sign in sign up
<<
Home , Alexander Lubotzky, Andrew Majda, ArviZ, David Masser, Generalized conic, Heini Halberstam

Anaheim Meetings Oanuary 9 -13) - Page 15

Notices of the American Mathematical Society

January 1985, Issue 239 Volume 32, Number 1, Pages 1-144 Providence, Rhode Island USA ISSN 0002-9920 Calendar of AMS Meetings

THIS CALENDAR lists all meetings which have been approved by the Council prior to the date this issue of the Notices was sent to the press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the American Mathematical Society. The meeting dates which fall rather far in the future are subject to change; this is particularly true of meetings to which no numbers have yet been assigned. Programs of the meetings will appear in the issues indicated below. First and supplementary announcements of the meetings will have appeared in earlier issues. ABSTRACTS OF PAPERS presented at a meeting of the Society are published in the journal Abstracts of papers presented to the American Mathematical Society in the issue corresponding to that of the Notices which contains the program of the meeting. Abstracts should be submitted on special forms which are available in many departments of and from the office of the Society. Abstracts must be accompanied by the Sl5 processing charge. Abstracts of papers to be presented at the meeting must be received at the headquarters of the Society in Providence. Rhode Island. on or before the deadline given below for the meeting. Note that the deadline for abstracts for consideration for presentation at special sessions is usually three weeks earlier than that specified below. For additional information consult the meeting announcements and the list of organizers of special sessions. MEETING# DATE PLACE ABSTRACT DEADLINE ISSUE 816 January 9-13, 1985 Anaheim, EXPIRED january (91 st Annual Meeting) 817 March 22-23, 1985 Chicago, Illinois january 23 March 818 April 12-13, 1985 Tucson, Arizona january 25 March 819 April 20-21, 1985 Worcester, Massachusetts january 28 March 820 May 3-4, 1985 Mobile, Alabama january 30 March 821 August 12-15, 1985 Laramie, Wyoming (89th Summer Meeting) October 26-27, 1985 Amherst, Massachusetts November 1-2, 1985 Columbia, Missouri january 7-11, 1986 New Orleans, Louisiana (92nd Annual Meeting) january 21-25, 1987 San Antonio, Texas (93rd Annual Meeting) january 6-11, 1988 Atlanta, Georgia (94th Annual Meeting) August 8-12, 1988 Providence, Rhode Island (AMS Centennial Celebration)

DEADLINES: Advertising (March 1985 Issue) February 7, 1985 (June 1985 Issue) April 24, 1985 News/Special Meetings (March 1985 Issue) january 25, 1985 (June 1985 Issue) April 8, 1985 Other Events Sponsored by the Society

May 1985, Symposium on Some Mathematical Questions in Biology, Plant Biology, Los Angeles, California. june 23-August 31, 1985, Joint Summer Research Conferences in the Mathematical Sciences, Humboldt State University, Arcata, California. June 30-july 13, 1985, AMS-SIAM Summer Seminar on Reacting Flows: Combustion and Chemical Re­ actors, , Ithaca, . July 8-26, 1985, AMS Summer Research Institute on Algebraic , Bowdoin College, Brunswick, Maine.

Suscribers' changes of address should be reported well in advance to avoid disruption of service: address labels are prepared four to six weeks in advance of the date of mailing. Requests for a change of address should a/ways include the member or subscriber code and preferably a copy of the entire mailing label. Members are reminded that U. S. Postal Service change-of-address forms are not adequate for this purpose. since they make no provision for several important items of information which are essential for the AMS records. Sutitable forms are published from time to time in the Notices (e.g. October 1984. page 728). Send change of address notices to the Soceity at Post Office Box 6248. Providence, Rl 02940. (Notices is published seven times a year (January, March. June. August. October. November. December) by the American Mathematical Society at 201 Charles Street. providence. Rl 02904. Second class postage paid at Providence. Rl and additional mailing offices. POSTMASTER: Send address change notices to Membership and Sales Department. American Mathematical Scoeity. P. 0. Box 6248. Providence. Rl 02940.) Publication here of the Society's street address. and the other information in brackets above. is a technical requirement of the U. S. Postal Service. All correspondence should be mailed to the Post Office Box. NOT the street address. Members are strongly urged to notify the Society themselves of address changes. since reliance on the postal service change-of-address forms is liable to cause delays in processing such requests in the AMS office. Notices of the American Mathematical Society

EDITORIAL COMMITTEE Volume 32, Number 1, January 1985 Paul F. Baum, Ralph P. Boas Raymond L. johnson, Mary Ellen Rudin Betram Walsh, Daniel Zelinsky Everett Pitcher (Chairman) MANAGING EDITOR Lincoln K. Durst ASSOCIATE EDITORS Hans Samelson, Queries Ronald L. Graham, Special Articles SUBSCRIPTION INFORMATION Subscription prices for Volume 32 (1985) are $65 list; $52 institutional member; 2 The Bierbach Conjecture: Retrospective $39 individual member. (The subscription Carl H. Fitzgerald price for members is included in the 7 News and Announcements annual dues.) A late charge of 10% of the subscription price will be imposed upon 9 Queries orders received from nonmembers after January 1 of the subscription year. Sub­ 11 NSF News & Reports scribers outside the and 13 News From Washington India must pay a postage surcharge of $5; subscribers in India must pay a 15 Future Meetings of the Society postage surcharge of $15. Subscrip- Anaheim, january 9-73, 15 tions and orders for AMS publications Chicago, March 22-23, 70 should be addressed to the American Mathematical Society, P.O. Box 1571, Tucson, April12-13, 73 Annex Station, Providence, Rl 02901. Worcester, April 20-21, 76 All orders must be prepaid. Mobile, May 3-4, 78 ADVERTISING & INQUIRIES The Notices publishes situations Symposium on Mathematical Biology, Los wanted and classified advertising, Angeles, May, 81 and display advertising for publishers 1985 AMS-SIAM Summer Seminar, 82 and academic or scientific organiza­ tions. Requests for information: 1985 Summer Research Institute, 83 Advertising: Wahlene Siconio Invited Speakers and Special Sessions, 86 Change of address or subscriptions: 87 Joint Summer Research Conference Series Eileen Linnane Book Order number 800-556-7774. 88 Special Meetings 94 New AMS Publications CORRESPONDENCE, including changes of address should be sent to American 97 Miscellaneous Mathematical Society, P.O. Box 6248, Personal Items, 97; Deaths, 97; Providence, Rl 02940. Visiting (Supplement), 97 Second class postage paid at 98 AMS Reports and Communications Providence, Rl, and additional mailing offices. Copyright © 1984 by the Recent Appointments, 98; American Mathematical Society. Reports of Past Meetings: 1984 Symposium Printed in the United States of America. on Mathematical Biology, 99; 1984 AMS­ The paper used in this journal is acid-free SIAM Summer Seminar, 100 and falls within the guidelines established to ensure permanence and durability. 101 Advertisements The Bieberbach Conjecture: Retrospective by Carl H. FitzGerald

For me, 1984 will recall the exciting word that [11, 24], [29], Scientific the Bieberbach conjecture was solved. There had American [37] and the student been rumors, then in late spring I received a 385 newspaper [40]. Suddenly Louis de Branges was page typed manuscript [9] of Louis de Branges of famous among mathematicians and known to all Purdue University purporting to give a proof. people with an interest in mathematics. There I was not hoping for the proof to be correct. was agreement that his illustrious solution was Two of my best papers [15, 16] showed the correct. Bieberbach conjecture was at least close to being With acceptance came many questions. How true. One showed the conjectured upper bounds was this proof missed all these years? Should on the magnitudes of coefficients of one-to-one Loewner have solved the problem fifty years ago? analytic functions were at most a few percent Is this mathematical progress? What of the off. The other showed the conjectured extremal scores of papers made obsolete by de Branges's function was at least approximately the extremal results? Were those papers the contributions function for late coefficients. I did not want these they were thought to be? Is progress made results superseded. by an accumulation of small insights or by an Aside from personal feelings, there were objec­ independent breakthrough? Were the methods tive reasons I was reluctant to take the manuscript developed in the efforts to solve the Bieberbach seriously. There were errors; and de Branges had conjecture important? made critical errors in previous work. Further­ The history of the Bieberbach conjecture makes more, many mathematicians have momentarily an interesting case study. Since there is an thought they had solved this particular problem. immense literature [4] and several surveys [3, 12, ("The Bieberbach conjecture is not difficult; I have 13, 18, 19, 38] only a sample of the highlights proved it dozens of times.") Then in mid-summer will be mentioned. The selection will be made I received a 13 page handwritten draft of a paper to present the path to de Branges's proof most in Russian on de Branges's proof the Bieberbach clearly. conjecture (cf. [7, 8]). The preprint was the We start with a comparatively elementary result of the geometric function theory seminar in theory. In the first decade of this century, the Leningrad which included G. V. Kuz'mina, E. G. coefficients of positive real part functions were Emel'anov and I. M. Milin. Louis de Branges had studied [39]. In particular the following bounds been visiting there and giving lectures. were found on the coefficients of the power series There was great excitement. Was the proof expansions. Let P(z) be analytic on the unit disk correct? (It is difficult to think about mathematics [) = {z: \z\ < 1}, satisfy ReP(z) > 0 on[), and be carefully when one's adrenalin level is high.) Ch. normalized so that P(O) = 1. Then the coefficients Pommerenke (from the Technische Universitat, of the power series expansion at the origin have ) and I were checking references, making magnitude less than or equal two. These bounds telephone calls, checking calculations, and study­ are attained by the functions ing approximations. We were not convinced (or (1 + eiz)/(1- ei4>z) = 1 + 2ei4>z + 2ei 24>z2 + .... did not want to believe). We wanted a more transparent argument. When a minor change The parallel study of univalent functions started made the proof more computational, we believed. with Koebe [23] in 1907. By proving a distortion de Branges's proof was short! It was correct! theorem, he, in effect, showed the following class Louis de Branges had accomplished the legendary of functions is compact. LetS denote{!: f(z) = feat that had defied eminent complex analysts of z+a2a2 +a3 z 3 +··· is one-to-one and analytic on this century. [)}. Thus, for every positive integer n, there is a We sent out an informal communication in July uniform bound on the magnitude of the coefficient to many people. In August we sent out a revised of zn for all f in S. communication with typographical corrections The first explicit statement of a putative sharp and some analysis of the proof. Between bound was made in 1916 by Ludwig Bieberbach the Russian preprint and Pommerenke's and [5] in a footnote to an article in which he showed my communications, the word was out that de \a2 \ ~ 2. The Bieberbach conjecture was that Branges had solved this 68 year old conjecture. \an!~ n for all finS and positive integers n. The Even the news media were interested: Science bound is attained only by rotations of the Koebe

2 function the last part. The Riemann map of D onto the complement of the retracted slit will have a series Kq,(z) = z/(1-ei ft and the Riemann map by ft(z). Note that, for takes J) onto the complex plane with a radial each t:;::.: 0, the arc ft and the function ft(z) are straight line from -ieid> to infinity deleted. uniquely defined. (Some people have argued against using Beiber­ For t > t1 ::::: 0 let '1/J(z, t, t1) = ft:1 o ftt (z). bach's name as a label [19] either because the Clearly, '1/J(·, t, t1) is a flow of the unit disk into conjecture was in the air already, or because he itself and '1/J(z, t1. t1) = z. By Schwarz's lemma the expressed objectionable racial and ethnic views flow takes every point z closer to the origin. [21]. Such arguments have had little effect.) If we grant that a'lj; I at exists and is analytic, At the same time [1] as Bieberbach's paper, then (at t = t1)a'lj;jat = -zP(z,t1), where the study of special classes [19] had started. Let Re P(z, t1) > 0 and P(O, tl) = 1. Since '1/J(·, t, t1) has range the unit disk with a slit coming in s* be {f : f belongs to s and has range that at one point, P(z, tl) [1 ~(ti)z]/[1- ~(t!)z], is starlike with respect to the origin}. If f is = + where J~(h)\ = 1. in then '1/J(z, t) 1[e-t f(z)] is a steady s*' = f- From the definition of '1/J, we have fto'lj;(z, t, t!) = flow for 0 and 0) Since Schwarz's t ::::: '1/J(z, = z. ft, (z). This equation can be differentiated with lemma implies each point z is moved towards the respect to t at t = tl to obtain aft/ at (aft! at) . origin, it is clear that 0) has + -1}i(z, = f(z)/ f'(z) (a¢/ at)= Hence, argument within 7r/2 of arg z. It follows that o. Re{zf'(z)/ f(z)} > 0. Conversely, supppose the oft! at= {[1 + ~(tt)z]/[1- ~(t1)z]}z(oft! az). real part condition holds. Note, for each z0 in D, that zof'(zo) is in the direction of the outer The usual notation is f = f(z, t) = ft(z). Then Loewner's differential equation is normal of the image of {z: Jz\ < Jz0 \} under f. It follows easily that if f(z) = z + ·· · and satisifies of 1 + ~(t)z of (1) -= z- the real part condition, it is in s*. This positive ot 1- ~(t)z az' real part characterization of starlike functions was used with the coefficient bounds on positive real where ~ is a continuous function with J~(t)J = 1. part functions to show inductively that if f is in From the geometrical construction, g(z) = f(z, 0). s*, then \an 1 ~ n for n = 1, 2, .... Thus, the set of all functions f(z, 0) of Sis a dense The Bieberbach conjecture was also proved for subset of S in the topology of normal convergence. another special class in 1931-1932 [10, 36]. If f Incidentally, it is easy to see that Loewner's is in S and has real coefficients, then Jan\ ~ n for differential equation describes an expanding flow. n=1,2, .... The last two factors at z = z0 represent an outer The next advance in the general theory was normal to the range of {z : \z\ ~ Jz0 \} under made in 1923 by Charles Loewner (Karl Lowner) f(·, t). And the first factor has positive real [27]. He showed that a dense subset of S can part; hence f(z0, t) is moving out of the image of be obtained from solutions of a partial differential {z: \z\ ~ \zo\}. equation. Using this result as a representation There are various ways to express (1) in terms formula, he showed Ja 3 J ~ 3. The method has of changing coefficients of power series. The also been found useful for problems not involving following formulation will be used in de Brange's coefficients-for example, bounding Jarg f'(z)\ in argument. Suppose f(z, t) = etz + ·· · satisifies (1) terms of JzJ. for some ~(t). Define ck(t) by One can understand de Branges's use of Loewner's differential equation without knowing (2) log f(~, t) = f ck(t)zk. a derivation of the equation. But to be complete e z k=l and to avoid being vague, we will sketch Loewner's Use Loewner's differential equation to connect the theory. results of applying a. ;at to (2) and of applrng For many problems, including coefficient es­ zo · /oz to (2). Identifying coefficients of z on timates, it suffices to consider functions g(z) = opposite sides, one finds 2 2 3 for in f(Rz)/ = z + a2Rz + a3R z + ·· · f k-1 S and 0 < R < 1 and Jz\ < 1. Clearly, such a function g has range bounded by an analytic (3) c~ = 2~(t)k + kck(t) + 2 L m~(t)k-mcm(t). Jordan curve. Fix the function g to be considered. m=l Let r be an arc coming from infinity to the Also note that since e-t f(z, t) is in S, for each boundary of the range of g and then moving k, the function ck(t) has bounded magnitude as about the boundary until it returns to the starting t--+ +oo. Only equation (3) and the boundedness point. No point should be covered twice by r of each ck(t) will be needed later. except the starting point on the boundary of the Returning to the historical development, we range of g. Now let r be retracted by erasing should consider a striking negative application of

3 Loewner's theory made by Fekete and Szego [14]. t --+ +oo for k = 1, 2, ... , n, then inequality (4) They showed there are odd functions in S with holds for C1, ... , Cn. las I > 1. Their example disproved the Littlewood­ Suppose { c1, ... , en} arises from a function I inS Paley conjecture [26] that odd functions in S have for which Loewner's differential equation applies. coefficients of magnitude bounded above by one. Then there is a continuous function ~~;(t) such An attraction of that conjecture was that, since I that the resulting functions ck(t) have bounded in S implies Jl(Z2) = z + · · · is in S and is odd, magnitude as t--+ +oo. De Branges's theorem an application of the Cauchy-Schwarz inequality implies that the Lebedev-Milin conjecture (4) would imply the Bieberbach conjecture. holds for this { c1, ... , c.,,.}. Since Loewner's Robertson [35] was then inspired to make differential equation holds for a dense subset of S, another conjecture, which, by the Cauchy­ the Lebedev-Milin conjecture follows. Schwarz inequality, would imply the Bieberbach The key ideas of de Branges's proof are now conjecture. Robertson conjectured: lf I is odd indicated [8, 17]. Consider a function and in S, then n 1/>(t) = E(kick(tW - ~ }k(t), L la2k-1l 2 ~ n for n = 1,2, .... k=l where the functions Tk are to be specified. It Another application of Loewner's differential is desired that 1/>(0) ~ 0 be the Lebedev-Milin equation was made by Goluzin (cf. [18]) to inequality (4). Thus, prove quadratic inequalities which characterize the (E1) Tk(O) = n + 1-k functions of S. Essentially the same inequalities had been proved by another method by Grunsky is required. Clearly 1/>(0) ~ 0 holds if 1/>'(t) ~ 0 [20]. These Grunsky inequalities proved to for t ~ 0 and if limt-++ooif>(t) = 0. The latter be a powerful tool in proving deep theorems. condition will be satisfied if The second proof of la41 ~ 4 [6] utilized these lim Tk(t) = 0, inequalities; also the first proofs of lasl ~ 6 [30, t-++oo 31, 32] and lasl ~ 5 [33] were based on the since for each k, lck(t)l is bounded for all t ~ 0. Grunsky inequalities. It is preferable that the inequality tf>'(t) ~ 0 follow Besides estimation of individual coefficients, from Loewner's differential equation in the form there was a tradition of estimates of the form (3) at time t, since otherwise information would lanl ~ Cn for all n. The first such estimate was be used about the coefficient body which is very obtained in 1925 by J. E. Littlewood [25] with difficult to obtain. A direct calculation of if>' is C = e. The value was lowered several times. easy to complete if In particular, in 1956 Milin (cf. [13]) lowered C to 1.243. The proof was based on the Grunsky (E2) Tk- Tk+l = -(T~jk + T~+lj(k + 1)) inequalities. (By a different use of the Grunsky where Tn+l = 0. The result of the calculation is inequalities I [15] lowered C to 1.081, and then David Horowitz [22] reduced C to 1.066.) Milin's work with the Grunsky inequalities led him to consider the coefficients of log(/(z)/z) = 2::;:'= ckzk for in S in the combination where 1 I k E~=l klckl 2(n + 1- k). Work of Lebedev and bk = L mK(t)-mcm(t). Milin concerning identities of the exponential m=l function [13, 28, 34] showed that the inequality Thus, the condition if>'~ 0 will be satisfied if (4) t kickl 2 (n+1-k)~4t n+~-k (P2) T~ ~ 0 for t ~ 0. k=l k=l Since equations (E1) and (E2) already determine would imply the Robertson conjecture. I will T1, .. ., Tn, the question becomes whether properties refer to (4) as the Lebedev"Milin conjecture [28]. (P1) and (P2 ) hold for these functions. Consider (They had been considering such an inequality n = 1. Then T2(t) = 0 and T1(t) = e-t. Clearly, since about 1966, but it was first publicized in T1(t)--+ 0 as t--+ +oo and T~(t) ~ 0. 1971.) Consider n = 2. Then Ta(t) =0,T 2(t) = e-2t, Now the theorem that de Branges proved can be and T1(t) = 4e-t- 2e-2t. Clearly, (P1) and (P2) formulated. Consider a set of complex numbers are easily checked. Thus, the Lebedev-Milin {c1, ..., en} and a continuous function ~(t) for conjecture has been proved for n ~ 2. That t ~ 0, with l~~;(t)l = 1 for t ~ 0. Consider the result implies the Robertson conjecture for n ~ 3, functions c1(t), ... , cn(t) obtained by solving the which, in turn, verifies the Bieberbach conjecture differential equations (3) with this ~~;(t) and initial for n ~ 3. conditions ck(O) = ck for k = 1, ... , n. De Branges Hand computation quickly becomes impractical. shows that if ck(t) has bounded magnitude as For n ~ 25, Walter Gautschi verified by computer

4 that the functions defined by equations (Et) and yields solutions to many problems. De Branges's (E2) have the properties (P1) and (P2). (The method may have wide application. Clearly, the Bieberbach conjecture then followed for n::; 26.) Bieberbach conjecture was an effective inspiration Later Gautschi discovered that, in 1976, and testing ground for new techniques. R. Askey and G. Gasper [2] had proved a theorem Many of us who worked on the conjecture that implies that the functions determined by lament its passing. equations (E ) and (E ) satisfy conditions (Pi) 1 2 References and (P2). Their work was in special functions, quite apart from this field of univalent functions. 1. J. W. Alexander, Jilunctions which map the interior The possibility of other weight functions was of the unit circle upon simple regions, Ann. of Math. (2) 17 (1915-16), 12-22. considered [17]. It was shown that the differential 2. R. Askey and G. Gasper, Positive Jacobi equation (E ) must hold if if>' ~ 0 is to follow from 2 polynomial sums. II, Amer. J. Math. 98 (1976), 709- Loewner's differential equation in the form (3) at 737. time t alone. 3. S. D. Bernardi, A survey of the development of the Also, the possibility of proving the Bieberbach theory of Schlicht functions, Duke Math. J. 19 (1952), conjecture directly was considered [17]. An 263-287. analysis of requirements on the corresponding 4. __ , Bibliography of Schlicht functions, weight functions showed the straightforward Mariner, Tampa, Fl, 1983. approach does not work. It appears essential 5. L. Bieberbach, Doer die Koejfizienten derjenigen that one have the Lebedev-Milin conjecture with Potenzreihen, welche eine schlichte Abbildung des Ein­ which to work. heitskreises vermitteln, S.-B. Preuss. Akad. Wiss. (1916), Now some response to the earlier questions 940-955. can be made. The conjecture of Lebedev and 6. Z. Charzytiski and M. Schiffer, A new proof of Milin would not have been made without a great the Bieberbach conjecture for the fourth coefficient, Arch. deal of support work, including the Robertson Rational Mech. Anal. 5 (1960), 187-193. conjecture, the Grunsky inequalities, and Milin's 7. L. de Branges, A proof of the Bieberbach earlier work showing lanl ::; 1.243n. Milin has conjecture, Steklov Math. Inst., LOMI, preprint E- given some credit to a paper of Pommerenke as 5-84, Leningrad, 1984, pp. 1-21. being an inspiration. Thus, there appears to be 8. __ , A proof of the Bieberbach conjecture (to a case for saying mathematics progressed by an appear). accumulation of insights-including, of course, 9. __ , Square summable power series, 2nd ed. (to appear). the major insight of Louis de Branges. Also, it 10. J. Dieudonne, Sur les fonctions univalentes, C. appears that many of these steps were necessary R. Acad. Sci. Paris 192 (1931), 1148-1150. and thus were important, even if now the results 11. D. Drasin, Letters, Science 226 (1984), 240. or conjectures are obsolete. 12. P. Duren, Coefficients of univalent functions, Bull. Certainly the estimation of the importance Amer. Math. Soc. 83 (1977), 891-911. of a contribution is not an exact science. As 13. __ , Univalent functions, Springer-Verlag, a thought experiment, suppose de Branges had 1983. done his work in the early 1970s, before the 14. M. Fekete and G. Szego, Eine Bemerkung iiber Askey-Gasper result was available. By direct ungerade schlichte Jilunktionen, J. London Math. Soc. 8 computation it would have been clear that (1933), 85-89. de Brange's techniques had proved the Bieberbach 15. C. H. FitzGerald, Quadratic inequalities and conjecture for many coefficients. For that reason I coefficient estimates for Schlicht functions, Arch. Ra­ suspect the acknowledgement of his contribution tional Mech. Anal. 46 (1972), 356-368. would have been about as great as it has been. (It 16. __ , Univalent functions with large late is amusing to note that the New York Times [29] coefficients, Journal d'Analyse Mathematique 42 indicates the proof is for n ::; 25.) (1982/83), 167-174. \Vhat about the work of Askey and Gasper? 17. C. H. FitzGerald and Ch. Pommerenke, The de If it had been done a few months after de Branges theorem on univalent functions, Trans. Amer. Branges's achievement, their work would have Math. Soc. (to appear). received great attention from people interested in 18. G. M. Goluzin, Geometric theory of functions ·of univalent functions as well as those interested in a complex variable, English transl., Amer. Math. Soc., Providence, RI, 1969. special functions. In fact, even now, an easily 19. A. W. Goodman, Univalent functions, Vols. I, II, accessible proof of the Askey-Gasper theorem Mariner, Tampa, Fl, 1983. would be of considerable interest. 20. H. Grunsky, Koejfizientenbedingungen fiir It is easier to document the importance of schlichte abbildende meromorphe Jilunktionen, Math. z. various methods generated or furthered by the 45 (1939), 29-61. Bieberbach conjecture. Loewner's theory has 21. G. H. Hardy, 50 years ago (Letter to Nature), been widely used. The Grunsky inequalities Math. Intelligencer 6 (1984), no. 3, 7. imply several coefficient estimates and analytic 22. D. Horowitz, A further refinement for coefficient continuation statements. The variational tech­ estimates of univalent functions, Proc. Amer. Math. Soc. nique, as developed by M. Schiffer and others, 71 (1978), 217-221.

5 23. P. Koebe, Uber die Uniformisierung beliebiger 31. ___ , An elementary proof of the Bieberbach analytischer Kurven, Nachr. Akad. Wiss. Gottingen, conjecture for the siuh coefficient, Kodai Math. Sem. Math.-Phys. Kl. (1907), 191-210. Rep. 21 (1969), 129-132. 24. G. Kalata, Surprise proof of an old conjecture, 32. R. N. Pederson, A proof of the Bieberbach Science 225 (1984), 1006-1007. conjecture for the sizth coefficient, Arch. Rational Mech. 25. J. E. Littlewood, On inequalities in the theory of Anal. 31 (1968), 331-351. functions, Proc. London Math. Soc. 23 (1925), 481- 33. R. N. Pederson and M. Schiffer, A proof of 519. the Bieberbach conjecture for the fifth coefficient, Arch. 26. J. E. Littlewood and R.E.A.C. Paley, A proof Rational Mech. Anal. 45 (1972), 161-193. that an odd schlichte function has bounded coefficients, J. 34. Ch. Pommerenke, Univalent functions, Vanden­ London Math. Soc. 7 (1932), 167-169. hoeck and Ruprecht, GOttingen, 1975. 27. C. Loewner (K. Lowner), Untersuchungen iiber 35. M. S. Robertson, A remark on the odd schlicht schlichte konforme Abbildungen des Einheitskreises. I, functions, Bull. Amer. Math. Soc. (1936), 366-370. Math. Ann. 89 (1923), 103-121. 36. W. Rogosinski, Uber positive harmonische 28. I. M. Milin, Univalent functions and orthonor­ Entwicklungen und typisch-reelle Potenzreihen, Math. mal systems, English trans!., Amer. Math. Soc., z. 35 (1932), 93-121. Providence, RI, 1977. 37. Scientific American Staff, Science and the citizen 29. New York Times Staff, Science Watch (Math {breaking Bieberbach}, Scientific American 251 (1984), Problem Verified), New York Times September 4, 75. 1984, p. 20. 38. D. C. Spencer, Some problems in conformal 30. M. Ozawa, On the Bieberbach conjecture for the mapping, Bull. Amer. Math. Soc. 53 (1947), 417-439. siuh coefficient, Kodai Math. Sem. Rep. 21 (1969), 97- 39. M. Tsuji, in modern function 128. theory, Chelsea, 2nd ed., 1975. 40. T. Todd, Math professor solves problem, The Purdue Exponent August 23, 1984, pp. 1, 10.

The article above is the ninth in the series of Special Articles published in the Notices. The author, CARL H. FITZGERALD, studied as an undergraduate first at the University of Texas in Austin, where he took four semesters of mathematics from R. L. Moore. He earned his S.B. degree in 1963 at M.l. T., and an M.A. (1965) and Ph.D. (1967) from Stanford, where he was Charles Loewner's last Ph.D. student. He is professor of mathematics at the at San Diego, La Jolla, and has held visiting positions at the University of Delaware, Johns Hopkins University, Imperial College of the and University of Maryland, College Park. He was an Alfred P. Sloan Research Fellow, 1973-1975. The series of Special Articles was created to provide a place for articles on mathematical subjects of interest to the general membership of the Society. The Editorial Committee of the Notices is especially interested in the quality of exposition and intends to maintain the highest standards in order to assure that the Special Articles will be accessible to mathematicians in all fields. The articles must be interesting and mathematically sound. They are first refereed for accuracy and (if approved) accepted or rejected on the basis of the breadth of their appeal 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 up to a maximum of $750. Manuscripts to be considered for this series should be sent to Ronald L. Graham, Associate Editor for Special Articles, Notices of the American Mathematical Society, Post Office Box 6248, Providence, Rhode Island 02940.

