372, 2440. 29-30. Decision Problems in Mathematies and Computer 6--8. Fifth International Symposium on Programming, Science, Bowling Green State University, Bowling Green, Torino, Italy. Ohio. Information: Istituto di Scienze dell'lnformazione, 42 corso Sponsor: Central State Universities Inc. M. d'Azeglio, I-10125 Torino, Italy. Speakers: Jean Ferrante, IBM and C. Ward Henson, 13-16. Sixth European Meeting on Cybernetiea and University of lllinois. Systems Reaeare.h, Vienna, Austria. Information: A. M. W. Glass, Department of Mathematics, Information: Organizing Committee of Sixth European Bowling Green State University, Bowling Green, Ohio Meeting, c/o Osterreich. Studiengesellschaft fiir 43403, (419)372-2636 or 2729. Kybern., 3 Schottengasse, A-1010 Wien 1, Austria. MA¥1982 13-16. GAMM-Tagung 1982, Budapest, Hungary. (October 1981, p. 547) 5-7. Fourteenth Annual ACM Symposium on the Theory 15-17. John H. Barrett Memorial Lectures in Dift"erential of Computing, San Francisco, California. (October 1981, Equations, University of Tennessee, Knoxville, Tennessee. p. 548) (January 1982, p. 75) 7. Sixth Symposium on the Unifleation of Finite Element&, 16-17. Pacifte Coast Conferenee on Mathematieal Modeling Finite Dift'erences and Caleulu& of Variation, University of Renewable Reaourees, Humboldt State University, of Connecticut, Storrs, Connecticut. Arcata, California. Program: The aim of the symposium is to present Purpose: The conference is designed to bring together recent advances in various numerical methods and, by members of the mathematics community and those emphasizing the analogy between them, to point out members of the natural resources community who have cases where they can be merged to ease the solution or interests in mathematical modeling. The purpose is to attain improvement of the results. There will be a to review the progress that has been made in the panel discussion at the conclusion of the symposium. mathematical modeling of renewable resources. Information: H. Kardestuncer (Chairman, Organizing Invited Speakers: Colin W. Clark (University of British Committee), University of Connecticut, U-37, Storrs, Columbia); Howard B. Stauffer (British Columbia Connecticut 06268. Ministry of Forests); Robert McKelvey (University of 10-14. Twenty-Sixth Annual Meeting of the Australian Montana); James C. Frauenthal (SUNY, Stony Brook); Mathematieal Society, Newcastle, Australia. (January A. R. Sen (Canadian Wildlife Service). 1982, p. 76) Information: Roland H. Lamberson, Department of 13-14. Optimi1ation Days 1982, Universite de Montreal, Mathematics, Humboldt State University, Arcata, Montreal, Canada. (January 1982, p. 76) California 95521. 16-28. NATO Advanced Study Institute on Nonlinear 16-17. Fifteenth Annual Small College Computing Sym­ Stochastic Problema, Algarve, Portugal. (January 1982, posium, North Dakota State University, Fargo, North p. 76) Dakota. (January 1982, p. 75) 17-19. Fourth Symposium on Mathematieal Programming 16-17. A Hundred Years of Algebra 1830-1930, Oxford, with Data Perturbations, Marvin Center, George England. (January 1982, p. 76) Washington University, Washington, D. C. (January 1982, 16-20. Conference on Representation Theory of Reduetive p. 76) Groups, Park City, Utah. 17-19. Seventeenth New Zealand Mathematics Colloquium, Support: Support is anticipated from the National Science University of Otago, Dunedin, New Zealand. (January Foundation. 1982, p. 76) Information: Ann Reed, Department of Mathematics, 17-21. Conference on Mathematieal Modela for Equitable University of Utah, Salt Lake City, Utah 84112. Alloeationa, The Citadel, Charleston, South Carolina. 22-23. Thirteenth Annual Pittsburgh Conference on Principal Speaker: William F. Lucas, Cornell University. Modeling and Simulation, University of Pittsburgh, Program: Professor Lucas will deliver a series of ten Pittsburgh, Pennsylvania. (October 1981, p. 547) lectures. Time will also be available for contributed papers and group discussions. 23-25. Journees relativistes, Lyon, France. Information: M. G. Collier, Department of Mathematics Information: E. Combet, Department of Mathematics, and Computer Science, The Citadel, Charleston, South 43 Boulevard 11 Novembre 1918, 69622 Vuleurbanne Carolina 29404, (803)792-6983. Cedex, Lyon, France. 17-June 5. Seeond Franco-Southeaat Aaian Mathematieal 24. Conferenee on Mathematies Learning and Teaehing, Conferenee, Quezon City, Philippines. (January 1982, p. Rutgers University, Newark, New Jersey. 76) Topics: Curriculum design, mathematization and problem solving, effective uses of microcomputers and software 24-27. Journees de statiatique, Brussels, Belgium. packages, mathematics and language, anxiety reduction, Information: Journees de statistique, Serv. Stat. et Rech. remedial and developmental mathematics teaching, and oper., Universite libre Bruxelles, CP 135, 50 av. F. D. problems of teaching geometry and calculus. Roosevelt, B-1050 Brussels, Belgium. Information: Arthur Powell, Rutgers University, Newark, 24-28. International Foreea&ting Conference, Valencia, New Jersey 07102, (201)648-5168. Spain. (October 1981, p. 548)

197 25-27. Twelfth International S)'Dlposium on Multivalued summary (at most 10 typed lines) should be sent before Logie, Paris, France. May 1, 1982, to the address indicated below. Information: Michel Israel, DE-CNAM, 292 rue Saint- Speakers: M. Akcoglu (Toronto), A. Badrikian (Clermont), Martin, 75141 Paris, Cedex 01, France. A. Bellow (Northwestern), R. V. Chacon (U.B.C.), J. 26--28. Advanced Seminar on the Theory of Dispened Mul­ Choksi (McGill), G. Choquet (Orsay), J. Christensen tiphase Flow, Mathematics Research Center, University (Copenhagen), J. Diestel (Kent), G. Edgar (Ohio), S. of Wisconsin, Madison, Wisconsin 53706. Graf (Erlangen), T. Hida (Nagoya), S. Kakutani (Yale), D. Kolzow (Erlangen), D. Maharam-Stone (Rochester), Program: The conference will cover recent developments and trends in the understanding of fluidization, R. D. Mauldin (North Texas), J. Mycielski (Colorado), J. suspension, sedimentation, aerosols and related subjects. Oxtoby (Bryn Mawr), R. R. Phelps.(U of Washington), There will be lectures by invited speakers. M. Sion (U.B.C.), A. Stone (Rochester), M. Talagrand (Paris), E. Thomas (Groningen), R. Wheeler (Northern Invited Speakers: A. Acrivos, G. D. Ashton, J. R. lllinois). Brock, B. Dahneke, Masao Doi, D. A. Drew, G. M. Homsy, R. Jackson, D. F. McTigue, J. W. Nunziato, Sponsors: National Sciences and Engineering Research G. Papanicolau, R. E. Rosensweig, W. B. Russell, S. B. Council of Canada, FCAC of Quebec, Canadian Savage and L. van Wijngaarden. Mathematical Society, Universite de Sherbrooke. Information: Gladys Moran, Mathematics Research Information: Organizing Committee, cfo J. M. Belley, J. Center, University of Wisconsin, 610 Walnut Street, Dubois, P. Morales, Departement de Mathematiques et Madison, Wisconsin 53706. d'Informatique, Universite de Sherbrooke, Sherbrooke, Quebec, Canada JlK 2Rl. 27. Trends and Applications 1982: Advances in Information Technology, National Bureau of Standards, Gaithersburg, 8-11. Conference in Modern Analysia and Probability (in Maryland. (January 1982, p. 76) honor of Shi1uo Kakutani), New Haven, Connecticut. (January 1982, p. 76) 30-June 1. Canadian Mathematical Society Summer Meeting, Carleton University, Ottawa, Ontario, Canada. 8-11. 1982 Short Course on Teaehing Computer Science in a Mathematica Department, Denison University, Invited Speakers: J. Cea (Nice), P. Conner (Louisiana), Granville, Ohio. (January 1982, p. 76) M. Fortin (Laval), R. Kane (Western Ontario), R. Swan (Chicago) and F. Treves (Rutgers). 14-18. Meeting on S)'Dlbolie Computation, Salisbury Call for Papers: Those wishing to contribute to special State College, Salisbury, Maryland. sessions of 15 minutes should send an abstract, ready Principal Lecturer: B. F. Caviness, University of Delaware. for photocopying (including author's name, and the Sponsor: MD-DC-VA Section of the MAA. title of the talk), before April 15, 1982, to M. Racine, Purpose: To make available to teachers in two- Department of Mathematics, University of Ottawa, and four-year colleges important topics in applicable Ottawa, Ontario KlN 9B4. mathematics. Information: B. M. Puttaswamaiah, Department of Math­ Information: B. A. Fusaro, Department of Mathematical ematics and Statistics, Carleton University, Ottawa, Sciences, Salisbury State College, Salisbury, Maryland Canada KlS 5B6. 21801, (301)546-3261, ext. 369. 30-June 2. 1982 Joint Meeting of the Claaliflcation Society 14-18. Fifth International Conference on Trenda in and the PI)'Chometrie Society, Universite du Quebec a Theory and Practice of Nonlinear Dift'erential Equations, Montreal, Montreal, Quebec, Canada. Department of Mathematics, University of Texas at Call for Papers: Twenty-minute talks are invited. Title Arlington, Arlington, Texas 76019. (January 1982, p. 77) and an abstract of no more than 500 words should be 15-17. Workshop on Low-Probability/High-Consequence sent to one of the addresses below by March 1. Risk Analysis, Hyatt Regency, Arlington, Virginia. Information: Pascale Rousseau, Departement de Mathematiques, Universite du Quebec Montreal, Sponsor: Society for Risk Analysis and the U.S. Nuclear a Regulatory Commission. Montreal, Canada H3C 3P8. Phone (514)282-3224; or Peter M. Bentler, Department of Psychology, UCLA, Information: George Flanagan, Oak Ridge National Los Angeles, California 90024. Phone (213)825-2893. Laboratory, P.O. Box X, Oak Ridge, Tennessee 37830. 15-28. Conference on Finite Groups, Montreat, Canada. JUNE 1982 Sponsor: Canadian Mathematical Society. Topics: Sporadic simple groups, modular forms, cubic 3-5. Statistical Society of Canada 1982 Annual Meeting, forms, exceptional groups, embeddings in Lie groups, University of Ottawa, Canada. geometries, graded Lie algebras, singularities. Information: William G. Warren, Forintek Canada Speakers: Conway, Griess, Kac, Kostant, Lepowsky, Corporation, Western Forest Products Laboratory, 6620 Moody, Ree, Steinberg, Tits. North West Marine Drive, Vancouver, British Columbia, Information: John McKay, Room 961, Concordia Canada V6T 1X2. University, 1455 Maisonneuve W., Montreal, H3G 1MB, 6--11. Conference on Approximation Theory, University Canada. of Alberta, Edmonton, Canada. (November 1981, p. 644; 16-18. Second International Conference on Boundary and January 1982, p. 76) Interior Layers-Computational and Asymptotic Methods 7-17. Seventh International Conference on Operator (BAIL D), Dublin, Ireland. (November 1981, p. 644) Theory, Timisoara-Herculana, Romania. 17-18. New Directions for Risk Analyli.....Second Annual Information: Seventh International Operator Theory Meeting of the Society for Risk Analysis, Hyatt Regency, Conference, Department of Mathematics, INCREST, Arlington, Virginia. 220 Bd. Pacii, R-79622 Bucharest, Romania. Information: J. R. Penland, Society for Risk Analysis, 7-18. Workshop on Meaaure Theory and ita Applications, P.O. Box 531, Oak Ridge, Tennessee 37830. Universite de Sherbrooke, Sherbrooke, Quebec, Canada. 20-July 2. Combinatorial Methods in Topology and Topics: Ergodic theory, Choquet representation theory, Algebraic Geometry, University of Rochester, Rochester, vector measures, measure theory and topology. New York 14627. Program: Three expository lectures of three hours Speakers: M.G. Barratt, S. Cappell, F. Cohen, M. Cohen, each, twenty-one invited lectures of one hour. Also R. Edwards, W. Metzler, B. Moishezon, M. E. Rudin, communications (about 20 minutes) are welcome and a W. T. Tutte.

198 Information: John R. Harper or Richard Mandelbaum, Information: Ninth Prague Conference, UTIA CSAV, Pod Department of Mathematics, University of Rochester, vodarenskou vezi 4, 182 08 Praha 8, Czechoslovakia. Rochester, New York 14627. 28-July 2. Second Bad Honnef Workshop on Stochastie 21-25. Queueing Networks and Applications, Johns Dill'erential Systema, Bonn, Federal Republic of Germany. Hopkins University, Baltimore, Maryland. Topics: Stochastic processes, martingale theory, limit Principal Speaker: Ralph L. Disney, Virginia Polytechnic theorems, stochastic control, filtering, stochastic models, Institute and State University. and related topics. Program: Professor Disney will deliver 10 research-level Information: Michael Kohlmann, Institute for Applied lectures on the theory and applications of queueing Mathematics, University of Bonn, Wegelerstr. 6-10, networks. Three additional speakers to be announced D5300 Bonn, Federal Republic of Germany. will present complementary material. Time will be 28-July 2. DUI'erential Geometrie Control Theory, reserved for small group discussions. Michigan Technological University, Houghton, Michigan. Participants: The conference will be limited in size, with (January 1982, p. 77) participants selected from applicants from universities, government and industry. Researchers in the field 28-July 2. Eleventh Conferenee on Stoehaatie Proee11es of queueing networks, as well as advanced graduate and their Applications, University of Clermont-Ferrand, students, are invited to apply. It is hoped that some France. (October 1981, p. 548) travel and subsistence funds will be 8VB.ilable. 28-July 3. Second World Conferenee on Mathematiu at Information: Alan F. Karr, Department of Mathemati­ the Serviee of Man, Las Palmas (Canary Islands), Spain. cal Sciences, Johns Hopkins University, Baltimore, (October 1981, p. 548) Maryland 21218, (301)338-7214. 29-July 2. Third S)'lllposium on Control of Distributed 21-25. Problem Solving, Salisbury State College, Parameter Systema, Toulouse, France. Salisbury, Maryland. Information: L. Le Letty, Symposium IFAC/CDPS, Principal Lecturer: A. H. Schoenfeld, University of CERT-DERA, 2, avenue Edouard Belin, B.P. 4025, Rochester. 31055 Toulouse Cedex, France. Sponsor: MD-DC-VA Section of the MAA. Purpose: To make available to teachers in two- and four-year colleges important topics in applicable JULY 1982 mathematics. Information: B. A. Fusaro, Department of Mathematical 5-11. Conferenee on Ordered Seta and Applications, Lyon, Sciences, Salisbury State College, Salisbury, Maryland France. 21801, (301)546-3261, ext. 369. Topics: Ordered sets and set theory; ordered structures; algebra and ordered sets; combinatoric& of ordered 21-25. mEE International S)'lllpollium on lulonnation sets; ordered sets and computer science; applications of Theory, Les Arcs, France. (October 1981, p. 548) ordered sets to social and economic sciences. 21-25. Ninth U. S. National Congreaa of Applied Program: There will be selected lectures intended to Mechaniea, Cornell University, Ithaca, New York. (August survey some broad areas. There will also be specialized 1981, p. 438) lectures, contributed lectures, and problem sessions. 22-30. International Conferenee on Population Biology, Speakers: C. Benzaken (Grenoble); E. Corominas (Lyon); University of Alberta, Edmonton, Alberta, Canada. P. Erdlls (Budapest); C. Flament (Aix-Marseille); F. Sponsor: Canadian Applied Mathematics Society. Fraisse (Marseille); G. Gratzer (Winnipeg); E. Harzheim (Dusseldorf); E. C. Milner (Calgary); D. Monk (Boulder); Principal Speakers: B. Charlesworth (Sussex, England), C. I. Rival (Calgary); I. G. Rosenberg (Montreal); J. Clark (Vancouver), J. Felsenatein (Seattle), B. S. Goh Rosenstein (Rutgers). (Australia), M. H. Hassell (Imperial College, England), S. Karlin (Stanford), N. Keyfitz (Harvard), S. Levin Information: R. Bonnet or M. Pouzet, Conference on (Cornell), D. Ludwig (Vancouver), J. Roughgarden Ordered Sets, Department of Mathematics, Universite (Stanford), M. Slatkin (Seattle), A. Templeton (St. Claude Bernard (Lyon I), 69622 Vllleurbanne Cedex, Louis), M. Turelli (Davis), P. Waltman (Iowa). France. Program: There will be contributed sessions and workshops 12-14. EURO V: Filth European Congre11 on Operations throughout. Principal topics are models of species Researeh, Lausanne, Switzerland. growth, predator-prey competition, mutualism, food Information: EURO V, c/o EPFL, Departement de webs, dispersion, age structure, stability, evolution Mathematiques, Av. de Cour 61, CH-1007 Lausanne, of ecological parameters, evolution of behavior, life Switzerland. history strategies, group and social selection, evolution of genetic systems. 12-14. Joint Meeting of Operations Researeh Society of America and The Institute of Management Scieneea, Coordinating Committee: J. Addicott, P. Antonelli, G. J. Butler, H. I. Freedman, K. Morgan and C. Stroebeck. Lausanne, Switzerland. Call for Papers: Contributed papers are invited. Abstracts Information: Operations Research Society of America, 428 should be sent in no later than April15, 1982. East Preston Street, Baltimore, Maryland 21202. Information and Abstracts: H. I. Freedman, Department of 12-16. CBMS Regional Conferenee on Competition Models Mathematics, University of Alberta, Edmonton, Alberta, in Eeology, Utah State University, Logan, Utah. Canada T6G 2Gl. Principal Lecturer: Paul E. Waltman. 28-30. 1982 National Educational Computing Conferenee, Program: The conference is intended to bring together Kansas City, Missouri. (November 1981, p. 644) mathematicians and mathematically-inclined ecologists who are interested in the application of modeling to 28-July 1. 8)'lllpollium on Random Walk• and their biological resource management. Waltman's twice­ Application to the Phyllieal and Biologieal Scienees, daily lectures, on models, global mathematical analysis, Gaithersburg, Maryland. and biological interpretation, will be supplemented by Information and Abstracts: George Weiss, Building 12A, invited addresses and contributed papers. Room 2007, National Institutes of Health, Bethesda, Support: NSF support, for travel and living expenses, is Maryland 20205. available for conference participants. 28-July 2. Ninth Prague Conferenee on lulonnation Information: Robert McKelvey, c/o Rocky Mountain Theory, Statiatieal Decillions and Random Proee11ea, Mathematics Consortium, Arizona State University, Prague, Czechoslovakia. Tempe, Arizona 85281.