6 News and Announcements

New Research Program position in the U.S. was as a research fellow of the in Discrete Mathematics Parnas Foundation at Johns Hopkins University, 1938-1939. The Office of Naval Research is pleased to He was on the faculty at Cornell University from announce the start of a new program in discrete 1939 to 1961 as an instructor (1939), assistant mathematics. The goal is to support research professor (1943), and full professor (1947). From that has potential application to naval problems. 1961 to 1981, he was professor of mathematics at Areas of particular interest include: (1) Graphi­ the , after which he moved cal algorithms, computational complexity, paral­ to the University of Southern California. lel programming, and heuristic algorithms, par­ He held a Guggenheim Fellowship in 1946-1947, ticularly, efficient algorithms that give nearly op­ which he spent at the University of Michigan and timal results with high probability; (2) Enumera­ at Cornell. He was a member of the Institute for tion of combinatorial configurations, asymptotic Advanced Study in 1951-1952. · enumeration, and properties of random graphs; (3) Kac was twice awarded the Mathematical Reconstruction problems, including investigations Association of America's for into pseudosimilarity, the development of isomor­ expository writing and in 1978 he received phism testing algorithms, and pattern recognition; the George David Birkhoff Prize in Applied (4) Combinatorial designs, particularly applica­ Mathematics, awarded jointly by the American tions to communication networks for efficient, Mathematical Society and Society for Industrial reliable, and secure transmission of information; and . He was the Society's (5) Graphical invariants, Ramsey theory, graphs Joshia Willard Gibbs Lecturer at the Annual and matrices, band width, and eigenvalues. Meeting in Houston in 1967; his title was Some Unsolicited proposals in these and other areas mathematical problems in the theory of phase of discrete mathematics will be considered. transitions. He gave the Colloquium Lectures at Proposals may be sent to Allen J. Schwenk, the Society's Annual Meeting in San Francisco in Mathematical Sciences Division, Code 411, Office January 1981; the topic of his lectures was Some of Naval Research, Arlington, Virginia 22217; mathematical problems suggested by questions in 202-696-4320. physics. He was a member of the U.S. National Academy Everett Pitcher Lecture Series of Sciences, the American Academy of Arts and Sciences, the American Philosophical Society, the The next series of Everett Pitcher lectures will Royal Netherlands Academy of Arts and Sciences, be held on Lehigh University's Bethlehem, Pen­ and the Royal Norwegian Academy, as well the nsylvania campus during the week of March 25, AMS, the MAA and the Institute of Mathematical 1985. They will be delivered by Jiirgen K. Moser Statistics (of which he was a fellow). From 1965 to of the Eidgenossische Technische Hochschule in 1967, he served as chairman of the mathematical Ziirich. The general topic is Stability of Hamil­ sciences division of the National Academy of tonian Systems. The lectures are open to the Sciences-National Research Council. public and are in honor of Everett Pitcher, Kac was a member-at-large of the AMS Council Secretary of the AMS, who served in the Math­ from 1950 to 1952 and was vice president of the ematics Department at Lehigh from 1938 until Society, 1965-1966. He was a member of the 1978, retiring as Distinguished Professor of Math­ Transactions and Memoirs editorial committee ematics. from 1956 to 1958. He gave invited addresses at two AMS meetings (Columbus, December 1948, and Middletown, October 1974) and spoke many 1914- 1984 times in special sessions, symposia and summer seminars. Mark Kac, professor of mathematics at the His mathematical interests included the theory University of Southern California, died October of probability, , and mathematical 26, 1984 at the age of 70. He was a member of physics (especially statistical mechanics). the Society for 45 years. Kac was born in Krzemieniec, Poland, on Langlands Selected August 3, 1914. He recieved a Ph.D. degree from for Common Wealth Award the Jan Kasimii' University in Lw6w, in June 1937. He worked for about a year as a junior Robert P. Langlands has been selected to actuary at the Phoenix Insurance Company in receive a Common Wealth Award of Distinguished Lw6w and moved to the United States in 1938 (he Service in Science. A cash award of $23,500 and a became a naturalized citizen in 1943). His first commemorative sculpture were presented to him.

7 The Common Wealth Awards, administered the Senior Scholar Fulbright Program, announced by Bank of Delaware, were established under that limited funds would be available to facilitate the will of Ralph Hayes, a Coca-Cola Company visits to interested institutions, especially to those executive and director of Bank of Delaware that have had little opportunity to participate in and the New York Community Trust. The educational exchange programs. awards can be made annually to reward and The Council has prepared a directory describing encourage outstanding achievement in the fields of this program and listing by disipline Fulbright dramatic arts, government, invention, literature, scholars, including those who welcome short-term mass communications, public service, science invitations. The entries include topics, home and sociology. Langlands was selected for and U.S. affiliations. A copy of this directory his achievements in and contributions to the can be obtained from Council for International development of mathematics. The selection Exchange of Scholars, 11 Dupont Circle, Suite committee, established by Sigmi Xi, The Scientific 300, Washington, D.C. 20036; 202-833-4979. Research Society, described him as "one of those rare individuals who combines mathematical William H. Roever Lectures power and great originality." in Geometry Langlands received his education at the Univer­ sity of British Columbia and . The third series of William H. Roever Lectures He has been on the faculties of Princeton and in Geometry will be held on January 14- Yale Universities and has been at the Institute of 18, 1985 at Washington University, St. Louis, Advanced Study in Princeton since 1972. He is an Missouri. They will be given by I. M. Singer, AMS member and is a fellow of the Royal Society of John D. MacArthur Professor of Mathematics at London and of the Royal Society of Canada. His the Massachusetts Institute of Technology, and research is in group representations-automor­ entitled The geometric interpretation of anomalies phic forms and number theory. in quantum field theory. The lectures, which are open to the public, have been established by his Fulbright Scholars sons to honor William H. Roever, Professor of Available for Lectures Mathematics at Washington University from 1908 until his death in 1951, and Chairman of the More than 800 visiting scholars from 86 Department of Mathematics from 1932-1944. countries have been awarded Fulbright grants Further information may be obtained by writing for university lecturing and advanced research in to the Department of Mathematics, Washington the United States during 1983-1984. University, Box 1146, St. Louis, Missouri 63130. Although most Fulbright scholars have a single institutional affiliation, many have broad Erratum academic interests and welcome opportunities to visit other colleges and universities. Many of them In a News Item in the October 1984 issue are available for occasional lectures, seminars and of Notices (page 618) AAAB was incorrectly special programs. The Council for International identified as the American Academy of Arts & Exchange of Scholars (ems), which administers Sciences. AAAS should have been identified as the Association for the Advancement of Science. We Unpublished Lecture Notes regret the error. The Notices will institute a column containing lists of unpublished lecture notes available from departments in the mathematical sciences, research institutes, and other organizations in the nonprofit sector. Readers are invited to submit material for this column; items submitted for inclusion in this section of the Notices should be accompanied by the following information: Name of author(s), title, year, number of pages, price; Address for orders and information about payment (postal surcharge, if any, or whether postpaid, to whom checks should be made). Items should be sent to the Providence office (Notices Lecture Notes, American Mathematical Society, Post Office Box 6248, Providence, Rhode Island 02940).

8 Queries Edited by Hans Samelson QUESTIONS ARE WELCOMED from AMS members regarding mathematical matters such as details of, or references to, vaguely remembered theorems, sources of exposition of folk theorems, or the state of current knowledge concerning published or unpublished conjectures. This is not intended as a problem corner, except for occasional lists of problems collected at mathematical meetings. REPLIES from readers will, when appropriate, be edited into a composite answer and published in a subsequent column. All answers received will be forwarded to the questioner. QUERIES and RESPONSES should be typewritten if at all possible and sent to Professor Hans Samelson, American Mathematical Society, P. 0. Box 6248, Providence, Rhode Island 02940. Queries is the characteristic polynomial of M, Ai = the eigenvalues, and Xi(x) = x(x)f(x->-i)· For another 318. 0. Hajek (Department of Mathematics formula for Mn, see Korn and Korn, Mathematical and Statistics, Case Western Reserve Univer­ handbook for scientists and engineers, McGraw­ sity, Cleveland, OH 44106). The quick and Hill, 1968, 13.4-13.7. For small none can derive easy formula yielding a function f analytic such formulas without denominator, valid also in at 0 froni its real part u(x, y), namely f(z) = the degenerate case. (Contributed by A. Parks, f(O) + 2u(z/2,z/2i), appears in Ahlfors' Complex P. Easthope, K. Larson) analysis. Who is the discoverer? It looks like 290. (vol. 30, p. 759, November 1983, Albert A. Euler. Mullin) Composite Mersenne numbers. Reply: 319. Themistoeles M. Rassias (University of La Through a combination of circumstances, the response in vol. 31, p. 480, came out garbled; Verne, Athens, Greece). Let f : R 2 -+ R 3 be a mapping (not necessarily continuous) such that the editor apologizes. It is certainly unknown at d(x, y) = 1 implies d(f(x), f(y)) = 1 for all x, y E present whether there are infinitely many primes p such that 2p 1 is also prime. What was R 2 • Must f be an isometry (onto its image)? + meant is this: (a) at the moment, looking for such 320. Peter Easthope (3760 72 Street, RR1, Delta, primes seems an efficient way of finding composite British Columbia, Canada V4K 3N2). For a Mersenne numbers; (b) the available evidence surface of the type of the sphere in R 3 , the suggests that there are infinitely many composite isoperimetric inequality states 367r V 2 /A3 s 1 (A = Mersenne numbers (see V. A. Golubev, Nombres surface area, V =enclosed volume), with equality de Mersenne ... , Mathesis 67 (1958), 257-262, only for the sphere. To what extent can one with the suspicion that the number of Mersenne describe the shape of the surfaces for a given value primes is finite, and D. B. Gillies, Three new of 367rV2 fA3 ( < 1)? Mersenne primes ... , Math. Comp. 18 (1964), 93- 321. Robert E. Vmograd (Division of Mathemati­ 97, who conjectures that the number of Mersenne cal Sciences, North Dakota State University, primes Mp, with p in [x, 2x], tends to 2 for Fargo, ND 58105). If P =I 0, I is a projection x -+ oo ). The question of bicomposites is still in a Euclidean or , and a is the unanswered. (Contributed by A. Boneh, H. Edgar, angle between the subspaces R = range P and L. Washington, P. Schumer, W. Staley) N =null P, then it is quite elementary to prove 288. (vol. 30, p. 759, November 1983, Seymour that \\P\\ =\II -PI\= csca. Nevertheless, I have Kass) The inequality. \ Ezi\P s E>-i-i>\zi\P for been unable to find this formula anywhere in its Ai > 0, 2:>-i = 1, p 2:: 1, once more (see pr~ explicit form. Does anybody know any references? vious responses vol. 31, pp. 164, 282, 480). Reply: The inequality, in essentially this form, Responses appears in J. Radon's paper on absolutely additive set functions (Akad. Wiss. Wien, Math.­ The editor would like to thank all those who Naturwiss. Kl. ITa, Sitzungsberichte 122 (1913), sent in replies. 1351, formula (20)). His derivation is similar to 294. (vol. 31, p. ;1.1, January 1984, Peter Lyall those given on the above pages, but uses the mean Easthope) Identities for powers of a matrix. value theorem instead of convexity of xP. Radon Reply: These identities come from the Cayley­ notes the equivalence with the Holder inequality Hamilton relation, which expresses Mn (and and derives the Minkowski inequality from it. He therefore also higher powers) in terms of lower notes that the latter implication seems to have powers. J. J. Sylvester noted (Works, vol. 4, been known at that time only for p = 2 (F. Riesz, p. 150): Since any polynomial p(M) (or power Math. Ann. 69(1910), 455) (Contributed by R. J. series) in M reduces via Cayley-Hamilton to a Gregorac) polynomial of degree < n, one can, in the case [The editor, who as a beginning student had of distinct eigenvalues, use Lagrange interpolation Radon as a teacher, would like to take the to get p(M) = EP(Ai)·(Xi(M)/Xi(Ai)), where x(x) occasion to express his gratitude to him for

9 maintaining his integrity during the difficult Nazi be the Hamiltonian of an atom (or ion) with N years in and for teaching an excellent electrons and Z protons. Let \II be the ground course in differential geometry.] state wave function, i.e., H\11 = E\11, E = infa(H). Let p be the ground state density, i.e., Correction to Problem List on Partial Differential Operators p(xl) = N ka ·· · k_.illl(xl, ... , XN )1 2d 3 x2· · · d3 xN (vol. 31, p. 631, October 1984) (x1 E R3). Clearly p(x) = p(jxi). Problem. Show In the October issue there was an error in p(r) is nonincreasing in r E (O,oo). Known results: the statement of problem 10 from the special (1) True if N 1. (2) True in (r0 , oo ), i.e., session on partial differential operators organized = true for sufficiently large r (M. and T. Hoffinann­ by Mark Kon, who apologizes for the error. The Osteiihof). (3) True for PTF, the Thomas-Fermi problem, due to J. Goldstein of Tulane University, approximation of p (E. Lieb, T. Gallouet and J. should read Morel). (This case requires Z 2': N.) On ){ = L2(R3N), let Note that the correction published in the November Notices (p. 785) should be disregarded. 1 1 N Z H=--Ll+ L -2:- 2 i

Axiomatic Set Theory

James E. Baumgartner, Donald A. Martin and , Editors Mathematicians interested in understanding the T. Carlson largely solves the pin-up problem. and directions of current research in set theory will not D. Velleman presents a novel construction of a want to overlook this book. which contains the Souslin tree from a morass. S. Todorcevic proceedings of the AMS Summer Research obtains the strong failure of the D principle from Conference on Axiomatic Set Theory. held in the Proper Forcing Axiom and A. Miller discusses Boulder. Colorado. June 19-25. 1983. This was properties of a new species of perfect-set forcing. the first large meeting devoted exclusively to set H. Becker and A. Kechris attack the third theory since the legendary 1967 UCLA meeting. Victoria Delfino problem while W. Zwicker looks and a large majority of the most active research at combinatorics on P.,(>.) and J. Henle studies mathematicians in the field participated. All areas infinite-exponent partition relations. A. Blass of set theory. including constructibility. forcing. shows that if every vector space has a basis then combinatorics and descriptive set theory. were AC holds. I. Anellis treats the history of set represented: many of the papers in the proceedings theory. and W. Fleissner presents set-theoretical explore connections between areas. Readers should axioms of use in general topology. have a background of graduate-level set theory. There is a paper by S. Shelah applying proper Contemporary Mathematics forcing to obtain consistency results on Volume 31, x + 259 pages (softcover) combinatorial cardinal "invariants" below the 1980 Mathematics Subject Classifications: continuum. and papers by R. David and 03E05, 03E10, 03E15, 03E25, 03E35 and others S. Freidman on properties of 0#. Papers by ISBN 0-8218-5026-1; LC 84-18457 A. Blass. H.-D. Donder. T. Jech and Publication date: November 1984 List price $25, institutional member $20, W. Mitchell involve inner models with measurable individual member $15 cardinals and various combinatorial properties. To order, please specify CONM/31 N

Shipping/Handling: 1st book $2, each add'l $1, max. $25;by air, 1st book $5, each add'l $3, max. $100 Prepayment is required. Order from American Mathematical Society, P.O. Box 1571, Annex Station, Providence, Rl 02901-1571, or call toll free 800-556-7774 to charge with Visa or MasterCard.

10 National Science Foundation News & Reports

National Science Foundation: Division and the time by which a decision on the Report on Mathematical Sciences proposal is desired. Finally, you should encourage faculty holding grants to check expiration dates and Science Engineering to determine early whether or not they need to As the new Division Director for the Division resubmit proposals at this time. of Mathematical Sciences, I am taking this Budget. The Congress has passed and the opportunity to introduce myself and bring you President has signed the FY 1985 Appropriation up to date on the changes that have taken place measure for the Foundation. We are entering this within the Division. I wish that I could do this year with a fairly clear understanding of budget on a more personal basis, but the mathematical levels and priorities. We expect a total of $47.8 sciences community is too widespread to permit million for FY 1985, an increase of 15.2% over the that. The former Division Director, Jim Infante, funds expended in FY 1984. Much of that increase gave our community a sense of purpose during the is targeted toward specific itmes such as enhanced last three years. With your help, I trust we can support of graduate students and postdoctorals move into a period where mathematical sciences and increased support for equipment. This research can maintain and enhance its position in continues the advances made in these areas in the scientific community. FY 1984. In submitting proposals for the coming Staff. The biggest organizational change of the year, your faculty should take into account the past year was the creation of the Divisions of increased availability of funding in these areas. Mathematical Sciences and Computer Research Advisory panel. The Advisory Committee for from the former Division of Mathematical and the Mathematical Sciences met September 17 Computer Sciences. That created some changes and 18, 1984. R. Gangolli of the University of in the administrative structure of the new division. Washington is the chairman. The committee's Also, we were given permission to add two new advice is very important to us in setting priorities staff at the program director level and two at the and developing long-range plans for the Division. secretarial level. The program staff for this year You and your faculty are welcome to attend or to includes: (Phone: 202-357-9764) suggest topics of discussion for future meetings. Classical Analysis John Ryft' The minutes of this meeting are available on Modern Analysis Frank Gilfeather request. Geometric Analysis Richard Millman Exciting mathematical interest. Researchers in Topology & Foundations Ralph Krause Algebra & Number Theory Bernard McDonald the mathematical sciences have no difficulty in Richard Draper becoming excited about new results in the field. Applied Mathematics Melvyn Ciment Those of us at NSF must not only learn of the John Lagnese exciting results in the fields, but convey in a Statistics & Probabilty Paul Shaman Peter Purdue meaningful way the excitement of our community Special Projects Alvin Thaler to those whose primary interest is in other fields. The Division's administrative staff includes: Your help in this task is essential and can be (Phone: 202-357-9669) provided by keeping us informed about important Division Director John Polking research results and giving us your ideas on Deputy Division Director Judith Sunley presenting those results to others. This is a crucial Administrative Assistant Fay Childress part of our role in keeping the mathematical Ciment and McDonald have joined Krause, sciences in public view. Ryff, Sunley and Thaler on the permanent staff. Science and engineering education. Al Buccino, Polking, Millman, Purdue, Shaman and Draper longtime friend of mathematics in the science are incoming rotators; and Gilfeather and Lagnese education arena has left the Foundation to be­ are continuing in their rotator positions. I would come Dean of the College of Eduication at the particularly like to thank Su-Shing Chen and University of Georgia. His departure coincided Jerome Sacks for their fine work during the past with significant reorganization of the Directorate year. for Science and Engineering Education. John Proposal submission. We continue to have no Thorpe of the State University of New York at deadline for the submission of standard research Stony Brook has recently been appointed as the proposals. Your faculty should be reminded program director who will have primary respon­ that it takes six to nine months to complete sibility for proposals in mathematics education the processing of a proposal. In particular, at the precollege level. The Directorate is still we recommend allowing at least seven months looking for additional personnel with expertise in between the time the proposal is received by the mathematics and its instruction. Ken Hoflinan of

11 MIT is the chairman of the Science and Engineer­ Cooperative Research with Eastern Europe ing Education Advisory Committee. I know he will keep us informed of developments on that NSF's Eastern Europe Cooperative Science front. Judy Sunley is acting as the liaison person program seeks to foster and support scientific between the Division of Mathematical Sciences and technological cooperation between the U.S. and the Science and Engineering Education Direc­ and Bulgaria, Hungary, and Romania. torate. The program offers financial support for three Advaneed seientifie computing. The Foundation types of activities: cooperative research projects, has made great strides on its initiative in the seminars and workshops, and scientific visits for advanced scientific computing arena. A central planning purposes. Proposals must be submitted office has been set up to deal on a Foundation­ to NSF by American institutions, and to the ap­ wide basis with the need for access to major propriate foreign agency by foreign institutions. facilities. Details on the activity can be obtained Proposals should be prepared according to ­ from staff members Ciment or Thaler. dard NSF guidelines, but must also contain a Final words. The coming year will provide all section on "International Cooperation," which of us with many challenges. Making individual describes the cooperative aspects of the work plan decisions on a large number of proposals within the and the mutual benefits to be obtained. Proposals total budget framework is becoming increasingly for joint research should be submitted at least intricate. I know we will have the cooperation nine months before the requested starting date; of the entire mathematical sciences community in for seminars 12 months, and for short-term visits, carrying out this task. If you have any questions six months. the next target date for research or are interested in following up any of the items proposals is May 1, 1985. For further information mentioned above, please feel free to contact me or contact Deborah Wince, Division of International any of the other members of the staff. Programs (357-9516). -NSF Bulletin John C. Polking, Division Director Division of Mathematical Sciences Computer Research Equipment Facilitation Awards for Handicapped The progress announcement (Brochure NSF Scientists and Engineers 84-59) for Computer Research Equipment is now available and may be requested on the The NSF encourages physically disabled scien­ Publications Order Form. tists and engineers to participate fully in its Proposals for the Computer Research Equip­ programs. Support to facilitate research and ment program must be received by December 1, education by disabled scientists and engineers is 1984. Further information may be obtained by described in a new announcement. Faciliation calling the Program Director, Computer Research Awards for Handicapped Scientists and Engineers Equipment, Division of Computer Research (357- (FAH) (NSF 84-62). The FAH activity provides 7349). -NSF Bulletin funds for special equipment or assistance neces­ sary to enable physically disabled individuals to Erratum conduct or participate in specific NSF-supported research or education projects. Copies of the Judith S. Sunley has been appointed Deputy announcement, and additional information on Division Director, Division of Mathematical the activity, may be obtained from the FAH Sciences. NSF had previously announced her ap­ Coordinator, A. B. Biscoe, Division of Research pointment as Deputy Division Director, Division of Initiation and Improvement (357-7552); TDD (357- Precollege Education in Science and Mathematics. 7492). -NSF Bulletin

12 News from Washington

New Board on Mathematics Board on Mathematical Sciences. Extensive work­ will Provide Focal Point ing familiarity with research in pure and applied mathematics and statistics, and experience with for Advice To Government study project management are required. from the U.S. Mathematical Community A Ph.D. in a directly relevant field and 7- The Commission on Physical Sciences, Mathe­ 10 years relevant professional experience are matics and Resources (CPMSR) announces the for­ strongly preferred. Evidence of management matio~ of a new Board on Mathematical Sciences. and communications skills are required. The The Board, to be chaired by National Academy of incumbent will have responsibility for designing, Sciences member of Massachusetts securing funding for, and managing an important Institute of Technology, will provide a unified program of studies. voice for advising the Government on mathe­ Please submit resume to: Lawrence E. McCray, matics, applied mathematics, and statistics. Associated Executive Director, Commission on Like other Boards within the Acacdemy com­ Physical Sciences, Mathematics, and Resources, plex, the Board on Mathema:tical S~iences will National Academy of Sciences/National Re­ operate mainly through specific proJects, each search Council, 2101 Constitution Avenue N.W., conducted by a committee of the best-qualified Washington, D.C. 20418. -NRC News Release experts available for the study topic. Topics will range from the research opportunities in mathe­ Exchanges with USSR matical sciences to advice on newly developed ap­ and Eastern European Academies plications of mathematics and statistics that can be used to improve Governmental performance. The National Academy of Sciences (NAS) The Board is presently recruiting a full-time staff invites applications from American scientists director. who wish to make visits during the period As is documented in the recent report, Renewing January 1, 1986-December 31, 1986 in the U.S. Mathematics, there is a real risk that USSR, Bulgaria, , the Germ~ support for mathematics research-which fo~s Democratic Republic, Hungary, Poland, Romarua a basis for scientific and technological advances m and Yugoslavia. Long-term research visits of many fields-will be inadequate to meet national five to twelve months' duration are encouraged, needs. The new Board can play a crucial role in particularly those where contact with colleagues preventing that from occurring. in the other country has already been established. Establishment of the Board has been made pos­ sible through support from the National Science Applicants must be U.S. citizens and ~ave a doctoral degree or its equivalent by the tnne of Foundation, Air Force Office of Scientific Re­ search, Office of Naval Research, Army Research the intended visit in mathematics; the physical, Office and the Department of Energy. Board biological, or engineering sciences; social or members are: behavioral sciences; or biomedical sciences. For Michael Artin (Chairman), Massachusetts In- the purpose of the exchange programs, emphasis stitute of Technology in the sociai and behavioral sciences is placed , on those which are oriented toward empirical and quantitative analysis and which on the Peter Bickel, University of California analysis of individual and group behavior. All Ralph Bradley, University of Georgia necessary expenses will be met by the NAS and Hirsh Cohen, ffiM Corporation the foreign academy, including reimbursement for Joseph Kohn, salary lost up to a predetermined maximum and Cathleen Morawetz, Courant Institute of Math- expenses for accompanying family members on ematical Sciences, visits of five months or more. Ronald Pyke, University of Washington Requests for applications should reach the Werner Rheinboldt, University of Pittsburgh National Academy of Sciences not later than Shing-Tung Yau, University of California at San February 15, 1985. Deadline for receiving c~m­ Diego, La Jolla pleted applications is March 4, 1985; applica­ For further information contact Lawrence E. tions must be postmarked by February 28, 1985. McCray, Associate Executive Director, CPSMR; For further information and applications contact 202-334-3061. -NRC News Release the National Academy of Sciences, Office of In­ ternational Affairs, USSR/EE, 2101 Constitution Staff Director-Mathematics Avenue, N.W., Washington, D.C. 20418; 202-334- 2644. -NRC News Release The National Academy of Sciences/National Research Council seeks a staff director for its

13 Amendments to the Bylaws at the Business Meeting of 10 January 1985 in Anaheim There are three amendments to consider. In the first, it is recommended by the Council that the name Mathematical Surveys be changed to Mathematical Surveys and Monographs. This corresponds to a modest redirection of the nature of the series. The change occurs in two places in the bylaws, to wit, in the name of the publication committee in Article m, Section 2, and in the name of the publication in Article IX, Section 1. The second amendment concerns the Executive Committee, which consists of four members elected from the Council by the Council and three members ex officiis. The term of office is prescribed in Article VII, Section 1 where it is stated that "[t]he term of office for elected members of the executive committee shall be two years, two of the elected members retiring annually." The Council recommends that the term be changed to four years, with one elected member retiring annually. The proposed change embodies the view of the executive committee and of the board of trustees (with whom the executive committee frequently meets jointly) that the turnover in the executive committee has been too rapid for its members to gather experience and for the Society to profit from that experience. The third amendment is concerned with corporate membership. The format of Article IX on Dues and Privileges of Membership is that classes of membership are handled in consecutive pairs of Sections, one on dues and the next on privileges. There is a break in format in that Section 4 sets dues of institutional members, Section 5 sets dues of corporate members, and Section 6 sets privileges of both by the same formula. It develops that the figure of $1,000 for minimum dues of corporate members set in Section 5 is too low and that the formula for their privileges in Section 6 does not correspond to their needs. The proposed change is to follow the format of the rest of the article without affecting privileges of institutional membership but to alter the rules concerning corporate membership. The new Section 5 is to consist of the old Section 6 with the bracketed words deleted, so that the new Section 5 is as follows: Section 5. The privileges of [a corporate or] an institutional member shall depend on its dues in a manner to be determined by the Council, subject to approval by the Board of Trustees. These privileges shall be in terms of Society publications to be received by the institution and of the number of persons it may nominate for ordinary membership in the Society. The new Section 6 shall replace the old Section 5 in its entirety by the following: Section 6. Dues and privileges of corporate members of the Society shall be established by the Council subject to approval by the Board of Trustees. Everett Pitcher Secretary