199 14-17. Third Geometry Symposium, Siegen, Federal 8-13. Fint lnterDational Conference on Teaching of Republic of Germany. Statistics, Sheffield, England. (January 1982, p. 77) Program: Invited speakers will hold 12 to 15 survey talks 9-10. International Conference on Phllosophy and Foun­ on geometric convexity and related topics. dations of Mathematics, Warsaw, Poland. University Information: J. M. Wills, Mathematics Institute, Organizers: Warsaw University Institutes of Mathematics Federal of Siegen, Holderlinstr. 3, D-5900 Siegen 21, and Philosophy, in cooperation with the Seminar on Republic of Germany. Philosophy and Mathematics of the Ecole Normale 19-23. SIAM Thirtieth Anniversary Meeting, Stanford Superieure in Paris. University, Stanford, California. Program: There will be invited lectures and organized Program: There will be six symposia and a number discussions. Participants will be able to present their of "mini-symposia" on various topics in applied results or views related to the topic of the conference. mathematics. The program also includes the first Information: Cecylia Rauszer, Institute of Mathematics, award of the SIAM Prize in Numerical Analysis and Warsaw University, PKin IX fl., 00-901 Warsaw, Poland. Scientific Computing, the John von Neumann Lecture, and a special lecture by Paul Switzer of Stanford 11-19.1nterDational Congress or Mathematicians, Warsaw, University. Poland. (August 1981, p. 426; see also announcement in Call for Papers: Contributions in all areas of applied this issue.) mathematics are welcome, but the following six 16-19. Instiute of Mathematical Statistics Annual Meeting, themes are especially sought: numerical solution of Cincinnati, Ohio. partial differential equations and their applications; the Information: American Statistical Association, 806 15th numerical solution of ordinary differential equations; Street, N.W., Washington, DC 20005. control and optimization; biomathematics; computer science; and methods in nonlinear analysis. Abstracts 19-21. Third American Time Series Meeting, Cincinnati, should be submitted on a standard SIAM abstract form, Ohio. obtainable from the address below. Abstracts must be Program: The conference will feature both invited and received by March 1, 1982. contributed papers. The purpose of the conference Information: Society for Industrial and Applied Mathe­ will be to discuss recent developments in the theory matics, Suite 1405, 117 South 17th Street, Philadelphia, and practice of time series analysis and forecasting, Pennsylvania 19103. and to bring practitioners together from diverse parent disciplines, work environments and geographical 25-August 7. Joint NATO/London Mathematical Society will be invited talks. Advanced Study Institute on Systems or Nonlinear locations. There Partial DifFerential Equations, Oxford, United Kingdom. Call for Papers: Abstracts of 150 words should be sent to (November 1981, p. 644) the address below as soon as possible. Offers to act as session chairmen are also being sought. 26-30. lnterDational Seminar on Funetional Analysis, Information: 0.-D. Anderson, ITSM Cincinnati, 9 Bolomorphy and Approximation Theory, State University Ingham Grove, Lenton Gardens, Nottingham NG7 2LQ, of Campinas, Brazil. ***(These dates have been changed. England. See August 2-6, 1982, below.)*** 19-27. Eighth Conference on Analytic Funetiona, 26-August 13. International Seminar on Data Analysis, Blazejewko, Poland. (August 1981, p. 438) Universite de Montreal, Montreal, Canada. Sponsors: NATO Advanced Study Institutes Program; 23-27. Eleventh lnterDational Symposium on Mathemati­ Ministry of Education of Quebec; Natural Sciences and cal Programming, University of Bonn, Bonn, West Engineering Research Council; Universite de Montreal. Germany. Program: Correspondence analysis, cluster analysis, Deadline for Abstracts: April1, 1982. analysis of categorical data, multivariate data analysis, Information: Math. Progr. Secretariat, c/o Institut fiir time series, data analysis for complex survey designs, Operations Research, Nassestrasse 2, D-5300 Bonn 1, graphical representation. West Germany. Y. Escoufier, Montpellier; J. C. Gower, Principal Speakers: 23-28. Equadift' 82, Wiirzburg, Federal Republic of Rothamsted Experimental Station; D. Hoaglin, Harvard; Germany. (January 1982, p. 77) G. G. Koch, North Carolina; G. Melard, Bruxelles; C. E. Sarndal, Montreal. 30-September 3. Eleventh International Symposium on Information: Ms. Ghislaine David, Seminaire de Mathematieal Foundations of Computer Science, Gdansk, Mathematiques Superieures, Universite de Montreal, Poland. (November 1981, p. 644) C.P. 6128, Montreal H3C 3J7, Canada. OCTOBER 1982 AUGUST 1982 October-November 1982. Workshop on Teaching or August 1982. lnterDational Conference on Finite Element Graduate and Undergraduate Mathematies, Chiangmai, Methode, Beijing, China. (January 1982, p. 77) Thailand. (January 1982, p. 77) 2-6. International Seminar on Functional Analysis, 17-21. International Conferenee on Mathematics, Univer­ Bolomorphy and Approximation Theory, State Univer­ sity of Riyadh, Riyadh, Saudi Arabia. sity of Campinas, Brazil. (November 1981, p. 644.) Sponsor: Arab Bureau of Education for the Gulf States. dates have been changed from those previously ***(These Program: There will be ten one-hour invited lectures and announced.)*** 15-minute contributed papers on the topics of algebra 2-6. Third Conference on Topology of Manifold• and and number theory, topology and geometry, analysis Homotopy Theory, Rio de Janeiro, Brasil. and differential equations, applied math and numerical Information: Antonio Conde, IMECC-UNICAMP, 13.100 analysis. Abstracts should be sent to the address below Campinas-SP. Brasil. by March 31, 1982. 3-10. Meeting on Binary Systema and Ring Theoretic Information and Abstracts: Secretary of the Organizing Methode in Univeraal Algebra, Czechoslovakia. (January Committee of the Conference, Arab Bureau of Education 1982, p. 77) for the Gulf States, P.O. Box 3908, Riyadh, Saudi Arabia. 8-13. Tenth IMACS World Congreas on Syatems Simulation and Scientific Computation, Montreal, Canada. (June 25-27. Sparae Matrix Symposium, Fairfield Glade, 1981, p. 348) Tennessee.

200 Program: The theme will be the construction and analysis of algorithms and mathematical software for sparse matrix calculations, both in basic linear algebra PROCEEDINGS OF SYMPOSIA problem areas and in specific applications. Speakers: lain S. Duft" and John R. Reid (AERE Harwell, IN PURE MATHEMATICS England), Stan C. Eisenstat (Yale University), Beresford (ISSN 0082-0717) N. Parlett (University of California, Berkeley), Mike T. Heath (Union Carbide Corp., Nuclear Division), AUTOMORPHIC FORMS, REPRESENTATIONS Wolfgang Fichtner and Don J. Rose (Bell Laboratories), AND L-FUNCTIONS Allen J. Pope (National Geodetic Survey), Michael Saunders (Stanford University). edited by A. Borel and W. Casselman Call for Papers: Papers relating to the theme are welcome; This book contains the proceedings of the those involving interesting applications of sparse matrix twenty-fifth AMS Summer Research Institute held at technology are encouraged. A short abstract (100.200 Oregon State University from July 11 to August 5, words, double-spaced) should be submitted no later than 1977. The Institute was financed by a grant from July 1. A software catalog containing announcements of the National Science Foundation. This volume con­ software will be compiled and distributed. Contributions sists of the Notes of the Institute, mostly in revised for the catalog should be submitted by July 1 on special form, and of a few paJlers written later. forms available from the contact given below. The book is intended as a comprehensive dis­ Information: Robert C. Ward, Union Carbide Corporation­ Nuclear Division, Computer Sciences Division, Box Y, cussion, with emphasis on the use of infinite dimen­ Bldg. 9704-1, Oak Ridge, Tennessee 37830. sional representations, of the £-functions attached to automorphic forms on, or automorphic represen­ tations of, reductive groups, of the local and global NOVEMBER 1982 problems pertaining to them, and of their relations 3-5. Twenty-third Annual IEEE S)'lllpoaium on Founda­ with the £-functions of algebraic number theory and tion• of Computer Science, Chicago, Dlinois. of algebraic geometry, such as the Artin £-functions Topics: Topics will include algorithms and data structures, and Hasse-Weil zeta functions. An effort has been computability and complexity theory, correctness of made to supply a considerable amount of background programs, theory of data bases, theory of formal material. Extensive treatment is provided of some languages and automata, theory of logical design cases. and layout, models of computation, and semantics of The papers in this volume are divided into four programming languages. broad sections. Section I is devoted to the structure Call for Papers: Papers presenting original research of reductive groups (Borel-Tits theory over arbitrary on theoretical aspects of computer science are sought. fields, Bruhat-Tits theory over local fields) and to in­ Ten copies of a detailed abstract (about 2500 words) finite dimensional admissible representations of re­ should be sent by April19, 1982, to the Program Com­ ductive groups over local fields. Section II is con­ mittee Chairman, Nicholas Pippenger, ffiM Research Laboratory K51/61F, 5600 Cottle Road, San Jose, cerned with automorphic forms and automorphic California 95193. representations, with emphasis on analytic theory. Information: David W. Bray, Department of Electrical Section III deals with automorphic representations and Computer Engineering, Clarkson College, Potsdam, and £-functions. Section IV relates the preceding to New York 13676. the £-functions of arithmetical algebraic geometry. Readers are assumed to be familiar with the LATE ENTRIES formalism of ideles and adeles in algebraic number theory, and with Lie groups and Lie algebras. Math­ Apri11982 ematicians interested in automorphic forms, infinite 13-27. Semimartingales and Stochastic Calculus on Manifolds, dimensional representations, nonabelian class field Centre Recherche Mathematiques Appliquees, Universite de theory, Artin £-functions, arithmetical algebraic Montreal, Montreal, Canada. geometry, and Shimura varieties should gain from Program: Laurent Schwartz will hold the Aisenstadt Chair this book a knowledge of recent results, basic tech­ at the University of Montreal. He will give two series of niques, and open problems in the subject matter of eight lectures, the second series to be held at the end of the the Institute. summer. Both series will be given in French. Information: Centre Recherche Mathematiques Appliquees, There is no other book which covers, from the Universite de Montreal, Montreal, Canada H3C 317, point of view of representations, the major recent (514)343-7501. developments in the study of automorphic forms, and of their relations with algebraic number theory and arithmetic algebraic geometry. Volume 33, Parts I, 2 August 1982 x + 322 pages (Part I); viii + 382 pages (Part 2) Each part: List price $22.40; institutional member $16.80; In a letter dated January 18, 1982, Witold Lipski, Jr., pro­ individual member $11.20 (soft cover) gram chairman, and Antoni Mazurkiewicz, conference chair­ Set: List price $38.00; institutional member $28.50; man, informed the Society that "due to the situation in individual member $19.00 (soft cover) Poland we do not see any chance to organize our 1982 Part 1: ISBN 0-8218-1435-4; LC 78-21184 Conference on Mathematical Foundations of Computer Sci­ Part 2: ISBN 0-8218-1437-0; LC 78-21184 Publication date: June 30, 1979 ence." This meeting was scheduled to be held in Gdansk To order, please specify PSPUM/33 (set), from August 30 to September 3, 1982. (See November 1981 PSPUM/33.1 (Part I); PSPUM/33.2 (Part 2) Notices, page 644.) Prepayment is required for all AMS publications. Order from AMS, PO Box 1571, Annex Station, Providence, Rl 02901, or call 800-556-7774 to charge with VISA or MasterCard.

201 MISCELLANEOUS

Personal Items corresponding member of the Austrian Academy of Sciences, Vienna. Elizabeth Berman Appelbaum of the University J. P. Kubilius, Rector of Vilnius University, of Missouri, Kansas City, has been appointed a U.S.S.R., was awarded an honorary doctoral degree by programmer for American Telephone and Telegraph in Greifswald University, German Democratic Republic. Kansas City, Missouri. Arienne S. Balser of Encino, California, has been Deaths appointed to a visiting assistant professorship at Loyola Marymount University, Los Angeles. Volodymyr Bohun-Chudyniv of Seton Hall Univer­ Heinz Bauer of the Mathematisches Institut, sity died on October 14, 1981, at the age of 87. He was Universitat Erlangen-Nurnberg, has been elected a a member of the Society for 30 years.

Baeklog of Mathematics Research Journals

Backlog. Information on the backlog of papers of the final revision and its publication may be much for research journals, primarily those published in shorter than is the case otherwise, so these figures are North America, is reported to the Providence Office by low to that extent. those editorial boards which elect to participate. The The observations are made from the latest issue figures are an estimate of the number of printed pages published before the deadline for this issue of the which have been accepted, but are in excess of the Notices from journals that have actually been received number required to maintain copy editing and printing by a subscriber in the Providence, Rhode Island, area; schedules. in some cases this may be two months later than Observed Waiting Time. The quartiles give a publication abroad. If the waiting time as defined measure of normal dispersion. They do not include above is not given in the journal, if no new issue has extremes which may be misleading. Waiting times are been received since the last survey, or if the latest issue measured in months from receipt of manuscript in final is for some reason obviously not typical, no times are form to publication of the issue. When a paper is given in this report and such cases are marked NA (not revised, the waiting time between an editor's receipt available or not applicable).

Editor's Estimated Observed Waiting Approximate Time for Paper Time in Latest Number Number Backlog of Submitted Currently Published Issue Issues Pages Printed Pages to be Published (In Months) Journal per Year per Year 12/15/81 5/31/81 (In Months) Q1 Q2 Q3

Acta Informatica 8 960 0 0 12 6 7 12 Aequationes Math. 3·6 400-640 40 400 12 NA American J. of Math. 6 1340 320 0 14 20 28 28 Annales Sci. Ecole Nor. Sup. 4 600 NR 312 12 11 13 19 Annals of Math. 6 1200 1000 600 18 16 16 17 Annals of Probability 4 1100 300 441 14 15 16 17 Annals of Statistics 4 1350 0 100 15 9 10 10 Applicable Analysis 8 NR NR NR NR 17 19 31 Appl. Math. & Optimization 4 NR NR NR NR 11 12 14 Arch. History of Exact Scis. 8 788 0 0 12 NA 18 NA Arch. of Rational Mech. Anal. 12 1200 0 0 13-14 14 15 17 Bull. Soc. Math. France 4 480 NR 277 18 8 11 11 Canad. J. of Math. 6 1524 900 1325 19 15 19 24 Canad. Math. Bulletin 4 512 256 437 16 20 21 24 Comm. Math. Physics 16 2432 0 0 5 6 7 9 Computing 8 768 0 390 8 9 15 15 Duke Math.). 4 NR NR 0 NR 5 6 8 Houston J. of Math. 4 600 300 300 6 18 22 24 Illinois J. of Math. 4 704 1321 1017 25 25 26 27 Indiana Univ. Math. J. 6 960 500 500 18 18 19 20 lnt'l. J. of Math. & Math. Scis. 4 800 200 200 15 9 13 17 lnventiones Math. 12 2100 0 0 9 8 11 12 Israel J. of Math. 12 1200 200 900 10 8 9 11 J. Amer. Stat. Assoc. 4 1000 50 NR NR 7 8 11

202 Editor's Estimated Observed Waiting Approximate Time for Paper Time in Latest Number Number Backlog of Submitted Currently Published Issue Issues Pages Printed Pages to be Published (In Months) Journal per Year per Year 12/15/81 5/31/81 (In Months) Q1 M 03 l. Assoc. for Comp. Mach. 4 800 600 800 24 16 16 17 J, Comp. & Sys. Sci. 6 850 0 0 12 9 9 9 l. D iff. Geometry 4 650 300 350 6 24 26 28 l. Math. Biology 4 600 150 NR 9 8 8 9 l. Math. Physics 12 3000 0 0 5-6 NA l. Math. Sociology 4 600 NR 0 2-3 NA l. Operator Theory 4 NR NR 500 NR 15 17 17 ]. Symbolic Logic 4 1000 0 0 20 19 24 26 Linear Algebra & Appl. 7 2128 300 300 8 10 12 12 Linear & Multilinear Alg. 6 540 270 80 10 13 13 26 Manuscripta Math. 12 1500 0 0 4 5 5 7 Math. Biosciences 10 1600 100 NR 6 7 8 8 Mathematical Programming 6 720 NR NR 20 12 13 13 Math. Systems Theory 4 NR NR NR NR 13 14 15 Math. of Comp. 4 1500 0 0 12 9 10 12 Math. of Operations Research 4 640 300 300 12 1 6 1 8 21 Math. Annalen 16 2300 0 0 4-6 6 7 10 Math. Zeitschrift 12 1740 0 0 8 8 9 11 Memoirs of AMS 6 1800 0 0 8 14 19 27 Michigan Math. J. 3 384 NR NR 9 14 16 18 Monatschefte fur Math. 8 704 100 100 9 10 11 12 Numer. Func. Anal. & Optim. 8 900 0 0 7 NA Numerische Math. 6 928 0 0 12 10 12 13 Operations Research 6 1200 100 200 12 NA Pacific J. of Math. 12 3000 NR NR 15 13 16 22 Proceedings of AMS 12 2000 0 0 10 10 11 14 Quarterly of Appl. Math. 4 560 400 150 10 18 19 19 Rocky Mtn. ]. Math. 4 768 450 450 25 23 27 29 Semigroup Forum 8 NR NR NR NR 4 4 5 SIAM]. Alg. & Disc. Methods 4 560 131 43 12 8 9 12 SIAM]. Appl. Math. 6 1350 407 520 14 13 14 17 SIAM j. on Computing 4 800 219 128 13 11 11 13 SIAM j. Control & Optim. 6 850 159 200 11 12 14 16 SIAM]. on Math. Anal. 6 1050 444 211 13 9 11 12 SIAM j. on Numer. Anal. 6 1300 229 272 11 13 15 19 SIAM J. on Sci. Stat. Comp. 4 500 0 0 7 8 11 14 SIAM Review 4 560 0 0 6 11 13 16 Stochastics 8 350 NR 0 2-3 NA Topology & Its Appl. 3 330 100 330 9-12 15 17 19 Transactions of AMS 12 4200 450 400 12 13 13 15 Z. Wahrscheinlichkeitstheorie 12 1680 0 0 10-11 5 10 13

NR means no response received. NA means not available or not applicable.

203 Assistantships and Fellowships in the Mathematical Sciences in 1982-1983 Supplementary List

The entries below supplement the December 1981 Special Issue of the Notices.

The number following "Faculty" is the number of faculty members in the department who are full time employees in the institution and at least half-time in the department; the number following "Published" is the number of those who have published a technical paper or book in the last three years.

Under the DEGREES AWARDED column the following terms have been used: Bachelor's by inst...... Number of bachelor's degrees awarded by the institution Bachelor's by dept...... Number of bachelor's degrees awarded by the department Master's by dept...... Number of master's degrees awarded by the department Ph.D. (78/81) ...... Doctoral degrees awarded during the last three years (1978-1979, 1979-1980 and 1980-1981) Abbreviations used ANT... Algebra or Number Theory S ....Statistics AFA ... Analysis or Functional Analysis CS ...Computer Science GT ....Geometry or Topology OR ...Operations Research L ..... Logic AM ... Applied Mathematics P ..... Probability ME ... Mathematics Education

Under the SERVICE REQUIRED column, hours per week section, "c" denotes contact hours.