14 Anaheim Meetings, January 7-13, 1985 Program

The January 1985 Joint Mathematics Meetings, 91st Annual Meeting of the AMS including the 91st Annual Meeting of the AMS, the January 9-13, 1985 68th Annual Meeting of the Mathematical Association of America, and the 1985 annual meetings of the Association for Symbolic Logic, the Association for Fifty-eighth Josiah Willard Gibbs Lecture Women in Mathematics, and the National Association The 1985 Gibbs lecture will be presented at for Mathematicians, will be held January 9-13 8:45 p.m. on Wednesday, January 9, by MICHAEL (Wednesday-Sunday), 1985, in Anaheim, California. 0. RABIN of and the Hebrew The meetings will be preceded by the AMS Short University of . Professor Rabin will speak Course on January 7-8 (Monday-Tuesday), 1985. on Randomization in mathematics and computer Sessions will take place in the Anaheim Convention sc2ence. Center, 800 West Katella; and the Anaheim Marriott Colloquium Lectures Hotel, 700 West Convention Way. The members of the Local Arrangements Com­ There will be a series of four Colloquium Lectures mittee are Lorraine T. Foster (publicity director), presented by DANIEL GORENSTEIN of Rutgers James 0. Friel, Robert M. Guralnick, Alfred W. University. The title of this lecture series is The Hales (chairman), Phocion G. Kolaitis, William J. classification of the finite simple groups. The LeVeque (ex-officio), Kenneth A. Ross (ex-officio), lectures will be given at 1:00 p.m. daily, Wednesday Hugo Rossi (ex-officio), Bernard Russo, David B. through Saturday, January 9-12. Wales, and Arthur Wayman. The Frank Nelson Cole Prize in Algebra WHERE TO FIND IT PAGE The 1985 Cole Prize will be awarded at 4:00 p.m. ANNUAL MEETING OF THE AMS 15 on Thursday, January 10. Gibbs Lecture, Colloquium Lectures, Prizes, Invited Addresses, Special Sessions, Contributed Invited Addresses Papers, Other Sessions, Council and By invitation of the Program Committee, there Business Meetings will be nine invited one-hour addresses. The names AMS SHORT COURSE 16 of the speakers, their affiliations, the titles of their EMPLOYMENT REGISTER 43 ANNUAL MEETING OF THE MAA 19 talks, the dates and times follow: Invited Addresses, Minicourses, RUTH M. CHARNEY, State University, Contributed Papers, Other Sessions, Some new approaches to moduli spaces, 9:00 a.m. Business Meeting, Board of Governors, Section Officers Wednesday. OTHER ORGANIZATIONS 24 Lours DE BRANGES, Purdue University, The AAAB,ASL,ATP,AWM,NAM,NSF,RMMC Riemann hypothesis for Hilbert spaces of entire TIMETABLE 23 f'J,nctions, 11:15 a.m. Thursday. OTHER EVENTS OF INTEREST 26 Book Sales, Exhibits, Information Table, MATHFILE, National Mathematics Department Chairmen's Meeting, Petition Table ACCOMMODATIONS 26 Hotels REGISTRATION DESK 34 Fees, Dates, Times, Locations, Services MISCELLANEOUS INFORMATION 38 Child Care, Disneyland, Local Information, Parking, Social Event, Travel, Weather MAP 30 PRESENTERS OF PAPERS 68 PROGRAM OF THE SESSIONS 45 IMPORTANT DEADLINES AMS Abstracts, For consideration for special sessions Expired Of contributed papers Expired MAA Abstracts, Of contributed papers Expired Employment Register (Applicants & Employers) Expired EARLY Preregistration and Housing Expired Preregistration and Housing Expired Motions for AMS Business Meeting Expired Preregistration eaneellations (50% refund) January 4 Dues credit for nonmembers/students February 13 Michael 0. Rabin, Gibbs Lecturer

15 American Mathematical Society Short Course Series Introductory Survey Lectures on Fair Allocation Anaheim, California, January 7-8, 1985

The American Mathematical Society, in conjunction with its ninety-first Annual Meeting, will present a two-day short course entitled Fair Allocation on Monday and Tuesday, January 7 and 8, at the Anaheim Convention Center in Anaheim, California. The program is being coordinated by H. Peyton Young, who is a professor at the School of Public Affairs at the University of Maryland, College Park. Fair allocation is concerned with principles and procedures for allocating objects among competing claimants according to standards of equity. It has important applications to public sector allocation problems, including the apportionment of representation, the sharing of common costs of public facilities, voting, and other problems of distribution and redistribution. One aspect of the question is the identification of normative principles of fairness and their logical consequences for the choice of method; another is to define appropriate measures or standards for making allocative decisions-such as measures of inequality. A third aspect is the design of different procedures for achieving fair allocations. Some of these methods are prescriptive-such as apportionment and costing "formulas"; others, such as voting and auctions, involve elements of competition, cooperation, and strategy. All of these topics will be covered and numerous applications will be made to problems based on real data. The mathematics is mainly combinatorial in spirit but also involves applications of real and convex analysis and game theory. While no special background in these subjects is presumed, some acquaintance with them would be helpful. A suggested reference in game theory is G. Owen, Game Theory, second edition, Academic Press, 1982 (Chapters 1, 2, 8, and 11). Synopses of the talks and accompanying reading lists appear in this issue of the Notices. The course will consist of six 75 minute survey lectures: "The Apportionment of Representation," by H. P. Young of the University of Maryland and M. L. Balinski of the Centre National de Recherche Scientifique, Paris; "Cost Allocation," by H. P. Young; ''Inequality Measurement," by J. E. Foster of the Krannert School, Purdue University; "Fairness and Strategies in Voting," by H. Moulin of the Virginia Polytechnic Institute (presented in two 75 minute lectures); and "Auctions and Competitive Bidding," by Robert J. Weber of the J. L. Kellogg Graduate School of Management, Northwestern University. The program will conclude with a discussion session with audience participation. The short course is open to all who wish to participate upon payment of the registration fee. Please refer to the section titled Registration at the Meetings for details. The short course was recommended by the Society's Committee on Employment and Educational Policy, whose members are Lida K. Barrett, Stefan A. Burr, Lisl Novak Gaal, Gerald J. Janusz, Irwin Kra and Donald C. Rung (chairman). The short course series is under the direction of the CEEP Short Course Subcommittee, whose members are Stefan A. Burr (chairman), Lisl Novak Gaal, Cathleen S. Morawetz, Barbara L. Osofsky, and Philip D. Straffin, Jr ..

16 Madison and University of Texas at Austin, 8:00 a.m. Wednesday and 8:30 a.m. Thursday. Max L. Benson, James W. Cannon, Marc Culler, William J. Floyd, Matt Grayson, Steve Kerckhoff, Walter D. Neumann, N. Smythe, , Kay Tatsuoka, and Philip Wagreich. Teichmuller theory for surfaces, graphs and hyperbolic manifolds, RuTH M. CHARNEY, , 9:00 a.m. Thursday and 2:15 p.m. Friday. Henry Glover, Lisa R. Goldberg, William M. Goldman, Matt Grayson, Steve Kerckhoff, Ronnie Lee, Jeffrey Mess, John Millson, Karen Vogtmann, and Steven H. Weintraub. Algebraic deformation theory, MuRRAY GERSTENHABER, University of Pennsylvania, 3:30 p.m. Wednesday and 8:00 a.m. Thursday. William Arveson, Murray Gerstenhaber, , Andy Magid, Joyce O'Halloran, Richard Rochberg, Samuel D. Schack, James Stasheff, and Clarence Wilkerson. , DORIAN GoLDFELD, University of Texas at Austin, 2:15 p.m. Wednesday, Daniel Gorenstein, Colloquium Lecturer 8:00 a.m. Thursday, and 1:00 p.m. Friday. Krish­ naswami Alladi, Enrico Bombieri, Boris Datskovsky, RoN DoNAGI, Northeastern University, Is a Leon Ehrenpreis, G. Freiman, Solomon Friedberg, variety determined by its periods?, 2:15 p.m. Patrick Gallagher, D. A. Goldston, Amait Ghosh, Wednesday. H. Halberstam, Jeffrey Hoffstein, Gerald Myerson, LAWRENCE CRAIG EVANS, University of Eugene K. S. Ng, A. M. Odlyzko, Ilya Piatetski­ Maryland, College Park, Some recent directions Shapiro, Ralph Phillips, H. M. Stark, Audrey Terras, in nonlinear elliptic partial differential equations, Jeffrey D. Vaaler, and David J. Wright. 9:00 a.m. Thursday. Ordinary differential equations, WILLIAM A. DORIAN GoLDFELD, University of Texas at HARRIS, JR., University of Southern California; Austin, On Gauss' class number problem, 10:15 and GEORGE R. SELL, University of , a.m. Wednesday. 9:00 a.m. and 2:15 p.m. Wednesday and 9:00 a.m. WILLIAM M. KANTOR, University of Oregon, Thursday. Werner Balser, Hyman Bass, Mel Berger, Some applications of the classification of finite Charles Conley, Jack K. Hale, William A. Harris, simple groups, 2:15 p.m. Saturday. Jr., David Hart, Po-Fang Hsieh, Russell Johnson, W. WILLIAM H. MEEKS III, Rice University, Beauty B. Jurkat, D. A. Lutz, John Mallet-Paret, Lawrence and symmetry in the theory of minimal surfaces, Markus, K. R. Meyer, David Perry, George R. Sell, 3:30 p.m. Wednesday. Yasutaka Sibuya, Barry Simon, Steven Sperber, and LAURENCE C. SIEBENMANN, University of Paris, Russell Walker. Orsay, On Gromov's horizon for combinatorially Infinite dimensional topology, JAMES P. HEN­ hyperbolic groups, 2:15 p.m. Friday. DERSON, Texas A & M University; and DENNIS J. W. HUGH WooDIN, California Institute of GARITY, Oregon State University, 3:30 p.m. Friday, Technology, Recent developments in set theory, and 1:00 p.m. Saturday. F. D. Ancel, Mladen Be­ 3:30p.m. Friday. stvina, Phillip L. Bowers, Doug Curtis, Jan Dijkstra, Tadeusz Dobrowolski, Terry L. Lay, Leonard R. Special Sessions Rubin, F. C. Tinsley, John J. Walsh, and David G. By invitation of the same committee, there will Wright. be twelve special sessions of selected twenty-minute Celestial mechanics, NEAL D. HuLKOWER, papers. The topics of these special sessions, the names TRW, Inc., 1:00 p.m. Saturday and 10:00 a.m. and affiliations of the mathematicians arranging Sunday. Roger Broucke, John G. Bryant, Robert them, the days and times they will meet, and lists of W. Easton, Joseph L. Gerver, Martin P. Kummer, speakers are as follows: Ernesto A. Lacomba, Richard McGehee, K. R. Meyer, Finite group theory, , Richard Moeckel, Filomena Pacella, Dieter Schmidt, California Institute of Technology, 2:15 p.m. Friday and John B. Urenko. and 3:20 p.m. Saturday. Alberto L. Delgado, J. Nonstrictly hyperbolic conservation laws, BAR­ Lepowsky, George Lusztig, Richard Lyons, Geoffrey BARA L. KEYFITZ, University of Houston, University Mason, Gary M. Seitz, Stephen D. Smith, Ronald Park, 9:00 a.m. and 2:15 p.m. Wednesday and 9:30 Solomon, and John H. Walter. a.m. Thursday. Matania Ben-Artzi, Moysei Brio, Asymptotic properties of hyperbolic groups, Eduard Harabetian, Harumi Hattori, Eli L. Isaacson, JAMES W. CANNON, University of Wisconsin, Daniel D. Joseph, Barbara Lee Keyfitz, Herbert C.

17 Kranzer, Brent Lindquist, Reza Malek-Madani, D. Business Meeting Marchesin, , Ralph A. Saxton, Michael The Business Meeting of the Society will take Shearer, M. Slemrod, and Blake Temple. place immediately following the award of the Cole Stochastic differential geometry, MARK A. Prize at 4:00 p.m. on Thursday, January 10. The PINSKY, Northwestern University, 8:00 a.m. Wed­ secretary notes the following resolution of the nesday and 10:15 a.m. Thursday. Rafael V. Chacon, Council: Each person who attends a Business I. Chavel, R. W. R. Darling, Jozef Dodziuk, Richard Meeting of the Society shall be willing and able Durrett, Gerard G. Emch, Samuel Goldberg, Leon to identify himself as a member of the Society. fu Karp, Peter March, M. Ann Piech, Daniel W. Stroock, further explanation, it is noted that each person and Dennis Sullivan. who is to vote at a meeting is thereby identifying Algebraic combinatorics, RICHARD P. STAN­ himself as and claiming to be a member of tfte LEY, Massachusetts Institute of Technology, 1:00 American Mathematical Society. For additional p.m. Friday, 3:20 p.m. Saturday, and 8:00 a.m. information on the Business Meeting, please refer Sunday. Louis J. Billera, Anders Bjorner, Paul to the box titled Committee on the Agenda for H. Edelman, Ira M. Gessel, Curtis Greene, Mark Business Meetings. Haiman, Phil Hanlon, Jeff Kahn, Gil Kalai, Robert MathSci (formerly MATHFILE) A. Proctor, David P. Robbins, Bruce Sagan, Richard P. Stanley, Dennis Stanton, Michelle Wachs, James MATHFILE is expanding its subject and time W. Walker, Dennis White, Dale R. Worley, and coverage and adding new subfiles. The database Thomas Zaslavsky. has been renamed MATHSCI to indicate its broader Differential geometry, KAREN K. UHLENBECK, scope. A presentation of the new features and ; PETER LI, Purdue University; additions in MATHSCI will be held on Friday, and WILLIAM H. MEEKS, III, Rice University; 1:00 January 11 at 4:45 p.m. p.m. and 3:30 p.m. Friday, 1:00 p.m. Saturday, and 9:00a.m. Sunday. Stephanie Alexander, Thomas P. Committee on the Agenda for Business Meetings Branson, Robert Brooks, Shiu-Yuen Cheng, Hyeong­ The Society has a Committee on the Agenda In Choi, Christopher Croke, Doris Fischer-Colbrie, for Business Meetings. The purpose is to make Gregory J. Galloway, Robert E. Greene, Joel Hass, Business Meetings orderly and effective. The David A. Hoffman, Qi-Keng Lu, Robert C. Reilly, committee does not have legal or administrative Steven Rosenberg, Ernst A. Ruh, Luen-Fai Tam, power. It is intended that the committee Chuu-Lian Terng, S. Walter Wei, B. Wong, and consider what may be called "quasi-political" Stephen S. T. Yau. motions. The committee has several possible September 26 was the deadline for submission courses of action on a proposed motion, includ­ of abstracts for consideration for inclusion in these ing but not restricted to special sessions. (a) doing nothing; Contributed Papers (b) conferring with supporters and opponents to arrive at a mutually accepted amended There will be sessions for contributed papers Wed­ version to be circulated in advance of the nesday morning and afternoon, Thursday morning, meeting; Friday and Saturday afternoons, and Sunday morn­ ing. October 17 was the deadline for submission (c) recommending and planning a format for of abstracts for contributed papers. debate to suggest to a Business Meeting; Late papers will not be accepted. (d) recommending referral to a committee; (e) recommending debate followed by referral Other AMS Sessions to a committee. Mathematics and Government Speaker There is no mechanism that requires automatic submission of a motion to the com­ REAR ADMIRAL J. B. MoONEY, JR., Chief of mittee. However, if a motion has not been Naval Research, Office of Naval Research, will give a submitted through the committee, it may be Special Address on Science and mathematics in the thought reasonable by a Business Meeting to Office of Naval Research at 2:15 p.m. on Thursday, refer it rather than to act on it without benefit January 10. of the advice of the committee. Panel Discussion The committee consists of Everett Pitcher The AMS Committee on Science Policy will sponsor (chairman), Marian B. Pour-El, David A. a Panel Discussion on The David Report and its Sanchez, and Guido L. Weiss. implementation at 7:00 p.m. on Thursday, January In order that a motion for the Business 10. The panelists are HIRSCH G. COHEN, RAMESH Meeting of January 10, 1985 receive the service GANGOLLI, and Gumo L. WEISS. offered by the committee in the most effective manner, it should have been in the hands of the Council Meeting secretary by December 10, 1984. The Council of the Society will meet at 2:00 Everett Pitcher, Secretary p.m. on Tuesday, January 8.

18 68th Annual Meeting of the MAA Minicourse #2: APL-A functional computer January 11-13, 1985 language for mathematicians is being organized by GARRY A. HELZER, University of Maryland, College Park. Part A is scheduled from 10:00 a.m. Invited Addresses to noon and Part B from 7:00p.m. to 9:00p.m. There will be eight invited fifty-minute ad­ on Friday, January 11. Total enrollment for this dresses. The names of the speakers, their Minicourse is limited to 30 persons. affiliations, the titles of their talks, the dates and This is a four-hour, self-contained, and hands­ times follow: on introduction to the APL computer language. The search for randomness, , No previous computer experience is expected. , 10:00 a.m. Sunday. The first session will introduce some of the Algorithms, geometry, and GL (n,Z), HELAMAN unique functions and operators defined in APL. R. P. FERGUSON, Brigham Young University, 9:00 The participants will then use these functions a.m. Saturday. and operators to do computations from among Toolkit for nonlinear dynamics, JoHN M. probability theory, calculus, matrix algebra, logic, GuCKENHEIMER, University of California, Santa and set theory. These computations will be done Cruz, 11:00 a.m. Saturday. without programming in APL's calculator mode. The many lives of invariant theory, GrAN­ The second session will emphasize the functional CARLO RoTA, Massachusetts Institute of Tech­ character of the language. Functional program­ nology, 10:00 a.m. Saturday. ming languages allow very flexible applications Some diophantine problems, MuRRAY M. packages to be easily built and maintained. This ScHACHER, University of California, Los Angeles, will not be a session on the details of entering 11:00 a.m. Sunday. and editing APL programs. Rather the structure Combinatorial set theory and its applications of a few such packages will be discussed and the to topology, FRANKLIN D. TALL, University of packages will be made available to the participants Toronto, 10:00 a.m. Friday. for hands-on experience. Examples will be chosen Some recent advances in real, complex, and from packages for descriptive statistics, linear al­ harmonic analysis, Gumo L. WErss, Washington gebra, number theory, two and three dimensional University, 9:00 a.m. Sunday. graphics, and polynomial arithmetic. Trusting computers, JOSEPH WEIZENBAUM, Minicourse #3: Teaching problem solving is Massachusetts Institute of Technology, 11:00 a.m. being organized by ALAN H. ScHOENFELD, Friday. . Part A is scheduled Minicourses from 10:00 a.m. to noon and Part B from 7:00 p.m. to 9:00 p.m. on Friday, January 11. Total Ten Minicourses are being offered by MAA. The enrollment for this Minicourse is limited to 80 names and affiliations of the organizers, the topics, persons. the dates and times of their meetings, and the The MAA Committee on the Teaching of enrollment limitations of each are as follows: Undergraduate Mathematics (CTUM) recommends Minicourse #1: The teaching of applied math­ that "a series of problem solving courses at various ematics is being organized by W. GILBERT levels of sophistication be developed and made STRANG, Massachusetts Institute of Technology. regular offerings in the standard curriculum." Part A is scheduled from 10:00 a.m. to noon and This Minicourse develops the following five themes Part B from 7:00p.m. to 9:00p.m. on Saturday, related to introducing a problem solving course: January 12. Total enrollment for this Minicourse 1. Heuristics la Polya. An introduction to is limited to 80 persons. a Polya's "basic" problem solving strategies, In this Minicourse one possible framework for with collections of sample problems. an introduction to modern applied mathematics 2. On thinking mathematically: The big picture. will be discussed. After basic courses in calculus What, beyond "basics", contributes to exper­ and linear algebra, there is an important need tise? The notion of "control" or "executive" that is not met by the traditional advanced decisions. calculus. The course should include both discrete and continuous problems, and numerical 3. What we know about thinking. Tidbits and combinatorial algorithms, bringing out their from the world outside mathematics, ranging analogies and developing the mathematical ideas from developmental psychology to artificial that are shared by different applications. The intelligence. organizer is convinced that this syllabus is also 4. What students don't know about thinking. the right way to organize the mathematics needed A close look at what really happens when by engineers and computer scientists; that subject students try to solve problems. does not have to be old-fashioned and boring. This 5. Teaching problem solving. A "nuts and bolts" course is the subject of the organizer's teaching discussion of problem solving in "ordinary" and writing, and he hopes for discussion and and special classes. Pointers to useful sources. correspondence about effective ways to introduce Minicourse #4: Applications of discrete mathe­ applied mathematics. matics is being organized by FRED S. RoBERTS,

19 Rutgers University. Part A is scheduled from syllogism before, but no advanced knowledge of 10:00 a.m. to noon and Part B from 7:00p.m. to logic is required. 9:00 p.m. on Friday, January 11. Total enrollment Minicourse #7: Linear programming is being for this Minicourse is limited to 80 persons. organized by CHARLES E. HAFF, University of One of the reasons that discrete mathematics Waterloo. Part A is scheduled from 9:00 a.m. has become so important is the enormous variety to noon and Part B from 2:00 to 5:00 p.m. on of applications of the subject. This Minicourse Sunday, January 13. Total enrollment for this will explore these applications. The emphasis Minicourse is limited to 80 persons. will be on several simple and traditional discrete Linear programming is the study of maximizing techniques: basic counting rules of combinatorics, or minimizing linear functions subject to linear the principle of inclusion and exclusion, the notion constraints. In addition to its theoretical richness, of graph coloring, and the concept of eulerian linear programming has wide applicability to such path. These techniques will be quickly reviewed real-world problems as capital budgeting, design (though prior knowledge of combinatorics or graph of diets, resource management, games of strategy, theory will not be necessary). Applications will economic growth prediction and transportation include switching functions in computer science, management. DNA chains in genetics, power in simple games This course is designed to acquaint the par­ in economics and political science, scheduling ticipant with the skills to formulate, solve and and operations research, engineering problems analyze solutions to linear programming problems. involving telecommunications and mobile radio Emphasis will be placed upon the computational transmission, urban sciences, computer graph techniques known as the simplex and revised plotting of electrical networks, and keypunching simplex algorithms and upon applications of errors in computing. duality theory. Also included will be pedagogical Minicourse #5: Groups, graphs, and computing pointers to the instructor who is new to the is being organized by EuGENE M. LuKs, Univer­ teaching of linear programming. Those who hope sity of Oregon. Part A is scheduled from 10:00 to gain the most from the course may wish to a.m. to noon and Part B from 7:00 p.m. to 9:00 review those parts of linear algebra dealing with p.m. on Saturday, January 12. Total enrollment solutions to systems of linear equations and with for this Minicourse is limited to 80 persons. elementary properties of vector spaces. The course will explore some exciting applica­ Minicourse #8: Microcomputer software in tions of group theory to problems in theoretical mathematics instruction is being organized by computer science. A focus will be on divide­ RoY E. MYERS, Pennsylvania State University, and-conquer algorithms for manipulating large New Kensington. Part A is scheduled from 10:00 permutation groups. These algorithms are the a.m. to noon and Part B from 7:00p.m. to 9:00 basic tools in the solutions of a number of p.m. on Saturday, January 12. Total enrollment problems, including some inspired by Rubik's for this Minicourse is limited to 30 persons. Cube. They also form the machinery behind some A wide variety of instructional software is new attacks on the computationally-significant becoming available for use with IBM compatible problem of testing graph isomorphism. microcomputers. It varies in nature, including Minicourse #6: PROLOG is being organized by drill and practice, tutorial, and materials for FREDERICK HoFFMAN, Florida Atlantic Univer­ use as lecture aids. Software is available for sity. Part A is scheduled from 10:00 a.m. to use in courses from introductory algebra through noon and Part B from 2:00 p.m. to 4:00 p.m. on calculus, statistics, differential equations, and Sunday, January 13. Total enrollment for this linear algebra. In this Minicourse, various types of Minicourse is limited to 30 persons. software will be demonstrated, and issues relating The intention of this Minicourse is to in­ to their uses will be discussed. It is planned that a troduce the programming language PROLOG large variety of software will be available and that (PROgramming in LOGic) to an audience of math­ Minicourse participants will have the opportunity ematicians. PROLOG is many things: mechanized to work with the software on microcomputers. logic; a good programming language for begin­ Minicourse #9: Teacher in-service programs (A ners; a major artificial intelligence language, with COMET Minicourse) is being organized by EUGENE applications to game playing, theorem proving, A. MAIER, Mathematics Learning Center and robot motion, natural language understanding Portland State University. Part A is scheduled and expert systems development; a powerful tool from 10:00 a.m. to noon and Part B from 2:00 for database management; and the initial choice to 4:00 p.m. on Sunday, January 13. Total for the "machine language" of the Japanese Fifth enrollment for this Minicourse is limited to 40 Generation Computer Project. In the Minicourse, persons. PROLOG will be described, evidence will be given Mathematicians are becoming more aware of that these statements are at least arguable, and the responsibility of the mathematics community some hands-on experience with microPROLOG will for developing programs to improve mathematics be provided. No computer background will be teaching at all levels in the schools. The CUPM assumed; those attending should have seen a Panel on Continuing Mathematical Education of

20 Teachers (COMET) is sponsoring this Minicourse Contributed Papers for mathematicians who are interested in design­ Papers were accepted on five topics in collegiate ing quality in-service programs. Mathematicians mathematics for presentation in contributed paper with no prior involvement in "math education" sessions at Anaheim. The topics, session leaders, are especially welcome. The course will inves­ their affiliations and days they will meet are: tigate strategies and procedures for offering con­ • Teaching introductory statistics: topics, tinuing education that serves to increase teachers' trends, and techniques (Ann Watkins, Pierce competence and confidence in teaching mathe­ College, Session Leader), Saturday morning. matics. Topics discussed will include: types of programs, funding, judging needs and interests of • Making mathematics majors marketable: un­ teachers, program design and selection of content, dergraduate training for nonacademic careers instructional approaches, examples of exemplary (Ann K. Stehney, Institute for Defense programs, and reflections of a as a Analyses, Session Leader), Sunday morning. mathematics educator. • Strategies, tactics, and techniques in teaching Minicourse #10: Constructing placement ex­ lower division and remedial courses (Ann aminations is being organized by RICHARD H. D. Holley, San Diego Mesa College, Session PROSL, College of William and Mary and Chair­ Leader), Sunday afternoon. man of the Committee on Placement Examina­ • Teacher training and retraining (Calvin T. tions. Part A is scheduled from 10:00 a.m. to Long, Washington State University, Session noon and Part B from 7:00 p.m. to 9:00 p.m. Leader), Friday morning. on Friday, January 11. Total enrollment for this • Does research in mathematics learning at Minicourse is limited to 80 persons. the college level exist? (James J. Kaput, Lectures and workshops will take participants, Southeastern Massachusetts University, Ses­ step-by-step, through the entire process of con­ sion Leader), Sunday afternoon. structing and implementing placement exams, in­ Presentations are normally limited to ten cluding: preliminary planning, writing test items, minutes, although selected contributors may be designing a test for establishing cut-off scores, and given up to twenty minutes. evaluating the test. Placement testing problems Individuals wishing to submit papers for any of participants' own institutions will be discussed of these sessions in Anaheim should have done so during question and answer periods. before November 15, 1984. The Minicourses are open only to persons Late papers will not be accepted. who have registered for the Joint Mathematics Other MAA Sessions Meetings and paid the Joint Meetings registration fee. The Panel on Remediation will sponsor a The Minicourses have separate registration fees Panel Discussion on Is there an alternative to of $25 each. This fee entitles the registrant remediation? on Saturday, January 12, at 7:00 to attend all sessions of the Minicourse for p.m. The moderator is DoNALD W. BusHAW, which he/she has registered. Please note in Washington State University. the descriptions the dates and times when these The Committee on Secondary School Lectures Minicourses meet. Participants are limited to two is sponsoring a Panel Discussion on How to give a Minicourses each. Payment of the fee(s) must be successful talk to secondary school students from made to the Minicourse Cashier at the meeting 9:00 a.m. to 10:30 a.m. on Saturday, January 12. registration desk in Anaheim two working hours There will be individual presentations by PETER prior to the beginning of the Minicourse, or the J. HILTON, DAVID E. LOGOTHETTI, and JEAN reservation will be relinquished to someone on J. PEDERSEN, followed by a Panel Discussion the waiting list. When making payment, the with five participants including Professors Hilton, participant should present the confirmation to Logothetti, and Pedersen. the Minicourse Cashier. "Standby" reservation The Committee on the Teaching of Under­ confirmations will be issued to participants whose graduate Mathematics (CTUM) is sponsoring an in­ preregistration was received after the Minicourse formation gathering session titled Teaching assis­ was filled. These individuals should check with tant and adjunct instructor competency. Panelists the Minicourse Cashier one working hour prior presenting information about programs at their to the Minicourse to see if any openings have universities will be FELIX E. BROWDER, WEN­ occurred. DELL H. FLEMING, LEON A. HENKIN, DAVID P. If the only reason for registering for the Joint KRAINES, AUDREY A. TERRAS, and the presider, Meetings is to gain admission to a Minicourse, BETTYE ANNE CASE. Participation in the dis­ this should have been indicated by checking cussion following is encouraged from departments the appropriate box on the preregistration form. employing adjunct instructors as well as from all Then, if the Minicourse is fully subscribed, full Ph.D. granting departments. This session will be refund can be made of the Joint Mathematics held from 11:00 a.m. to noon on Sunday, January Meetings preregistration fee. Otherwise, the Joint 13. Meetings preregistration will be processed, and A Panel Discussion on Calculus instruction: then be subject to the 50 percent refund rule. Crucial but ailing will take place from 10:00