TYPE OF ASSISTANCE STIPEND FEES SERVICE REQUIRED DEGREES AWARDED (number anticipated paid to student paid by hours type Academic year 1982-1983) dollars months student($) per week of service 1980-1981

CALIFORNIA

California State University, Fullerton 92634 DEPARTMENT OF MATHEMATICS Applications due: 5/1/82 Bachelor's by inst. 3021 james 0. Friel, Chair Faculty 30; Published 14 Bachelor's by dept. 19 Master's by dept. 4 Teaching Assistantship (6-8) 3482-6961 9 115.50-130.50 3-6 Teaching San Jose State University, San Jose 95192 DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE Applications due: 4/15/82 Bachelor's by inst. 3600 john Mitchem, Chairman Faculty 42; Published 20 Bachelor's by dept. 65 Master's by dept. 6 Teaching Fellowship (18-20) 3475-6950 9 130.50* 3-6c Teaching *Nonresidents & Foreign Students pay an additional $94.50 per unit. University of California, Irvine 92717 DEPARTMENT OF MATHEMATICS Applications due: 4/2/82 Bachelor's by inst. 1626 james). Yeh, Chair Faculty 26 Bachelor's by dept. 25 Master's by dept. 6 (22) Teaching Assistantship 7922 9 864 15* Ph.D. (78/81) ANT 2, L 1, *Class, lab, and office hours, and time preparing for class. P 1, S 2. Total: 6

DISTRICT OF COLUMBIA

American University, Washington 20016 DEPARTMENT OF MATHEMATICS, STATISTICS AND COMPUTER SCIENCE Applications due: 4/1/82 Bachelor's by inst. 1307 Basil Korin, Chairman Faculty 22; Published 15 Bachelor's by dept. 129 Master's by dept. 33 Fellowship (2) 4500 12 Teaching Assistantship (12) 4000 9 15 Teaching, Ph.D. (78/81) S 5. Total: 5 Tutoring Scholarship (2) 500-1000 15 Tutoring

204 TYPE OF ASSISTANCE STIPEND FEES SERVICE REQUIRED DEGREES AWARDED (number anticipated paid to student paid by hours type Academic year 1982-1983) dollars months student ($) per week of service 1980-1981

George Washington University, Washington 20052 DEPARTMENT OF STATISTICS Faculty 8; Published 6 Bachelor's by inst. 4688 Hubert Lilliefors, Chairman Bachelor's by dept. 11 Master's by dept. 10 Teaching Assistantship (5} 3100-3400 9 10 Grading, Ph.D. (78/81} S 9. Total: 9 Tutoring

GEORGIA

Georgia Institute of Technology, Atlanta 30332 DEPARTMENT OF INFORMATION AND COMPUTER SCIENCE Applications due: 1/1/82 Bachelor's by inst. 1449 Raymond E. Miller, Director Faculty 23; Published 19 Bachelor's by dept. 80 Master's by dept. 60 Fellowship (3} 6500 12 Ph.D. (78/81} CS 3. Total: 3 Teaching Assistantship (1 *) 14000-26000 12 Research Assistantship (1 *} 14000-26000 12 *Per full time equivalent.

HAWAII

University of Hawaii, Honolulu 96822 PUBLIC HEALTH SCIENCES-BIOSTATISTICS Applications due: 3/1 /82 Master's by dept. 4 Chairman C. S. Chung, Faculty 4; Published 3 Ph.D. (78/81} S 1. Total: 1 Teaching Assistantship (1} 482/mo. 9 15 Lab. section

INDIANA

Purdue University, West Lafayette 47907 DEPARTMENT OF STATISTICS Applications due: 5/31/82 Bachelor's by inst. 4750 Shanti S. Gupta, Head F acuity 19; Published 17 Bachelor's by dept. 4 Master's by dept. 16 Fellowship (5} 4800 12 210 Teaching Assistantship (30} 4900-5500 10 210 6c Teaching Ph. D. (78/81} P 1, S 12. Research Assistantship (8} 3900-5500 10 21 0 20 Research Total: 13

KENTUCKY

Eastern Kentucky University, Richmond 40475 DEPARTMENT OF MATHEMATICAL SCIENCES Applications due: Open Bachelor's by inst. 1600 Marijo LeVan, Chairman Faculty 26; Published 10 Bachelor's by dept. 20 Master's by dept. 2 Teaching Assistantship (5} 2800-5600 9 662 3-6 Teaching University of Kentucky, Lexington 40506 DEPARTMENT OF COMPUTER SCIENCE Applications due: * Bachelor's by inst. 2774 Raymond Cox, Acting Chairman Faculty 10; Published 6 Bachelor's by dept. 20 Master's by dept. 11 Fellowship (1} 5200 9 752** Teaching Assistantship (25} 5200 9 752** 20 Teaching Internship (6} 4200-7000 9-12 752** 18-20 Programming *Fellowships: 2/1/82; Assistantships: 3/15/82. **In-state portion only. DEPARTMENT OF STATISTICS Applications due: * Bachelor's by inst. 2774 joseph Gani, Chairman Faculty 15; Published 12 Ph.D. (78/81} S 8. Total: 8 Fellowship (2} 4800-6000 816 0-5 Teaching Assistantship (13-18} 5200-5800 816 20 *Fellowships: 2/1 /82; Assistantships: 4/1/82. University of Louisville, Louisville 40292 DEPARTMENT OF MATHEMATICS Faculty 13; Published 7 Master's by dept. 6 W. Wiley Williams, Chairman Teaching Fellowship (4-6} 6200-6500 9 Remitted Teaching

205 TYPE OF ASSISTANCE STIPEND FEES SERVICE REQUIRED DEGREES AWARDED (number anticipated paid to student paid by hours type Academic year 1982-1983) dollars months student($) per week of service 1980-1981

LOUISIANA University of Southwestern Louisiana, Lafayette 70504 DEPARTMENT OF COMPUTER SCIENCE Applications due: 3/1/82 Bachelor's by inst. 1556 Terry M. Walker, Head Faculty 14; Published 12 Bachelor's by dept. 57 Master's by dept. 15 Fellowship (4) 5000 12 Ph.D. (78/81) CS 10. Total: 10 Teaching Assistantship (20) 3000-7000 12 * Research Assistantship (16) 3000-8000 9·12 20 Research Scholarship (3) 500-1000 9·12 *Teaching 1 or 2 courses.

MARYLAND Johns Hopkins University, Baltimore 21205 DEPARTMENT OF BIOSTATISTICS Faculty 12; Published 12 Master's by dept. 3 Charles A. Rohde, Chairman School Scholarship (7) 425/mo. 9 6000 16 Ph.D. (78/81). Other 7. Total:7

MISSOURI University of Missouri-Columbia 65211 DEPARTMENT OF STATISTICS Applications due: 3/1/82 Bachelor's by inst. 3360 Asit P. Basu, Chairperson Faculty 1 0; Published 8 Bachelor's by dept. 3 Master's by dept. 6 Teaching Assistantship (8) 5600-6000* 9 ** 6c Teaching Ph.D. (78/81) S 8. Total: 8 Research Assistantship (2) 5600-6000* 9 ** 20 Research *Current stipends. It is anticipated these will be higher for 1982-83. **Fees are currently $504 per semester. University of Missouri-Kansas City 64110 DEPARTMENT OF MATHEMATICS Applications due: 5/15/82 Bachelor's by inst. 1100 Paul Liebnitz, Chairman Facuity 12; Published 8 Bachelor's by dept. 7 Master's by dept. 1 915 5·6c Teaching Assistantship (6) 5850-6000 9 Ph.D. (78/81) GT 1, AM 1. Total: 2

NEW JERSEY Montclair State College, Upper Montclair 07043 DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE Faculty 32; Published 4 Bachelor's by inst. 1834 Kenneth C. Wolff, Chairman Bachelor's by dept. 73 Master's by dept. 13 Teaching Assistantship (2) 3000 9 Waived 6c Basic Skills Lab/Courses (4) 3000 9 Waived 15

NEW MEXICO

University of New Mexico, Albuquerque 87131 DEPARTMENT OF COMPUTER SCIENCE Applications due: 7/1/82 Bachelor's by inst. 1813 Cleve B. Moler, Chairman Faculty 12; Published 9 Bachelor's by dept. 13 Teaching Fellowship (1) 4000-6000 9 * .50 FTE Teaching Assistantship (6) 4000-6000 9 * .50 FTE Research Assistantship (2) 6.05/hr.-9.30/hr. *Over 9 hours, $28 per credit hour.

NEW YORK City University of New York, Hunter Colle9e, New York 10021 DEPARTMENT OF MATHEMATICAL SCIENCES Applications due: 2/20/82 Bachelor's by inst. 1410 Brian Shay, Chairman Faculty 17; Published 10 Bachelor's by dept. 14 Master's by dept. 9 Teaching Fellowship (2) 8279-8752 9 75/cr. 7 Teaching Teaching Assistantship (20) 5040-5495 9 75/cr. 7 Teaching

206 TYPE OF ASSISTANCE STIPEND FEES SERVICE REQUIRED DEGREES AWARDED (number anticipated paid to student paid by hours type Academic year 1982-1983) dollars months student ($) per week of service 1980-1981

Clarkson College of Technology, Potsdam 13676 DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE Applications due: 3/1/82 Bachelor's by inst. 816 Mark ). Ablowitz, Chairman Faculty 22; Published 17 Bachelor's by dept. 23 Master's by dept. 4 Teaching Assistantship (1 5) 6400* 12 12c Teaching, Ph.D. (78/81) Grading AFA 2, S 1, Research Assistantship (1) 6400* 12 12 Research AM 1. Total: 4 *PI us tuition.

University of Rochester, Rochester 14627 DEPARTMENT OF COMPUTER SCIENCE Applications due: 8/1/82 Bachelor's by inst. 1029 Joel I. Seiferas, Chairman Faculty 12; Published 12 Bachelor's by dept. 5 Master's by dept. 7 Fellowship (18) 5000-5500 9 15 Grading, Research Ph.D. (78/81) CS 8. Total: 8 Teaching Assistantship (17) 5000-5500 9 15 Research

OHIO University of Akron, Akron 44325 DEPARTMENT OF MATHEMATICAL SCIENCES Applications due: 3/1/82 Bachelor's by inst. 2667 William H. Beyer, Head Faculty 29; Published 10 Bachelor's by dept. 1 5 Master's by dept. 3 Teaching Assistantship (30) 3600-4200 9 15·20 Teaching OKLAHOMA University of Oklahoma, Norman 73019 DEPARTMENT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE Faculty 21; Published 20 Bachelor's by inst. 2403 Seun K. Kahng, Director Bachelor's by dept. 8 Master's by dept. 8 Teaching Assistantship (6) 3600-7500 9 211.50* 20 Ph.D. (78/81) CS 2, Other 10. Research Assistantship (1 0) 4000-7200 12 211.50* 20 Total: 12 Grader/Lab. Assistantship (74) 1800-4500 9 211.50* 20 *Plus facility fee ($25.00), health fee ($15.00) and an additional $15.00 fee if an International student.

OREGON Oregon State University, Corvallis 97331 DEPARTMENT OF STATISTICS Applications due: 2/15/82 Bachelor's by inst. 2716 Lyle D. Calvin, Chairman Faculty 16; Published 15 Master's by dept. 8 Teaching Fellowship (10) 4200-4800 9 85/term 12·15 Ph.D. (78/81) S 15, OR 1. Teaching Assistantship (10) 4200-7500 9·12 85/term 12·20 Total: 16

TENNESSEE

Vanderbilt University, Nashville 37235 DEPARTMENT OF COMPUTER SCIENCE Applications due: 2/1/82 Bachelor's by dept. 26 Patrick C. Fischer, Chairman Faculty 10; Published 8 Master's by dept. 8 Fellowship (1) 4050-4950 9 Ph.D. (78/81) CS 7. Total: 7 Teaching Assistantship (14) 4050-4950 9 Research Assistantship (2) 4050-4950 9

TEXAS Texas A&M University, College Station 77843 INSTITUTE OF STATISTICS Faculty 18; Published 18 Bachelor's by inst. 5327 W. B. Smith, Director Bachelor's by dept. 12 Master's by dept. 1 0 Fellowship (1) 5400 9 200 Teaching Assistantship (13) 5400 9 200 20 Teaching Ph.D. (78/81) S 15. Total: 15 Research Assistantship (2) 5400 9 200 20 Research Nonteaching Graduate Assistantship (2) 5400 9 200 20 Teaching related

207 TYPE OF ASSISTANCE STIPEND FEES SERVICE REQUIRED DEGREES AWARDED (number anticipated paid to student paid by hours type Academic year 1982-1983} dollars months student ($) per week of service 1980-1981

University of Texas, Austin 78712 DEPARTMENT OF COMPUTER SCIENCES Applications due: 2/1/82 Bachelor's by inst. 7265 Alfred G. Dale, Chairman Faculty 26; Published 21 Bachelor's by dept. 115 Master's by dept. 32 Fellowship (6) 9 Ph.D. (78/81) CS 24.Total: 24 Teaching Assistantship (24) 9 10 or 20 Research Assistantship (40) 12 Varies VIRGINIA George Mason University, Fairfax 22030 DEPARTMENT OF MATHEMATICAL SCIENCES Applications due: Open Bachelor's by inst. 1372 Richard Draper, Chairman Faculty 32; Published 9 Bachelor's by dept. 15 Master's by dept. 3 Teaching Assistantship (2) 3500-4300 9 10 Virginia Polytechnic Institute and State University, Blacksburg 24061 DEPARTMENT OF STATISTICS Applications due: 1/31/82 Bachelor's by inst. 3435 jesse C. Arnold, Head Faculty 18; Published 18 Bachelor's by dept. 9 Master's by dept. 15 Teaching Assistantship (25) 5760-6660 9 409/qtr. 20 Teaching, consulting Ph.D. (78/81) S 14. Total: 14 Research Assistantship (7) 5760-6660 9 409/qtr. 20 Research, consulting Tuition Grants (6) 40/qtr. CANADA Acadia University, Wolfville, Nova Scotia BOP 1XO DEPARTMENT OF MATHEMATICS Applications due: 3/15/82 Bachelor's by inst. 570 F. Chipman, Head Faculty 11; Published 8 Bachelor's by dept. 20 Master's by dept. 1 Fellowship (2) 4000-5000 9 1375 Carleton University, Ottawa, Ontario K1S 5B6 DEPARTMENT OF MATHEMATICS AND STATISTICS Applications due: 3/1/82 Bachelor's by inst. 1797 Kenneth S. Williams, Chairman Faculty 38; Published 24 Bachelor's by dept. 27 Master's by dept. 17 Fellowship (30) 1 000-6000 12 900 Teaching Fellowship (25) 3200 9 10 Ph.D. (78/81) ANT 2, AFA 1, Teaching Assistantship (25) 3200 9 900 10 GT 1, P 5, S 1, OR 1, AM 1. Scholarship (30) 1 000-6000 12 900 Total: 12 McMaster University, Hamilton, Ontario LSS 4K1 DEPARTMENT OF MATHEMATICAL SCIENCES Applications due:* Bachelor's by inst. 1988 T. Husain, Chairman Faculty 42; Published 32 Bachelor's by dept. 76 Master's by dept. 6 Teaching Assistantship (1 0) 4547 12 ** 10 Grading, marking, teaching Ph.D. (78/81) ANT 5, AFA 3, Scholarship (1 0) 2439-4093 12 GT 1, S 1. Total: 10 *Open, but not later than May 15, 1982. **Visa: $1 028; Statistics students: $2410. Simon Fraser University, Burnaby, British Columbia VSA 1S6 DEPARTMENT OF MATHEMATICS Applications due: 8/1/82 Bachelor's by inst. 1177 G. A. C. Graham, Chairman Faculty 33; Published 30 Bachelor's by dept. 24 Master's by dept. 3 Teaching Assistantship (50) 8835-1047012 610 15 Research Assistantship (5) 8400 12 610 15 Ph.D. (78/81) L 2, Other 3. Total: 5 University of British Columbia, Vancouver, British Columbia V6T 1W5 DEPARTMENT OF COMPUTER SCIENCE Applications due: 4/1/82 Bachelor's by dept. 45 P. C. Gilmore, Head Faculty 16; Published 16 Master's by dept. 4 Ph.D. (78/81) CS 5. Total: 5 Teaching Assistantship (21) 4920-5110 8 1000 12 Teaching Research Assistantship (8) 8400 12 1000 12 Research Scholarship (11) 8000-9350 12 1000 12 Research University of Saskatchewan, Saskatoon, Saskatchewan S7N OWO DEPARTMENT OF MATHEMATICS Applications due: 2/28/82 Bachelor's by inst. 2000 R. Servranckx, Head Faculty 27; Published 20 Bachelor's by dept. 75 Master's by dept. 1 Teaching Fellowship (8) 3900* 8 740 6c Teaching or equivalent Ph.D. (78/81) AFA 2, GT 1. Scholarship (2) 3700* 8 740 Total: 3 *Plus up to $1850 if research is continued throughout summer months.

208 TYPE OF ASSISTANCE STIPEND FEES SERVICE REQUIRED DEGREES AWARDED {number anticipated paid to student paid by hours type Academic year 1982-1983) dollars months student {$) per week of service 1980-1981 Jniversity of Toronto, Toronto, Ontario M5S 1A1 )EPARTMENT OF MATHEMATICS Applications due: 4/31/82 Bachelor's by inst. 6950 , McCool, Chairman Faculty 58; Published 55 Bachelor's by dept. 1 0 Master's by dept. 8 ~SERC Fellowship (8) 8500 12 * '{esearch Fellowship (1 0) 6500 12 * Ph.D. (78/80) ANT 2, AFA 7, Jniversity of Toronto GT 4, L 2, AM 2. Total: 17 Open· Fellowship (3) 4500 12 * 'Canadian $1050; non-Canadian visa student: $2300. Additional financial lSsistance available in summer session. DEPARTMENT OF STATISTICS Applications due:* Bachelor's by inst. 6950 D. A. S. Fraser, Chairman Faculty 16; Published 15 Bachelor's by dept. 20 Master's by dept. 5 University of Toronto Fellowship (5) 5100-5300 12 ** Ph.D. (78/81) S 5. Total: 5 Teaching Assistantship (25) 3516-4043 8 ** 10 Tutoring, marking Research Assistantship (5) 500-4000 1·8 ** Research OGS (3) 5700-9350 ** NSERC (6) 5700-9350 ** *Assistantship: No deadline; Fellowship: 2/1/82. **Canadian: $1064.50; foreign: $2349.50. University of Western Ontario, London, Ontario N6A 589 DEPARTMENT OF STATISTICAL AND ACTUARIAL SCIENCES Faculty 10; Published 10 Bachelor's by inst. 3000 I. B. MacNeill, Chairman Bachelor's by dept. 16 Teaching Assistantship (10) 8100 12 10 Ph.D. (78/81) S 3. Total: 3 London Life Scholarship (4) 1000 12 York University, Downsview, Ontario M3J 1P3 DEPARTMENT OF MATHEMATICS Applications due: 4/1/82 Bachelor's by inst. 3303 G. Denzel, Chairman Faculty 28; Published 19 Bachelor's by dept. 33 Master's by dept. 3 Teaching Assistantship (18) 4400* 9 ** 10 Problem session, grading Research Assistantship (6) 500 9 ** Scholarship (2) 3000 9 ** Graduate Assistantship 500 9 ** *Under negotiation with union. **Canadian citizen or landed immigrant: $1035; Foreign: $2300.

Erratum An incomplete entry was given in the December 1981 issue listing for the UNIVERSITY OF LOUIS­ VILLE, Louisville, Kentucky. The whole entry has been printed in this supplement.

Critical, Historical, or Expository Theses Supplementary List

The list below supplements the list published on page 733 of the December 1981 Notices. DISTRICT OF COlUMBIA Degree NEW MEXICO Degree American University University of New Mexico Department of Mathematics, Statistics, Department of Computer Science Ph.D. and Computer Science Ph.D. KENTUCKY TENNESSEE University of Kentucky Vanderbilt University Department of Computer Science Ph.D. Department of Computer Science Ph.D.

209 AMS REPORTS AND COMMUNICATIONS

Recent Appointments Reports of Past Meetings Committee members' terms of office on standing The October Meeting in Amherst committees expire on December 31 of the year given in parentheses following their names, unless The seven hundred eighty-ninth meeting of the otherwise specified. American Mathematical Society was held at the University of Massachusetts, Amherst, on October 16-17, 1981. The Five Colleges (Amherst, Hampshire, John P. D'Angelo {1984) and Paul T. Bateman {1984) Mt. Holyoke, and Smith Colleges, and the University have been appointed by Alex Rosenberg, Chairman of Massachusetts, Amherst) were joint hosts for this of the Board of Trustees, to the Committee on meeting. There were 304 registrants, including 207 Membership of the Board of Trustees, with Professor members of the Society. Bateman appointed as chairman of the committee. Continuing members of the committee are Frederick Invited Addresses. By invitation of the Committee W. Gehring {1982) and Jack K. Hale {1983). to Select Hour Speakers for Eastern Sectional Meetings, there were four invited one-hour addresses as follows: J. Ian Richards {1983) has been appointed to the Committee to Select Hour Speakers for Central MELVYN S. BERGER, University of Mas­ Sectional Meetings by President Andrew M. Gleason. sachusetts, Amherst, The confinement problem ·in Continuing members of the committee are Richard A. nonlinear gauge theories and in nonlinear analysis. Askey {1983), M. S. Ba.ouendi, chairman {1982), Paul 0. BETTANCOURT, Courant Institute of Math­ T. Bateman (ex officio), and R. H. Bing {1982). ematical Sciences, New York Univeristy, A com­ putational method for 3-D nonlinear magneto­ By action of the Executive Committee, in November hydrodynamics. 1981, that section of the Society formerly referred to J. H. SAMPSON, Johns Hopkins University, as the Western Section was designated the Central Aspects of harmonic mappings. Section. CHUNG-TAO YANG, University of Pennsylvania, Topological problems arising from the Blaschke Robert W. McKelvey {1983) has been appointed to conjecture. the Committee on Employment and Educational Policy by President Andrew M. Gleason. Continuing Special Sessions. By invitation of the same members of the committee are Lida K. Barrett, committee, there were ten sessions of selected twenty­ chairman {1982), Irwin Kra {1984), Donald C. Rung minute papers. The topics of these special sessions, the {1984), Robert J. Thompson {1982), and Barnet M. organizers, and the speakers are listed below. Weinstock {1983). Graph theory, MICHAEL 0. ALBERTSON and JOAN HUTCHINSON, Smith College. The speakers Harold J. Stolberg {1984) has been appointed to were Bela Bollobas, F. R. K. Chung, V. Chvatal, the Committee on Opportunities in Mathematics Paul H. Edelman, Paul Erdos, Marianne L. Gardner, for Disadvantaged Groups by President Andrew M. Curtis Greene, Phil Hanlon, Alan J. Hoffman, Michael Gleason. Continuing members of the committee are Saks, Vera T. S6s, Joel Spencer, Allen Tucker, Sue H. Manuel P. Berriozabal {1982), James A. Donaldson, Whitesides, and Herbert S. Wilf. chairmim {1984), Roland F. Esquerra {1984), Gloria F. Gilmer {1982), and Scott Warner Williams {1983). Nonlinear generalizations of Maxwell's equa­ tions, MELVYN S. BERGER, University of Mas­ Barbara Keyfitz {SIAM, 1984) has been appointed sachusetts, Amherst, and LESTER J. SENECHAL, by President Seymour V. Parter of SIAM to the joint Mt. Holyoke College. The speakers were Judith M. AMB-MAA-NCTM-SIAM Committee on Women in Arms, Frederick Bloom, Arthur M. Jaffe, N. Prakash, Mathematics. Continuing members of the committee Donald J. Rose, Walter Strauss, Clifford H. Taubes, are Pamela Cook-Ioannidis (SIAM, 1982), Etta Z. Craig Tracy, Karen Uhlenbeck, Ricardo Weder, and Falconer {AMS, 1982), Phyllis Fox {SIAM, 1983), Mary Robin Wells. W. Gray, chairman (AMS, 1983), John L. Kelley (AMS, Algebraic geometry, DAVID A. Cox, Amherst 1984), Edith H. Luchins {MAA, 1982), Jacquelin C. College. The speakers were David A. Cox, Bruce Moss (MAA, 1981), Katherine L. Pedersen {NCTM, C. Crauder, David Harbater, Robert La.zarsfeld, Rick 1982), Alice T. Schafer {AMS, 1983), Joel E. Schneider Miranda, David R. Morrison, Peter A. Norman, Walter {NCTM, 1982), Barbara Searle {NCTM, 1982), and Parry, Ziv Ran, Loring W. Tu, and Steven Zucker. Gail A. Williams (MAA, 1983). Hyperbolic geometry, ALAN H. DURFEE, Smith Tilla Klotz Milnor and Barry M. Mitchell were College, and MARK KIDWELL, Amherst College. appointed by President Andrew M. Gleason to be the The speakers were William Abikoff, H. S. M. Coxeter, tellers in the election of 1981. A report on the results Jane Gilman, William M. Goldman, John L. Harer, of the election appears in this issue of the Notices. Robert Penner, John G. Ratcliffe, and William F. Reynolds.

210 Kac-Moody Lie theory, HOWARD GARLAND, in conjunction with the AMS meeting. Alice T. Schafer Yale University, and JAMES HURLEY, University was the principal speaker. of Connecticut. The speakers were Mark Adler, Etsuro Date, Vinay V. Deodhar, Howard D. Fegan, Raymond G. Ayoub Alex J. Feingold, Igor B. Frenkel, Howard Garland, University Park, Pennsylvania Associate Secretary Eugene Gutkin, James F. Hurley, Victor G. Kac, James Lepowsky, Arne E. Meurman, Jun Morita, Alvany Rocha-Caridi, Peter Slodowy, and Gregg J. The November Meeting in Austin Zuckerman. The seven hundred ninetieth meeting of the Ameri­ Combinatorial set theory, JAMES M. HENLE can Mathematical Society was held at the Sheraton­ and STANLEY WAGON, Smith College. The Crest Inn, Austin, Texas, on Friday and Saturday, speakers were Donna M. Carr, E. F. Cornelius, Jr., November 6-7, 1981. There were 241 registrants, Marcia J. Groszek, James M. Henle, Thomas J. Jech, including 222 members of the Society. Donald H. Pelletier, Ned I. Rosen, Juris Steprans, Franklin D. Tall, Alan D. Taylor, Ronald J. Watro, and Invited Addresses. By invitation of the Committee William S. Zwicker. to Select Hour Speakers for Western Sectional Meetings, there Cluster analysis, MELVIN F. JANOWITZ, were the following four invited one-hour addresses: University of Massachusetts, Amherst. The speakers M. SALAH BAOUENDI, Purdue University, Over­ were Forrest B. Baulieu, Hamparsum Bozdogan, Jack determined systems of complex vector fields and Bryant, C. H. Chen, William H. E. Day, Robert M. C. R. functions. Haralick, M. F. Janowitz, Enrique H. Ruspini, Stanley JOHN M. FRANKS, Northwestern University, L. Sclove, D. N. Spinelli, and Danny W. Turner. Structurally stable diffeomorphisms of compact Differential geometry and ergodic theory, A. surfaces. KATOK, University of Maryland, College Park. The CAMERON MeA. GORDON, University of Texas, speakers were Michael Brin, Robert Brooks, Patrick Austin, Concordance of classical knots. Eberlein, Richard H. Escobales, Jr., Vladislav V. EDGAR REICH, University of Minnesota, Goldberg, Brian Marcus, John N. Mather, Steven Minneapolis, Plane quasiconformal mappings Rosenberg, Peter Sarnak, Wolfgang Ziller, and Robert and analytic functions- analytic and geometric J. Zimmer. aspects of the boundary value problem. Topological transformation groups, LARRY N. The presiding officers at these four lectures were MANN and J. C. Su, University of Massachusetts, Raghavan Narasimhan, Robert F. Williams, Steve Amherst. The speakers were Karl Heinz Dovermann, Armentrout, and Albert Marden. Steven M. Kahn, Mei-Chin Ku, Ronnie Lee, T. Y. Lin, Special Sessions. By invitation of the same Frank Raymond, David C. Royster, Reinhard Schultz, committee, there were six special sessions of selected and McKenzie Y. Wang. twenty-minute papers. Discrete geometry and its applications, MAR­ Low-dimensional topology, R. H. BING, Univer­ JORIE SENECHAL, Smith College. The speakers sity of Texas, Austin. The speakers were Steve were Donald L. D. Caspar, Robert Connelly, Ralph 0. Armentrout, James W. Cannon, Robert J. Daver­ Erickson, Jacob E. Goodman, David Harker, Herbert man, William T. Eaton, David S. Gillman, Wolfgang Hauptman, Evelyn Fox Keller, David Klamer, Arthur Haken, Mary Elizabeth Hamstrom, John P. Hempel, L. Loeb, Richard Pollack, Alburt Rosenberg, Richard James P. Henderson, Chung-Wu Ho, Jim E. Hoste, L. Roth, Doris Schattschneider, Walter Whiteley, Shin1ichi Kinoshita, L. Duane Loveland, William W. Stephen J. Willson, and Hans J. Zassenhaus. Menasco, Robert Myers, Richard P. Osborne, Dale Contributed Papers. There were four sessions for Rolfsen, T. Benny Rushing, Michael Starbird, Gerard contributed papers. A. Venema, David G. Wright, and Thomas Perrin Wright, Jr. Maxwell Symposium. A symposium, held on Inverse and/or not-well-posed problems in par­ Friday, October 16, to commemorate the 150th tial differential equations, JOHN R. CANNON, anniversary of the birth of James Clerk Maxwell, University of Texas, Austin, and Washington State was arranged by the AMS, the Five Colleges Applied University. The speakers were John R. Cannon, Paul Mathematics Group, and the Center for Applied C. DuChateau, Richard E. Ewing, Richard S. Falk, Mathematics of the University of Massachusetts, Howard A. Levine, M. Zuhair Nashed, Lawrence E. Amherst. It was supported in part by a grant Payne, William Rundell, and Eutiquio C. Young. to the Five Colleges from the NSF. Lecturers in Smooth dynamical systems, CAROLYN C. this symposium included S. Adler, Melvyn S. Berger, NARASIMHAN, DePaul University, and ROBERT F. 0. Bettancourt, Leon Cooper, Andre Lichnerowicz, WILLIAMS, Northwestern University. The speakers George Mackey, Roger Penrose, Irving Segal, and were Marcy Barge, Steven L. Batterson, Paul R. C. N. Yang. Other participants included Frederick Blanchard, Louis S. Block, Alan Dankner, Sue E. Byron, Wolfgang Fichtner, Arthur Jaffe, Robert Keyes, Goodman, Michael Handel, Michael Hurley, John Herman Statz, and Maurice Wilkes. Smillie, Helena S. Wisniewski, and Lai-Sang Young. Association for Women in Mathematics. The The theory of Banach spaces, EDWARD W. Association for Women in Mathematics held a meeting ODELL, JR. and HASKELL P. ROSENTHAL,

211 University of Texas, Austin. The speakers were on locally symmetric spaces; he was introduced by Dale E. Alspach, Alfred D. Andrew, Spiros Argyros, Joseph A. Wolf. Steven F. Bellenot, Gerald A. Edgar, John H. Elton, Special Sessions. By invitation of the same Carlos E. Fino!, Aggie G. Ho, William B. Johnson, committee, there were five special sessions of selected Joram Lindenstrauss, Heinrich P. Lotz, N. Tenney papers. The topics of these special sessions, the names Peck, Shlomo Reisner, James W. Roberts, Stanislaw of the organizers and the lists of speakers are as follows: Nicole Tomczak-Jaegermann, and John E. J. Szarek, Group representations, PETER TROMBI, Wolfe. University of Utah. The speakers were Henryk Hecht, Quasiconformal mappings, BRUCE P. PALKA, Dragan Milii~ic, David A. Vogan, and Joseph A. Wolf. University of Texas, Austin. The speakers were Stephen models and analysis in the social Agard, Glen D. Anderson, David Drasin, Frederick P. Network C. JOHNSEN, University of Gardiner, Frederick W. Gehring, Jane P. Gilman, sciences, EUGENE Barbara. The speakers were Phillip F. David Lesley, Albert Marden, Ruth Miniowitz, Brad California, Santa Paul Boyd, Linton C. Freeman, Paul G. Osgood, Bruce P. Palka, Glenn E. Schober, and Bonacich, John R. Allen Weitsman. W. Holland, Stephen B. Seidman, and Douglas also a general discussion led by Number theory and related parts of analysis, White. There was Matthew Witten. JEFFREY D. V AALER, University of Texas, Austin. The speakers were Bruce C. Berndt, Brian Conrey, Rings and modules, JULIUS M. ZELMAN­ Thomas W. Cusick, P. D. T. A. Elliot, Paul Erdos, OWITZ, University of California, Santa Barbara. The Ronald J. Evans, John B. Friedlander, Mary Elizabeth speakers were Victor P. Camillo, Laszlo Fuchs, John Gbur, Dorian Goldfeld, Steven M. Gonek, James Lawrence, T. H. Lenagan, Bruno J. Mueller, W. K. Lee Hafner, Heini Halberstam, Donald G. Hazelwood, Nicholson, Stanley S. Page, and S. P. Smith. Dennis A. Hejhal, Douglas A. Hensley, Jeffrey C. Convexity in fv.nctional analysis, KY FAN and Lagarias, Kevin S. McCurley, Julia Mueller, Gerald STEPHEN SIMONS, University of California, Santa Myerson, Melvyn B. Nathanson, Carl B. Pomerance, Barbara. The speakers were Gerald A. Beer, Robert J. Ian Richards, Wolfgang M. Schmidt, Eira J. C. James, Isaac Namioka, R. R. Phelps, Simeon Reich, Scourfield, Kenneth B. Stolarsky, and John W. Van Wolfgang Ruess, and Stephen Simons. Horne. Theoretical computer science, MICHAEL L. Contributed Papers. There were five sessions of FREDMAN, University of California, San Diego. The contributed ten-minute papers, for which David Drasin, speakers were Leonard M. Adleman, Ronald V. Book, John H. Elton, John J. Sarraille, Ralph E. Showalter, Patrick W. Dymond, Michael L. Fredman, Maria and David M. Young, Jr., served as presiding officers. Klawe, George S. Lueker, and Nicholas Pippenger. Of the 25 ten-minute papers listed in the program of Contributed Papers. There were two sessions the meeting, 3 were withdrawn, so that 22 ten-minute of contributed ten-minute papers of six and seven papers were actually presented. speakers each. They were chaired by H. Y. Mochizuki and J. S. Rao respectively. Paul T. Bateman Other Events. The MAA program included an Urbana, Illinois Associate Secretary hour address by Neal J. A. Sloane, entitled Some remarkable new sphere packings. There was also The November Meeting in Santa Barbara an MAA special session on Number Theory and Combinatorial Analysis. The seven hundred ninety-first meeting of the Amer­ The SIAM program included an hour address by ican Mathematical Society was held at the University Joel Franklin entitled Mathematical methods of of California, Santa Barbara, on Friday and Saturday, economics. November 13-14, 1981. The meeting was held in The featured speaker at the Saturday luncheon was conjunction with meetings of the Southern California Mark Kac; the title of his talk was The search for the sections of the Mathematical Association of America meaning of independence. (MAA) and the Society for Industrial and Applied Mathematics (SIAM). There were 226 registrants Hugo Rossi including 138 members of the Society. Adil Yaqub, Salt Lake City, Utah Associate Secretary with the assistance of Patty Minnich, served as the local organizer of this meeting. Invited Addresses. By invitation of the Committee The Annual Meeting in Cineinnati to Select Hour Speakers for Far Western Sectional Council Meeting Meetings, there were two invited one-hour addresses. THOMAS J. ENRIGHT of the University of The Council met at 2:00 p.m. on January 12, 1982 California, San Diego, lectured on Representations of in Room 23 of the Cincinnati Convention-Exposition Lie groups and connections with Lie algebras over Center. President Gleason was in the chair. commutative rings; he was introduced by Henryk The Council established a two-part formula for dues Hecht. of ordinary members. First, dues are to be increased JOHN MILLSON of the University of California, each year when necessary a whole dollar amount Los Angeles, spoke on Cycles and harmonic forms equivalent to the percentage increase in average salary