21 a.m. to noon on Friday, January 11. The co­ of Science (AAAS) project, is scheduled for 8:00 organi:llers are RoNALD G. DouGLAS, on leave p.m. on Friday, January 11. JAMES C. CRIMMINS, at the University of California, Berkeley and executive producer of this seven-part film series for STEPHEN B. MAURER of Swarthmore College and schools, will discuss the problem of making a film the Alfred P. Sloan Foundation. The speakers are series on problem solving. The presentation will LIDA K. BARRETT, Northern lllinois University; describe how the production team, working closely JOHN W. KENELLY, Clemson University; PETER with a distinguished advisory board, designed D. LAx, Courant Institute of the Mathematical the series not only to illustrate problem solving Sciences; and DoNALD B. SMALL, Colby College. concepts, but also to involve students through This panel is jointly sponsored by the AMS and the films and accompanying teaching materials in MAA. the challenge of devising and solving their own There will be a presentation of, and discussion nonroutine problems. It will also focus on the role about, a preliminary proposal from the Panel of ffims in schools, what they can do in motivating on Discrete Mathematics. This session, led by students and enlarging the classroom environment MARTHA J. SIEGEL, Towson State University, and what they cannot do. will take place from 8:00 a.m. to 9:50 a.m. on DEANE ARGANBRIGHT of Whitworth College Friday, January 11. The panel will have published will make a presentation titled The electronic its preliminary report by December 1, 1984, and spreadsheet-a creative program for mathematics invites the MAA membership to react to it in an and mathematicians. The presentation is open discussion session. Copies of the report will scheduled from 1:00 p.m. to 1:50 p.m. on Sunday, be made available from the Washington, DC office January 13. of the MAA and at the MAA Book Sale in Anaheim. A special program on computer science is being There will be a Panel Report of the Fifth In­ sponsored by the ACM/MAA Joint Committee on ternational Congress on Mathematical Education Retraining for Computer Science. There will from 9:30 a.m. to 10:50 a.m. on Sunday, January be three separate, but related, events which 13. The presider will be DoNALD M. HILL of will take place on Friday morning, Saturday Florida Agricultural and Mechanical University. morning, and Sunday morning. There will Professor Hill is Chairman of the U.S. Commis­ be five 40-minute talks in a special session sion on Mathematical Instruction. Members of the on Advanced topics for mathematicians teaching panel are Henry L. Alder, Katherine P. Layton, undergraduate computer science, scheduled on Warren Page and Henry 0. Pollak. Friday and Sunday. This session will consist of There will be a Panel Discussion on Sunday five talks of forty minutes each on advanced topics afternoon, January 13, from 2:00 p.m. to 3:30 in computer science that can be incorporated into p.m., sponsored by the Committee on Computers the undergraduate computer science curriculum. in Mathematics Education (CCIME). This session, The talks will be geared towards mathematicians organi:lled by CHRISTOPHER NEVISON of Colgate with a firm foundation in computer science-such University, will concern the use of computing in upper level undergraduate courses. as that obtained at the Institute for Retraining in Computer Science (IFRICS). Particular emphasis There will be a Panel Discussion on Project will be placed on indicating where the material EQuality, an undertaking of the College Board, fits within the undergraduate program. from 2:00 p.m. to 3:30 p.m. on Sunday, January 13. This Panel Discussion is cosponsored by the The main goal of this session is to present MAA and the National Council of Teachers of enrichment material that will help the mathe­ Mathematics (NCTM). matician responsible for maintaining an under­ A get-together cocktail hour for those interested graduate computer science curriculum. A second in two-year college mathematics will be held from goal is to describe some of the current areas of 4:30 p.m. to 6:00 p.m. on Friday, January 11. research in computer science. It will be hosted by DONALD J. ALBERS, Menlo There will be workshops on Friday and Saturday College, Second Vice President and chairman of on The nature of computer science: Now that the Committee on Two-Year Colleges, and will you know how to program... There is more include the following: Discussion and distribution to computer science than programming and of the recommendations of the Sloan Foundation discrete mathematics. Knowing a programming conference New directions in two-year college language (or even several) is not enough. There mathematics DONALD J. ALBERS, STEPHEN are many subtle problems whose understanding Rom, and ANN E. WATKINS; review of the requires more than a rapid study of a textbook. continuing work of the CUPM Panel on the Indeed, mastering computer science (even at the Mathematics Curriculum in Two-Year Colleges by undergraduate level) involves the study of an the panel chairman, RoNALD M. DAVIS; report increasingly difficult sequence of concepts and on the College Mathematics Journal by its editor, techniques. WARREN PAGE; and an open forum to identify The purpose of this workshop is to discuss, in concerns of those assembled. detail, several problems that appear to be easy A presentation of Challenge of the Unknown, but, in fact, require sophisticated machinery to an American Association for the Advancement develop their efficient solution.

22 TIMETABLE (Pacific Standard Time) The final version oi the Timetable and Program including room assignments will be distributed at the meeting ' ' AMERICAN MATHEMATICAL SOCIETY SHORT COURSE SERIES

MONDAY, January 7 FAffi ALLOCATION 9:00a.m. - 4:00p.m. REGISTRATION (Short Course Only) Outside California Room A

10:30 a.m. - 10:45 a.m. Introduction 10:45 a.m. - noon The apportionment oi representation Michael L. Balinski and H. Peyton Young 2:00p.m. - 3:15 p.m. Cost allocation H. Peyton YOtmg 3:45p.m. - 5:00 p.m. Inequality measurement James E. Foster

TUESDAY, January 8 8:00 a.m. - 2:00p.m. REGISTRATION (Short Course Only) Outside California Room A

9:00 a.m. - 10:15 a.m. Fairness and strategy in voting Herve Moulin 10:45 a.m. - noon Fairness and strategy In voting (continued) Herve Moulin 2:00p.m. - 3:15 p.m. Auctions and competitive bidding Robert J. Weber 3:45p.m. - 4:45 p.m. Discussion

JOINT MATHEMATICS MEETINGS Mathematical Association oi America TUESDAY, January 8 American Mathematical Society and Other Organizations 2:00p.m. - 10:00 p.m. COUNCIL MEETING California RoomE 4:00p.m. - 8:00 p.m. REGISTRATION North Lobby 7:00p.m. - 10:00 p.m. American Association for the Advancement of Science - SYMPOSIUM: Order in chaos Title to be announced Mitchell Feigenbaum Solving the unsolvable; predicting the unpredictable Joseph Ford Detecting strange attractors In experiments Jerry P. Gollub

WEDNESDAY, January 9 AlliS MAA and other Organizations

8:00a.m. - 5:00 p.m. REGISTRATION

SPECIAL SESSION 8:00a.m. - 11:50 a.m. Stochastic differential geometry I

SESSIONS FOR CONTRIBUTED PAPERS 8:00a.m. - 11:55 a.m. General topology

8:00 a.m. - 12:10 p.m. Number theory

8:15 a.m. - 11:25 a.m. Algebra

8:30 a.m. - 11:55 a.m. Complex analysis

9:00 a.m. - 10:00 a.m. INVITED ADDRESS Some new approaches to moduli spaces R nth M. Charney

23 Assuming no prerequisite in computer science, This will be the first of an annual series of the first session will present background material symposia, intended by Section A to help bring and outline the problems to be considered. mathematics and the parts of science using and Participants will then be challenged to use the needing new mathematical methods together. material presented to solve these problems. The The Association for Symbolic Logie (ASL) will second session will discuss the correct solutions as hold its 1985 Annual Meeting on Saturday and well as many seemingly correct, but nevertheless Sunday, January 12-13. In addition .to the false, solutions. contributed papers, there will be six invited talks. There will also be a Panel Discussion on Satur­ The speakers are Lou VAN DEN DRIES, LEo day on Undergraduate computer science is not A. HARRINGTON, JOHN McCARTHY, THEODORE just mathematics. This panel discussion will SLAMAN, KIT FINE, and HOWARD BECKER. center on the relationship between undergraduate (Note that the related AMS Invited Address on mathematics and computer science. The panelists logic by W. Hugh Woodin has been scheduled for are research computer scientists with considerable 3:30p.m. on Friday, January 11.) teaching experience at both the undergraduate The ATP Prize Committee (ATP) will award and graduate levels. They will discuss the un­ the 1984 Milestone Prize in Automated Theorem dergraduate computer science curriculum, tech­ Proving to J. A. RoBINSON on Friday, January 11 niques for teaching computer science at the un­ at 7:00p.m. for his fundamental contributions to dergraduate level, the role of mathematics within the field. Professor Robinson's address will follow the computer science program and the knowledge the presentation. and skills included in the undergraduate computer The fifth annual Emmy Noether Lecture will science program that are not direct extensions of be presented to the Association for Women in those learned in elementary mathematics. Mathematics (AWM) at 9:00 a.m. on Friday, Business Meeting January 11, by JANE CRONIN SCANLON, Rutgers University. Professor Scanlon will speak on A The Business Meeting of the MAA will take place at 4:30 p.m. on Saturday, January 12. The 1985 model of a cardiac fiber: Problems in singularly Award for Distinguished Service to Mathematics, perturbed equations. the Chauvenet Prize, and the MAA Book Prize AWM will sponsor a Panel Discussion on will be presented. This meeting is open to all Nonacademic careers in mathematics at 10:15 members of the Association. a.m. on Thursday, January 10. The moderator for this panel is PATRICIA C. KENSCHAFT, Board of Governors Montclair State College. Panelists include MARIA The MAA Board of Governors will meet at 9:00 M. KLAWE, ELIZABETH W. RALSTON, BONNIE a.m. on Thursday, January 10. This meeting is SAUNDERS, and MARGARET C. W AID. open to all members of the Association. The AWM Business Meeting will be held at 11:15 Section Officers a.m. on Thursday, January 10. There will be a Section Officers' meeting at 7:00 A reception is being planned by AWM for 5:45 p.m. on Thursday, January 10. p.m. on Thursday, January 10. DAVID W. Fox, Director of the Mathematical ACTMTIES OF OTHER ORGANIZATIONS and Information Sciences Directorate of the Section A of the American Association for the Air Force Office of Scientific Research, will Advancement of Science (AAAS) will sponsor a speak at 5:45 p.m. on Wednesday, January 9, special symposium on Order in chaos, to be held on the Interagency Commission for Extramural from 7:00p.m. to 10:00 p.m. on Tuesday, January Mathematics Programs (ICEMAP). 8. The National Association of Mathematicians Recent work in many fields of science, as (NAM) will receive the William W. S. Claytor different as meteorology, turbulence of fluids, Lecture at 10:00 a.m. on Saturday, January physiological control mechanisms, and molecular 12, from DAVID BLACKWELL, Department of action, show that apparently dissimilar types of Statistics, University of California, Berkeley, random behavior in these fields all have common who will speak on Some recent developments features susceptible to mathematical modelling. in statistics. The work raises new mathematical problems, NAM will sponsor a Panel Discussion titled and affords opportunities for application of Graduate students in mathematics: "Increasing many areas of pure mathematics. The three the pool" at 11:15 a.m. on Saturday, January speakers, MITCHELL FEIGENBAUM of Cornell 12. The panel will be moderated by ROGERS University, JosEPH FoRD of the Georgia Institute NEWMAN, Southern University. Panelists are of Technology, and JERRY P. GOLLUB of TEPPER GILL, GLORIA HEWITT, J. ARTHUR Haverford College, all professors of physics, all JONES, and DWIGHT LAHR. among the leaders in this new area of science. The NAM Business Meeting will take place at The discussion is intended to be expository, to 6:30 p.m. on Friday, January 11. introduce mathematicians to the new field, and to JOHN C. POLKING, Director of the Division indicate directions for new mathematical research. of Mathematical Sciences of the National Science

24 TIMETABLE All sessions are at the Anaheim Convention Center, unless noted as follows: AMH~Anaheim Marriott Hotel

Mathematical Association of America WEDNESDAY, January 9 American Mathematical Society and Other Organizations SPECIAL SESSIONS 9:00 a.m. - 11:50 a.m. Nonstrictly hyperbolic conservation laws I

9:00 a.m. - 11:50 a.m. Asymptotic properties of hyperbolic groups I

9:00 a.m. - 11:50 a.m. Ordinary differential equations I

SESSIONS FOR CONTRIBUTED PAPERS 9:00a.m. - 11:55 a.m. Operator theory I 9:00 a.m. - 11:30 a.m. Functional analysis I 9:00a.m. - 9:55 a.m. Algebraic geometry 10:00 a.m. - 11:10 a.m. Lie groups 10:00 a.m. - 11:10 a.m. General session

10:15 a.m. - 11:15 a.m. INVITED ADDRESS On Gauss' class number problem Dorian Goldfe ld COLLOQUIUM LECTURES 1:00 p.m. - 2:00 p.m. Lecture I: The classification of the finite simple groups Daniel Gorenstein I 1:00 p.m. - 5:00 p.m. EXHIBITS Anaheim Room 1:00 p.m. - 5:00 p.m. A:MS BOOK SALE MAA BOOK SALE Anaheim Room Anaheim Room 2:15 p.m. - 3:15 p.m. INVITED ADDRESS Is a variety determined by its periods ? Ron Donagi SPECIAL SESSIONS 2:15 p.m. - 5:45 p.m. Analytic number theory I

2:15 p.m. - 4:35 p.m. Nonstrictly hyperbolic conservation laws II

2:15 p.m. - 5:35 p.m. Ordinary differential equations II

SESSIONS FOR CONTRIBUTED PAPERS 2:15p.m. - 4:25 p.m. Linear algebra 2:15 p.m. - 5:25 p.m. Probability 2:15p.m. - 5:40p.m. Partial differential equations 2:15p.m. - 4:25 p.m. Operator theory II 2:15 p.m. - 4:40p.m. Topology 2:15p.m. - 4:40 p.m. Functional analysis II 2:15 p.m. - 4:40p.m. Mathematical economics 2:15p.m. - 5:25p.m. Differential geometry

3:30 p.m. - 4:30 p.m. INVITED ADDRESS Beauty and symmetry in the theory of minimal surfaces William H. Meeks III SPECIAL SESSION 3:30 p.m. - 5:50 p.m. Algebraic defor mat!on theory I

4:45 p.m. - 5:45 p.m. Federal support for the mathematical sciences: Research and education John C. Polking, Director Division of Mathematical Sciences, NSF

25 Foundation (NSF) will speak at 4:45 p.m. on p.m. by two parallel sessions on The relationship Wednesday, January 9, on Federal support for the between mathematics and computer science in the mathematical sciences: Research and education. same department and How to develop a successful At 7:15 p.m. on Wednesday, January 9, the research department. Office for Advanced Scientific Computing of Attendance at these sessions is not restricted the NSF will present a discussion of The NSF to department chairmen and all interested math­ supercomputer initiative. LARRY LEE, Program ematicians are encouraged to attend. Director for Supercomputer Centers, is organizing this presentation, and will speak from 7:15 to 7:45 Book Sales p.m. There will be three additional speakers. Books published by the AMS and MAA will be The NSF will again be represented at a booth sold for cash prices somewhat below the usual in the exhibit area. NSF staff members will be prices when these same books are sold by mail. available to provide counsel and information on These discounts will be available only to registered NSF programs of interest to mathematicians from participants wearing the official meeting badge. 9:00 a.m. to 5:00 p.m., Thursday and Friday, VIsA and MASTERCARD credit cards will be January 10-11. accepted for book sale purchases at the meeting. The Rocky Mountain Mathematics Consortium The book sales will be open the same days {RMMC) Board of Directors will meet on Thursday, and hours as the Exhibits and are located in January 10, from 2:00 p.m. to 4:00 p.m. the Anaheim Room of the Anaheim Convention Center. OTHER EVENTS OF INTEREST Exhibits National Mathematics Department The book and educational media exhibits are Chairmen's Meeting located in the Anaheim Room of the Anaheim The Joint Policy Board for Mathematics, AMS, Convention Center and will be open Wednesday, MAA, and the Society for Industrial and Applied January 9, through Saturday, January 12. The Mathematics, will sponsor a keynote address by exhibits will be open from 1:00 p.m. to 5:00 p.m. LESTER H. LANGE, Dean of the College of on Wednesday; from 9:00 a.m. to 5:00 p.m. on Science at San Jose State University, who will Thursday and Friday; and from 9:00 a.m. to noon speak on What does the administration expect Saturday. All participants are encouraged to visit from department chairmen?, at 7:30 p.m. on the exhibits during the meeting. Participants Friday, January 11. This will be followed at 8:00 visiting the exhibits will be asked to display their meeting badge in order to enter the exhibit area. Petition Table MATHFILE At the request of the AMS Committee on Human Rights of Mathematicians, a table will The MATHFn..E demonstration will be held in be made available in the meeting registration the exhibit area during regular exhibit hours. area at which petitions on behalf of named Many new features and additions to the database individual mathematicians suffering from human will be explained, and sample searches will be rights violations may be displayed and signed performed on the DIALOG and BRS systems. by meeting participants acting in their individual MATHFn..E is expanding: At present the file capacities. contains 400,000 MR. citations dating back to 1973 Signs of moderate size may be displayed at the (with the text of the reviews from 1979 on). table, but must not represent that the case of the By next year 200,000 additional entries from MR. individual in question is backed by the Committee 1959-1972 will be searchable online. on Human Rights unless it has, in fact, so voted. The currency of MATHFILE will improve greatly Volunteers may be present at the table to provide when Current Mathematical Publications (CMP) information on individual cases, but notice must becomes an integral part of MATHFn..E at the be sent at least seven (7) days in advance of the end of 1984. It will then be possible to search meeting to the Meetings Department in Providence simultaneously both printed publications: MR. (telephone 401-272-9500). Since space is limited, back to 1959 and the most current issues of CMP. it may also be necessary to limit the number of volunteers present at the table at any one time. ACCOMMODATIONS The Committee on Human Rights may delegate a person to be present at the table at any or all times, Hotels taking precedence over other volunteers. Any material which is not a petition (e.g., The rates listed below are subject to an 8 advertisements, resumes) will be removed by the percent sales tax. The number in parentheses staff. When registration eloses, any material on after the name of the hotel is the number it carries the table will be discarded, so individuals placing on the map. The estimated walking distance petitions on the table should be sure to remove from the hotel to the Anaheim Convention Center them prior to the close of registration. is given in parentheses following the telephone number.

26 TIMETABLE All sessions are at the Anaheim Convention Center, unless noted as follows: AMH = Anaheim Marriott Hotel

Mathematical Association of America WEDNESDAY, January 9 American Mathematical Society and Other Organizations 5:45 p.m. - 6:00 p.m. Interagency Commission for Extramural Mathematics Programs (ICEMAP) David W. Fox, Director of the Mathematical and Information Sciences Directorate, Air Force Office of Scientific Research (AFOSR)

7:15 p.m. - 8:15 p.m. The NSF supercomputer initiative Larry Lee, Program Director for Supercomputer Centers, NSF

8:45 p.m. - 9:45 p.m. JOSlAH WILLARD GIBBS LECTURE I Randomization in mathematics and computer science Michael 0. Rabin

THURSDAY, January 10 AMS MAA and Other Organizations

8:00 a.m. - 4:00p.m. REGISTRATION North Lobby SPECIAL SESSIONS 8:00 a.m. - 10:50 a.m. Algebraic deformation theory II 8:00 a.m. - 11:50 a.m. Analytic number theory II

SESSIONS FOR CONTRIBtJTED PAPERS 8:00 a.m. - 11:55 a.m. Abstract analysis H:OO a.m. - 11:55 a.m. Combinatorics 8:15 a.m. - 11:55 a.m. General session

SPECIAL SESSION 8:30 a.m. - 11:50 a.m. Asymptotic properties of hyperbolic groups II

SESSION FOR CONTRIBUTED PAPERS 8:30 a.m. - 11:55 a.m. Group theory

9:00 a.m. - 10:00 a.m. INVITED ADDRESS Some recent directions in nonlinear elliptic partial differential equations Lawrence Craig Evans 9:00 a.m. - 9:30 a.m. EMPLOYMENT REGISTER ORIENTATION SESSION

9:00 a.m. - 4:00 p.m. IMAA - BOARD OF GOVERNORS' MEETING

9:00 a.m. - 5:00 p.m. EXHIBITS Anaheim Room 9:00 a.m. - 5:00 p.m. AMS BOOK SALE MAA BOOK SALE Anaheim Room Anaheim Room SPECIAL SESSIONS 9:00 a.m. - 11:50 a.m. Teichmuller theory for surfaces, graphs and hyperbolic manifolds I 9:00 a.m. - 11:50 a.m. Ordinary differential equations m 9:30 a.m. - 11:50 a.m. Nonstrictly hyperbolic conservation laws III

9:30 a.m. - 4:00 p.m. EMPLOYMENT REGISTER REGISTRATION

SESSION FOR CONTRIBUTED PAPERS 9:30 a.m. - 11:40 a.m. Mathematical education

SPECIAL SESSION 10:15 a.m. - 12:05 p.m. Stochastic differential geometry II

27 Participants should be aware that it is general Information Table hotel practice in most cities to hold a non­ The information table at Joint Meetings of guaranteed reservation until6:00 p.m. only. When the AMS and MAA is set up in the registration one guarantees a reservation by paying a one­ area for the dissemination of information of night's deposit in advance, however, the hotel a nonmathematical nature of possible interest usually will honor this reservation up until check­ to the members. The administration of the out time the following day. If the individual information table is in the hands of the AMS­ holding the reservation has not checked in by MAA Joint Meetings Committee, as are all then, the room is then released for sale, and the arrangements for such joint meetings. The hotel retains the deposit. If you hold a guaranteed following rules and procedures apply. reservation at a hotel, but are informed upon arrival that there is no room for you, there are 1. Announcements submitted by participants certain things you can request the hotel do. First, should ordinarily be limited to a single sheet no they should provide for a room at another hotel more than 8 14". !"X in town for that evening, at no charge (you have 2. A copy of any announcement proposed already paid for the first night when you made for the table is to be sent to: H. Hope Daly, your deposit). They should pay for taxi fares American Mathematical Society, Post Office to the other hotel that evening, and back to the Box 6248, Providence, Rhode Island 02940 to meetings the following morning. They should also arrive at least one week before the first day of pay for one telephone toll call so that you can the scientific sessions. let people know you are not at the hotel you 3. The judgment on the suitability of an expected. They should make every effort to find a announcement for display rests with the Joint room for you in their hotel the following day, and, Meetings Committee. It will make its judge­ if successful, pay your taxi fares to and from the ments on a case by case basis to establish second hotel so that you can pick up your baggage precedents. and bring it to the first hotel. Not all hotels in 4. Announcements of events competing in time all cities follow this practice, so your request for or place with the scheduled scientific program these services may bring mixed results, or none at will not be accepted. all. 5. Copies of an accepted announcement for Please make all changes to or cancellations of the table are to be provided by the proponent. hotel reservations with the Mathematics Meetings Announcements are not to be distributed in any Housing Bureau in Providence before January 1, other way at the meeting (for example, not by 1985. The telephone number in Providence is posting or personal distribution of handbills). 401-272-9500 (extension 239). After that date, 6. It may be necessary to limit the number changes should be made directly with the hotel. of events or the quantity of announcements Cancellations must be made 48 hours prior to distributed at a meeting. date of arrival. 7. At the close of registration, the table will Hilton at the Park (5) be swept clean. A proponent who wishes the 1855 South Harbor Boulevard return of extra copies should remove them. Anaheim, California 92802 Telephone: 714-750-1811 (2 minutes) Participants should be aware that when major Singles $ 60 conventions occur in any large city, additional Doubles/Twin Doubles$ 60 (1 or 2 beds) safety problems are created, especially at night. Triples $ 70 (2 beds) Those who are attending the meetings alone, or $ 70 (2 beds plus cot) who are concerned about walking to and from the Quads $ 80 (2 beds) meetings after dark, are encouraged to choose a Suites $155-$380 hotel in close proximity to the Convention Center. Children of any age are free in same room Participants are also urged to read the Words to with parents. No advance deposit is required the Wise in the centerfold of the program they for room reservations. The Hilton will request receive at the meetings. deposits when confirmations are sent; payment Reservations at these hotels cannot be made by for deposits may be made by check, American calling the hotel directly until after December 31. Express, Diners Club, and Carte Blanche. Balance Also, after that date, the rates below may not due may be paid in the same manner, as well as apply. by VrsA and MASTERCARD. There is a $1 daily In all cases "single" refers to one person in parking fee for guests of the Hilton with in/out one bed; "double" refers to two persons in one privileges. Airport bus will discharge passengers bed; "twin" refers to two persons in two single at the Grand Hotel where a Hilton phone is beds; and "twin double" refers to two persons in available to request shuttle service to the hotel. A two double beds. A rollaway cot for an extra 48-hour cancellation notice is required. person can be added to double or twin rooms Holiday Inn-Anaheim (6) only; however, not all hotels are willing to do so. 1850 South Harbor Boulevard

28 TIMETABLE All sessions are at the Anaheim Convention Center, unless noted as follows: AMH ~Anaheim Marriott Hotel

Mathematical Association of America American Mathematical Society THURSDAY, January 10 and Other Organizations 10:15 a.m. - 11:15 a.m. Association for Women in Mathematics PANEL DISCUSSION: Nonacademic careers in mathematics Patricia C. Kenschaft (moderator) Maria !Vl. Klawe Elizabeth W. Ralston Bonnie Saunders Margaret C. Waid

11:15 a.m. - 12:15 p.m. INVITED ADDRESS The Riemann hypothesis for Hilbert spaces of entire functions Louis de Branges 11:15 a.m. - 12:55 p.m. AWM- BUSINESS MEETING

COLLOQUIUM LECTURES 1:00 p.m. - 2:00 p.m. Lecture II: The classification of the finite simple groups Daniel Gorenstein 2:00 p.m. - 4:00 p.m. Rockv Mountain Mathematics Consortium BOARD OF DIRECTORS' MEETING

2:15 p.m. - 3:15 p.m. SPECIAL INVITED ADDRESS Science and mathematics in the Office of Naval Research Rear Admiral J. B. Mooney, Jr., Chief of Naval Research, ONR I 4:00 p.m. - 5:30 p.m. COLE PRIZE SESSION AND BUSINESS MEETING

5:45p.m. AWM- RECEPTION

7:00 p.m. - 8:30 p.m. Committee on Science Policy PANEL DISCUSSION: The David Report and its implementation

7:00 p.m. - 8:30 p.m. MAA - SECTION OFFICERS' MEETING

FRIDAY, January 11 AMS MAA and Other Organizations

8:00 a.m. - 4:00 p.m. REGISTRATION North Lobby morning MAA - CONTRIBUTED PAPER SESSION Teacher training and retraining Calvin T. Long

8:00 a.m. - 9:50 a.m. MAA - Panel on Discrete Mathematics PANEL DISCUSSION: A preliminary proposa Martha .J. Siegel (presider)

8:00 a.m. - 10:00 a.m. ACM/MAA - Joint Committee on Retraining for Computer Science SPECIAL SESSION on Advanced topics for mathematicians teaching undergraduate computer science, Part A

9:00 a.m. - 9:50 a.m. AWM- EMMY NOETHER LECTURE A model of a cardiac fiber: Problems in singularly perturbed equations Jane Cronin Scanlon

9:00 a.m. - 5:00 p.m. EXHIBITS Anaheim Room 9:00 a.m. - 5:00 p.m. AMS BOOK SALE IMAA BOOK SALE Anaheim Room Anaheim Room 9:00 a.m. EMPLOYMENT REGISTER DISTRIBL'TION OF SCHEDULES

9:30 a.m. - 5:30 p.m. EMPLOYMENT REGISTER INTERVIEWS

29 BALL RD. BALL RD.

CERRITOS AVE. !i5 enl­ w c:i $: DISNEYLAND >..J lXl a: FREEDMAN WAY 0 lXl a: <( J:

KATELLA AVE. KATELLA AVE. 4 CD 0 CD • ANAHEIM ~CONVENTION ...... , CENTER !i5 CONVENTION WAY a: CD CD w !ii <( G) CD CD J: @ ORANGEWOOD AVE. ORANGEWOOD AVE.