212 at institutions reporting salary data to the American the Executive Committee to prepare a response for the Association of University Professors for the last ten Society. The Chairman of the Executive Committee is years. Second, there are two levels of dues for ordinary President Andrew M. Gleason and the Secretary is a members, the lower level being about three-quarters member. Either may be addressed at the Providence of the higher level. The division point is to be office of the Society. established at a round thousand dollar amount which The Council recessed for dinner and adjourned at places about 60% of the ordinary members in the 9:30p.m. category of lower dues. The Council empowered the Bwiness Meeting Executive Committee to apply the formula, to set the division point, and to forward the results directly to the The Business Meeting followed the session for the Trustees for their approval. The Trustees have already award of Cole Prizes and was held on January 14, approved the formula subject to Council action. It 1982 in the North Meeting Room of the Cincinnati was noted that had this formula been put into effect Convention-Exposition Center. in 1973, the dues for 1982 would be within a dollar The Secretary reported on actions of the Council as of what they are now and the division point would detailed above. probably be $21,000 rather than the current $20,000. He noted that, with the cloud cast over the The Society had the opportunity to comment on a International Congress of 1982, the program of the proposal for voluntary prepublication review of papers Summer Meeting in Toronto in the interval August 23- which might be of interest to the National Security 27, 1982 is not being curtailed. There is to be a full Agency. The NSA was attempting to carry out program of speakers, including Colloquium Lectures by a suggestion formulated by the Pubic Cryptography Morris W. Hirsch. Study Group, which was sponsored by the American Saunders Mac Lane addressed the Business Meeting Council on Education. (The PCSG report was printed briefly on issues related to the proposed revision of in full in the October 1981 Notices, pages 517 to 526.) Circular A-21. The Council, acting under the authority of Article IV, Frederick W. Gehring introduced a resolution of Sections 2 and 8, of the bylaws, passed the following thanks to the Committee on Arrangements, particularly resolution in four parts. its Chairman, Edward P. Merkes, the Program 1. The Society as an organization should not become committee and Associate Secretary Frank T. Birtel, involved in any phase of the administration of a and the staff from the Providence office. It was passed plan of voluntary prepublication review of papers in by acclamation. cryptology. The meeting adjourned at 5:20 p.m. 2. In particular, neither the editors of Society journals nor the Providence office should inquire Everett Pitcher whether a paper submitted to or accepted by a Society Bethlehem, Pennsylvania Secretary journal has been offered for review. 3. The Society should not make recommendations of names to any appeal panel that is set up in the review Eleetion Results of 1981 process. 4. On the other hand, the Notices should publicize, The two newly elected Vice-Presidents of the Society without endorsement, any request by NSA for are Michael Artin and Elias M. Stein. The newly individuals to participate in the review process. elected Members-at-Large of the Council are Peter A. The Council passed the following resolution by Fillmore, Melvin Hochster, Robert P. Langlands, M. acclamation: Susan Montgomery, and Hector J. Sussmann. The Council notes with pleasure the facts that the Ronald L. Graham was elected to the position of backlog at the Mathematical Reviews editorial Trustee. The President-elect is Julia B. Robinson. All office has been cleared, and that the journal candidates in noncontested elections were elected to now appears on time. The Council congratulates their respective offices. the entire staff for accomplishing this task and The candidates elected to the Nominating Com­ commends the Executive Editor, John L. Selfridge, mittee of 1982-1983 are David Mumford, Ralph S. and the Managing Editor, William B. Woolf, for Phillips, Linda Preiss Rothschild, and George W. their leadership in directing it. Whitehead. The composition of the Council of 1982 The Council considered issues connected with the follows. Names of persons elected in 1981 are marked 1979 version of Circular A-21 from the Office of with an asterisk. Management and Budget and dated February 26, 1979. COUNCIL FOR 1982 It is concerned with what was once known as ''time President: Andrew M. Gleason and effort reporting" and is now sometimes called President-elect: Julia B. Robinson* "monitored workloads and personal activity reporting." Vice Presidents: Michael Artin* Copies are available in university grants offices. The Paul R. Halmos occasion of re-examination is coincidental with the Elias M. Stein* publication in the Federal Register on January 7, 1982 Secretary: Everett Pitcher of a proposed revision with a deadline sixty days hence for the return of comments. The Council empowered

213 Associate Secretaries: Raymond G. Ayoub Paul T. Bateman* Frank T. Birtel PROCEEDINGS OF SYMPOSIA Hugo Rossi* IN APPLIED MATHEMATICS Treasurer: Franklin P. Peterson Associate Treasurer: Steve Armentrout GAME THEORY AND ITS APPLICATIONS MEMBERS-AT-LARGE edited by William F. Lucas Donald L. Burkholder Richard S. Millman This volume contains the lecture notes prepared Peter A. Fillmore* M. Susan Montgomery* by the speakers in the short course on Game Theory Frederick W. Gehring Marian B. Pour-El and its Applications given in Biloxi, Mississippi in Melvin Hochster* Mary Ellen Rudin 1979. Alan J. Hoffman Paul J. Sally, Jr. Game theory has been a topic of broad interest Linda Keen David A. Sanchez as a purely theoretical subject which has relation· Robert P. Langlands* I. M. Singer ships to many other mathematical areas, and also as a subject widely Lee Lorch Hector J. Sussmann* used in applications over a large variety of problem areas. It is concerned with mathe· 0. Carruth McGehee matical models for situations involving conflict and/ COMMUNICATIONS COMMITTEE or cooperation. These arise in a fundamental way throughout the behavioral and decision sciences. Chairman, Committee to Monitor Problems in Game theory has become a basic modeling technique Communication: Robert G. Bartle in much of modern economic theory, political sci­ PUBLICATIONS COMMITTEES ence, sociology, and operations research, and it has frequently been applied to many other fields. It is a Bulletin Editorial Committee subject highly suitable for joint research of an inter­ Felix E. Browder Calvin C. Moore* disciplinary nature. Meyer Jerison This volume is concerned mostly with the n-per­ Colloquium Editorial Commmittee son theory (n # 3), although chapter 6 also describes John W. Milnor* Elias M. Stein several basic two-person models. The first five chap­ Stephen Smale ters deal for the most part with the multiperson co­ operative games in the characteristic function (coali­ Proceedings Editorial Committee tional) form. The normal (strategic) form and the Thomas H. Brylawski Reinhard E. Schultz extensive (tree) form of a noncooperative game are David M. Goldschmidt* J. Jerry Uhl, Jr.* stressed in chapter 6, although some basic definitions William E. Kirwan II Lawrence A. Zalcman for the normal form do appear in an earlier chapter. David J. Lutzer Selected applications of the theory which are covered Transactions and Memoirs Editorial Committee here in some detail include economic market games, Michael Artin Steven Orey measuring power in political systems, equitable allo­ cation of costs, and auctions. Many of the important William B. Johnson* Paul H. Rabinowitz recent uses of game theory have involved the n-per­ Jan Mycielski R. 0. Wells, Jr. son cooperative models. Walter David Neumann* These lectures were presented to an audience of Mathematical Reviews Editorial Committee mature mathematicians. Nevertheless, this volume Paul T. Bateman Carl M. Pearcy could also serve as a textbook for a general course Morton Lowengrub* in game theory at the upper division or graduate levels. Mathematical Surveys Editorial Committee Donald W. Anderson* Jane Cronin Scanlon William F. Lucas, The multiperson cooperative games William F. Lucas, Applications of cooperative games R. James Milgram to equitable allocation Mathematics of Computation Editorial Louis j. Billera, Economic market games Committee L. S. Shapley, Valuation of games James H. Bramble Morris Newman L. S. Shapley, Measurement of power in political Carl de Boor Daniel Shanks* systems AMS Representatives, Board of Editors Robert J. Weber, Noncooperative games of American Journal of Mathematics 1980 Mathematics Subject Classification: 90 D Victor W. Guillemin Richard G. Swan Volume 24, viii + 128 pages Hard cover prices: List $18, institutional member $13.50, individual member $9 Soft cover prices: List $12, institutional member $12, all individuals $6 ISBN 0·8218-0025-6; LC 81-12914 Publication date: October 1981 To order, please specify PSAPMSI24N (soft cover) PSAPM{24N (hard cover) Prepayment is required for all AMS publications. Order from AMS, PO Box 1571, Annex Station, Providence, Rl 02901, or call 800-556-7774 to charge with VISA or MasterCard.

214 CLASSIFIED ADVERTISEMENTS

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THE RATE IS $.40 per word with a minimum of $4.00. The same ad in 7 consecutive issues is $2.50 per word. Type will be set solid unless c~ntering and spac­ ing are requested. A centered line of any length or the equivalent in white space is $4.00. A word is defined as a group of characters With space at each end. Prepayment is required of individuals but not of institutions. DEADLINES are listed on the inside front cover.

U. s. LAWS PROHIBIT discrimination in employment on the basis of color, age, sex, race, religion or nation~! o~igi~. 11 Positions A~ail~bl~" advertisements from institutions outside the U. s. cannot be published unless they are accompanied by a statement that the mst1tution ~oes not d1scnmmate on these grounds, whether or not it is subject to U.S. laws. Details and specific wording may be found on page 95 of the January 1982 1ssuc of the Notices. SITUATION WANTED advertisements are accepted under terms spelled out on page A-355 of the April1979 Notices. (Deadlines are the same as for other classi­ fied advertisements.) SEND AD AND CHECK TO: Advertising Department, AMS, P.O. Box 6248, Providence, Rhode Island 02940. Individuals are requested to pay in advance, in­ stitutions are not required to do so.

POSITIONS AVAILABLE MICHIGAN TECH UNIV DEPT OF MATH & COMP SCI HOUGHTON, Ml 49931 Assistant Professor, Computer Science. Initial three-year appointment. Possibility of reappointment and eventual About 5 tenure-track positions in applicable mathematics tenure. Qualifications include demonstrated research in (e.g., probability, fluid mechanics, ODE, POE, functional computer science and ability and interest in teaching under­ analysis, calculus of variations, control theory, etc.), statis­ graduate courses in computer science and mathematics. Ph.D. tics, differential geometry, numerical analysis and computer required. Write to Professor Martin Arkowitz, Chairman, science as well as visiting positions are available. Assistant or Department of Mathematics, DARTMOUTH COLLEGE, associate professors preferred. Excellent research and teach· Bradley Hall, Hanover, NH 03755 (Attn: Recruiting). EO/ AA. ing are required. MTU is a strong engineering school with good students and consulting possibilities. Houghton has temperatures moderated by Lake Superior with a great deal The Department of Mathematics and Statistics at of snow and recreational activities. To apply write Dr. MISSISSIPPI STATE UNIVERSITY anticipates two or more Richard Millman, Head. MTU is an equal opportunity educa· tenure-track positions beginning with the 1982-1983 aca· tional institution/equal opportunity employer. demic year. A Ph.D. is preferred. Applicants with expertise in some area of applicable mathematics are especially wel­ comed. Responsibilities include teaching and research. Rank DEPARTMENT OF MATHEMATICS and salary "commensurate with qualification and experience. Candidates should submit a vita and three letters of recom· AND COMPUTER SCIENCE mendation by February 15, 1982, to j. L. Solomon, Head, SOUTHWEST TEXAS STATE UNIVERSITY Department of Mathematics and Statistics, Mississippi State, Applications invited for positions beginning fall 1982: Mississippi 39762. Assistant or Associate Professorships in Computer Science, Affirmative Action/Equal Opportunity Employer tenure and non-tenure-track. Applicants should have a Ph.D. in Computer Science and demonstrate potential for excel· TEXAS A&M UNIVERSITY AT GALVESTON. Assistant lence in teaching graduate and undergraduate courses in Professor, tenure-track, starting Fall 1982. Requires Ph.D., Computer Science. Professional activity is expected. teaching excellence and research, or research potential, Assistant or Associate Professorships in Mathematics, tenure Undergraduate Math through Differential Equations and and non·tenure·track. Applicants should have a Ph.D. in Applied Math for Engineers. TAMU at Galveston, a growing Mathematics (or closely related area) and demonstrate poten· institution, presently offers Bachelor degrees in Marine· tial for excellence in research and teaching. Preference will related programs: Administration, Biology, Engineering, Sci· be given candidates with research interests in Topology ences, Transportation. Graduate programs: Biology, Wildlife (topology of low dimensional manifolds, decomposition & Fisheries Science. Math faculty teaches in all degree pro­ space theory, and algebraic topology), Number Theory grams through the Department of General Academics. Send (analytic or algebraic), Mathematics Education (elementary dossier, including vita and three letters of recommendation or secondary), and Differential Equations (fixed points, to: variational methods, nonlinear functional analysis, continuum Dr. Anthony P. Blozinski mechanics, numerical methods, functional DE's, bifurcation Math/General Academics theory, dynamical systems). Applicants in Operations Re­ Texas A&M University at Galveston search and Quadratic forms are also invited to apply. Post Office Box 1675 Galveston, Texas 77553 Instructorships, non-tenure-track. Applicants should have an TAMU at Galveston is an Equal Opportunity/Affirmative M.A. or equivalent in Mathematics (or closely related area), Action Employer. demonstrate teaching ability or teaching potential, and be willing to participate in faculty seminars and committee MATHEMATICS: The Virginia Military Institute, a state projects. supported undergraduate college, anticipates an opening at Salary and rank commensurate with qualifications and ex­ the instructor or assistant professor level in the Department perience. Further information concerning specific positions of Mathematics in August 1982. The applicant should have is available from: Dr. john Spellmann, Chairman, Department a strong interest in teaching undergraduates in a military of Mathematics and Computer Science, Southwest Texas college environment. Send your resume by February 28, State University, San Marcos, Texas 78666. Applications 1982 to Department of Mathematics, The VIRGINIA should be received by February 15, 1982 (late applications MILITARY INSTITUTE, Lexington, VA 24450. will be considered if openings exist). SWTSU is an equal AA/EEO Employer. opportunity/affirmative action employer.

215 POSITIONS AVAILABLE Department of Mathematics and Computer Science UNIVERSITY OF MIAMI PROFESSOR/ASSOCIATE PROFESSOR Applications are invited for tenure-track positions, beginning PURE MATHEMATICS August, 1982. Ranks and salaries are open, commensurate Boston University announces a search for a tenure level with qualifications of the applicants. Preference will be given appointment (professor or associate professor) in pure math· to candidates in the areas of applied mathematics, computer ematics. Field unrestricted. A record of distinguished science and analysis. Candidate must have the Ph.D. degree achievements in research and a sustained commitment to ex· and excellent research record, or a definite research potential, cellence in teaching are required. Women and minorities are with a strong commitment to teaching and research. Appli· especially encouraged to apply. Nominations and applications cants should send vitae and three letters of reference to: to: Shair Ahmad, Chairman Dennis D. Berkey, Chair Department of Mathematics and Computer Science Department of Mathematics University of Miami Boston University Coral Gables, FL 33124 Boston, MA 02215 The University of Miami is a private, independent, interna· First closing january 30, 1982. tiona! university and an equal opportunity and affirmative BOSTON UNIVERSITY is an Equal Opportunity/Affirmative action employer. Action Employer. ------VILLANOVA UNIVERSITY ASSISTANT PROFESSORSHIPS IN MATHEMATICS ASSIST ANT/ ASSOCIATE PROFESSORSHIPS AVAILABLE FALL 1982 Boston University announces several openings at the rank of assistant professor. Field unrestricted. Strong potential for Applications are invited for the position of Assistant or excellence in both teaching and research are required. Women Associate Professor in Mathematics. Several appointments and minorities are especially encouraged to apply. VIta and will be made for up to three years with the possibility of three letters of reference to: tenure-track. Candidates should possess the Ph.D. degree and Dennis D. Berkey, Chair have a strong interest in undergraduate and graduate teaching Department of Mathematics as well as mathematical research. Expertise in computer sci· Boston University ence is preferred but not required. Applicants should send a Boston, MA 02215 resume and three letters of recommendation to: First closing january 30, 1982. Frederick W. Hartmann Chairman, Mathematics Department BOSTON UNIVERSITY is an Equal Opportunity/Affirmative Villanova University Action Employer. Villanova, PA 19085 PROFESSOR/ASSOCIATE PROFESSOR Villanova University is an Equal Opportunity/Affirmative IN DYNAMICAL SYSTEMS Action Employer. Boston University announces the search for a tenure level Department of Mathematics & Statistics appointment (professor or associate professor) in dynamical UNIVERSITY OF SOUTH CAROLINA, Columbia, SC 29208 system theory or one of the related fields. The successful candidate will play a leadership role in a group of ten pro· The Department invites applications for tenure-track fessors working in these areas. A distinguished record in positions in mathematics and statistics beginning Fall of scholarship and a sustained commitment to excellence in 1982. The Department is committed to continued growth teaching are required. Women and minorities are especially and development of its pure and applied programs. The Ph.D. encouraged to apply. Nominations and applications to: degree and strong potential for excellence in teaching and Dennis D. Berkey, Chair research are required. The standard teaching load is two Department of Mathematics courses per semester. Boston University Applicants should submit a resume and arrange for four Boston, MA 02215 letters of recommendation to be sent to Professor W. T. First closing january 30, 1982. Trotter, Jr., Chairman. The University of South Carolina is an affirmative action/equal opportunity employer. BOSTON UNIVERSITY is an Equal Opportunity/Affirmative Action Employer. UNIVERSITY OF CALIFORNIA, RIVERSIDE Faculty Position in Computer Science SENIOR LEVEL POSITION IN COMPUTER SCIENCE Applications are invited for a permanent position in The Department of Mathematics at Boston University an· Computer Science beginning with the 1982-1983 academic nounces the search for a tenure level appointment (professor year. Applicants must have a Ph.D. and a commitment to or associate professor) in computer science. Field is unre· teaching and research in computer science. Candidates from stricted. Substantial productivity in research, a record of all areas of specialization in computer science will be effective teaching, and the capability for leadership are re· considered. quired. Industrial experience is a plus. The computer science Rank and salary are open; candidates for senior rank must programs provide instruction at all levels from introductory have leadership ability and a proven research record. through Ph.D. Research interests are balanced in both theory and applications. Vita and three letters of reference to: To apply, send resume with names of three references to Dennis D. Berkey, Chair Professor Sudhir Aggarwal Department of Mathematics Chairman, Search Committee Boston University Department of Mathematics Boston, MA 02215 University of California Women and Minorities are especially encouraged to apply. Riverside, CA 92521 BOSTON UNIVERSITY is an Equal Opportunity/Affirmative The University of California is an Equal Opportunity/ Action Employer. Affirmative Action Employer.