N

1 c:i >..J w~i)..-E lXl a: T 0 lXl s a: <( J: CHAPMAN AVE. CHAPMAN AVE.

List of Anaheim Hotels/Motels Q) Inn of Tomorrow @ Holiday Inn- Anaheim (6) Magic Lamp Q) Marriott Hotel- Anaheim @ Magic Carpet @ Quality Inn- Anaheim @ Jolly Roger Inn ® Anaheim Town and Country Inn @ Hilton at the Park @ Anaheim Travelodge International Inn

SCALE 0 .5 1.5 MILES 0 .5 1.5 2 KILOMETERS COPYRIGHT© 1984 ONE KILOMETER EQUALS .62 MILE AUTOMOBILE CLUB OF SOUTHERN CALIFORNIA

30 TIMETABLE All sessions are at the Anaheim Convention Center, unless noted as follows: AMH =Anaheim Marriott Hotel

Mathematical Association of America FRIDAY, January 11 American Mathematical Society and Other Organizations 10:00 a.m. - 10:50 a.m. MAA - INVITED ADDRESS Combinatorial set theory and its applications to topology Franklin D. Tall

10:00 a.m. - noon ACM/MAA- Joint Committee on Retraining for Computer Science WORKSHOP- The nature of computer science: Now that you know how to program.•• Part I

10:00 a.m. - noon AMS/MAA PANEL DISCUSSION Calculus instruction: Crucial but ailing Ronald G.\ Douglas (co-organizer) Stephen B. Maurer (co-organizer) Lida K. Barrett John v.:. Kenelly Peter D. Lax Donald B. Small

10:00 a.m. - noon MAA - MINICOURSE i/2 (Part A) APL - A functional computer language for mathematicians Garry A. Helzer

10:00 a.m. - noon MAA - MINICOURSE i/3 (Part A) Teaching problem solving Alan H. Schoenfeld

10:00 a.m. - noon MAA - MINICOURSE !14 (Part A) Applications of discrete mathematics Fred S. Roberts

10:00 a.m. - noon MAA - MINICOURSE i/10 (Part A) Constructing placement examinations Richard H. Pros\

11:00 a.m. - 11:50 a.m. MAA - INVITED ADDRESS Trusting computers Joseph Weizenbaum

COLLOQUIUM LECTURES 1:00 p.m. - 2:00 p.m. Lecture III: The classification of the finite simple groups Daniel Gorenste!n SPECIAL SESSIONS 1:00 p.m. - 2:10 p.m. Differential geometry I

1:00 p.m. - 5:20 p.m. Algebraic comhinatorics I

1:00 p.m. - 6:20 p.m. Analytic number theory III

SESSIONS FOR CONTRIBUTED PAPERS 1:00 p.m. - 5:25 p.m. Differential equations

1:00 p.m. - 5:10 p.m. Computer science and numerical analysis

1:00 p.m. - 3:40 p.m. Lattices

2:15 p.m. - 3:15 p.m. INVITED ADDRESS On Gromov' s horizon for combinator!ally hyperbolic groups Laurence C. Siebenmann SPECIAL SESSION 2:15 p.m. - 4:20 p.m. Finite group theory I

SESSION FOR CONTRIBUTED PAPERS 2:15 p.m. - 3:40 p.m. Commutative rings

31 Anaheim, California 92802 Telephone: 714-772-9450 (7 minutes) Telephone: 714-7 50-2801 ( 3 minutes) NOTE: It is the practice of this motel not to Singles $58 send out confirmations. The acknowledgment sent Twin Doubles $64 (2 beds) by the Mathematics Meetings Housing Bureau in Triples $70 (2 beds) Providence will serve as confirmation of room $70 (2 beds plus cot) reservation. Quads $76 (2 beds plus cot) Singles $28 Children 12 years of age and under are free; Doubles $32 (1 or 2 beds) $6 will be charged if a cot is used. A $50 room Triples $36 (2 beds) deposit is required by cheek made payable to $38 (2 beds plus cot) AMS, or VIsA or MASTERCARD. Balance due Quads $38 (2 beds) may be paid in the same manner, as well as $40 (2 beds plus cot) by American Express, Diners Club and Carte Children 3 years of age and under are free; Blanche. Airport bus will discharge passengers at $2 will be charged if a cot is used. A $50 the Grand Hotel where a Holiday Inn phone is room deposit is required by cheek made payable available to request shuttle service to the motel. to AMS, or VISA, MASTERCARD, or American A 48-hour cancellation notice is required. Express. Balance due may be paid in cash or Inn of Tomorrow (1) by any of the credit cards indicated above; no 1110 West Katella Avenue personal cheeks will be accepted. Airport bus will Anaheim, California 92802 discharge passengers at the Grand Hotel where Telephone: 800-854-8175 (10 minutes) phones are available to request shuttle service to the motel. A 48-hour cancellation notice is Singles $36 required. Doubles $40 (1 or 2 beds) Triples $44 (2 beds) Magie Lamp (2) $48 (2 beds plus cot) 1030 West Katella Avenue Quads $48 (2 beds) Anaheim, California 92802 $52 (2 beds plus cot) Telephone: 714-772-7242 (7 minutes) Children 18 years of age and under are free; NOTE: It is the practice of this motel not to $4 will be charged if a cot is used. A $50 send out confirmations. The acknowledgment sent room deposit by cheek made payable to AMS, or by the Mathematics Meetings Housing Bureau in MASTERCARD, VIsA, American Express, Carte Providence will serve as confirmation of room Blanche, or Diners Club. Balance due may be paid reservation. in the same manner. Airport bus will discharge Singles $28 passengers at the Grand Hotel where the Inn of Doubles $32 {1 or 2 beds) Tomorrow meets incoming arrivals. A 48-hour Triples $36 (2 beds) cancellation notice is required. $38 (2 beds plus cot) Jolly Roger Inn (4) Quads $38 (2 beds) · 640 West Katella Avenue $40 (2 beds plus cot) Anaheim, California 92802 Children 3 years of age and under are free; Telephone: 714-772-7621 (6 minutes) $2 will be charged if a cot is used. A $50 Singles $41 room deposit is required by cheek made payable Doubles $42 (1 or 2 beds) to AMS, or VISA, MASTERCARD, or American Triples $45 (2 beds) Express. Balance due may be paid in cash or $47 (2 beds plus cot) by any of the credit cards indicated above; no Quads $45 (2 beds) personal cheeks will be accepted. Airport bus will $47 (2 beds plus cot) discharge passengers at the Grand Hotel where phones are available to request shuttle service free Children 3 years of age and under are to the motel. A 48-hour cancellation notice is with parents. Cribs, complete in same room required. with linen are available for this age group at no charge. A $50 room deposit is required by cheek Marriott Hotel-Headquarters (7) made payable to AMS, or VISA or MASTERCARD. 700 West Convention Way Balance due may be paid in the same manner. Anaheim, California 92802 Airport bus will discharge passengers at the Grand Telephone: 714-750-8000 ( 4 minutes) Hotel where phones are available to request shuttle Singles $55 service to the motel. A 24-hour cancellation notice Doubles $60 (1 or 2 beds) is required. Triples $66 (2 beds) Magie Carpet (3) $70 (2 beds plus cot) 1016 West Katella Avenue Quads $68 (2 beds) Anaheim, California 92802 $72 (2 beds plus cot)

32 TIMETABLE All sessions are at the Anaheim Convention Center, unless noted as follows: AMH = Anaheim Marriott Hotel Mathematical Association of America American Mathematical Society FRIDAY, January 11 and Other Organizations SPECIAL SESSION 2:15 p.m. - 4:05 p.m. Teichmuller theory for surfaces, graphs and hyperbolic manifolds II

3:30 p.m. - 4:30 p.m. ~~~~~e~~~:,!::ts in set theory I W. Hugh Woodin. SPECIAL SESSIONS 3:30 p.m. - 4:50 p.m. Differential geometry II

3:30 p.m. - 5:50 p.m. Infinite dimensional topology I

4:30 p.m. - 6:00 p.m. MAA - Committee on Two-Year Colleges SOCIAL HOUR & DISCUSSION Donald J. Albers (host) Ronald M. Davis Warren Page Stephen Rod! Ann E. Watkins

4:45 p.m. - 5:30 p.m. MathSci Taissa Kusma 6:30 p.m. - 7:30 p.m. National Association of Mathematicians BUSINESS MEETING

7:00 p.m. - 8:00 p.m. ATP PRIZE COMMITTEE 1984 Milestone Prize in Automated Theorem Proving J. A. Robinson

7:00 p.m. - 9:00 p.m. MAA - MINICOURSE i/2 (Part B) APL - A functional computer language for mathematicians Garry A. Helzer

7:00 p.m. - 9:00 p.m. MAA - MINICOURSE i/3 (Part B) Teaching problem solving Alan H. Schoenfeld

7:00 p.m. - 9:00 p.m. MAA - MINICOURSE i/4 (Part B) Applications of discrete mathematics Fred S. Roberts

7:00 p.m. - 9:00 p.m. MAA - MINICOURSE i/10 (Part B) Constructing placement examinations Richard H. Proal

7:30 p.m. - 9:30 p.m. NATIONAL MATHEMATICS DEPARTMENT CHAIRMEN'S MEETING 7:30p.m. Vl'hat does the administration expect from department chairmen? Lester H. Lange

8:00p.m. The relationship between mathematics and computer science in the same department

8:00 p.m. How to develop a successful research department

8:00 p.m. - 9:00 p.m. MAA- PRESENTATION Challenge of the unknown (an American Association for the Advancement of Science project) James C. Crimmins

8:00 p.m. - 11:00 p.m. Association for Symbolic Logic COUNCIL MEETING

8:30 p.m. - 11:00 p.m. ND-HOST COCKTAIL PARTY

33 in one's employment or other trade or business Telephone: 714-971-9393 (8 minutes) or (ii) meet express requirements of an employer Singles $40 or a law imposed as a condition to retention of Doubles $40 (1 or 2 beds) employment, job status, or rate of compensation. Triples $40 (2 beds) This is true even for education that leads to a $44 (2 beds plus cot) degree. Quads $42 (2 beds) Registration fees may be paid at the meetings $46 (2 beds plus cot) in cash, by personal or travelers' check, or by VrsA Suites $75-79 or MASTERCARD credit card. Canadian checks $95-99 must be marked for payment in U.S. funds. Children 12 years of age and under are free; There is no extra charge for members of the $4 will be charged if a cot is used. A $50 families of registered participants, except that all room deposit is required by check made payable professional mathematicians who wish to attend to AMS or VrsA, MASTERCARD or American sessions must register independently. Express. Balance due may be paid by these credit All full-time students currently working toward cards only. Complimentary breakfast is included a degree or diploma qualify for the student in room rate. Airport bus discharges passengers registration fees, regardless of income. at the Grand Hotel where phones are available A 48- The unemployed status refers to any person to request shuttle service to the motel. cancellation notice is required; however, a $5 currently unemployed, actively seeking employ­ hour for cancellation will be charged. merit, and who is not a student. It is not intended penalty to include any person who has voluntarily resigned or retired from his or her latest position. Registration Desk Persons who qualify for emeritus membership in either the Society or the Association may register Registration at the Meetings at the emeritus member rate. The emeritus status Meeting preregistration and registration fees refers to any person who has been a member of only partially cover expenses of holding meetings. the AMS or MAA for twenty years or more, and is All mathematicians who wish to attend sessions retired on account of age from his or her latest are expected to register, and should be prepared position. to show their meeting badge, if so requested. Nonmembers who register at the meetings and Badges are required to enter the exhibit area, pay the $109 nonmember registration fee are to obtain discounts at the AMS and MAA Book entitled to a discount of the difference between the Sales, to cash a check with the meeting cashier, member registration fee of $72 and the nonmember and to attend sessions scheduled in the Pacific registration fee of $109 as a $37 credit against Room of the Anaheim Convention Center. (If dues in either the AMS or MAA or both, provided a preregistrant should arrive too late in the day they apply for membership before February 13, to pick up his/her badge, he/she may show the 1985. acknowledgment received from the Mathematics Nonmember students who register at the Meetings Housing Bureau as proof of registration.) meetings and pay the $18 registration fee are The fees for Joint Meetings registration at the entitled to a discount of the difference between meeting listed below are 30 percent more than the the student preregistration fee of $14 and the preregistration fees. registration fee of $18 as a $4 credit against dues Joint Mathematics Meetings in either the AMS or MAA or both, provided they apply for membership before February 13, 1985. Member of AMS, ASL, MAA, NCTM $ 72 Nonmembers and nonmember students who Emeritus Member of AMS, MAA $ 18 $109 thus qualify may apply for membership at the Nonmember $ 18 meetings, or by mail afterward up to the deadline. Student/Unemployed Employment Register Registration Dates, Times, and Locations Employer $100 AMS Short Course Applicant $ 20 California Room, Anaheim Convention Center AMS Short Course Monday, January 7 9:00a.m. to 4:00p.m. Student/Unemployed $ 10 Tuesday, January 8 8:00 a.m. to 2:00 p.m. All Other Participants $ 30 Joint Mathematics Meetings One-day Fee (Se~ond Day Only) $ 15 [and MAA Minicourses (until filled)] MAA Minicourses #1 through #10 North Lobby, Anaheim Convention Center All Participants $ 25 each Tuesday, January 8 4:00p.m. to 8:00p.m. Wednesday, January 9 8:00 a.m. to 5:00p.m. U.S. Treasury regulation §1.162-5 allows an Thursday, January 10, income tax deduction for education expenses through 8:00 a.m. to 4:00 p.m. (registration fees, cost of travel, meals, and Saturday, January 12 lodging) incurred to (i) maintain or improve skills

34 TIMETABLE All sessions are at the Anaheim Convention Center, unless noted as follows: AMH ~ Anaheim Marriott Hotel

Mathematical Association of America SATURDAY, January 12 American Mathematical Society and O:her Organizations 8:00 a.m. - 10:00 a.m. ACM/MAA Joint Committee on Retraining for Computer Science - WORKSHOP The nature of computer science: Now that you know how to program. . . Part II

8:00 a.m. - 4:00 p.m. REGISTRATION North Lobby morning MAA - CONTRIBUTED PAPER SESSION Teaching introductory statistics: Topics, trends, and techniques Ann Watkins

9:00 a.m. - 9:50 a, m. MAA - INVITED ADDRESS Algorithms, geometry, and GL (n, Z) Helaman R. P. Ferguson

9:00 a.m. - 10:30 a.m. MAA - Committee on Secondary School Lectures - PANEL DISCUSSION: How to give a successful talk to secondary school students Peter J. Hilton David E. Logothett! Jean J. Pedersen

9:00 a.m. - noon EXHIBITS Anaheim Room 9:00 a.m. - noon AMS BOOK SALE IMAA BOOK SALE Anaheim Room Anaheim Room 9:00 a.m. EMPLOYMENT REGISTER DISTRIBUTION OF SCHEDULES

9:30 a.m. - 5:30 p.m. EMPLoYMENT REGISTER INTERVIEWS

9:30 a.m. - 10:30 a.m. ASL - INVITED ADDRESS Tarski's problem, exponential sets, and Ffaffian functions Lou van den Dries

10:00 a.m. - 10:50 a.m. MAA - INVITED ADDRESS The many lives of invariant theory Gian-Carlo Rota

10:00 a.m. - 11:00 a.m. ACM/MAA Joint Committee on Retraining for Computer Science- PANEL DISCUSSION Undergraduate computer science is not just mathematics

10:00 a.m. - 11:00 a.m. NAM- WILLIAM W. S, CLAYTOR LECTURE Some recent developments in statistics David Blackwell

10:00 a.m. - noon MAA - MINICOURSE ill (Part A) The teaching of applied mathematics W.

10:00 a.m. - noon MAA- MINICOURSE i/5 (Part A) Groups, graphs, and computing Eugene M. Luks

10:00 a.m. - noon MAA - MINICOURSE i/8 (Part A) Microcomputer software in mathematics instruction Roy E. Myers

10:45 a.m. - 11:45 a.m. ASL - INVITED ADDRESS Nonmonoton!c reasoning John McCarthy

35 in one's employment or other trade or business Assistance and fuformation Desk or (ii) meet express requirements of an employer Heritage Lobby, Anaheim Convention Center or a law imposed as a condition to retention of Sunday, January 13 8:30 a.m. to 1:30 p.m. employment, job status, or rate of compensation. This is true even for education that leads to a Registration Desk Services degree. AMS/MAA Information Registration fees may be paid at the meetings and activities in cash, by personal or travelers' check, or by VISA Information on the publications organizations may be obtained at this or MASTERCARD credit card. Canadian checks of both must be marked for payment in U.S. funds. section of the registration desk. There is no extra charge for members of the Assistance, Comments and Complaints families of registered participants, except that all A log for registering participants' comments professional mathematicians who wish to attend or complaints about the meeting is kept at the sessions must register independently. Transparencies section of the registration desk. All full-time students currently working toward All participants are encouraged to use this method a degree or diploma qualify for the student of helping to improve future meetings. Comments registration fees, regardless of income. on all phases of the meeting are welcome. If The unemployed status refers to any person a written reply is desired, participants should currently unemployed, actively seeking employ­ furnish their name and address. ment, and who is not a student. It is not intended Participants with problems of an immediate to include any person who has voluntarily resigned nature requiring action at the meeting should see or retired from his or her latest position. the Director of Meetings, who will try to assist Persons who qualify for emeritus membership in them. either the Society or the Association may register Audio-Visual Assistance at the emeritus member rate. The emeritus status A member of the A.MS /MAA staff will be available refers to any person who has been a member of to advise or consult with speakers on their audio­ the AMS or MAA for twenty years or more, and is visual requirements. retired on account of age from his or her latest Rooms where special sessions and contributed position. paper sessions will be held are equipped with an Nonmembers who register at the meetings and overhead projector and screen. Blackboards will pay the $109 nonmember registration fee are not be available. entitled to a discount of the difference between the Check Cashing member registration fee of $72 and the nonmember registration fee of $109 as a $37 credit against The meeting cashier will cash personal or dues in either the AMS or MAA or both, provided travelers' checks up to $50, upon presentation of they apply for membership before February 13, the official meeting registration badge, provided 1985. there is enough cash on hand. Canadian checks Nonmember students who register at the must be marked for payment in U.S. funds. It is meetings and pay the $18 registration fee are advisable that participants bring travelers' checks entitled to a discount of the difference between with them. When funds are low the meetings the student preregistration fee of $14 and the cashier will not be able to cash checks and registration fee of $18 as a $4 credit against dues travelers' checks can be easily cashed at local banks or hotels. in either the AMS or MAA or both, provided they apply for membership before February 13, 1985. Local fuformation Nonmembers and nonmember students who This section of the desk will be staffed by mem­ thus qualify may apply for membership at the bers of the Local Arrangements Committee and meetings, or by mail afterward up to the deadline. other volunteers from the Anaheim mathematical Registration Dates, Times, and Locations community. AMS Short Course Lost and Found California Room, Anaheim Convention Center See the meeting cashier. Monday, January 7 9:00 a.m. to 4:00 p.m. Mail Tuesday, January 8 8:00 a.m. to 2:00 p.m. All mail and telegrams for persons attend­ Joint Mathematics Meetings ing the meetings should be addressed to the [and MAA Minicourses (until filled)] participant, c/o Joint Mathematics Meetings, North Lobby, Anaheim Convention Center Anaheim Convention Center, 800 West Katella Tuesday, January 8 4:00 p.m. to 8:00 p.m. Avenue, Anaheim, California 92802. Mail and Wednesday, January 9 8:00 a.m. to 5:00 p.m. telegrams so addressed may be picked up at the Thursday, January 10, mailbox in the registration area during the hours through 8:00 a.m. to 4:00 p.m. the registration desk is open. U.S. mail not Saturday, January 12 picked up will be forwarded after the meeting

36 TIMETABlE All sessions are at the Anaheim Convention Center, unless noted as follows: AMH ~ Anaheim Marriott Hotel

Mathematical Association of America American Mathematical Society SATURDAY, January 12 and Other Organizations 11:00 a.m. - 11:50 a.m. MAA - INVITED ADDRESS Toolkit for nonlinear dynamics John M. Guckenheimer

11:15 a.m. - 12:30 p.m. NAM- PANEL DISCUSSION Graduate students in mathematics: "Increasing the pool" Tepper Gill Gloria Hewitt J. Arthur Jones Dwight Lahr Rogers Newmann (moderator)

COLLOQUIUM LECTURES 1:00 p.m. - 2:00 p.m. Lecture IV: The classification of the finite simple groups Daniel Gorenstein SPECIAL SESSIONS 1:00 p.m. - 4:50 p.m. Celestial mechanics I

1:00 p.m. - 3:50 p.m. Infinite dimensional topology II

1:00 p.m. - 4:20 p.m. Differential geometry III

SESSIONS FOR CONTRIBUTED PAPERS 1:00 p.m. - 2:55 p.m. Analysis Santa Ana Room 2 1:00 p.m. - 3:55 p.m.

2:00 p.m. - 3:00 p.m. ASL - INVITED ADDRESS Good grief1 More about priority arguments Leo A. Harrington

2:15 p.m. - 3:15 p.m. INVITED ADDRESS Some applications of the classification of finite simple groups William M. Kantor SESSION FOR CONTRIBUTED PAPERS 2:15 p.m. - 3:55 p.m. Algebraic number theory

3:15 p.m. - 5:40 p.m. ASL- SESSION FOR CONTRIBUTED PAPERS

SPECIAL SESSIONS 3:20 p.m. - 4:55 p.m. Finite group theory II

3:20 p.m. - 4:30 p.m. Algebraic combinatorics II

4:30 p.m. - 5:30 p.m. MAA- BUSINESS MEETING

5:45 p.m. - 7:15 p.m. ASL - RECEPTION

7:00 p.m. - 9:00 p.m. MAA - MINICOURSE ill (Part B) The teaching of applied mathematics W. Gilbert Strang

7:00 p.m. - 9:00 p.m. MAA - MINICOURSE i/5 (Part B) Groups, graphs, and computing Eugene M. Luks

7:00 p.m. - 9:00 p.m. MAA - MINICOURSE i/8 (Part B) Microcomputer software in mathematics instruction Roy E. Myers

37 to the mailing address given on the participant's three years of age are free). Disneyland will registration record. be closed Monday and Tuesday, January 7-8, Personal Messages but will be open from 10:00 a.m. to 6:00 p.m. Wednesday through Friday, January 9-11 and Participants wishing to exchange messages from 10:00 a.m. to 7:00 p.m. on Saturday and during the meeting should use the mailbox Sunday, January 12-13. The park will be closed mentioned above. Message pads and pencils are on Monday, January 14, but will be open from provided. It is regretted that such messages left 10:00 a.m. to 6:00 p.m. on Tuesday, January in the box cannot be forwarded to participants 15. The Exchange Cards are good for the period after the meeting is over. January 5-15. Telephone Messages Local Information A telephone message center is located in the Taxis presently cost $1.40 plus $1.20 per mile registration area to receive incoming calls for participants. The center is open from January for one to five persons. Most local trips within the Convention Center area are under $3. The 8 through 12 only, during the hours that the Joint Mathematics Meetings registration desk is County Transit District (OCTD) operates open. Messages will be taken and the name of any buses throughout Orange County. Local fares individual for whom a message has been received are 60 eents midday, weekends, and holidays, but will be posted until the message has been picked 75 cents during weekday rush (6:00-9:00 a.m. up at the message center. The telephone number and 3:00-6:00 p.m.). Note that riders must have of the message center is 714-635-8440. exact change for the fare; bus drivers do not carry change. Transparencies Several sight-seeing and shopping shuttles Speakers wishing to prepare transparencies in operate in the area. Fun Bus offers scheduled and advance of their talk will find the necessary daily door-to-door service from most Convention materials and copying machines at this section of Center area hotels and motels to Disneyland, the registration desk. A member of the staff will Knott's Berry Farm, Movieland Wax Museum assist and advise speakers on the best procedures and Buena Park Shopping Center; prices vary and methods for preparation of their material. according to route. The City Shopper provides There is a modest charge for these materials. convenient transportation to the City Shopping Please note that this service will not be available Center in Orange and local hotels; the fare is $1. on Sunday, January 13. The Anaheim Plaza Express operates during mall Visual Index hours daily providing roundtrip transportation to An alphabetical list of registered participants, including local addresses, arrival and departure dates, is maintained in the registration area. MISCELLANEOUS INFORMATION Child Care The Marriott Hotel has eight sitters on call at $5 per hour. All of the other hotels which are blocking rooms for the meeting provide telephone numbers of bonded babysitting agencies and/or licensed individual babysitters. Rates vary from $4 to $5, some with initial four-hour minimums, ranging from $23 to $26. Agency rates are subject to change. It is therefore advisable to contact the individual agency to establish their particular hourly rate and any transportation fees. Disneyland The Local Arrangments Committee has nego­ tiated a special discount in the adult rate at Dis­ neyland for participants in the January 1985 Joint Mathematics Meetings. Disneyland Exchange Cards may be purchased through preregistration or at the meeting for $9 each. This card may be exchanged at the Disneyland main entrance ticket booth or Monorail station for one Disneyland Passport Ticket. The current rates for these tickets are $14 for adults and $9 for children from three to eleven years of age (children under

38 TIMETABLE All sessions are at the Anaheim Convention Center, unless noted as follows: AMH = Anaheim Marriott Hotel

Mathematical Association of America SATURDAY, January 12 American Mathematical Society and other Organizations 7:00 p.m. - 9:00 p.m. MAA - Panel on Remediation PANEL DISCUSSION: Is there an alternative to remediation? Donald W. Bushaw (moderator)

8:15 p.m. - 11:15 p.m. ASL - COUNCIL MEETING

BUNDA Y, January 13 AMS MAA and other Organizations

8:00 a.m. - 11:00 a.m. ACM/MAA - Joint Committee on Retraining for Computer Science - SPECIAL SESSION on Advanced topics for mathematicians teaching undergraduate computer science, Part B

morning MAA - CONTRIBUTED PAPER SESSION Making mathematics majors marketable: Undergraduate training for nonacademic careers Ann K. Stehney

SPECIAL SESSION 8:00 a.m. - noon Algebraic comhinatorics 1li

8:30a.m. - 1:30 p.m. ASSISTANCE & INFORMATION DESK Heritage Lobby SPECIAL SESSION 9:00 a.m. - 11:50 a.m. Differential geometry IV

SESSION FOR CONTRIBUTED PAPERS 9:00 a.m. - 10:40 a.m. Statistics

9:00 a.m. - 9:50 a.m. MAA - INVITED ADDRESS Some recent advances in real, complex, and harmonic analysis Guido L. Weiss

9:00 a.m. - noon MAA - MINICOURSE #7 (Part A) Linear programming Charles E. Haff

9:30 a.m. - 10:30 a.m. ASL - INVITED ADDRESS Definability in substructures of the Turing degrees Theodore Slaman

9:30 a.m. - 10:50 a.m. MAA - PANEL REPORT Fifth International Congress on Mathematical Education Henry L. Alder Donald M. Hill (presider) Katherine P. Layton Warren Page Henry 0. Pollak

SPECIAL SESSION 10:00 a.m. - 11:50 a.m. Celestial mechanics II

10:00 a.m. - 10:50 a.m. MAA - INVITED ADDRESS The search for randomness Persi Diaconis

10:00 a, m. - noon MAA - MINICOURSE #6 (Part A) PROLOG Frederick Hoffman

39 Anaheim Meeting-SuperPhone Exelusive 800-556-6882 US61R.. FLY TO ANAHEIM WITH AMERICAN OR USAm AND SAVE SUPERPHONE exclusive does it again! Discount roundtrip airfare for Anaheim is available for the Joint Mathematics Meetings, January 7-13, 1985. SUPERPHONE guarantees you a minimum 35% discount on all American and USAir flights going into the Los Angeles area airports (additional restrictions may apply from Canada). Depending on your city of origin you may be eligible for up to a 45% discount. Tickets must be purchased 14 days prior to your travel. Seats are limited so the earlier you book the more likely you are to maximize your savings. SUPERPHONE also offers its exclusive fare check system that guarantees that you get the lowest possible fare. FARE CHECK will automatically rewrite your ticket if a lower price becomes available. Remember these special fares are available ONLY THROUGH THE ANAHEIM MEETING SUPERPHONE EXCLUSIVE. Call toll-free today-800-556-6882-and save!!

(In Rhode Island and outside the Continental U.S. call 401-884-9500.) Hours of Operation: 9:00a.m. to 7:00p.m. EST, Monday through Thursday, Fridays until 6:00p.m. Anaheim Plaza from local Anaheim hotels; the The Anaheim Convention Center is located near fare is $1. the junction of the Santa Ana Freeway (Interstate 5) In addition to the local Anaheim attractions and Harbor Boulevard, 27 miles from downtown Los mentioned above, offers an Angeles. enormous variety of cultural, historical, and All major airlines provide regular service to the recreational attractions. Information on these will Los Angeles International Airport (LAX). Airport be available at the Local Information section of Service, Inc. (telephone 714-778-3141) operates the registration desk. "The Airport Bus" between LAX and Anaheim with frequency varying between 20 minutes and 60 minutes Parking depending on the hour of the day. No reservations There is adequate parking at the Anaheim are required for the bus. Present cost is about $9 Convention Center. The charge is $2.50 per day. A per person and the trip takes from one to one-and­ new charge is incurred if the car is taken from the lot one-half hours. Buses board passengers at all LAX and returned. The parking lot opens in the morning terminals and stop at several major hotels near the and closes after the last events. There is no parking Anaheim Convention Center. in the residential areas surrounding the Convention To reach Anaheim from LAX by car, take the Center. Cars parked in this area risk being ticketed. San Diego Freeway (Interstate 405) South to Artesia There is parking available at the surrounding Freeway (Highway 91) East, to Santa Ana Freeway hotels. The Hilton Towers has its own five-level (Interstate 5) South, and exit on Harbor Boulevard. parking structure. Self-parking there is $3 for a 24- The trip by car takes at least 45 minutes. hour period. The car can be removed and returned at Some major airlines fly daily to the no additional charge. The Hilton Towers is adjacent (Orange County) Airport (SNA). There are direct to the Anaheim Convention Center. flights to Orange County from Chicago, Dallas, Parking at the Anaheim Marriott is free for guests Phoenix, Salt Lake City and many cities in California. and $3 per day otherwise. There are no in and out The trip by bus from the Orange County Airport privileges. to the Anaheim Convention Center takes about 40 Soeial Events minutes. The present bus fare is $3.60 per person. The Local Arrangements Committee has arranged Participants are warned, however, that service is infrequent and they should be prepared to wait an a No-Host Cocktail Party for Friday, January 11, from 8:30 p.m. to 11:00 p.m. at the Anaheim Marriott. hour or more depending upon the arrival time of their flight. To reach Anaheim from the Orange Travel County Airport by car, take the Costa Mesa Freeway In January, Anaheim is on Pacific Standard Time. (Highway 55) North to Santa Ana Freeway (Interstate

40 TIMETABlE All sessions are at the Anaheim Convention Center, unless noted as follows: AMH = Anaheim Marriott Hotel Mathematical Association of America SUNDAY, January 13 and Other Organizations 10:00 a.m. - noon MAA - MINICOURSE !19 (Part A) Teacher in-service programs (A COMET Minicourse) Eugene A. Maier

10:45 a.m. - 11:45 a.m. ASL - INVITED ADDRESS ·what is a variable ? Kit Fine

11:00 a.m. - 11:50 a.m. MAA - INVITED ADDRESS Some diophantine problems Murray M. Schacher

11:00 a.m. - noon MAA - Committee on the Teaching of Under­ graduate Mathematics - SESSION on Teaching assistant and adjunct instructor competency­ an informal exchange Felix E. Browder Bettye Anne Case (presider) Wendell H. Fleming Leon A. Henkin David P. Kraines Audrey A. Terras

afternoon MAA - CONTRIBUTED PAPER SESSION Strategies, tactics, and techniques in teach­ ing lower division and remedial courses Ann D. Holley

afternoon MAA - CONTRIBUTED PAPER SESSION Does research in mathematics learning at the college leve I exist ? James J. Kaput

1:00 p.m. - 1:50 p.m. MAA- PRESENTATION The electronic spreadsheet-a creative pro­ gram for mathematics and mathematicians Deane Arganbright

2:00 p.m. - 3:00 p.m. ASL - INVITED ADDRESS Jump operators and inner model operators Howard Becker

2:00 p.m. - 3:30 p.m. MAA - Committee on Computers in Mathe­ matics Education- PANEL DISCUSSION The use of computing in upper level undergraduate courses Christopher Nevison (organizer)

2:00 p.m. - 3:30 p.m. MAA/NCTM- PANEL DISCUSSION Project Equality, an undertaking of the College Board

2:00 p.m. - 4:00 p.m. MAA - MINICOURSE !16 (Part B) PROLOG Frederick Hoffman

2:00 p.m. - 4:00 p.m. MAA - MINICOURSE #9 (Part B) Teacher in-service programs (A COMET Minicourse) Eugene A. Maier

2:00 p.m. - 5:00 p.m. MAA- MINICOURSE #7 (Part B) Linear programming Charles E. Haff

3:15 p.m. - 5:15 p.m. ASL- SESSION FOR CONTRIBUTED PAPERS

41 5) and exit on Harbor Boulevard. This trip takes Weather about 20 minutes. Winters in Anaheim are generally mild. The Los Angeles can be reached by car via I-5 from average high temperature in January is 68°F while the the north and south, and I-10, I-15, and I-40 from average low is 44°F. On rare occasions, temperatures the east. There is a major AMTRAK terminal in may range from the upper twenties to the eighties. downtown Los Angeles and an AMTRAK station in Contrary to popular belief, it does rain in Southern Anaheim itself. California. The average rainfall in January is slightly over three inches.

AMS Book Exhibit at Anaheim 10 Percent OFF already low AMS individual member prices Stop by the new AMS exhibit to view a display of books published by the society. The displayed books, as well as all the books listed in our catalogue, are marked down an extra 10 percent from the 40 percent discount already given to individual members. Purchase these quality books for just 50 percent of their list price. These low prices will apply to books paid for at the annual meeting only, so take advantage of them while you can. In the interest of serving you more efficiently; this year we have chosen to bring only selected new publications as well as some of the more popular backlist books. Please note that this reduction in books on display in no way effects the number of books you have to select from. For your convenience we have compiled a catalogue of AMS publications grouped together by subject classifications, making it easier for you to locate books relating to your specific areas of interest. Any book either on display or in the catalogue is available at the Anaheim meeting with the 50 percent discount. To get your copy of this new catalogue, just stop by our exhibit booth and pick one up. Look through it at your leisure, select the books which you wish to purchase. Then before leaving the meeting stop by our booth and place your order, paying only half the list price. Just think, no more standing in line waiting to search through a table of books hunting for those of special interest to you. We think you will agree that this is a far better use of your time. We look forward to seeing you in Anaheim.

42 Mathematical Sciences Employment Register January 1985 Meeting in Anaheim The Mathematical Sciences Employment Register, held annually at the Joint Mathematics Meetings in January, provides opportunities for mathematical scientists seeking professional employment to meet employers who have positions to be filled. Job listings (or descriptions) and resumes prepared by employers and applicants are displayed at the meeting for the participants so that members of each group may determine which members of the other group they would like t~ have an opportunity to interview. A computer program assigns the appointments, matchmg requests to the extent possible, using an algorithm which maximizes the number of interviews which can be scheduled subject to constraints determined by the number of time periods available, the numbers of applicants and employers, and the pattern of requests. The report below outlines the operation of the register, indicating some of the procedures involved for the benefit of those not familiar with its operation. The Mathematical Sciences Employment Register is apparently unique among employment services offered by professional organizations in the sciences, engineering and the humanities. The computer programs used are constructed around a matching program, devised by Donald R. Morrison and based on an algorithm described in his paper "Matching Algorithms" in Journal of Combinatorial Theory, volume 6 {1969), pages 20 to 32; see also "Matching Algorithms" {abstract) Notices, August 1967, page 630. The number of interviews arranged by the program is ~ignificantly greater than the number possible at the employment registers of other organizations, m many cases greater by an order of magnitude. 1985 Employment Register in Anaheim be accommodated depending on the availability of The Employment Register at the Anaheim meeting participants. The scheduling program does not have will take place in the Marriott Hall of the Anaheim a provision allowing participants to specify particular Marriott Hotel on Thursday, Friday, and Saturday, times for interviews beyond the choice of session (day, January 10, 11, and 12, 1985. A short (optional) and morning or afternoon). Such requests cannot be orientation session will be conducted by the AMS­ accommodated. MAA-SlAM Committee on Employment Opportunities Requests for interviews to take place during at 9:00 a.m. on Thursday, January 10. The the two sessions on Friday must be submitted purpose of the orientation session is to familiarize on Thursday between 9:30 a.m. and 4:00 p.m. participants with the operation of the Register Requests for interviews to take place during the and with the various forms involved. Following Saturday sessions must be submitted on Friday orientation, participants of the Employment Register before 4:00 p.m. can pick up their interview request forms. Computer­ On Friday and Saturday mornings at 9 a.m. all scheduled interviews will be held on Friday and schedules for applicants and employers for the day Saturday, January 11 and 12. No interviews will be (both the morning and afternoon sessions) will be held on Thursday. available for distribution in the Marriott Hall Foyer. Fifteen-minute intervals are allowed for interviews, The Saturday afternoon session is the annual including two or three minutes between successive "employers' choice" session. For this session inter­ interviews. The interviews are scheduled in half­ views will be scheduled on the basis of requests made day sessions: Friday morning and afternoon, and by employers. Applicants do not submit specific Saturday morning and afternoon, amounting to four interview requests for this session; but, in order to half-day sessions for interviews. There are ten time participate they must indicate their availability for periods (9:30-11:45 a.m.) in which interviews can the session by filing the Interview Request Form be scheduled in the morning sessions and fourteen for Saturday, indicating that they will attend the time periods (1:15-5:00 p.m.) in the afternoon afternoon session that day. Request Forms for the sessions. It is possible that an applicant or employer "employers' choice" session must be submitted by may be scheduled for the maximum number of 4:00 p.m. on Friday in order for the interviews to interviews in a session. Requests for interviews will be scheduled for Saturday afternoon. Applicants should be aware of the fact that Background of Applicants interviews arranged by the Employment Register represent only an initial contact with employers, and Employers who preregistered for the Employment that hiring decisions are not ordinarily made during Register in January 1984 sought to fill 178 or immediately following such interviews. Applicants positions, 10 of which were nonacademic jobs. are advised to bring a number of copies of their For 98% of the positions, holders of doctoral vitae or resumes so that they may leave them with degrees were preferred, for 62% of the positions prospective employers. only applicants with doctorates were acceptable, Employers and applicants who wish to par­ for 28% of the positions, holders of masters degrees were considered eligible. One of the nonacademic ticipate in the Register and who have neither employers indicated an interest in holders of preregistered nor paid the Employment Register bachelors degrees in mathematics. fee must go to the Joint Mathematics Meetings registration desk in the North Lobby of the

43 Anaheim Convention Center in order to complete The MSER registration fee for employers covers the their registration. Registration for the Joint cost of a copy of the December Issue of Employment Meetings is required to use the Employment Information in the Mathematical Sciences (ElMS). Register facilities. (No provision will be made This publication contains printed copies of the to handle cash transactions at the site of the resumes of applicants who preregistered prior to the Employment Register in the Marriott Hall Foyer.) deadline; it also contains a copy of the summary Additional fees for participation in the Employment Winter List of Applicants. The resumes themselves Register were $75, for employers, and $15 for will be posted at the site of the Register in addition applicants, if paid before the preregistration deadline. to the resumes of those who register at the meeting. Registration, if paid at the meeting, is $100 for Additional copies of the December Issue of ElMS and employers and $20 for applicants. both the summary Winter Lists (of Applicants and Employers and applicants who have completed of Employers) will be available for sale at the AMS registration for the Employment Register, and Book Sale at the meeting, as long as supplies last. employers and applicants who have preregistered, Prices at the meeting are $2 each for the summary may pick up their MSER material after 9:30 a.m. on lists and $3 for the December issue. Any copies Thursday, January 10, in the Marriott Hall Foyer, remaining after the meeting will be available from where the Employment Register will be held. All the Providence office of the Society for $3 and $6, who wish to have interviews scheduled for Friday respectively. (Attention is called to the fact that the or Saturday, must submit their Interview Request December issue of ElMS contains the Winter List of Forms on the preceding day by 4:00 p.m. Those Applicants, but does not contain the Winter List of who fail to do so cannot be included in the Employers.) pool of available participants when the matching The Winter List of Employers consists of sum­ program which schedules the interviews is run maries of the position listings submitted by the on the computer that night. This applies both employers who preregistered for the meeting; it will to preregistered employers and applicants, and to be distributed to the applicants participating in the those registering at the meeting. Register. Others may purchase the Winter List of These forms are given to participants at the Employers at the AMS Book Sale at the meeting or meeting. These are not the forms that are from the Providence office later, as long as the supply completed with preregistration. lasts. (See previous paragraph for prices.) Employers who do not plan to participate in the The Mathematical Sciences Employment Register Employment Register, but who wish to display job is sponsored by the American Mathematical Society, descriptions, may do so (subject to approval) using the Mathematical Association of America, and the special forms available at the Employment Register. Society for Industrial and Applied Mathematics; it A fee of $15 will be charged for listings. The fee is operated by members of the AMS staff under should be paid at the Joint Mathematics Meetings the general supervision of the joint AMS-MAA-SIAM desk before the material can be exhibited. Committee on Employment Opportunities.

44 Program of the Sessions All AMS sessions will take place in the Anaheim Convention Center. The time limit for each contributed paper in the AMS general sessions is ten minutes. In the special sessions, the time limit varies from session to session and within sessions. To maintain the schedule, time limits will be strictly enforced. Abstracts of papers presented in AMS sessions at this meeting will be found in the January 1985 issue of Abstracts of papers presented to the American Mathematical Society, ordered according to the numbers in parentheses following the listings below. For papers with more than one author, an asterisk follows the name of the author who plans to present the paper at the meeting.

Wednesday, January 9, 1985, 8:00a.m.

Special Session on Stoehastie Differential Geometry, I 8:00- 8:20 (1) Convergence of martingales on manifold8 of negative curvature. R. W. R. DARLING, University of Southern California (816-60-82) 8:30- 8:50 (2) Random walk.! on covering spaces. RICHARD DuRRETT, University of California, Los Angeles (816-60-22) 9:00- 9:20 (3) The limiting angle of certain Riemannian Brownian motions. Preliminary report. PETER MARCH, Courant Institute of Mathematical Sciences, New York University (816-60-47) 9:30- 9:50 (4) Applications of Brownian motion to the function theory of manifolds. SAMUEL GOLDBERG, University of Illinois, Urbana-Champaign (816-99-521) 10:00-10:20 (5) The Laplace-Beltrami operator on a Riemannian-Wiener manifold. M. ANN PIECH, State University of New York, Buffalo (816-58-93) 10:30-10:50 (6) Stochastic geometry and descriptions of the physical world. GERARD G. EMCH, University of Rochester (816-60-66) 11:00-11:20 (7) Heat diffu,sion on submanifolds of spaces of constant curvature. Preliminary report. LEON KARP, Herbert H. Lehman College, City University of New York (816-60-192) 11:30-11:50 (8) The in Riemannian manifolds. I. CHAVEL *, City College, City University of New York, and E. A. FELDMAN, Graduate School, City University of New York (816-60-96)

Wednesday, January 9, 1985, 8:00a.m. Session on General Topology 8:00- 8:10 (9) Remainders of H-closed extensions. MoHAN TIKOO, Southeast Missouri State University (816-54-280) 8:15- 8:25 (10) G0 -sets in countably metacompact, first countable spaces. Preliminary report. DENNIS K. BuRKE, Miami University (816-54-314) 8:30- 8:40 (11) Weakly closed functions. DAVID A. RosE, Francis Marion College (816-54-199) 8:45- 8:55 (12) On chain conditions in Moore spaces, II. ERIC K. VAN DOUWEN, University of Wisconsin, Madison, and GEORGE M. REED*, Ohio University (816-54-141) 9:00- 9:10 (13) On densely homogeneous spaces. BEN FITZPATRICK, JR.*, Auburn University, and NORMA F. LAUER, West Virginia Institute of Technology (816-54-11) 9:15- 9:25 (14) On z-embedding and extension of semi-continuous functions. Preliininary report. JOHAN SwART, University of Natal, South Mrica and San Diego State University (816-54-16) 9:30- 9:40 (15) Strong characteristic 0: A generalization of equicontinuity. SAROOP K. KAUL *, University of Regina, and JEONG S. YANG, University of South Carolina, Columbia (816-54-103) 9:45- 9:55 (16) A characterization of closed images of metric spaces. LESLIE FoGED, University of Texas, El Paso (816-54-176) (Sponsored by Joe A. Guthrie) 10:00-10:10 (17) On products of projective Tychonov spaces. Preliminary report. ANANDA V. GUBBI, Youngstown State University (816-54-218) 10:15-10:25 (18) On a question by Davis and Smith. Preliminary report. JoE MASHBURN, University of Dayton (816-54-290) 10:30-10:40 (19) Linear extenders and metrization. Preliminary report. DAVID LUTZER, Miami University (816-54-327) 10:45-10:55 (20) Remote points and locally finite families. Preliminary report. THOMAS J. PETERS, Computervision Corporation (816-54-435) 11:00-11:10 (21) Some reflections on collectionwise normality. FRANKLIN D. TALL, University of Toronto (816-54-436) 11:15-11:25 (22) A finite space of Bessel-Hagen type. Preliminary report. F. E. J. LINTON, Wesleyan University (816-54-451)

45 11:30-11:40 (23) Co-Namioka space. J. P. LEE, State University of Old Westbury, and Z. PIOTROWSKI*, Youngstown State University (816-54-471) 11:45-11:55 (24) When is continuous convergence topological? FRIEDHELM SCHWARZ, University of Toledo (816-54-477)

Wednesday, January 9, 1985, 8:00 a.m. Session on Number Theory 8:00- 8:10 (25) On the Es construction of the Leech lattice. Preliminary report. SHERWOOD WASHBURN, Seton Hall University (816-11-30) 8:15- 8:25 (26) A note on polygonal numbers. BUDMON DAVIS* and R. SITARAMACHANDRARAO, University of Toledo (816-11-60) (Sponsored by Stephen E. Spielberg) 8:30- 8:40 (27) Algebraic groups and small transcendence degree: Periodic case. Preliminary report. RoB TuBBS, University of Texas, Austin (816-11-67) 8:45- 8:55 (28) Character sum analogues for Mnomial coefficient identities over finite fields. Preliminary report. JOHN GREENE, Southern illinois University, Carbondale (816-11-200) 9:00- 9:10 (29) On the natural density of the Niven numbers. RoBERT E. KENNEDY* and CuRTIS N. CooPER, Central Missouri State University (816-11-219) · 9:15- 9:25 (30) On an asymptotic formula for the Niven numbers. CURTIS N. CooPER* and RoBERT E. KENNEDY, Central Missouri State University (816-11-220) 9:30- 9:40 (31) Fermat's Last Theorem. Preliminary report. CHIEN WENJEN, Seal Beach, California (816-11-188) 9:45- 9:55 (32) On a theorem of LP discrepancy. Preliminary report. JAU-SHYONG SHIUE, Saginaw Valley State College (816-11-194) 10:00-10:10 (33) A problem in additive arithmetic. R. SITARAMACHANDRARAO, University of Toledo (816-11-98) (Sponsored by Martin Pettet) 10:15-10:25 (34) A ring associated with the Jacobi-Perron algorithm. PAUL S. PEDERSEN, University of Denver (816-11-230) 10:30-10:40 (35) The sum of cl1(n) over integers with restricted prime factors. Preliminary report. DONALD G. HAZLEWOOD, Southwest Texas State University (816-11-243) 10:45-10:55 (36) The construction of unramified cyclic quartic extensions of Q( ..jm). THERESA P. VAUGHAN, University of North Carolina, Greensboro (816-11-244) 11:00-11:10 (37) Differences between squares and powerful numbers. CHARLES VANDEN EYNDEN, illinois State University (816-11-305) 11:15-11:25 (38) Probabilistic evidence for the 3x + 1 Coniecture. , Smith College (816-11-362) 11:30-11:40 (39) A generalization of a theorem of Euler for regular chains of complex quadratic irrationalities. NORMAN RICHERT, Marquette University (816-11-442) 11:45-11:55 (40) A sieve for all primes of the form x2 + (x + 1)2. PANAYIOTIS TSANGARIS, Athens University, Greece (816-11-469) 12:00-12:10 (41) Some thoughts on Goldbach's coniecture. BETTY C. LYON, University of Nebraska, Omaha (816-11-483) (Sponsored by Hugo Rossi)

Wednesday, January 9, 1985, 8:15 a.m. Session on Algebra 8:15- 8:25 (42) Bivariant long exact in homological algebra. TEMPLE H. FAY*, University of Southern Mississippi, and KEITH A. HARDIE, University of Capetown, Republic of South Africa (816-18-446) 8:30- 8:40 (43) N-systems of polynomials. Preliminary report. J. J. MALONE* and B. C. McQuARRIE, Worcester Polytechnic Institute (816-16-179) 8:45- 8:55 (44) A decomposition of right FPF rings. GARY F. BIRKENMEIER, Kuwait University (816-16-190) 9:00- 9:10 (45) A commutativity theorem. EVAGELOS PSOMOPOULOS, University of Thessaloniki, Greece, HrsAo TOMINAGA, Okayarna University, Japan, and ADIL Y AQUB*, University of California, Santa Barbara (816-16-197) 9:15- 9:25 (46) Prime ideals in differential operator rings and crossed products of infinite groups. WILLIAM CHIN, University of Wisconsin, Madison (816-16-335) 9:30- 9:40 (47) Properness of Lie algebras and enveloping algebras. WALTER MicHAELIS, State University of New York, Buffalo (816-16-373) 9:45- 9:55 (48) Group-graded rings and duality. DECLAN QUINN, University of Wisconsin, Madison (816-16- 453)

46 10:00-10:10 (49) A characterization of Morita equivalence. LILLIAN E. PETERS RUPERT, Loyola University of Chicago (816-16-484) 10:15-10:25 (50) Special simple Jordan triple systems over fields. THOMAS J. E. ScHWARZ, Western Washington University (816-17-143) 10:30-10:40 (51) Simple locally (-1,1) nil rings. IRVIN R. HENTZEL and HARRY F. SMITH*, Iowa State University (816-17-148) 10:45-10:55 (52) A Euclidean interpretation of Dynkin diagrams and its relation to root systems. D. DRUCKER* and D. FROHARDT, Wayne State University (816-17-177) 11:00-11:10 (54) A categorical analogue of Zn. ALEXANDRU SoLIAN, University of North Carolina, Charlotte (816-18-105) 11:15-11:25 (55) On the notion of precohomology. GoRo KATO, California Polytechnic State University (816-18-140)

Wednesday, January 9, 1985, 8:30a.m. Session on Complex Analysis 8:30- 8:40 (56) A property of entire functions admissible in the sense of Hayman. ALBERT EDREI, (816-30-224) 8:45- 8:55 (57) Distributional Laplacian of the star-function. Preliminary report. J. R. QUINE, Florida State University (816-30-311) 9:00- 9:10 (58) Coefficient inequalities for a subclass of starlike functions. R. D. BERMAN, Wayne State University, and H. SILVERMAN*, College of Charleston (816-30-259) 9:15- 9:25 (59) On fixed points of composite meromorphic functions. FRED GRoss*, University of Maryland, Baltimore County, and CHARLES F. OsGOOD, Naval Research Laboratory, Washington, D.C. (816-30-45) 9:30- 9:40 (60) Dominating sets of measures for Hardy spaces. Preliininary report. DANIEL H. LUECKING, University of Arkansas, Fayetteville (816-30-315) 9:45- 9:55 (61) An entire function that gives the Fibonacci numbers at the integers. A. W. GoODMAN, University of South Florida (816-30-129) 10:00-10:10 (62) A note on Toeplitz operators. DMITRY KHAVINSON, University of Arkansas, Fayetteville (816-30-495) 10:15-10:25 (63) On the behavior at the boundary of harmonic functions of Beurling type. Preliininary report. JoHN A. KELINGOS, Vanderbilt University (816-30-262) 10:30-10:40 (64) The remaining continued fractions in Ramanujan's Second Notebook. Preliininary report. RoBERT L. LAMPHERE, Francis Marion College (816-30-333) (Sponsored by David Rose) 10:45-10:55 (65) Functions with harmonic characteristic. Preliininary report. F ARUK F. ABI-KHUZAM, American University of Beirut, Lebanon (816-30-503) 11:00-11:10 (66) On some classes of first-order differential subordinations. SANFORD S. MILLER*, State University of New York, Brockport, and PETRU T. MoCANU, Babes-Bolyai University, Romania (816-30-505) 11:15-11:25 (67) Monge-Ampere measures associated to extremal plurisubharmonic functions in en. NoRMAN LEVENBERG, University of Kentucky (816-32-198) 11:30-11:40 (68) A small boundary for H""(D) on a strictly pseudoconvex domain. ANTONELLA CuPILLARI, Behrend College, Pennsylvania State University (816-32-261) 11:45-11:55 (69) Some applications of the Lie algebra of a Banach space. Preliminary report. THOMAS BARTON, Memphis State University (816-32-459)

Wednesday, January 9, 1985, 9:00a.m. Invited Address 9:00-10:00 (70) Some new approaches to moduli spaces. RUTH M. CHARNEY, Ohio State University, Columbus (816-14-374)

Wednesday, January 9, 1985, 9:00 a.m.

Special Session on Nonstrictly Hyperbolic Conservation Laws, I 9:00- 9:20 (71) A survey of non-strictly hyperbolic conservation laws. BARBARA LEE KEYFITZ, University of Houston, University Park (816-35-231) 9:30- 9:50 (72) A non-strictly hyperbolic system of conservation laws with characteristic speeds which vary in the same direction. BARBARA L. KEYFITZ, University of Houston, and HERBERT C. KRANZER*, Adelphi University (816-35-161) 10:00-10:20 (73) Phase jumps near the Maxwell line. MICHAEL SHEARER, Duke University (816-35-86)

47 10:30-10:50 (74) The Riemann problem for a van der Waals fluid. HARUMI HATTORI, West Vrrginia University (816-35-160) 11:00-11:20 (75) 'I'ravelling waves in non-linearly viscoelastic media and shock structure in elastic media. Preliminary report. STUART S. ANTMAN, University of Maryland, College Park, and REZA MALEK-MADANI*, United States Naval Academy (816-35-400) 11:30-11:50 (76) The initial value problem for incompressible elasticity RALPH A. SAXTON*, University of California, Los Angeles, and DAVID G. EBIN, State University of New York, Stony Brook (816-73-369)

Wednesday, January 9, 1985, 9:00 a.m.