216 POSITIONS AVAILABLE Siena College- Mathematics Department The mathematics department has two openings for the THE UNIVERSITY OF ARKANSAS - J, William Fulbright 1982-1983 academic year. One opening is a tenure-track College of Arts and Sciences is seeking a distinguished per· position, the other is a one-year sabbatical replacement. son to direct its Honors Program. The director will admin· Both positions will be filled at the assistant professor level. ister existing programs and help to develop a four-year in­ Siena College is an undergraduate teaching college located terdisciplinary component. Evidence of scholarly or creative in the Capital District of New York. The full-time teaching achievement teaching excellence, and administrative poten· load is 12 credits/semester. We offer a mathematics major tial is Rank is open; salary and fringe benefits are requir~d. and provide service courses to the Physics, Biology, Chem· competitive. The committee began reviewing applications on istry and Computer Science Departments. January 1, 1982; the job will become available july 1, 1982. Please send a letter of application; a complete vitae; a state­ We seek mathematicians who have completed their Ph.D., ment describing view on the place of an honors program in who are committed to excellence in teaching and who enjoy a liberal education; and the names, addresses, and telephone interacting with students in and outside of the classroom. numbers of five persons who are thoroughly familiar with The person who is hired for the tenure-track position must your qualifications to: be capable and willing to teach Algebra and Number Theory. Interested persons should send a resume, transcripts and Dr. Randall B. Woods at least three letters of recommendation to Dr. L j. Putnick, Associate Dean Chairman, Mathematics Department, Siena College, Loudon­ j. William Fulbright ville, NY 12211. Applications received prior to March 15 College of Arts and Sciences are guaranteed consideration. Siena College is an affirmative Vol Walker Hall -122 action, equal opportunity employer. University of Arkansas Fayetteville, Arkansas 72701 The University of Arkansas is an affirmative action/equal Research Positions in Theoretical and opportunity institution. Computational Fusion Physics The Magnetofluid Dynamics Division of the Courant Mathematics Positions (two)-Rank Open-Tenure-track. Institute of Mathematical Sciences, New York University, is Salary Competitive. The regular teaching load is 12 semester seeking candidates for full-time research positions in theo· hours of undergraduate mathematics courses at the lower retical and computational fusion physics. The MFD Division and upper division levels and first year graduate courses. One has been an active participant in the world fusion program requires a Ph.D. degree in any of the modern applied mathe· for over twenty years and specializes in those areas of fusion matics areas such as: modeling, combinatorics, applied sta· physics which benefit from a sharper mathematical viewpoint. tistics, optimization. The other requires a Ph.D. In Mathe­ Present research concerns theoretical problems of both main­ matics. The candidates should show high promise to become line and alternate magnetic confinement fusion approaches, excellent teachers. Persons interested in the above should and close contact is maintained with national laboratory submit a n!sum~ along with a letter of application and three programs. An on-site mini user service center of the MFE letters of reference by March 15, 1982 to Dr. Vasily C. national computer network has been established by DOE. Cateforis, Department of Mathematics, State University Interaction with the Courant Institute staff engaged in varied College of Arts and Science at Potsdam, Potsdam, New York research programs provides a stimulating scientific environ· 13676. An Equal Opportunity/Affirmative Action Employer. ment. Rank and salary will depend on education and ex­ perience. MATHEMATICS/COMPUTER SCIENCE-Full-time tenure· Send resume and three letters of recommendation to track position. Rank, salary dependent on qualifications and Director, Magnetofluid Dynamics Division, New York Uni· experience. Ability to teach all levels of undergraduate versity, Courant Institute of Mathematical Sciences, 251 mathematics is required. Ability to teach upper-level com­ Mercer Street, New York, New York 10012. puter science courses is desired. A doctorate in mathematics or a masters in computer science with a strong background in mathematics is required. SOUTHWEST STATE UNIVER­ CLAREMONT MCKENNA COLLEGE is seeking a SITY is a four-year liberal arts and technical institution in qualified person for a three-year visiting assistant professor· a rural setting. Current enrollment is approximately 2000 ship teaching mathematics and computing. Applicants undergraduates. The Department offers a major in Mathe· should have a Ph.D. in computer science, mathematics or a matics and a minor in Computer Science. Appointment closely related field, have a strong commitment to teaching, date: September 1982. Closing date for applications: and show promise in research. Background and interest in March 15, 1982 (subject to budget considerations). Address numerical analysis, mathematical modelling, data base letters of inquiry to Malcolm Tobey, Search Committee, design, or statistics would be especially appropriate. Mathematics/Computer Science Department, South west State University, Marshall, MN 56258. Southwest State University Claremont McKenna College (formerly Claremont Men's is an Affirmative Action/Equal Employment Opportunity College) is a coeducational, liberal arts college with a cur­ Employer. ricular emphasis on economics and political science and is one of the Claremont Colleges. The standard teaching load TENURE-TRACK POSITION(S) IN MATHEMATICS is five courses per year ranging from freshman introductory courses to advanced undergraduate courses. The College THE UNIVERSITY OF MISSISSIPPI shares a VAX 11 with three other Claremont Colleges and UNIVERSITY, MS 38677 students have access via twelve ports. Assistant or Associate Professors of Mathematics, position(s) Resumes and letters of recommendation should be sent pending funding and administrative approval, tenure-track, to: beginning Fall 1982. Ph.D. required, with interest in research. Normal teaching load is currently 9 credit hours per semes­ Professor James B. Lucke, Chairman ter. Send resume, graduate transcript, reprints, dissertation Department of Mathematics abstract, and three letters of recommendation to Dr. Eldon Claremont McKenna College L. Miller, Chairman, Department of Mathematics, University Claremont, California 91 711 of Mississippi, University, MS 38677, before March 15, 1982, Claremont McKenna College is an Equal Opportunity/ to ensure consideration. Equal Opportunity Employer. Affirmative Action Employer.

217 POSITIONS AVAILABLE COMPUTER SCIENCE UNIVERSITY OF MARYLAND BALTIMORE COUNTY THE AUSTRALIAN NATIONAL UNIVERSITY The UMBC Mathematics Department invites applications The Department of Mathematics under Professor D. W. from computer scientists for tenure-track or tenured faculty Robinson, FAA, is one of ten departments in the Research positions at the assistant, associate, or full professor level, School of Physical Sciences and carries out research in the beginning September 1982. Candidates should have Ph.D. following areas: Operator Algebras and Mathematical Physics in computer science or in a closely related field, demon­ (D. W. Robinson), Partial Differential Equations and Geom· strable research potential, and strong ability to teach a etry (L. Simon), Foundations (R. E. Edwards), Lie Groups broad range of basic computer science courses and graduate and Algebraic Groups (R. W. Richardson), Ordinary Differ· courses in one's field of specialty. The Department offers a entia! Equations and Control Theory (W. A. Coppei), Global B.A. program in mathematics, a B.S. program in computer Analysis (S. Yamamuro), and Group Theory (L. G. Kovacs, science, M.S. and Ph.D. programs in applied mathematics. M. F. Newman). Current graduate course offerings are grouped in the follow­ ing areas: applied analysis, computer science, control sys­ The School conducts competitions twice yearly for two­ tems, numerical analysis, operations research, statistics and year Postdoctoral Fellowships for outstanding young post· probability. Send a curriculum vitae, reprints and/or pre· researchers in any relevant field of research in the doctoral prints, names of at least three references to: Y. M. Lynn, Salaries are within the range $A 18068 to $A20699 School. Chairman, Department of Mathematics, University of Mary­ per annum, according to qualifications and experience. land Baltimore County, Catonsville, Maryland 21228. Further particulars are available from The Registrar, The EQUAL OPPORTUNITY/AFFIRMATIVE ACTION Australian National University, P. 0. Box 4, Canberra, EMPLOYER. ACT 2600, Australia, with whom applications for such fel· lowships commencing in 1983 close on 31 March and 30 OPERATIONS RESEARCH September 1982. UNIVERSITY OF MARYLAND BALTIMORE COUNTY Department invites applications DEPARTMENT OF MATHEMATICS The UMBC Mathematics for a tenure-track assistant or associate professor position in OF WESTERN ONTARIO THE UNIVERSITY Operations Research beginning September 1982. Candidates The Department of Mathematics invites applications for should have Ph.D., demonstrable research potential and a limited term appointment at the Assistant Professor level. strong teaching ability. Experience or ability to teach under­ The appointment, which is subject to the availability of graduate courses in computer science is desirable. The funds, will be for the period September 1, 1982, to May 31, Department offers a B.A. program in mathematics, a B.S. 1983. Candidates should have a Ph.D. in an area of pure program in computer science, M.S. and Ph.D. programs in mathematics. Duties will include teaching and research. applied mathematics. Current graduate course offerings are Canadian Immigration regulations require that Canadians or grouped into the following areas: applied analysis, computer Landed Immigrants to Canada be given preference for this science, control systems, numerical analysis, operations re· position. Applications, including the names of three referees, search, statistics and probability. Send a curriculum vitae, should be sent to: reprints and/or preprints, names of at least three references Chairman, Department of Mathematics, Dr. D. Borwein, Head to: Y. M. Lynn, County, Catonsville, Department of Mathematics University of Maryland Baltimore EQUAL OPPORTUNITY/AFFIRMATIVE Middlesex College Maryland 21228. The University of Western Ontario ACTION EMPLOYER. London, Ontario, Canada N6A 5B7 TENURE TRACK POSITION UNIVERSITY OF MARYLAND BALTIMORE COUNTY Indiana State University is searching for a chairperson in the The UMBC Mathematics Department invites applications Department of Mathematics/Computer Science effective in for a tenure-track assistant or associate professor position August 1982. Candidates must have a Doctorate, an estab­ beginning September 1982. Candidates should have Ph.D., lished record of research, grant-writing and administrative strong teaching ability, and demonstrable research potential experience, plus a commitment to quality teaching. The with interests in discrete mathematics and/or in fields cur­ chairperson will administer the Department consisting of rently represented on the faculty (applied and complex approximately 26 staff members and 400 Mathematics and/ analysis, computer science, control systems, numerical analy­ or Computer Science Majors. Salary and rank are dependent sis, operations research, statistics and probability). Experience upon candidates' qualifications. Send credentials and 3 let­ or ability to teach undergraduate computer science courses ters of recommendation to Dr. R. D. Pethtel, Chairman, is desirable. The Department offers a B.A. program in mathe· Chairperson Search Committee, Math/Computer Science matics, a B.S. program in computer science, M.S. and Ph.D. Department, Indiana State University, Terre Haute, IN programs in applied mathematics. Send a curriculum vitae, 47809. The deadline for applications is March 15, 1982. reprints and/or preprints, names of at least three references Affirmative Action/Equal Opportunity Employer. to: Y. M. Lynn, Chairman, Department of Mathematics, University of Maryland Baltimore County, Catonsville, Maryland 21228. EQUAL OPPORTUNITY/AFFIRMATIVE WASHINGTON UNIVERSITY IN ST. LOUIS ACTION EMPLOYER. DEPARTMENT OF MATHEMATICS UNIVERSITY OF MAINE AT ORONO at the Assistant Professor Assistant Professor. A position DEPARTMENT OF MATHEMATICS, ORONO, ME 04469 level starting Fall 1982 or 1983. Candidates should have outstanding research ability in a field represented in the Department Chairperson, rank and salary open. Earned doc­ Department, and evidence of excellence in teaching. Appli­ torate in mathematical sciences, demonstrated scholarship. cations will be accepted until the position is filled. Send a Must provide leadership to 27-person department with letter of application and vita, and have three letters of diverse interests and have the ability to articulate effectively reference sent to: R. H. McDowell, Chairman, Department the departmental goals and needs to higher levels of admin­ of Mathematics, Box 1146, Washington University in istration. Send vita and names of three references imme­ St. Louis, St. Louis, MO 63130. Washington University is diately to Chair Search Committee. Equal Opportunity/ an affirmative action/equal opportunity employer. Affirmative Action Employer.

218 POSITIONS AVAILABLE The Department of Mathematics and Statistics, UNIVERSITY OF SOUTH ALABAMA, is accepting applications for pos­ DEPARTMENT OF MATHEMATICS sible tenure-track positions at the rank of Assistant Professor OREGON STATE UNIVERSITY or higher. A successful applicant must possess a Ph.D. in CORVALLIS, OR 97331 mathematics; a strong background in numerical analysis, differential equations, or operations research is preferred. One year appointments-in pure or applied mathematics Consideration will also be given to candidates with research or in mathematics education. Ph. D. or equivalent training interests in functional analysis, geometric topology, or num­ and experience is required. All professional ranks will be ber theory. The duties attendant to this position include considered. The visiting rank will be the same as the person's teaching undergraduate and graduate mathematics courses, rank at the home institution. Preference will be given to carrying out research or other creative activity, and contrib­ those applicants who augment areas of current research uting to a scholarly atmosphere. The appointment would activity in the department, and to those with expertise to begin September 1982. Applicants should send a detailed meet specific instructional needs. Either full or part-time resume, transcripts, and three letters of recommendation to appointment can be arranged. Full-time duties include Dr. Gene Crossley, Chairman, Department of Mathematics teaching six to eight class hours per week. Closing date is and Statistics, University of South Alabama, Mobile, AL March 1, 1982. 36688. The closing date is March 15, 1981. Write to Dr. R. M. Schori, Chairman USA is an equal opportunity/affirmative action employer. Department of Mathematics Oregon State University ASSISTANT PROFESSORS Corvallis, OR 97331 Attn: Staff Selection Committee The Department of Mathematics of Carnegie-Mellon Univer­ sity is conducting a search for three mathematicians at the Oregon State University is an Affirmative Action/Equal rank of assistant professor. Special attention will be given Opportunity Employer and complies with Section 504 of to candidates in mathematical optimization, general analysis the Rehabilitation Act of 1973. and numerical analysis. Joint appointments with other Departments are possible. Candidates will be expected to play a major role in the Department's Applied Mathematics The Department of Mathematical Sciences Program. This will require not only potential excellence in North Dakota State University teaching, but also sufficient breadth to develop and teach New faculty position in mathematics beginning Fall 1982, courses in diverse areas of applied mathematics. Research with salary and rank commensurate with qualifications. potential must be strong, and special consideration will be Applicants should have mathematics (or related) Ph.D., and given to candidates who can work on problems that are of excellence in teaching and research. Our 35 member depart­ interest in engineering and physical sciences, or the manage­ ment has over $500,000 in NSF and private grants in both ment and social sciences. Carnegie-Mellon University is an teaching and research, and extensive computing, statistical and Affirmative Action/Equal Opportunity Employer. Com­ operations research hardware and software. North Dakota munications should be addressed to Professor George J. is oil and coal rich, with extensive recreational opportunities. Fix, Head, Department of Mathematics, Carnegie-Mellon Send vita and the names of three references to James Olsen, University, Pittsburgh, Pennsylvania 15213. Mathematical Sciences, North Dakota State University, Fargo, North Dakota 58105, by February 15, 1982, or Faculty Positions- All Levels thereafter until filled. EOE/AA Computer Science Department UNIVERSITY OF LOWELL COMPUTER SCIENCE-Assistant Professor level, tenure­ Applications are encouraged for several tenure-track po­ track appointment to begin August 1982. Joint appointment sitions at assistant, associate and full professor ranks. Inno­ with Department of Mathematical Sciences in the School of vative candidates in all areas of Computer Science will be Arts and Sciences and Division of Technical Studies in the considered. Preference will be given to those with interests School of General Studies and Professional Education. Teach variety of computer science and related courses in degree in DBMS, Software Engineering, Office Automation or programs in Computer Science-Mathematics and Computer Distributed Processing. Science-Information Science. Ph.D. required in Computer University of Lowell is a Massachusetts state university, Science, Mathematics, Statistics, or related field. Some in­ located in the center of the world's minicomputer activity dustrial experience desirable. Competitive salary and fringe and the 128/495 high technology belt. We are within 15 benefits. Send letter of application, curriculum vitae, and miles of the corporate headquarters and R&D development references by March 31, 1982, to Computer Science Search centers for DG, DEC, WANG LABS, PRIME, COMPUTER­ VISION, APOLLO, ANALOG DEVICES, CULLINANE, Committee, School of General Studies and Professional Education, SUNY-Binghamton, Binghamton, New York LEXIDATA, •.. ; the Boston academic centers are within easy commuting distances. Faculty cooperative and ex­ 13901. An equal opportunity /affirmative action employer. change programs are being negotiated with a number of firms. Lowell is convenient to Boston and to all the cul­ SKIDMORE COLLEGE-Faculty member, Department of tural and recreational areas for which New England is Mathematics, beginning September 1982. Tenure-track. To famous. Our undergraduate program is projected to double teach courses including the following topics: computer or­ (to 800 students) by FALL 1983. M.S. and Ph.D. pro­ ganization and assembly language, data structures, formal grams are under consideration and their development is sup­ ported by the high-technology community. language theory, and compiler design. We especially invite Applicants should hold Ph.D. or equivalent in Computer applications from candidates interested in the development Science or a related discipline. ABO candidates with strong of a computer science curriculum in a liberal arts setting. experience will be considered for junior level appointments. Candidates should have a Ph.D. in computer science, or an Please send current vita and recommendations to: M.A. in computer science with work toward a Ph.D., or a Ph. D. in mathematics with extensive computer experience. Dr. Thomas Costello Rank and salary according to the qualifications of the can­ Chairman Computer Science Department didate. Applications with CV and three letters of recom­ University of Lowell, Lowell, MA 01854 mendation by March 1 to Richard Speers, Chairman, 617-452-5000, ext. 2389 Department of Mathematics, Skidmore College, Saratoga The University of Lowell is an Equal Opportunity/ Springs, NY 12866. AA/EOE. Affirmative Action Title IX 504 Employer.

219 POSITIONS AVAILABLE AMERICAN MATHEMATICAL SOCIETY The Translations Department at AMS headquarters has an AUSTIN PEAY STATE UNIVERSITY, DEPARTMENT OF opening for an analyst with a reading knowledge of Russian. MATHEMATICS AND COMPUTER SCIENCE, CLARKS· Specialization in differential equations and related func· VILLE, TENNESSEE 37040. Possibly three tenure-track tional analysis would be particularly desirable. The work positions for fall of 1982 at Assistant or Associate Professor involves translating and editing Russian publications at the level in areas of computer science, statistics or applied current research level. Qualified applicants should respond mathematics, and mathematics education. Ph.D. or Ed.D. with details of background, addressed to the American preferred with strong interest in undergraduate teaching. Mathematical Society, Translations Department, P. 0. Box Application deadline March 15, or until the positions are 6248, Providence, Rl 02940. The Society is an equal oppor· filled. Send resume, transcripts and three letters of reference tunity employer. The building is accessible to handicapped to Professor William G. Stokes, Chairman. APSU is an persons. Affirmative Action/Equal Opportunity Employer.

CHAIRPERSON, DEPARTMENT OF MATHEMATICS AND TEMPLE UNIVERSITY COMPUTER SCIENCE, Tennessee Technological University. The Department of Mathematics expects to have the follow· Effective 1 September 1982. ing positions available beginning September 1982. Minimum qualifications: Ph.D. in Mathematics; 6 years col· {1) Lawton Lectureships-candidates should have Ph.D., legiate teaching in mathematical sciences; established research strong research interests and a commitment to excellence in ability. Administrative experience preferred. Request appli­ teaching. Salary is competitive and based upon background cation and detailed job description from D. C. Ramsey, and experience, Preference will be shown to those whose Chairman, Search Committee, P. 0. Box 5054, Tennessee research interests are compatible with those of present fac· Technological University, Cookeville, TN 38501. Closing ulty. Teaching load is five courses per year. Appointment is date for receiving applications is 1 March 1982. for one year with possible renewal for second year. {2) Tenure-track Assistant or Associate Professorships­ An AA/EEO Employer. candidates must have strong research interest and a com· mitment to excellence in teaching. Salary is competitive and COLLEGE OF USF NEW based upon background and experience. Preference will be ASSISTANT PROFESSOR: Tenure-track position in a shown to those in applied fields but all strong candidates small, highly selective liberal arts college with a strong com· will be considered. mitment to student independent study and research and Applications including a resume and three letters of close student-faculty interaction. recommendation should be sent to Qualifications: A Ph.D. in mathematics or applied mathe· Leon Steinberg, Chairman matics, an excellent potential for teaching and scholarship Department of Mathematics 038· 16 broadly defined. Temple University The salary will be competitive. Philadelphia, PA 19122 Applications should include a statement of teaching philoso­ Temple University is an Affirmative Action/Equal Oppor­ phy, resume, and three letters of reference; send to Profes· tunity Employer. sor Soo Bong Chae, Division of Natural Sciences, New College of USF, Sarasota, FL 33580. EO/AA employer. EAST CAROLINA UNIVERSITY CHAIRPERSON DEPARTMENT OF MATHEMATICS The Office of Vice-President for Research and Graduate Studies of the UNIVERSITY OF PANAMA has an opening The Search Committee will continue to receive and review beginning May 3, 1982 in a multi-national M.Sc. Program in applications for the position of Chairperson of the Depart· Mathematics for a qualified applicant in Applied Mathematics ment of Mathematics through April 2, 1982. Applicants (with strong background and experience in numerical meth· should submit dossier with three letters of reference. Can· ods, optimization on Operations Research) and Mathematical didates must have Ph.D. in mathematics/mathematical sci· Statistics. ences and should furnish evidence of effectiveness in teach· ing, of ability to lead and administer a multifaceted depart· Applicants must hold a Ph.D. in Mathematics and should ment, and of scholarly achievement involving research, ere· be able to communicate in Spanish. Responsibilities include activity, publications, etc. Rank and salary commen­ teaching a graduate course per semester and directing thesis ative research. surate with qualifications. The Mathematics Department has 34 full-time members in mathematics, mathematics educa· Terms of Contract: Initially 1 year, renewable up to a tion, computer science, and statistics, and offers B. A. in maximum of 3 years; salary: US $20,000 to US $24,000 per mathematics, B. A. in computer science, and B.S. in mathe· annum (tax-free) commensurate with qualifications and aca· matics for preparation of teachers, and the master's degree, demic credentials; medical expenses in a Government Social as well as service courses for all university students. Send Security hospital, one month vacation, and round trip air· application to Professor Eugene E. Ryan, Chair, Search fare for spouse from hometown to Panama City, moving ex· Committee, Department of Mathematics, East Carolina Uni· penses of US $800. versity, Greenville, NC 27834; 919·757-6121. An AA/EO Applicants should send their Curriculum Vitae with three Employer. references to the following address: Dr. Abdiel ). Adames Division de Investigaciones y Postgrado Universidad de Panama Estafeta Universitaria Panama, Republica de Panama FOR SALE The Canadian journal of Statistics will be published four times a year, starting with Volume 10 (1982). Publica­ tion will be in March, june, September, and December. Re­ ISTITUTO NAZIONALE search papers intended for publication should be sent to the Dl ALTA MATEMATICA FRANCESCO SEVERI Editor, Professor Sudhish G. Ghurye, Department of Statis­ ROME- ITALY tics and Applied Probability, The University of Alberta, Central Academic Building CAB593, Edmonton, Alberta, Recent publications: Canada T6G 2G1. Free boundary problems All back issues are available (vol. 1-9, 1973-1981, 2 Proceedings of a seminar held in Pavia issues per volume). Orders should be placed with the Man­ September-October 1979 by: S. Albertoni, H. W. Alt, A. aging Editor, Professor George P. H. Styan, Department of Ambrosetti, L. Amerio, I. Athanasopoulos, C. Baiocchi, ). Mathematics, McGill University, Burnside Hall, Room 1238, Bear, M. Biroli, P. Boieri, C. M. Brauner, H. Brezis, M. 805 ouest, rue Sherbrooke, Montreal, Quebec, Canada Bulgarelli, L. A. Caffarelli, ). R. Cannon, A. Capelo, G. H3A 2K6. Capriz, V. Casulli, ). Cea, M. Chipot, G. Cimatti, L. Citrini, The Canadian journal of Statistics is the official journal L. Collatz, V. Comincioli, B. Coppi, P. Cortey-Dumont, of the Statistical Society of Canada and publishes original C. W. Cryer, B. D'Acunto, A. Damlamian, E. De Giorgi, contributions deemed to be informative to the statistical A. S. Demidov, E. Di Benedetto, ). Douglas, G. Duvaut, world and of theoretical, applied or pedagogical interest. A. Fasano, A. Franchi, ). Frehse, A. Friedman, F. Gastaldi, The 1982 subscription rate for libraries and nonmembers is G. Geymonat, G. Gilardi, B. Glowinski, L. Guerri, C. $45; orders should be placed with the Managing Editor. The Guillope, W. Hager, G. D. lanculescu, R. jensen, S. Kamin, 1982 Society membership dues of $25 include a subscription ). L. Lions, P. L. Lions, G. Maier, U. Maione, G. Meyer, to the journal; inquiries concerning membership should be ). C. Miellou, M. Miranda, U. Mosco, B. Nicolaenko, J. A. sent to the Treasurer of the Statistical Society of Canada, Nitsche, ). R. Ockendon, G. A. Pozzi, M. Primicerio, G. Professor Peter D. M. Macdonald, Department of Mathe­ Prouse, ). W. Rogers, L. I. Rubinstein, G. Sacchi, A. Taroni, matical Sciences, McMaster University, 1280 Main Street R. Temam, F. Tomarelli, A. Torelli, B. Turkington, P. West, Hamilton, Ontario, Canada L8S 4K1. Villaggio, A. Visintin. Two volumes: 523 + 606 pages, $70. Learn about computers. Send $7 for our 50-page workbook, the Computer Primer, or write for our free brochure. Orders must be prepaid and should be addressed to: American Reveille Publishing Company, Box 7436, Chicago lstituto Nazionale di Alta Matematica Francesco Severi 60680. P. le Aldo Moro, 5 Citta Universitaria 00185 ROMA, ltalia American Mathematical Society Mathematical Who's Where 1982. Lists, by department and A set of four Colloquium Lectures was presented by alphabetically, 2000 mathematicians at universities in the Dennis Sullivan of the Graduate School and University UK and Eire. Copies of this 64-page booklet are available, Center, City University of New York, at the annual meeting price $2 post free, from I. M. )ames, Mathematical Institute, of the Society in Cincinnati, Ohio in january 1982. Copies 24-29 St. Giles, Oxford. Please make checks payable to of the lecture notes, entitled Geometry, iteration, and group I. M. james. theory (11 pages) are still avail able. Requests for copies should be accompanied by a check MATH SCI PRESS, 53 Jordan Rd., Brookline, MA 02146. or money order for $3.20 per copy to cover the costs of 617-738-0307. Publisher (32 titles) of cross-disciplinary handling, and mailed to the Society at P. 0. Box 1571, work between geometry and Lie groups (history and fron­ Annex Station, Providence, Rhode Island 02901. The notes, tiers), physics and systems. Translations of Klein, Lie, Ricci which were distributed to those who attended the Collo­ and Levi-Civita. Discounts to scholars, students and to quium Lectures in Cincinnati, do not constitute a formal libraries for large or standing orders. publication. Please note that informally distributed manu­ scripts and articles should be treated as personal communi­ Bulletin, Monthly, Math Magazine, Math Teacher, 1957- cations and are not for library use. Reference to the con­ Reasonable. Would donate to library. CHC, Math, S RSC, tents of such an informal publication should have the prior Slippery Rock, PA 16057. 412-794-7307. approval of the author.

THREE PAPERS ON DYNAMICAL SYSTEMS formation on qualitative properties of some long by A. G. Kusnirenko, A. B. Katok, and known problems. V. M. Alekseev The literature on smooth dynamical systems is A. G. Kusnirenko, Problems in the general theory of substantial. In selecting material for their lectures dynamical systems on a manifold the authors have set themselves a twofold aim. On A. B. Katok, Dynamical systems with hyperbolic the one hand they have tended to give a more or less structure connected account of a number of contemporary re- V. M. Alekseev, Quasirandom oscillations and quail- suits associated with general problems of the classifi- tative questions in celestial mechanics cation of dynamical systems, by describing "rough" Volume 116, vi + 169 pages (hard cover) and "typical" properties, etc. On the other hand they List price $32.40, institutional member $24.30, individual member $16.20 wish to emphasize that the general constructions ISBN 0·8218·3066-X; LC 81·4981 arising here are connected with ideas going back to Publication date: May 1981 the classics, and they permit one to obtain new in- To order, please specify TRANS2/116N Prepayment is required for all AMS publications. Order from AMS, P.O. Box 1571, Annex Station, Providence, Rl 02901, or call toll free 800-556-7774 to charge with Visa or MasterCard.

221 The Ohio State University Department of Mathematics

The Department of Mathematics of The Ohio State University hopes to fill the position of full professor created by the DEPARTMENT impending retirement of Professor Hans Zassenhaus effective Autumn Quarter, OF MATHEMATICS 1982. Applications are invited from out­ AND STATISTICS standing research mathematicians. Nomina­ tions for suitable candidates are also wel­ come. Other things being equal, applicants The Department of Mathematics in algebra and number theory will be given and Statistics, The University of Calgary, to budgetary approval, priority. Applications will be accepted until will have, subject several vacancies at the ASSISTANT the position is filled. PROFESSOR level commencing July 1 , Interested persons should write to: 1982. Areas of particular interest will be: Professor Dijen K. Ray-Chaudhuri (1) Statistics: Experimental Design, Sampling, Time Series, Department of Mathematics Biostatistics (one position) The Ohio State University (2) Pure and Applied Modern 231 W. 18th Avenue Analysis: (two positions) (3) Modern and Applied Math­ Columbus, Ohio 43210 ematics: Optimization, Control The Ohio State University is an affirma­ Theory, Numerical Analysis (one tive action and an equal opportunity position) (4) Pure Mathematics: (one employer. position) Duties will include teaching at the undergraduate and graduate levels, «•·<(••<(• ·oC• ·. •> •• ,. ••>• .,. •• ,.. •> •• ,. research and direction of graduate students. Candidates should possess the Ph.D. degree or expect to possess it by the commencement date. Candidates UNIVERSITY OF MARYLAND should present strong evidence of excel­ COLLEGE PARK, MD 20742 lence and continuing activity in their par­ ticular field of mathematical research. DEPARTMENT OF MATHEMATICS Some University level teaching experi­ ence is expected. Successful applicants A chair position has become vacant in must be able to make a significant and lively contribution to the research and Geometry/Topology. We invite the area of academic life of the Department. applicants for a senior position in the gen­ Starting salary will be in the range eral area of GEOMETRY (ranging from of $25,484-$32,596 p.a. (1981 scales). Algebraic Geometry through Differential This represents the lower half of the Geometry to Geometric Analysis). range for Assistant Professor. Citizens and permanent residents of Canada will A successful applicant will be expected be given preference. Applications, in­ to generate activity and interact with cur­ cluding a current curriculum vitae, plus rent faculty in the area. Other duties and 3 letters of reference, should be sent salary are negotiable. All inquiries will be as soon as possible, and no later than February 15th, 1982to: treated confidentially. Application (including Curriculum Vitae) Prof. P.J. Browne, Head or inquiries should be sent to Walter Department of Neumann, Geometry Search Committee. Mathematics and Statistics, Calgary, applications The University of To ensure full consideration, 2500 University Drive N.W., should be received by March 1, 1982. Calgary, Alberta T2N 1N4 The University of Maryland is an Equal Opportunity/Affirmative Action Employer. • 222 Seminaire de Chaire mathematiques Aisenstadt superieures Editor : Anatole Joffe This series, is assigned tor publication of all conferences Editor : Gert Sabidussi given since 1970 at the Centre de recherches mathemati­ This series, presents the notes of the lectures given at the ques of the Universite de Montreal. The generous finan­ Seminaire de mathematiques superieures. This seminar cial aid of Mr. Andre Aisenstadt, doctor in theoretical has been organized each summer since 1962 by the physics of University of Zurich, enables the Centre de Department of Mathematics and Statistics of the Faculty recherches math8matiques to invite famous research of Arts and Sciences of the Universite de Montreal and is scientists and publish their conferences at Les Presses de now under the auspices of the National Research Council I· Universite de Montreal. of Canada and the Ministry of Education of the Govern­ ment of Quebec. These meetings are meants for mathe­ PHYSICAL ASPECTS OF LIE GROUP THEORY maticians and for graduate students in mathematics. Robert Hermann, Universite de Boston 1974, 272 p. (2-7606-0256-7) D 16$ 72. Homological Invariants of Modules Over QUELQUES PROBLEMES MATHEMATIQUES Commutative Rings EN PHYSIQUE ST A TISTIQUE PAUL ROBERTS Mark Kac, Universite Rockefeller, New York.., University of Utah 1974, 88 p. (2-7606-0260-5) u 13$ 1980, 112 p. (2-7606-0499-3) D 13$ LA TRANSFORMATION DE WEYL ET LA 73. Representations of Valued Graphs FONCTION DE WIGNER : UNE FORME VLASTIMIL DLAB ALTERNATIVE DE LA MECANIQUE Universite d'Ottawa QUANTI QUE 1980, 192 p. (2-7606-0503-5) D 14$ Sybren R. De Groot, Institut de physique theorique d 'Amsterdam 74. Groupes abeliens sans torsion 1975, 86 p. (2-7606-0279-6) D 13$ KHALID BENABDALLAH MARIAGES STABLES ET LEURS RELATIONS Universite de Montreal AVEC D'AUTRES PROBLEMES 1981, 184 p. (2-7606-0545-0) D 14$ COMBINATOIRES Donald E. Knuth, Universite de Stanford 75. Lie Groups, Lie Algebras and Representation 1976, 1o8 p. <2-7606-0342-3) 14$ Theory D HANS ZASSENHAUS SUR QUELQUES QUESTIONS D:ANALYSE, University of Ohio DE MECANIQUE ET DE CONTROLE OPTIMAL 1981,288 p. (2-7606-0546-9) D 15$ Jacques Louis Lions, College de France 1976,212 p. (2-7606-0339-3) D 18$ 76. Birational Geometry for Open Varieties SYMETRIES, JAUGES ET VARIETES DE M. SHIGERU IITAKA GROUPES University of Tokyo 1981, 96p. (2-7606-0561-2) D 13$ Yuval Ne'eman, Universite de Tel Aviv 1979, 144p. (2-7606-0441-1) D 14$ 77. Lectures on Hilbert Modular Surfaces LA THEORIE DES SODS-GRADIENTS ET SES FRIEDRICH HIRZEBRUCH APPLICATIONS A L'OPTIMISATION University of Bonn Fonctions convexes et non convexes GERARD VAN DER GEER R. Tyrrell Rockafellar, Universite de Washington, University of Amsterdam Seattle 1981,196p. (2-7606-0562-0) D 15$ 1979, 112 p. (2-7606-0436-5) D 15$

ORDER FORM D Please keep me informed of any new publication in mathematics. 0 Please send me copies of the titles marked above. D Payment enclosed (cheque or money order) plus 10% for shipping cost. Name'------Address'------·------·------Postal Code, ______Agent in U.S.A. :Global Library Marketing Service, Rt. 127, Contoocook, New Hampshire 03229

223 UNIVERSITY OF MARYLAND SWISS FEDERAL INSTITUTE COLLEGE PARK, MD 20742 OF TECHNOLOGY ZURICH PROFESSOR OF APPLIED MATHEMATICS The Swiss Federal Institute of Technology Applications are invited for a research Zurich invites applications for a position of professorship in Applied Mathematics to be assistant professor of mathematics. held jointly in the Department of Mathe­ matics and the Institute for Physical Science Duties of the new professor will include and Technology. Applicants should have an teaching and research in mathematics, outstanding record of research in a field of especially in statistics. It is expected that applied mathematics such as numerical applicants are working on important con­ analysis, fluid mechanics, solid mechanics, tributions in their field. They must be etc., and should be able to interact effec­ willing and competent to provide instruction tively with other faculty members. The at all university levels, some of it for non­ teaching load consists of one graduate mathematicians, and to cooperate with course per semester. The salary is negotia­ colleagues. ble. All inquiries will be treated confiden­ Applications should be submitted with tially. curriculum vitae and list of publications Applications, which should include a before March 31st, 1982, to the President curriculum vitae, should be sent to Profes­ of the Swiss Federal Institute of Tech­ sorS. S. Antman or Professor F. W.J. nology Zurich, Prof. H. Ursprung, CH-8092 Olver; those received by 1 May, 1982 will Zurich, Switzerland. be assured full consideration. The University of Maryland is an Equal Opportunity/Affirmative Action Employer.

ssssssss~ssssssss EXXON FELLOWSHIP in APPLIED MATHEMATICS at NORTHWESTERN UNIVERSITY The DEPARTMENT OF ENGINEERING SCIENCES AND APPLIED MATHEMATICS announces a special fellowship funded by the EXXON EDUCATION FOUNDATION to support graduate study in Applied Mathematics at NORTHWESTERN UNIVERSITY. The Fellowship The Exxon fellowship will support a program of study and research leading to a Ph.D. degree in Applied Mathematics. This three year fellowship provides full tuition and fees and annual stipends of $12,000, $13,500 and $15,000. The Program The Ph.D. program in Applied Mathematics trains students in the formulation and solution of problems in the physical, engineering and life sciences. Programs of study are designed to meet the needs of the individual student. This includes courses in mathematical modelling and methods and in various areas of application. Application for the Fellowship All applicants to the Applied Mathematics program will be considered for the Exxon fellowship. Applicants must indicate their intention to begin graduate study in the fall of 1982. Completed applications should be received at the Graduate School by March 1, 1982. Notification of the award will be made on or about April 1, 1982. For application forms and additional information, write to Professor W. E. Olmstead - Department of Engineering Sciences and Applied Mathematics Northwestern University - Evanston, I L 60201

224 A complete, practical information source and guide to statistical methods, techniques and applications for virtually every professional discipline and business

ENCYCLOPEDIA OF STATISTICAL SCIENCES Edited by Samuel Kotz and Norman L. Johnson

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SELECfA by Szolem MANDELBROJT

By publishing this book, the Comit~ National Fran<;ais des Mathematiciens wanted to pay a tribute to Professor Mandelbrojt, one of the leading ftgures of the Ecole Mathema­ tique Fran<;aise. The works of S. Mandelbrojt, spreading over half a century, include more than 200 books covering all the fields of mathematical analysis. In the present volume, you will find a text written in 1926, with the contribution of J. Hadamard, on Taylor•s series and its developments. This text is followed by lectures which were given in ·Eriglish at the Rice Institute. A! an introduction, these texts will be very useful for those who want to penetrate the fruitful works of S. Mandelbrojt. 640 pages. 15,5 em x 24. Bound. 180 FF

PAUL LEVY'S COMPLETE WORKS

Paul levy, who died in 1971, has left considerable scientific works which cover general analysis and the theory of probabilities. Most of the memoirs published later in his scien­ tific life are devoted to the latter.