Special Session on Asymptotic Properties of Hyperbolic Groups, I 9:00- 9:20 (77) Rotation numbers of products of circle homeomorphisms. MARK JANKINS, College of Charleston, and WALTER D. NEUMANN*, University of Maryland, College Park (816-54-408) 9:30- 9:50 (78) Length functions on free groups. MARK CULLER, Rutgers University and Mathematical Sciences Research Institute (816-20-409) 10:00-10:20 (79) Growth functions of Fuchsian groups. PHILIP WAGREICH, University of illinois, Chicago (816-51-460) 10:30-10:50 (80) Constructing the sphere at infinity. WILLIAM J. FLOYD, University of Michigan, Ann Arbor, and Virginia Polytechnic Institute and State University (816-20-56) 11:00-11:50 (81) Limit sets of Kleinian and Julian sets. Preliminary report. DENNIS SuLLIVAN, Graduate School and University Center, City University of New York (816-30-481)

Wednesday, January 9, 1985, 9:00 a.m. Special Session on Ordinary Differential Equations, I 9:00- 9:20 (82) Periodic orbits of nonlinear oscillators. Preliminary report. DAVID HART, University of Florida (816-34-272) 9:30- 9:50 (83) Global simplification of a Hamiltonian system with multi-transition points. HARRY GINGOLD, West Virginia University, and Po-FANG HSIEH*, Western Michigan University (816-34-57) 10:00-10:20 (84) Lyapunov exponents and oscillatory behavior in linear differential-delay equations with negative feedback. Preliminary report. JOHN MALLET-PARET*, , and GEORGE R. SELL, , (816-39-415) 10:30-10:50 (85) Normal forms for general equilibrium. K. R. MEYER, University of Cincinnati (816-34-14) 11:00-11:20 (86) Central configurations. CHARLES CONLEY, University of Minnesota, Minneapolis (816-34-419) 11:30-11:50 (87) Local reductions in functional differential equations. JACK K. HALE, Brown University (816-34-40)

Wednesday, January 9, 1985, 9:00 a.m. Session on Operator Theory, I 9:00- 9:10 (88) Tensor products and joint essential spectra of commuting systems of operators. RAM U. VERMA, University of Puerto Rico, San Juan (816-47-35) 9:15- 9:25 (89) Consequences of maximal decomposibility. Preliminary report. GARY W. SHULBERG, Pennsylvania State University, Delaware County Campus (816-47-41) 9:30- 9:40 (90) On the Daugavet property. Preliminary report. DAVID MoTTE, Auburn University (816-47-104) 9:45- 9:55 (91) Reductive algebras containing a direct sum of the unilateral shift and a certain other operator are selfadjoint. MOHAMAD A. ANsARI, Pennsylvania State University, Berks Campus (816-47-124) 10:00-10:10 (92) Factorization of diagonally dominant operators on £1. Preliminary report. P. W. SMITH, Old Dominion University, and J. D. WARD*, Texas A&M University, College Station (816-47-126) 10:15-10:25 (93) Convergence rates for Wiener's theorem for contraction semigroups. Preliminary report. MicHAEL BALLOTTI, Western Washington University (816-47-130) 10:30-10:40 (94) Compact weighted composition operators on Sobolev related spaces. HERBERT KAMOWITZ* and DENNIS WoRTMAN, University of Massachusetts, Boston (816-47-151) 10:45-10:55 (95) Generalized Cesaro operators on£2. CRAWFORD RHALY, Millsaps College (816-47-172) 11:00-11:10 (96) Factorization of diagonally dominant operators on L1([0, 1],X). KEVIN T. ANDREWS*, Oakland University, and JOSEPH D. WARD, Texas A&M University, College Station (816-47-173) 11:15-11:25 (97) Maxwell's principle for locally Lipschitzian functions. GREGORY B. PASSTY* and RICARDO TORREJON, Southwest Texas State University (816-47-267)

48 11:30-11:40 (98) Approximation of the parallel sum of nonlinear operators. CARROLL BANDY, GREGORY B. PASSTY and RICARDO TORREJON*, Southwest Texas State University (816-47-358) 11:45-11:55 (99) Non-sublinear transformations and adjoints of continuous linear transformations. MARY EMBRY­ WARDROP, Central Michigan University (816-47-308)

Wednesday, January 9, 1985, 9:00 a.m.

Session on Functional Analysis, 9:00- 9:10 (100) Precursors of the geometric Hahn Banach theorem JOHN J. SACCOMAN, Seton Hall University (816-46-31) 9:15- 9:25 (101) Topological algebras with finitely-generated bases. , McMaster University, and SALEEM WATSON*, Pennsylvania State University, Delaware County Campus (816-46-38) 9:30- 9:50 (102) Permanence and universal family theorems for conull FK spaces. Preliminary report. MATTHEW ScHAFFER* and A. K. SNYDER, Lehigh University (816-46-313) 9:45- 9:55 (103) Results on multipliers of inifinite matrices. Prelimi.nary report. WILLIAM H. RucKLE, Clemson University (816-46-277) 10:00-10:10 (104) A theorem of Burgess and Mauldin and its application to operators in C(K). LUTZ WEIS, Louisiana State University, Baton Rouge (816-46-112) 10:15-10:25 (105) Uniform operator u-additivity of indefinite integrals induced by scalar-type spectral operators. Preliminary report. S. OKADA*, San Diego State University, and W. RICKER, Australian National University, (816-46-203) 10:30-10:40 (106) A reflexive LUR Banach space that lacks normal structure. MARK A. SMITH, Miami University, and BARRY TURETT*, Oakland University (816-46-221) 10:45-10:55 (107) A permanence theorem for sums of sequence spaces. A. K. SNYDER, Lehigh University (816-46-279) 11:00-11:10 (108) C*-algebra of inverse semigroups. JOHN DuNCAN, University of Arkansas, Fayetteville (816-46-316) 11:15-11:30 (109) Extremely non-nice operators into CK and continuous mappings into the Hilbert cube. P. GREIM*, University of California, Santa Barbara, S. KOPPELBERG, Freie Universitaet, Federal Republic of Germany, and M. RAJAGOPALAN, Cochin University, India (816-46-343)

Wednesday, January 9, 1985, 9:00 a.m.

Session on Algebraic Geometry 9:00- 9:10 (110) Rings of invariants of vector fields on G/B with a unique zero. Preliminary report. ERSAN AKYILDiz* and YILMAZ AKYILDIZ, University of Petroleum and Minerals (816-14-102) 9:15- 9:25 (111) The classification of cubic curves. Preliminary report. DAVID WEINBERG, Texas Tech University (816-14-107) 9:30- 9:40 (112) On linking double lines. JuAN MIGLIORE, Northwestern University (816-14-340) 9:45- 9:55 (113) A semi-algebraic Heine-Bore! theorem. Preliminary report. CHARLES N. DELZELL, Louisiana State University, Baton Rouge (816-14-380)

Wednesday, January 9, 1985, 10:00 a.m. Sessi.m on Lie Groups 10:00-10:10 (114) Compactly generated groups. R. W. BAGLEY, University of Miami, T. S. Wu, Case Western Reserve University, and J. S. YANG*, University of South Carolina, Columbia (816-22-122) 10:15-10:25 (115) On pseudocompact Abelian groups. W. W. COMFORT* and LEWIS C. ROBERTSON, Wesleyan University (816-22-206) 10:30-10:40 (116) Connectedness of complete metric groups. T. CHRISTINE STEVENS, Arkansas State University (816-22-366) 10:45-10:55 (117) Maximal compact normal subgroups. M. REZA PEYROVIAN, University of Miami (816-22-387) 11:00-11:10 (118) The exponential mapping in Clifford algebras. NIKOS SALINGAROS, University of Texas, San Antonio (816-99-169)

Wednesday, January 9, 1985, 10:00 a.m. General Session 10:00-10:10 (119) Riccati's use of analogous logarithms to define sinh and cosh. JosEPH MACDONNELL, Fairfield University (816-01-33) 10:15-10:25 (120) Combinatory predicate logic. ALAIN L. GAUDEFROY, Centre National de Ia Recherche Scientifique, France (816-03-207)

49 10:30-10:40 (121) A many-valued semantics for propositional logic. JOHN SIMMS, Marquette University (816-03- 394) 10:45-10:55 (122) The relative consistency of a "Large Cardinal" property for w1. RoBERT MIGNONE, College of Charleston (816-04-236) 11:00-11:10 (123) A generalized partition property in set theory without choice. RONALD J. WATRO, Villanova University (816-04-367)

Wednesday, January 9, 1985, 10:15 a.m. Invited Address 10:15-11:15 (124) On Gauss' class number problem. DoRIAN GoLDFELD, University of Texas, Austin (816-12-184)

Wednesday, January 9, 1985, 1:00 p.m. Colloquium Lectures: Lecture I 1:00- 2:00 (125) The classification of the finite simple groups. DANIEL GoRENSTEIN, Rutgers University

Wednesday, January 9, 1985, 2:15 p.m. Invited Address 2:15- 3:15 (126) Is a variety determined by its periods? RoN DONAGI, Northeastern University (816-99-522)

Wednesday, January 9, 1985, 2:15 p.m. Special Session on Analytic Number Theory, I 2:15- 3:05 (127) Primes in large progression. Preliminary report. ENRICO BOMBIERI, Institute for Advanced Study (816-11-185) (Sponsored by Dorian Goldfeld) 3:15- 4:05 (128) Poincare series and Kloosterman sums. Preliminary report. DANIEL BUMP, University of Texas, Austin, SoLOMON FRIEDBERG*, Harvard University, and DORIAN GoLDFELD, University of Texas, Austin (816-11-186) 4:15- 5:05 (129) The winding number for the scattering matrix and the deformation of discrete groups. Preliminary report. RALPH PHILLIPs*, Stanford University, and , Stanford University and Courant Institute of Mathematical Sciences, New York University (816-11-133) 5:15- 5:45 (130) An infinite series related to modular forms of weight one. Preliminary report. H. M. STARK, Massachusetts Institute of Technology and University of California at San Diego, La Jolla (816-11-250)

Wednesday, January 9, 1985, 2:15 p.m. Special Session on Nonstrictly Hyperbolic Conservation Laws, II 2:15- 2:35 (131) Approximate Riemann solvers and numerical flux functions. Preliminary report. STANLEY OSHER, University of California, Los Angeles (816-65-191) 2:45- 3:05 (132) Characteristic fields of the MElD equations. Preliminary report. MoYSEY BRio* and CHENG­ CHIN Wu, University of California, Los Angeles (816-35-109) (Sponsored by Barbara L. Keyfitz) 3:15- 3:35 (133) The generalized Riemann problem and numerical schemes for compressible duct flows. MATANIA BEN-ARTZI, Institute of Technology and University of California, Berkeley (816-76- 289) 3:45- 4:05 (134) The scalar Riemann problem in two spatial dimensions: Piecewise smoothness of solutions. BRENT LINDQUIST, Courant Institute of Mathematical Sciences, New York University (816-35-293) 4:15- 4:35 (135) A Cauchy-Kovalevsky theorem for conservation laws with piecewise analytic initial data. EDUARD HARABETIAN, Institute for Computer Applications in Science and Engineering (816-35-88)

Wednesday, January 9, 1985, 2:15 p.m. Special Session on Ordinary Differential Equations, II 2:15- 2:35 (136) White noise illuminates black holes. Preliminary report. LAWRENCE MARKUS, University of Minnesota, Minneapolis (816-34-264) 2:45- 3:05 (137) Lyapunov exponents for dynamical systems. GEORGE R. SELL, University of Minnesota, Minneapolis (816-34-418) 3:15- 3:35 (138) Floquet exponents for non-periodic linear systems. RussELL JoHNSON, University of Southern California and University of Heidelberg, Federal Republic of Germany (816-34-420) 3:45- 4:05 (139) A numerical study of the spectrum of a Schrodinger operator with quasi-periodic potential. DAVID PERRY, 3M Corporation (816-34-413)

50 4:15- 4:35 (140) Smoothness of the density of states in one-dimensional random difference equations. BARRY SIMON, California Institute of Technology (816-34-136) 4:45- 5:05 (141) Reduction of scalar meromorphic differential equations of second order to special forms. W. B. JuRKAT* and H. J. ZwiESLER, Universitii.t Ulm, Federal Republic of Germany (816-34-465) (Sponsored by W. A. Harris) 5:15- 5:35 (142) Diagonalization of nonlinear polynomial ordinary differential operators. Preliminary report. MEL S. BERGER, University of Massachusetts, Amherst (816-34-440)

Wednesday, January 9, 1985, 2:15 p.m.

Session on Linear Algebra 2:15- 2:25 (143) Matrices as sums of squares: a conjecture of Griffin and Krusemeyer. Preliminary report. DAVID R. RICHMAN, University of South Carolina, Columbia (816-15-253) 2:30- 2:40 (144) Generalized inverses of substochastic matrices. Preliminary report. CECIL EuGENE RoBINSON, JR., University of Southern Mississipi (816-15-254) 2:45- 2:55 (145) Convergence of periodic matrix valued continued fractions. WYMAN FAIR* and R. BusBY, University of North Carolina, Wilmington (816-15-344) 3:00- 3:10 (146) Some comments concerning nonsingular principal submatrices. Preliminary report. MELVYN W. JETER* and W. C. PYE, University of Southern Mississippi (816-15-405) 3:15- 3:25 (147) An efficient geometric characterization of the generalized inverses of a matrix. Preliminary report. JIMMIE GILBERT, Louisiana Tech University (816-15-425) 3:30- 3:40 (148) Generalized inverses of infinite matrices. K. P. S. BHASKARA RAo, Michigan Technological University (816-15-428) 3:45- 3:55 (149) An inequality involving determinants of positive definite hermitian matrices. Preliminary report. THEODORE TOLLIS, University of lllinois, Urbana-Champaign (816-15-431) 4:00- 4:10 (150) Some decompositions of Mm,n· Preliminary report. ANDREW MATCHETT, University of Wisconsin, La Crosse (816-15-449) 4:15- 4:25 (151) On the minimum rank of regular classes of matrices of zeros and ones. RICHARD A. BRUALDI and RACHEL MANBER, University of Wisconsin, Madison, and JEFFREY A. Ross*, Bell Communications Research (816-15-113)

Wednesday, January 9, 1985, 2:15 p.m.

Session on Probability 2:15- 2:25 (152) Some models for nonlinear random oscillators. RENATO SPIGLER, Courant Institute of Mathematical Sciences, New York University (816-60-09) 2:30- 2:40 (153) Comparison of optimal value and constrained maxima expectations for independent random variables. RoBERT P. KERTZ, Georgia Institute of Technology (816-60-127) 2:45- 2:55 (154) Evaluations of barrier crossing probabilities of Wiener paths when the barrier has negative jumps. CRULL PARK, Miami University (816-60-168) 3:00- 3:10 (155) C""' densities for weighted sums of independent random variables. JAKOB I. REICH, Bernard M. Baruch College, City University of New York (816-60-170) 3:15- 3:25 (156) On dynamical systems driven by Markov processes. Preliminary report. ANDRZEJ KoR­ ZENIOWSKI, University of Texas, Arlington (816-60-196) 3:30- 3:40 (157) Weak compactness in the space H 1 of martingales. NICOLAE DINCULEANU, University of Florida (816-60-227) 3:45- 3:55 (158) A strong law of large numbers for generalized £-statistics. RoBERT J. SERFLING, Johns Hopkins University (816-60-282) 4:00- 4:10 (159) Extreme value distribution for the largest cube in a random lattice. R. W. R. DARLING* and MICHAELS. WATERMAN, University of Southern California (816-60-292) 4:15- 4:25 (160) On random walks in multidimensional time. JANOS GALAMBOS*, Temple University, and IMRE KATAI, L. Eotvos University, Hungary (816-60-319) 4:30- 4:40 (161) The il-metric and central limit theorems. PAUL SHIELDS, University of Toledo (816-60-356) 4:45- 4:55 (162) Operator-normed domains of attraction and regular variation. Preliminary report. MARK M. MEERSCHAERT, Vector Research, Incorporated (816-60-371) 5:00- 5:10 (163) Stochastic integral representation of stable processes. Preliminary report. JAN RoSINSKI, University of North Carolina, Chapel Hill (816-60-450) 5:15- 5:25 (164) On some properties of normal random variables. G. G. HAMEDANl*, Marquette University, and M. N. TATE, Universitate of Humanities and Arts, Iran (816-60-486)

51 Wednesday, January 9, 1985, 2:15 p.m. Session on Partial Differential Equations 2:15- 2:25 (165) The operator equationAl XA2-B1 XB2 = Q with possibly unbounded At,A2,Bi,B2,Q. TAPAS MAZUMDAR, Wright State University (816-35-195) 2:30- 2:40 (166) Existence and uniqueness of the solution of a nonlinear wave equation. P ARVIZ KHAJEH KHALILI, Southwest Texas State University (816-35-202) 2:45- 2:55 (167) Asymptotic results on cylinders. Preliminary report. CLYDE CoLLINS, Louisiana State University, Baton Rouge (816-35-208) 3:00- 3:10 (168) Existence results using local and asymptotic estimates. R. KENT NAGLE, University of South Florida (816-35-456) 3:15- 3:25 (169) The use of a parabolic operator in an existence theory problem of the Vlasov-Poisson system. STEPHEN WoLLMAN, Bernard M. Baruch College, City University of New York (816-35-222) 3:30- 3:40 (170) Periodic boundary value problem for first order partial differential equation. A. S. V ATSALA, University of Southwestern Louisiana (816-35-265) 3:45- 3:55 (171) Remarks on an s-shaped bifurcation curve. RATNASINGHAM SHIVAJI, Southwest Texas State University (816-35-269) 4:00- 4:10 (172) Approximate solution of nonlinear problems. G. ADOM1AN, University of Georgia (816-35-504) 4:15- 4:25 (173) Exceptional boundary sets for solutions of partial differential inequalities. G. N. HILE* and R. Z. YEH, University of Hawaii (816-35-270) 4:30- 4:40 (17 4) Scattering of solitary waves in multiple dimensions. Preliminary report. HENRY A. W ARCHALL, University of Texas, Austin (816-99-515) 4:45- 4:55 (175) Generalized singular quadratic control problem. Preliminary report. SuNG J. LEE, University of South Florida (816-49-123) 5:00- 5:10 (176) A new algorithm for linear programming. GEZA ScHAY, University of Massachusetts, Boston (816-49-382) 5:15- 5:25 (177) On the existence of optimal feed-back law. Preliminary report. WANDA SzPUNAR-LOJASIEWICZ, Rochester Institute of Technology (816-49-424) 5:30- 5:40 (178) A proximal subgradient formula in Hilbert space. Preliminary report. JAY TREIMAN, Lehigh University (816-49-213)

Wednesday, January 9, 1985, 2:15 p.m. Session on Operator Theory, n 2:15- 2:25 (179) Cyclic vectors for backward hyponormal weighted shifts. Preliminary report. SHELLEY WALSH, Purdue University, West Lafayette (816-47-318) 2:30- 2:40 (180) Self-adjointness in separable Banach spaces. TEPPER L. GILL* and VERNISE STEADMAN, Howard University (816-47-359) · 2:45- 2:55 (181) Spectra associated with invariant operator ranges. Preliminary report. RIDGLEY LANGE, Central Michigan University (816-47-284) 3:00- 3:10 (182) Feynman's operational calculus, generalized Dyson series and the Feynman integral. Preliminary report. GERALD W. JOHNSON, University of Nebraska, Lincoln, and MICHELL. LAPIDUS*, University of Southern California and Mathematical Sciences Research Institute (816-47-361) 3:15- 3:25 (183) Surjectivity theorems for multi-valued mappings of accretive type. Preliminary report. CLAUDIO H. MORALES, University of Alabama, Huntsville (816-47-443) 3:30- 3:40 (184) Bishop's condition beta. JoN C. SNAm;R, University of South Florida (816-47-455) 3:45- 3:55 (185) Spectral analysis of the ergodic Hilbert transform. Preliminary report. JAMES T. CAMPBELL, Memphis State University (816-47-458) 4:00- 4:10 (186) A hyperplane of eigenvalues. KATHERINE A. YERION, Gon~aga University (816-47-487) 4:15- 4:25 (187) Quasisimilar operators in the commutant of a cyclic subnormal operator. MARC RAPHAEL, University of Missouri, Rolla (816-47-499)

Wednesday, January 9, 1985, 2:15 p.m. Session on Topology 2:15- 2:25 (188) The fiber of the transfer. ROBERT P1ACENZA, University of Alaska, Fairbanks (816-55-20) 2:30- 2:40 (189) Higher-order products in the Steenrod algebra. JAMES H. FIFE, University of Richmond (816-55-271) 2:45- 2:55 (190) Almost-free torus actions. CHRISTOPHER J. ALLDAY*, University of Hawaii, and VoLKER PUPPE, Universitiit Konstanz, Federal Republic of Germany (816-55-295)

52 3:00- 3:10 (191) Polynomial invariants for /mots and links. W. B. R. LICKORISH, , , and KENNETH C. MILLETT*, Mathematical Sciences Research Institute (816-57- 55) 3:15- 3:25 (192) Homotopy RO(G)-bundles and transversality. Preliminary report. J.P. E. HoDGSON, AdelpLi University (816-57-147) 3:30- 3:40 (193) Smoothing foliations of codimension one. JOHN CANTWELL, St. Louis University, and LAWRENCE CONLON*, Washington University (816-57-171) 3:45- 3:55 (194) Non simply connected manifolds with four critical points. JOHN D. BLANTON, St. John Fisher College (816-57 -298) 4:00- 4:10 (195) 1r1-bijective mappings of compact 3-manifolds. JOHN KALLIONGis*, Southwest Texas State University, and DARRYL McCuLLOUGH, University of Oklahoma, Norman (816-57-494) 4:15- 4:25 (196) Nonseparated manifolds and completely unstable flows. SuDHIR K. GOEL, University of Houston, Downtown (816-58-329) (Sponsored by Richard A. Alo) 4:30- 4:40 (197) Equivariant homotopy type of Fredholm manifolds. Preliminary report. MICHAEL R. CoLVIN, Northern Arizona University (816-58-390)

Wednesday, January 9, 1985, 2:15 p.m.

Session on Funetional Analysis, II 2:15- 2:25 (198) The Cesaro operator on HP. Preliminary report. ARISTOMENIS G. SISKAKIS, University of lllinois, Urbana-Champaign (816-46-372) 2:30- 2:40 (199) On a property of the Hardy space H 1(U). S. SWAMINATHAN, Dalhousie University (816-46-330) 2:45- 2:55 (200) Banach spaces with an ultrapower isometric to an ultrapower of co. S. HEINRICH, Academy of Sciences, German Democratic Republic, C. WARD HENSON, University of illinois, Urbana-Champaign, and L. C. MoonE, JR.*, Duke University (816-46-332) 3:00- 3:10 (201) On BK spaces containing isomorphic copies of co. Preliminary report. JEFF CoNNOR, Kent State University (816-46-397) 3:15- 3:25 (202) Operators on Banach lattices and the Radon-Nikodym Theorem. WILLIAM FELDMAN, University of Arkansas, Fayetteville (816-46-429) 3:30- 3:40 (203) Tsirelson superspaces and lp. STEVEN F. BELLENOT, Florida State University (816-46-474) 3:45- 3:55 (204) Closed ideals in algebras of analytic functions on the annulus. Preliminary report. TOVEY BACHMAN, University of Michigan, Ann Arbor (816-46-454) 4:00- 4:10 (205) Pettis integrability and the equivalence of the norms of the weak* integral and Dunford integral. Preliminary report. ELIZABETH BATOR, North Texas State University (816-46-445) 4:15- 4:25 (206) On the point's cone of a finite dimensional compact convex set. C. H. SUNG* and B. S. TAM, University of California at San Diego, La Jolla, San Diego State University and Tamkang University, Republic of China (816-99-519) 4:30- 4:40 (207) An abstract Banach-Stone type theorem. Preliminary report. D. R. HART, Texas A&M University, College Station (816-46-276)

Wednesday, January 9, 1985, 2:15 p.m. Session on Mathematieal Eeonomies 2:15- 2:25 (208) Solutions for n-person coalitional games. Preliminary report. WILLIAM F. LucAs, Claremont Graduate School, and JOHN C. MACELI*, Ithaca College (816-90-125) 2:30- 2:40 (209) Power indeces for multicandidate voting games. EDWARD BOLGER, Miami University (816-90- 396) (Sponsored by David Lutzer) 2:45- 2:55 (210) Second-order necessary conditions in nonsmooth optimization. ROBIN W. CHANEY, Western Washington University (816-90-225) 3:00- 3:10 (211) An algorithm for constrained convex optimization. RoBERT W. OWENS*, Lewis and Clark College, and V. P. SREEDHARAN, Michigan State University (816-90-364) 3:15- 3:25 (212) Thermodynamic modeling of merger versus conflict. Preliminary report. DENNIS G. CoLLINS, University of Puerto Rico, Mayagiiez (816-90-52) 3:30- 3:40 (213) Absorbing set for n-person games. Preliminary report. CHIH CHANG, Cornell University (816-90-211) 3:45- 3:55 (214) Using UNIX and C in the preparation of computer contracts and other legal documents. Preliminary report. R. KEOWN, University of Arkansas, Fayetteville (816-90-430) 4:00- 4:10 (215) Imposition of stability on vector ARMA models with rational expectations. Preliminary report. ALBERT E. PARISH, JR., College of Charleston (816-90-457) 4:15- 4:25 (216) Inset entropies on open domains. BRUCE EBANKS, Texas Tech University (816-94-444)

53 ·4:30- 4:40 {217) An environ analysis for nonlinear compartment models. M. N. ANTONIOS, Memphis State University {816-93-506)

Wednesday, January 9, 1985, 2:15 p.m. Session on Differential Geometry 2:15- 2:25 (218) Differential geometry of one-dimensional real Mange-Ampere foliations. ROBERT L. FooTE, Texas Tech University {816-53-283) 2:30-- 2:40 {219) Geodesic completeness in standard static space-times. Preliminary report. DEAN ALLISON, University of Missouri, Columbia {816-53-297) 2:45- 2:55 {220) Characterizing Gauss maps. STEVE WILKINSON, University of North Carolina, Chapel Hill {816-53-357) 3:00-- 3:10 {221) Higher order flatness of spheres. Preliminary report. GREGORY A. FREDRICKS*, Texas Tech University, and PHILLIP E. PARKER, Wichita State University {816-53-73) 3:15-- 3:25 {222) A linearizability condition for a three-web in the plane. Preliminary report. VLADISLAV V. GOLDBERG, New Jersey Institute of Technology {816-53-383) 3:30- 3:40 {223) Strongly unstable manifolds. RALPH HowARD, University of South Carolina, Columbia, and S. WALTER WEI*, University of California, Los Angeles, and Michigan State University {816-53-478) 3:45-- 3:55 {224) On differential geometry in modules: The generalized Bianchi formula. PETRU P APADOPOL, University of Alabama at Tuscaloosa, University {816-53-376) 4:00- 4:10 {225) Fold singularities in pseudo Riemannian geodesic tubes. Preliminary report. MAREK KossowsKr, Rice University {816-53-510) 4:15-- 4:25 {226) Sectional curvature on 3-manifolds. Preliminary report. PHILLIP E. PARKER, Wichita State University {816-53-500) 4:30-- 4:40 {227) Asymptotic approximation by harmonic functions on closed sets. MYRON GoLDSTEIN*, Arizona State University, and WELLINGTON H. Ow, Michigan State University {816-99-514) 4:45-- 4:55 {228) Para-¢-structures with parallelizable kernel on manifolds. ANDRZEJ BucKr, Maria Curie­ Sklodowska University, Poland {816-53-512) 5:00-- 5:10 {229) Some characterizations of Euclidean motions. J. A. LESTER, California State University, Los Angeles {816-99-518) 5:15-- 5:25 {230) On quasi-Euclidean spaces. ROBERT WILLIAMSON* and LUDVIK JANOS, Claremont Graduate School {816-99-520)

Wednesday, January 9, 1985, 3:30 p.m. Invited Address 3:30-- 4:30 {231) Beauty and symmetry in the theory of minimal surfaces. WILLIAM H. MEEKS, Rice University {816-53-426)

Wednesday, January 9, 1985, 3:30 p.m. Special Session on Algebraic Deformation Theory, I 3:30- 4:00 {232) Dimension of varieties of simple representations. ANDY MAGID*, University of Oklahoma, Norman, and ALEXANDER LUBOTZKY, Hebrew University, Israel (816-20-43) 4:10-- 4:40 {233) Representation varieties of nilpotent groups. ALEXANDER LuBOTZKY*, Hebrew University, Israel, and ANDY MAGID, University of Oklahoma, Norman {816-20-42) 4:50- 5:20 {234) Rigid associative algebras and the Bockstein as an obstruction map. MuRRAY GERSTENHABER, University of Pennsylvania, and SAMUEL D. SCHACK*, State University of New York, Buffalo (816-16-406) 5:30- 5:50 {235) Deformations of nilpotent Lie algebra structures. Preliminary report. FRITZ GRUNEWALD, Universitat Bonn, Federal Republic of Germany, and JoYCE O'HALLORAN*, University of Wisconsin, Milwaukee {816-14-144)

Wednesday, January 9, 1985, 8:45 p.m. Josiah Willard Gibbs Lecture 8:45- 9:45 {236) Randomization in. mathematics and computer science. MICHAEL 0. RABIN, Harvard University and Hebrew l]niversity of Jerusalem, Israel

Thursday, January 10, 1985, 8:00 a.m. Special Session on Algebraic Deformation Theory, n 8:00- 8:30 {237) Cohomology and deformation of triangular algebras. Preliminary report. MURRAY GERSTENHABER*, University of Pennsylvania, and S. D. SCHACK, State University of New York, Buffalo {816-18-464)

54 8:40- 9:10 (238) Algebra deformations as cohomological perturbations. JAMES STASHEFF, University of North Carolina, Chapel Hill (816-18-187) 9:20- 9:50 (239) Hopf algebraic techniques in deformation theory. Preliminary report. CLARENCE W. WILKERSON, Wayne State University (816-55-492) 10:00-10:20 (240) Uniqueness of symplectic structures. WILLIAM ARVESON, University of California, Berkeley (816-81-485) 10:30-10:50 (241) Deformation of uniform algebras. RicHARD RocHBERG, Washington University (816-46-153)