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• COMITES UNDllS DIS SUNC!S DE • BULLETIN DES SCIENCES L'ACAD!MtE DIS SCIENCES MATI:ItMATIQUES Series l : Mathematics Createdin 1870byG.DARBOUX \V:eekly.l981 :tomes 294-295 2,200 FF Editorial Board : V J. ARNOLD, H. CABANNES, L. CARLESON, • ANNAUS SCIIN'r!flQUIS DEL'800LE R.. DEHEUVELS, A. OOLD, L. EHR.ENPR.EIS, NORMAL~ S1.1'8RJEUU F. HIR.ZEBR.UCH, P. MALLIA YIN, C. PISOT.(I)i.rector) Cteatedin 1864 by Louis PASTEUR 4 issues per year 1982 : tome 106 S3S FF pursued frem .~ . · 1872 tlt.l.$8i by H. t883to 1888 by R Y · to1900byC. TE • ANNALES DE L'INSTITUI' 1 to 1~17byG.DARBOUX HENRI POINCARE 1Uo 1941 by E. PICAliD . Section B : Probability calculus and statistics 94t·l~7byP.MONTEL. Foundeurs: N~wam: CH. MA UR.AINt. EMILE BOREL ; J. PERRIN, M~.B~G~. L. BOUTET de MONVEL, M. HERMAN, r. LANGE'VIN F. LAUDENBACH, P.A. MEYER, M. R.A YNAUD Chairman of Scientific Board-: 4 issues ~r year 1981 : tome 14 630 FF Louis de BROGLIE Editorial Board : .• JOlJRMAL DEMA'I'H8MATIQUES PUUS 1. NEVEU, J.P. BENZ2CR.I, l. GEFFROY, ET APPUQU8ES P. MALLIA ¥IN Ct;elted in 1.8l6 an published until 1874 by 4 issues per year 1982 : volum 18 341FF laseph LIOUVlLLE fi\trsued from. : 1375 to 1&84 by.Henti J.WiAJ. . • MIMOIRES DE LA SoedTB tal$ to 1921.fW ~.J~liD.A;N 191!2 to 1972 &y Hmd Vl'LLAT MATI:8tATIQUE DE FRANC! Each issue is devoted to a single topic : Bditotial board : . ;Gi~CHQQVET, Y. CHOQVET-BRlJBAT,.P.GJRMAIN, New series no 1 : e. 'GOULA01JI(;, P. LELONG, .J. ~J;AY, U .. LION$, 06fonnations equisinguli&res des germes de COUf· . P~ l4AUJAVl'N, Y. ME'YER besfauches reduites, 4~tl ....)'ta,r 1982.: tome 61 571 FF by . BRIA~ON, A. GAWGO, M. GRANGER 29FF .• '11.JI..LI'ON DE LA~ New series no 2 : •.. MATRIMAnQIJE J)l I'&ANCE Fonctions ab6lieanes et nombres transcendants, of• «Socl1te. Matb.ernttkple de France Joumees Mathematiques, Universit6- S.M.F. - JoUrnal » CN.R.S. -&ole Polytechnique, Mai 1979, · Bditodal Board ;-· · by D. BERTR.AND,M. WALDSCHMIDT 48FF J.M. FONTAINE, L.. ILJ,.US!E; M. METIVIElt, New series no 3 : H. SKODA. M. USMAN (:Dire¢tot) 06nombrement des types de KwHomotopie. ~ 4 issues+ 4memoirs per year 1982 :tome 110 rie de Ia defonnation, by Y. FEUX 21 FP . . . 54tPP New series no 4 : Dualit6 sur un corps local a corps residuel aW­ briquement clos, by L. BEGUERI 49 PF Se:nd yottr order to : .. New series no 5 : C.DA -Ceatra1edetRale$B.P.ao 119 Signature Modulo 16, invariants de Kervaire ge., . tltt4110NTUULCSDIX -PitANCI neralis6s et nombres caract6ristiques dans la K­ . . .. . tlleorie reeUe, by S. OCHANINE 75 FF CLEMSON UNIVERSITY DEPARTMENT OF MATHEMATICAL SCIENCES The Clemson University Department of Mathe­ WAYNE STATE UNIVERSITY matical Sciences anticipates two or more positions DETROIT, MICHIGAN available beginning Fall Semester, 1982. One posi­ tion would be at the PROFESSOR/ASSOCIATE DEPARTMENT OF MATHEMATICS PROFESSOR level and another at the ASSOCIATE PROFESSOR/ASSISTANT PROFESSOR level. Applicants should have a Ph.D. Degree in algebra/ Applications are invited for the position of combinatorics, analysis, computational mathemat­ ics, operations research or statistics. It is desirable Chair of the Department of Mathematics, that applicants have research interests in the appli­ effective Fall, 1982. Candidates for the cation of the mathematical sciences to the solution should have an established record of real world problems. The positions would be position 9-month, tenured or tenure-track positions. Salaries of excellence in research, commitment to would be commensurate with rank and experience. teaching, and the capability for leadership The Department of Mathematical Sciences at Clemson embraces algebra/combinatorics, analysis, and administration. Applicants should computational mathematics, operations research and forward a resume together with the names statistics and integrates these mathematical sciences of four references to: into its B.A., B.S., M.S., and Ph.D. programs. Appli­ cations will be accepted until any approved posi­ Dean Martin T. Wechsler, Secretary tions are filled. Mathematics Chairperson Search Committee Vitae (with names and telephone numbers of three references), nominations, and requests for fur­ 554 Mackenzie Hall ther information should be sent to: Wayne State University PROFESSOR JOHN D. FULTON, Head Detroit, Michigan 48202 Department of Mathematical Sciences 0-103 Martin Hall An equal opportunity/affirmative action Clemson, South Carolina 29631 employer. Phone: (803) 656-3434 CLEMSON UNIVERSITY IS AN AFFIRMATIVE ACTION/EQUAL OPPORTUNITY EMPLOYER.

MATHEMATICAL SCIENCES 1982 administrative directory

PROFESSIONAL MATHEMATICAL ASSOCIATIONS ACADEMIC INSTITUTIONS-DEPARTMENTS IN THE MATHEMATICAL SCIENCES AND OTHER FACILITIES in the U.S., Canada, Central America, and the Caribbean, coded according to the highest degree offered MATHEMATICAL UNITS IN NONACADEMIC ORGANIZATIONS HEADS AND KEY PERSONNEL of a selected group of government agencies EDITORS OF JOURNALS in the mathematical sciences OFFICERS AND COMMITTEE MEMBERS in more than 25 professional mathematical organizations AN INDEX OF ACADEMIC INSTITUTIONS $12.60 Publication date: February 15,1982 Code: ADMDIR82 - Prepayment Required american mathematical society p. o. box 1571, annex station, providence, r. i. 02901

228 NEW PUBLICATIONS FROM L'ENSEIGNEMENT MATHEMA TIQUE GENEVA EM

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THEORIE ERGODIQUE- Proceedings of a Seminar Lectures by P. Arnoux, P.-L. Aubert, P. de laHarpe and K. Jhabvala, M. Misiurewicz, C. Series, B. Weiss. 112 pages, 1981; 34 Swiss Francs. Provides an introduction to a few chapters of ergodic theory in connection with interval exchange transformations, SL2 (Z) and Fuchsian groups, geometry of the plane, variational principle, con­ tinued fractions and orbit equivalence.

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229 Mathematical Reviews Sections

ENJOY THE CONVENIENCE OF HAVING MATHEMATICAL REVIEWS AT YOUR DESK. HAVE YOU THOUGHT HOW REALLY HANDY IT WOULD BE TO HAVE THE SECTIONS RELEVANT TO YOUR RESEARCH RIGHT BEFORE YOUJ MR has been divided into 37 affordable Sets for individual subscribers. Each month you can receive the Section Sets you have chosen with an author index. With your june sets you will receive a semiannual author index (just as you would forM R) and in December an annual author and subject index (as with MR). Also available for 1982 Section subscribers are three-ring binders of sturdy quality in the familiar tangerine color of MR to hold your subscription. The binders have a two-inch spine and are adequate to hold 400 pages. Section Sets are divided into Class 1 and Class 2 according to the estimated number of pages per year. Set Sections Subjects 021 42,43, 44,45 Harmonic analysis, integral OlA 00,01 General, history, biography transforms/equations (Class 2) (Class 1) 0 1) 46 Functional analysis (Class 1) 0 lB 03,04 L'(;ic, foundations, set theory 0 lK 47 Operator theory (Class 1) Class 1) 02) 49 Calculus of variations, optimiz- 0 lC 05 Combinatorics (Class 1) ation (Class 2) 02A 06,08 Order, lattices, general systems 02K 51, 52 Geometry, convex sets (Class 2) (Class 2) 0 ll 53 Differential geometry (Class 1) 010 10 Number theory (Class 1) 0 2L 54 General topology (Class 2) 02B 12 Algebraic number theory, field 55,57 See 1 E (18, 55, 57) theory, polynomials (Class 2) OlM 58 Global analysis, analysis on 02C 13,14 Commutative rings and algebras, manifolds (Class 1) algebraic geometry (Class 2) 0 lN 60 Probability theory and stochas- 020 15 Linear and multilinear algebra, tic processes (Class 1 ) matrix theory (Class 2) 0 lP 62 Statistics (Class 1) 02E 16, 17 Associativefnonassociative 0 lQ 65 Numerical analysis (Class 1) rings, algebras (Class 2) 0 lR 68 Computer science (including 0 lE 18, 55, 57 Category theory, algebraic automata) (Class 1) topology, manifolds (Class 1) 02M 70,73 Mechanics of particles, systems, 0 lF 20 Group theory, generalizations (Class 2) (Class 1) 02N 76, 78,80 Fluid mechanics, optics, elec- 02F 22 Topological groups, Lie groups tromagnetics, thermodynam- (Class 2) ics (Class 2) 02G 26,28 Real functions, measure, inte- 0 lS 81 Quantum mechanics (Class 1) gration (Class 2) 02P 82, 83, 85, 86 Other physics, astronomy, astro- DlG 30, 31, 32, 33 Complex analysis, potential physics, geophysics (Class 2) theory, special functions on 90 Economics, operations re- (Class 1) search, programming, games OlH 34 Ordinary differential equations (Class 1) (Class 1) 02Q 92 Biology and behavioral sci- 011 35 Partial differential equations ences (Class 2) (Class 1) 0 lU 93 Systems theory; control (Class 1) 02H 39, 40,41 Finite differences, sequences, DlV 94 Information and communica- approximations (Class 2) tion, circuits (Class 1)

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231 REVIEWS IN RING THEORY Compiled and Edited by Lance W. Small Department of Mathematics, University of California, San Diego

These volumes collect 5,396 reviews from Mathematical Reviews of papers in noncommutative ring theory. All reviews of papers in ring theory from Volume 21 (1960) through Volume 58 (1979) appear here. Additionally, the editor has collected those papers from Volume 1 through Volume 20 which are necessary background. Papers on group rings, homological questions, and enveloping algebras with ring theoretic interest are also included. Each review has an "appearance number" specifying the location of the review by chapter, section and number within the section. By and large, reviews within one section are arranged in "rough" chronolog­ ical order (i.e., by appearance in Mathematical Reviews). The principal exceptions are papers in a series and very closely related papers. If a cited review occurs in these volumes, then its appearance number is listed after the review in which it is cited. Cross-references are given at the beginning of some sections and chapters to inform the reader of closely related reviews appearing elsewhere. These cross-references may also be useful to the reader as a guide to finding reviews which do not appear where the reader thinks they should. These volumes are a research tool. There are no other books containing the information herein except Mathematical Reviews itself. The editor's previous work includes over 40 papers in ring theory. He has been a reviewer for Mathe­ matical Reviews since 1968. The work is divided into 31 chapters each subdivided into 3 to 21 sections. Chapter headings are:

1. Primitive, prime and semi-prime rings 16. Injective modules, self-injective rings and generalizations 2. Theory of radicals 17. Von Neumann regular rings and their generalizations 3. Nil, nilpotent and radical rings 18. Artin rings 4. Simple and semi-simple Artin rings 19. Quasi-Frobenius (QF) rings and their generalizations 5. Division rings 20. Perfect, semi-perfect rings and modules and their general- 6. Matrices over commutative rings and fields and linear izations algebra (ring theoretic) 21. Integral domains 7. Classical orders, integral representation theory, arith­ 22. Goldie's theorem, rings of quotients matic in algebras 23. Noetherian rings 8. Separable algebras, Azumaya algebras and their generaliz­ 24. Group rings zations 25. Homological and categorical methods in ring theory 9. Galois theory 26. Torsion theories 10. Hopfalgebras-algebraic theory 27. Automorphisms, endomorphism& and derivations on rings 11. Rings satisfying a polynomial identity 28. Commutativity theorems. Generalizations of commutative 12. Rings with involution rings 13. Lie and Jordan structures on rings 29. Topological rings and modules. Ordered rings 14. Module theory (general) 30. Other rings and algebras. Miscellaneous topics and results 15. Projective modules, flat modules and their generalizations 31. Books, conference proceedings and surveys Published in 2 volumes, xii + 1,114 pages (soft cover). List price $160.00, institutional member $120.00, individual member $40.00, student $20.00. ISBN o-82111-0215-1; LC 81-10770. Publication date: August 1981. To order, please specify REVRING. Prepayment is required.

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232 Finite Algebra and Multiple-Valued Logic

edited by B. CSAKANY, and I. ROSENBERG, I. Chajda, K. N. Cimev, D. Clark, Y. Coufalova, B. Csakany, G. Czedli, A. F. Danii'Cenko, COLLOQUIA MATHEMATICA SOCIETATIS J. Dassow, J. Demetrovics, T. Evans, F. Ferenci, JANOS BOLYAI, Vol. 28 T. Gavalcova, F. Gecseg, K. Glazek, P. GorallJfk, V. A. Gorbunov, L. Hannak, J. Henno, T. Hikita, 1981. 880 pages. Price: US $135.00/Df/. 290.00 T. Kepka, R. A. Knoebel, V. Koubek, D. Lau, ISBN 0-444-85439-8 H. Machida, S. S. MarlJenkov, M. Miyakawa, This volume contains 41 papers, mainly detailed I. Nemeti, A. Nozaki, P. 0. Palfy, V. Pinkava, versions of lectures delivered at the Colloquium A. P. Pixley, L. Polak, R. Poschel, L. R6nyai, on Finite Algebra and Multiple-Valued Logic R. W. Quackenbush, I. G. Rosenberg, J. Rosicky, held in Szeged, Hungary, in August 1979. D. M. Smirnov, J. D. H. Smith, I. Strazdins, L. SzabO, A. Szendrei, D. Uhlig, E. Varmonostory, CONTRIBUTORS: H. Andreka, R. A. BaTramov, H.-J. Vogel, H. Werner, P. ZlatoS.

Studies on Graphs and Discrete Programming

edited by P. HANSEN R. Chandrasekaran; Y. P. Aneja and K. P. K. Nair; NORTH-HOLLAND MATHEMATICS STUDIES, N. Christofides and M. Gerrard; K. Darby­ Vol. 59 Dowman and G. Mitra; M. A. Frumkin; T. Gontijo Annals of Discrete Mathematics (11), Rocha et a/.; P. L. Hammer, T. lbaraki and Editor: Peter L. Hammer U. N. Peled; P. Hansen, D. Peeters and J.-F. Thisse; F. S. Hillier and N. E. Jacqmin; 1981 viii + 396 pages Price: US $83.00/Dfl. 195.00 A. Hilton; W. L. Hsu; M. S. Hung, A. D. Warren ISBN D-444-86216-1 and W. D. Rom; T. lbaraki, [. Kameda and This volume contains the proceedings of the S. Toida; T. lbaraki and U. N. Peled; M. Minoux; Workshop on Applications of Graph Theory to G. L. Nemhauser and L. A. Wolsey; Management, held at the European Institute for A. H. G. Rinnooy Kan and J. Telgem; P. Serra Advanced Studies in Management in Brussels, and A. Weintraub; G. L. Thompson; I. Tomescu; March 20- 21, 1979. J. Tomlin B. Villareal and M. Karwan; CONTENTS: Foreword. Papers by: E. Balas; D. De Werra. C. Berge; R. E. Burkard and U. Derigs;

stochastic control by Functional Analysis Methods by ALAIN BENSOUSSAN Chapter IV outlines the theory of Stochastic STUDIES IN MATHEMATICS AND ITS Control with complete information (when the APPLICATIONS, Volume 11 control only affects the drift term). Chapter V presents the theory of filtering and prediction 1982 xvi + 410 pages Price: US $58.25/Dfl. 125.00 for linear stochastic differential equations, ISBN 0-444-86329-X which leads to the Kalman filter. Chapter VI This book is an advanced text on stochastic deals with the variational approach to control. It is self-contained and presents most stochastic control, in two situations, one with of the results on stochastic control, relying on complete observation and one with incomplete functional analysis methods and the theory of observations. Chapter VII is devoted to optimal partial differential equations. stopping problems which are solved by the Chapter I presents the elements of Stochastic theory of variational inequalities. The final Calculus and Stochastic Differential Equations, chapter covers the theory of impulsive control Chapter II presents the theory of partial and its solution by the method of quasi differential equations and Chapter Ill discusses variational inequalities - thus the last five the Martingale problem - thus the first three chapters deals with the theory of stochastic chapters are devoted to background. control.

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STURMIAN THEORY FOR ORDINARY DIFFERENTIAL EQUATIONS William T. Reid 1981 /559 pp./ paper $28.50 GAUSS Applied Mathematical Sciences, Volume 31 A Biographical Study ISBN 0-387-90542-1 W.K. Buhler 1981 /208 pp./9 illus./ cloth $16.80 NUMERICAL SOLUTIONS OF PARTIAL ISBN 0-387-10662-0 DIFFERENTIAL EQUATIONS Theodor Meis and Ulrich Marcowitz MATHEMATICS TOMORROW 1981 /541 pp./ paper $24.00 Lynn Arthur Steen Applied Mathematical Sciences, Volume 32 1981 /250 pp./12 illus./ cloth $18.00 ISBN 0-387-90550-2 ISBN 0-387-90564-2

REGULAR STRUCTURES MARSTON MORSE Lectures in Pattern Theory, Volume 3 Selected Papers Ulfe Grenander Edited by Raoul Bott 1981 /569 pp./ paper $24.00 1981 /882 pp./22 illus. I cloth $36.00 Applied Mathematical Sciences, Volume 33 ISBN 0-387-905324 ISBN 0-387-90560-X QUANTUM PHYSICS PERTURBATION METHODS IN A Functional Integral Point of View APPLIED MATHEMATICS James Glimm and Arthur Jaffe J. Kevorkian and J.D. Cole 1981 /417 pp./43 illus. 1981 /558 pp./79 illus./ cloth $42.00 paper $16.80; cloth $28.00 Volume 34 Applied Mathematical Sciences, ISBN 0-387-90562-0 (paper) 0-387-90551.0 ISBN 0-387-90507-3 THE NON-EUCLIDEAN HYPERBOLIC APPLICATIONS OF CENTRE PLANE MAN I FOLD THEORY and Consistency Jack Carr Its Structure Paul Kelly and Gordon Mathews 1981 /142 pp./ paper $14.00 1981 /333 pp./201 illus./ paper $24.00 ~ Applied Mathematical Sciences, Volume 35 LU Q ISBN 0-387-90552-9 0 ISBN 0-387-905774 N "O:t 0'1 0'1 8 N Prices subject to change without notice. a:- VI Q BASIC THEORY OF ALGEBRAIC N -I GROUPS AND LIE ALGEBRAS § < ct: Order Your Copies Today, Write: u Qj~ Gerhard P. Hochschild z i= \.I 1981 /267 pp./ cloth $32.00 VI c: Springer-Verlag New York Inc. VI < a.• Graduate Texts in Mathematics :::E :!~ Dept. S5150 LU ,. ISBN 0-387-90541-3 - 0 P. 0. Box 2485 VI ::I: ... Secaucus, New Jersey 07094 r :::E 1- Q.. APPLIED FUNCTIONAL ANALYSIS < < oci (" 1981 /313 pp./ cloth $34.00 u Q Applications of Mathematics