Thursday, January 10, 1985, 8:00 a.m. Special Session on Analytic Number Theory, II 8:00- 8:20 (242) On Riemann's zeta function. Preliminary report. DANIEL BuMP, University of Rochester, an

Thursday, January 10, 1985, 8:00 a.m. Session on Abstract Analysis 8:00- 8:10 (249) Invariant Sp(1)-instantons on 8 2 X 8 2 . Preliminary report. FRANK R. UNGER, Oregon State University (816-99-513) 8:15- 8:25 (250) On the Mhaskar-Saff extreme! property and asymptotics of the greatest zero of orthogonal polynomials. Preliminary report. STANFORD S. BoNAN, University of Rhode Island (816-41- 404) 8:30- 8:40 (251) A new quadrature formula associated with the ultraspherical polynomials. PAUL NEVAI, Ohio State University, and A. K. VARMA*, University of Florida (816-41-437) 8:45- 8:55 (252) On the degree of weak convergence of a sequence of finite measures (J.Ln)nEN to the unit measure Ox 0 , ill. Preliminary report. GEORGE A. ANASTASSiou, University of Rhode Island (816-41-275) 9:00- 9:10 (253) Some theorems concerning holomorphic Fourier transforms. Preliminary report. R. A. ZALIK, Auburn University (816-42-114) 9:15- 9:25 (254) Double trigonometric series with bounded partial sums on a set and g~. J. M. AsH, DePaul University (816-42-355) 9:30- 9:40 (255) Highly oscillatory singular integrals along curves. Preliminary report. MICHAEL F. ZIELINSKI, University of Wisconsin, Madison (816-42-384) 9:45- 9:55 (256) Oscillatory behavior of orthogonal polynomials. ATTILA MATE*, Brooklyn College, City University of New York, and PAUL NEVA! and VILMOS ToTIK, Ohio State University (816-42-342) 10:00-10:10 (257) Bounded synthesis and Bochner's property. Preliminary report. DAVID COLELLA, St. Lawrence University (816-43-309) 10:15-10:25 (258) Which amalgams are convolution algebras? JAMES STEWART*, McMaster University, and SALEEM WATSON, Pennsylvania State University, Media (816-43-328) 10:30-10:40 (259) Harmonic functions on homogeneous spaces of commutator induced extensions of compact groups. R. E. LEWKOWICZ, Wright State University (816-43-278) 10:45-10:55 (260) Representation for the dual- Weierstrass-Laguerre transform. DEBORAH TEPPER HAIMO, University of Missouri, St. Louis (816-44-341) 11:00-11:10 (261) L1 estimates of a function from its Radon transform. Preliminary report. JAMES V. PETERS, C. W. Post Center, Long Island University (816-44-106) 11:15-11:25 (262) An isomorphism theorem for subalgebras of crossed products. JusTIN PETERS, Iowa State University (816-45-274)

55 11:30-11:40 (263) Ultimate behavior for equations with infinite delay. Preliminary report. HERMINIO CASSAGO, JR., Universidade de S~o Paulo, Brazil, and C. CoRDUNEANU*, University of Texas, Arlington (816-45-379) 11:45-11:55 (264) A reduction method for solving an integral inequality. EuTIQUIO C. YoUNG, Florida State University (816-45-49)

Thursday, January 10, 1985, 8:00 a.m. Session on Combinatories 8:00- 8:10 (265) A group of a graph and Harary reconstructions. STEPHEN LIPSCOMB, Mary Washington College (816-05-100) 8:15- 8:25 (266) Some equivalents of the Erdos sum of reciprocals conjecture. NEIL HINDMAN, Howard University (816-05-216) 8:30- 8:40 (267) A combinatorial proof of Wedderburn's theorem. JuDITH LONGYEAR, Wayne State University (816-05-12) 8:45- 8:55 (268) The Catlerian identity. Preliminary report. DoN RAWLINGs, California Polytechnic State University (816-05-181) 9:00- 9:10 (269) Dual operators and Lagrange inversion in several variables. Lurs VERDE-STAR, Universidad Aut6noma Metropolitana, Mexico (816-05-182) 9:15- 9:25 (270) Pseudo-Boolean functions and the random local improvement algorithm. Preliminary report. KATHY WILLIAMSON HOKE, University of North Carolina, Chapel Hill (816-05-70) 9:30- 9:40 (271) Mo:r:imal, minimal connectivity in graphs. KEN PETERS, RENU LASKAR* and STEPHEN HEDETNIEMI, Clemson University (816-05-229) 9:45- 9:55 (272) Classification by isomorphism of the reduced latin squares of order ~ 7. LARRY J. BRANT*, National Institute on Aging, and GARY L. MULLEN, Pennsylvania State University, University Park (816-05-233) 10:00-10:10 (273) Predicates with periodic mo:r:imallength functions. MICHAEL GILPIN* and RoBERT SHELTON, Michigan Technological University (816-05-235) 10:15-10:25 (274) The toroidal splitting number of the complete graph. NORA HARTSFIELD, Western Washington University (816-05-237) (Sponsored by Michael Ballotti) 10:30-10:40 (275) Bipartite regulation numbers. YoUSEF ALAVI, GARY CHARTRAND, LINDA LESNIAK* and 0RTRUD OELLERMANN, Western Michigan University (816-05-238) 10:45-10:55 (276) Adjacency based topology of a raster screen. Preliminary report. LAWRENCE N. STOUT, illinois Wesleyan University (816-05-310) 11:00-11:10 (277) On constructing t- (v, k, A.) designs with group actions. NEAL BRAND, North Texas State University (816-05-325) 11:15-11:25 (278) The constant term of a non-commutative multinomial. Preliminary report. NICHOLAS PAS SELL*, PRESTON BusH and PAMELA LIPKA, University of Wisconsin, Eau Claire (816-05-348) 11:30-11:40 (279) Transformations which are compositions of three idempotents. Preliminary report. BoRis M. ScHEIN, University of Arkansas, Fayetteville (816-05-423) 11:45-11:55 (280) Finite planes and graphs. Preliminary report. JosEPH RoTMAN, University of lllinois, Urbana-Champaign (816-05-468)

Thursday, January 10, 1985, 8:15 a.m. General Session 8:15- 8:25 (281) Boundedness and stability of solutions of an integra-differential ~ystem. W. E. MAHFOUD, Murray State University (816-34-268) 8:30- 8:40 (282) Minimal existence of nonoscillatory solutions in functional differential equations with deviating arguments. BHAGAT SINGH, University of Wisconsin, Manitowoc County Center (816-34-441) 8:45- 8:55 (283) On a generalized fundamental equation of information. PL. KANNAPPAN, University of Waterloo (816-39-201) 9:00- 9:10 (284) Criteria for right disfocality of linear difference equations. PAUL ELOE, University of Dayton (816-39-19) 9:15- 9:25 (285) On the uniqueness of solutions of nonlinear boundary value problems. A. R. AFTABIZADEH* and JosEPH WIENER, Pan American University (816-34-447) 9:30- 9:40 (286) On nicely spread out sequences of points on a circle. Preliminary report. THOMAS M. ZACHARIAH, University of Alaska, Fairbanks (816-40-306) (Sponsored by John Patrick Lambert) 9:45- 9:55 (287) Correcting the partial sums of a positive-term series. DoNALD R. SNOW, Brigham Young University (816-40-381) 10:00-10:10 (288) On the set of subsums of an infinite series. Preliminary report. J. A. GuTHRIE and J. E. NYMANN*, University of Texas, El Paso (816-40-434)

56 10:15-10:25 {289) On statistical convergence. JOHN FRIDY, Kent State University {816-40-217) 10:30-10:40 (290) Summability methods constructed from coin tosses. Preliminary report. DEBORAH A. FRANTZ, Western Kentucky University {816-40-291) 10:45-10:55 {291) Ordered planes. Preliminary report. DAVID SACHS, Wright State University {816-51-174) 11:00-11:10 {292) 'Jiypical convex curves on convex surfaces. TUDOR ZAMFIRESCU, University of Dortmund, Federal Republic of Germany {826-52-307) {Sponsored by John W. Woll, Jr.) 11:15-11:25 {293) A simplicial3-arrangement of21 planes. Preliminary report. G. L. ALEXANDERSON, University of Santa Clara, and JoHN E. WETZEL*, University of illinois, Urbana-Champaign {816-51- 511) 11:30-11:40 {294) Class of generalized conic sections and their applications to orbital analysis. Preliminary report. SHELDON P. GORDON, Adelphi University {816-51-470) {Sponsored by Robert Payton) 11:45-11:55 {295) Convex sets, homeomorphisms, and profiles. MANGHO AHUJA, Southeast Missouri State University {816-52-281)

Thursday, January 10, 1985, 8:30a.m.

Special Session on Asymptotic Properties of Hyperbolic Groups, II 8:30- 8:50 {296) A generalization of Dehn's algorithm. Preliminary report. KAY TATSUOKA, University of Wisconsin, Madison {816-57-375) {Sponsored by James W. Cannon) 9:00- 9:20 {297) Stereo optics in hyperbolic space. MATT GRAYSON, Mathematical Sciences Research Institute {816-51-410) 9:30- 9:50 {298) Infinite words and geodesics in moduli space. Preliminary report. STEVE KERCKHOFF, Mathematical Sciences Research Institute {816-58-490) (Sponsored by Robion Kirby) 10:00-10:20 {299) Some examples of national growth in class 2 nilpotent groups. Preliminary report. MAx L. BENSON, University of Minnesota, Duluth {816-20-68) 10:30-10:50 {300) Growth functions of groups and Euler series. N. SMYTHE, Australian National University, Australia {816-20-48) 11:00-11:50 (301) Asymptotic properties of hyperbolic groups. Preliminary report. JAMES W. CANNON, University of Texas, Austin, and University of Wisconsin, Madison {816-53-299)

Thursday, January 10, 1985, 8:30 a.m.

Session on Group Theory 8:30- 8:40 {302) Infinite groups satisfying the weak chain conditions for finitely generated subgroups. MANFRED KARBE, University of Kentucky {816-20-117) {Sponsored by Paul Eakin) 8:45- 8:55 (303) Representation extension properties of normal bands. SYDNEY BULMAN-FLEMING* and KENNETH McDOWELL, Wilfrid Laurier University {816-20-06) 9:00- 9:10 {304) Left absolutely flat generalized inverse semigroups. KENNETH McDOWELL* and SYDNEY BULMAN-FLEMING, Wilfrid Laurier University {816-20-07) 9:15- 9:25 (305) Pi-blocks of pi-separable groups. MICHAEL C. SLATTERY, Marquette University {816-20-150) {Sponsored by Suzanne L. Larson) 9:30- 9:40 {306) Near F'rattini subgroups of amalgamated free products of groups. Preliminary report. MoHAMMAD K. AzARIAN, Saint Louis University {816-20-183) 9:45- 9:55 {307) Subgroups of the exceptional groups. Preliminary report. DoNNA M. TESTERMAN, University of Oregon {816-20-255) 10:00-10:10 (308) On large centralizers in finite solvable groups. Preliminary report. EDWARD A. BERTRAM*, University of Hawaii, Manoa, and MARCEL HERZOG, University, Israel {816-20-256) 10:15-10:25 {309) Prefrattini subgroups and nonsaturated formations. Preliminary report. MARK HoFFMAN, St. Lawrence University {816-20-258) 10:30-10:40 (310) Locally complemented formations. Preliminary report. H. BECHTELL, University of New Hampshire {816-20-360) 10:45-10:55 {311) Groups that are very nearly isomorphic. CHARLES HoLMES, Miami University {816-20-378) 11:00-11:10 {312) Verbal embeddings into groups, I. KENNETH W. WESTON* and LEO P. COMERFORD, JR., University of Wisconsin, Parkside {816-20-461) 11:15-11:25 {313) Verbal embeddings into groups, IT. LEO P. COMERFORD, JR.* and KENNETH W. WESTON, University of Wisconsin, Parkside {816-20-462) 11:30-11:40 {314) Rank 3 permutation modules over a field of characteristic dividing the degree. Preliminary report. MICHAEL R. LEWY, California Institute of Technology {816-20-475) 11:45-11:55 {315) On idempotent generated ideals in finite group rings. JAMES WISEMAN, Rochester Institute of Tecl... ~ogy {816-99-516) (Sponsored by George Georgantas)

57 Thursday, January 10, 1985, 9:00 a.m. Invited Address 9:00-10:00 (316) Some recent directions in nonlinear elliptic PDE. LAWRENCE CRAIG EVANS, University of Maryland, College Park (816-35-26)

Thursday, January 10, 1985, 9:00 a.m. Special Session on Teiehmuller Theory for Surfaces, Graphs and Hyperbolic Manifolds, I Garden Grove Room 4 9:00- 9:20 (317) Cohomology of Sp4(Z) and related groups and spaces. RoNNIE LEE, Yale University, and STEVEN H. WEINTRAUB*, Louisiana State University, Baton Rouge (816-14-64) 9:30- 9:50 (318) Symplectic geometry of deformations of flat bundles over surfaces. Preliminary report. WILLIAM M. GoLDMAN, Mathematical Sciences Research Institute (816-57-99) 10:00-10:20 (319) A dynamical class of entire functions. LISA R. GOLDBERG* and LINDA KEEN, Graduate School and University Center, City University of New York (816-30-121) 10:30-10:50 (320) Torsion in the mapping class group and its cohomology. HENRY GLOVER*, Ohio State University, and Gumo MlsLIN, Eidgenossische Technische Hochschule, Switzerland (816-55-149) 11:00-11:20 (321) Going to infinity in moduli space. Preliminary report. STEVE KERCKHOFF, Mathematical Sciences Research Institute (816-57-489) (Sponsored by Robion Kirby) 11:30-11:50 (322) Characteristic classes and moduli spaces. RoNNIE LEE, Yale University (816-14-370)

Thursday, January 10, 1985, 9:00 a.m. Special Session on Ordinary Ditferential Equations, m 9:00- 9:20 (323) The nth roots of solutions of linear ordinary differential equations. WILLIAM A. HARRIS, JR.*, University of Southern California, and YASUTAKA SIBUYA, University of Minnesota, Minneapolis (816-34-416) 9:30- 9:50 (324) A note on some recent results of Harris-Sibuya. STEVEN SPERBER, University of Minnesota, Minneapolis (816-34-414) 10:00-10:20 (325) Connection problems for ordinary differential equations. WERNER BALSER, Universitat Ulm, Federal Republic of Germany (816-34-155) (Sponsored by William A. Harris) 10:30-10:50 (326) Perturbations of singular differential equations. D. A. LuTZ*, University of Wisconsin, Milwaukee, and R. ScHAFKE, Universitat Essen, Federal Republic of Germany (816-34-79) 11:00-11:20 (327) Polynomial flows in the plane. HYMAN BAss*, Columbia University, and GARY MEISTERS, University of Nebraska, Lincoln (816-34-134) 11:30-11:50 (328) Cohomological characterization of regular singularities ~'n several variables. Prelhninary report. YASUTAKA SIBUYA*, University of Minnesota, Minneapolis, and HIDEYUKI MAJIMA, Hitotsubashi University, Japan (816-34-417)

Thursday, January 10, 1985, 9:30a.m. Special Session on Nonstrictly Hyperbolic Conservation Laws, m 9:30- 9:50 (329) Examples and classification of non-strictly hyperbolic systems of conservation laws. Preliminary report. ELI L. ISAACSON*, University of Wyoming, and J. BLAKE TEMPLE, University of Wisconsin, Madison (816-35-399) 10:00-10:20 (330) Systems of conservation laws with coinciding shock and rarefaction curves. BLAKE TEMPLE, University of Wisconsin, Madison (816-35-496) 10:30-10:50 (331) A model for two phase flow with hysteresis. Preliminary report. D. MARCHESIN*, H. B. MEDEIROS and P. J. P AES-LEME, Pontificia Universidade Catolica do Rio de Janeiro, Brazil (816-35-87) 11:00-11:20 (332) Hyperbolicity of the flow of viscoelastic fluids. DANIEL D. JoSEPH, University of Minnesota, Minneapolis (816-35-162) (Sponsored by M. Slemrod) 11:30-11:50 (333) Viscosity-capillarity admissibility criteria for dynamic phase transitions. M. SLEMROD, Rensselaer Polytechnic Institute (816-35-21)

Thursday, January 10, 1985, 9:30 a.m. Session on Mathematical Education 9:30- 9:40 (334) A sabermetric model for predicting the AL East baseball standings in 1984: Analysis and future implications. STEVE KREVISKY, University of Wisconsin, Washington County (816-98-111) 9:45- 9:55 (335) Computer literacy and computer mathematics. Prelhninary report. MoNTY STRAUss* and DERALD WALLING, Texas Tech University (816-98-167) 10:00-10:10 (336) Writing as a learning device in calculus. CaREEN METT, Radford University (816-98-215)

58 10:15-10:25 {337) Some interesting inequalities. Preliminary report. PHILIP W. McCARTNEY, Northern Kentucky University {816-98-226) (Sponsored by James Sehnert) 10:30-10:40 {338) Dealing with student deficiencies. Preliminary report. RoTRAUT CAHILL, University of Wisconsin, Washington County Center {816-98-232) 10:45-10:55 {339) Nothing and everything are the same. Preliminary report. PAUL FJELSTAD, St. Olaf College {816-98-273) (Sponsored by Thomas Q. Sibley) 11:00-11:10 {340) Constructing bijections: How it can benefit the undergraduate mathematics major. Preliminary report. ROGER W. ALLEN, JR., Francis Marion College {816-98-339) 11:15-11:25 {341) The University of Minnesota Talented Youth Mathematics Project (UMTYMP}-Implications for education of the gifted. HARVEY B. KEYNES and CHRIS ENNIS*, University of Minnesota, Minneapolis {816-98-351) 11:30-11:40 {342) Observations on mathematics education in Botswana, Africa. RITA M. EHRMANN, Villanova University {816-98-353) (Sponsored by Frederick W. Hartmann)

Thursday, January 10, 1985, 10:15 a.m. Special Session on Stochastic Differential Geometry, II 10:15-10:35 {343) A large deviation result for the long-time behavior of certain diffusions. DANIEL W. STROOCK, Massachusetts Institute of Technology {816-60-13) 10:45-11:05 {344) Random walks on graphs and Brownian motion on manifolds. JozEF DoozruK, Queens College, City University of New York {816-58-131) 11:15-11:35 {345) An extension of Feller's theorem. RAFAEL V. CHACON, University of British Columbia {816-60-509) {Sponsored by Mark A. Pinsky) 11:45-12:05 {346) Harmonic functions, Riemannian manifolds and fundamental groups. DENNIS SuLLIVAN, Graduate Center, City University of New York, and Institut des Hautes Etudes Scientifique, France {816-58-320)

Thursday, January 10, 1985, 11:15 a.m. Invited Address 11:15-12:15 {347) The Riemann hypothesis for Hilbert spaces of entire functions. Lours DE BRANGES, Purdue University, West Lafayette {816-11-75)

Thursday, January 10, 1985, 1:00 p.m. Colloquium Lectures: Lecture ll 1:00- 2:00 {348) The classification of the finite simple groups. DANIEL GoRENSTEIN, Rutgers University

Thursday, January 10, 1985, 2:15 p.m. Invited Address 2:15- 3:15 {349) Science and mathematics in the Office of Naval Research. J. B. MOONEY, JR., Office of Naval Research

Thursday, January 10, 1985, 4:00 p.m. Cole Prize Session and AMS Business Meeting

Thursday, January 10, 1985, 7:00 p.m. AMS Committee on Science Policy, Panel Discussion, The David Report and its hnplementation Pacific Room

Friday, January 11, 1985, 10:00 a.m. AMS/MAA Panel Discussion Calculus Instruction: Crucial but Ailing

Friday, January 11, 1985, 1:00 p.m. Colloquium Lectures: Lecture ill 1:00- 2:00 {350) The classification of the finite simple groups. DANIEL GoRENSTEIN, Rutgers University

Friday, January 11, 1985, 1:00 p.m.

Special Session on Differential Geometry, I 1:00- 1:20 {351) Surfaces minimizing area in their homology class. JOEL HAss, Mathematical Sciences Research Institute {816-53-157)

59 1:25- 1:45 (352) Deformations and rigidity of minimal surfaces. Preliminary report. HYEONG IN CHOI, Mathematical Sciences Research Institute (816-53-317) 1:50- 2:10 (353) The Liouville theorem and regularity of minimizing harmonic maps into strongly unstable manifolds. S. WALTER WEI, University of California, Los Angeles, and Michigan State University (816-53-479)

Friday, January 11, 1985, 1:00 p.m.

Special Session on Algebraic Combinatories, I 1:00- 1:20 (354) Some matroids on graphs and digraphs. Preliminary report. THOMAS ZASLAVSKY, University of Evansville (816-05-83) 1:30- 1:50 (355) Some results from the theory of shifted young tableaux. DALE R. WORLEY, Massachusetts Institute of Technology (816-05-137) 2:00- 2:20 (356) Hybrid tableaux and the Littlewood-Richardson Rule. Preliminary report. DENNIS WHITE, University of Minnesota, Minneapolis (816-05-156) 2:30- 2:50 (357) A class of shellable lattices, JAMES W. WALKER, University of South Carolina, Columbia (816-06-44) 3:00- 3:20 (358) Generalized quotients of Coxeter groups. ANDERS BJORNER, Massachusetts Institute of Technology, and MICHELLE WAcHs*, University of Miami (816-05-90) 3:30- 3:50 (359) Sign variations of the rank 2 Macdonald identities. Preliminary report. DENNIS STANTON, University of Minnesota, Minneapolis (816-05-39) 4:00- 4:20 (360) Intersection homology, toric varieties, and the Dehn-Sommerville equations. Preliminary report. RICHARD P. STANLEY, Massachusetts Institute of Technology (816-52-23) 4:30- 4:50 (361) Shellability of exponential structures. Preliminary report. BRUCE SAGAN, Middlebury College (816-05-108) 5:00- 5:20 (362) Determinants and alternating sign matrices. DAVID P. RoBBINs* and HowARD RuMSEY, JR., Institute for Defense Analyses (816-05-28)

Friday, January 11, 1985, 1:00 p.m. Speeial Session on Analytie Number Theory, m 1:00- 1:20 (363) On density of discriminants of cubic extensions. BoRis DATSKOVSKY, Tufts University (816-11-242) 1:30- 1:00 (364) Transcendental numbers, entire functions, and PDE. Preliminary report. LEON EHRENPREIS, and Temple University (816-11-159) (Sponsored by Marvin I. Knopp) 2:00- 2:20 (365) Meditationes metaplecticae. Preliminary report. DANIEL BuMP, University of Texas, Austin, and University of Rochester, and JEFFREY HoFFSTEIN*, University of Rochester (816-11- 204) (Sponsored by Dorian Goldfeld) 2:30- 2:50 (366) Some simple aspects of the theory of automorphic forms for the general linear group. AUDREY TERRAs, University of California at San Diego, La Jolla (816-11-97) 3:00- 3:20 (367) Applications of automorphic forms. Preliminary report. G. FREIMAN, Tel-Aviv University, Israel (816-11-350) (Sponsored by Dorian Goldfeld) 3:30- 4:20 (368) L-functions for automorphic forms. Preliminary report. ILYA PIATETSKI-SHAPIRO, Tel Aviv University, Israel (816-11-251) 4:30- 4:50 (369) Mean values of class numbers of forms. DAVID J. WRIGHT, Massachusetts Institute of Technology (816-11-346) 5:00- 5:20 (370) Polynomials with low height and prescribed vanishing. Preliminary report. JEFFREY D. VAALER*, University of Texas, Austin, and ENRICO BoMBIERI, Institute for Advanced Study (816-11-132) 5:30- 6:20 (371) Zeros of the zeta-function. AMIT GHOSH, Oklahoma State University (816-11-467)

Friday, January 11, 1985, 1:00 p.m. Session on Differential Equations 1:00- 1:10 (372) On VanDer Pol equations on a torus. JING-HUANG TIAN, Academia Sinica, People's Republic of China (816-34-03) 1:15- 1:25 (373) Cobifurcating branches of solutions of semilinear hyperbolic problems. Preliminary report. RITA IANNACCI, Universita della Calabria, Italy, and MARIO U. MARTELLI*, Bryn Mawr College (816-34-32) 1:30- 1:40 (374) Singular solutions of Riccati matrix differential equations. Preliminary report. JOHN JONES, JR.* and T. J. JoNEs, Air Force Institute of Technology (816-34-34) 1:45- 1:55 (375) Trichotomy of systems of ordinary differential equations. SABER ELAYDI, University of Colorado, Colorado Springs (816-34-61)

60 2:00- 2:10 (376) Nonnegative solution.s to boundary value problems for nonlinear ordinary differential equations. Preliminary report. JAIRO SANTANILLA, Michigan Technological University (816-34-63) 2:15- 2:25 (377) Multipoint boundary value problems for ordinary differential equations by matching solution.s. JoHNNY HENDERSON, Auburn University (816-34-80) 2:30- 2:40 (378) Eventual disconjugacy of a linear differential equation, II. WILLIAM F. TRENCH, Drexel University (816-34-178) 2:45- 2:55 (379) Asymptotic behavior of solutions of a certain nth order differential equation about an irregular singular point. T. K. PUTTASWAMY, Ball State University (816-34-263) 3:00- 3:10 (380) Multi-time-scale singularly perturbed linear stochastic systems. Preliminary report. G. S. LADDE and 0. SIRISAENGTAKSIN*, University of Texas, Arlington (816-34-266) 3:15- 3:25 (381) Singular perturbations of linear systems with multi-parameters and multiple time scales. Preliminary report. G. S. LADDE and S. G. RAJALAKSHMI*, University of Texas, Arlington (816-34-488) 3:30- 3:40 (382) Dynamics of a class of autonomous systems in R 3 with specified sign constraints. DANIEL S. LEVINE, University of Texas, Arlington (816-34-345) 3:45- 3:55 (383) Periodic boundary value problems for first order integra-differential systems of Volterra-type. S. LEELA, State University of New York, Geneseo (816-34-349) 4:00- 4:10 (384) Lower bounds for the eigenvalues of boundary problems. HYUN JoaN AHN, Indiana State University (816-34-363) 4:15- 4:25 (385) Distribution of zeros of a fourth order differential equation. ABDELALI BENHARBIT, Pennsylvania State University, York (816-34-386) 4:30- 4:40 (386) A note on cubic systems in the plane. Preliminary report. T. R. BLows*, Northern Arizona University, and N. G. LLOYD, UniverJity College of Wales, Wales (816-34-389) 4:45- 4:55 (387) Global analysis of limit cycles. Preliminary report. LAWRENCE M. PERKO, Northern Arizona University (816-34-391) (Sponsored by John Hagood) 5:00- 5:10 (388) The existence of homoclinic orbits and the method of Melnikov for systems in Rn. JosEPH R. GRUENDLER, National Bureau of Standards (816-34-422) 5:15- 5:25 (389) Concepts of topological hyperbolicity. Preliininary report. RusSELL WALKER, Montana State University (816-34-498)

Friday, January 11, 1985, 1:00 p.m.

Session on Computer Seienee and Numerieal Analysis 1:00- 1:10 (390) A fast elliptic solver using incomplete factorization. Preliminary report. LALA B. KRISHNA, University of Akron (816-65-119) 1:15- 1:25 (391) Numerical solution of random nonlinear equations. MELVIN D. LAx, California State University (816-65-175) 1:30- 1:40 (392) Estimating eigenvalues by conformal maps combined with intermediate methods using truncation. JAMES R. KUTTLER, Johns Hopkins University (816-65-212) 1:45- 1:55 (393) On two-dimen.sional van der Corput sequences. Preliininary report. J. P. LAMBERT, University of Alaska, Fairbanks (816-65-285) 2:00- 2:10 (394) Convergence of SOR for positive real matrices. JANE M. DAY*, San Jose State University, and MELVIN HENRIKSEN, Harvey Mudd College (816-65-336) 2:15- 2:25 (395) A sixth order imbedded Runge-Kutta algorithm with continuously variable weights. CuRTIS OUTLAW*, LEROY DERR and DIRAN 8ARAFYAN, University of New Orleans (816-65-337) 2:30- 2:40 (396) Continuity of Runge-Kutta processes of lower order. DIRAN SARAFYAN, University of New Orleans (816-65-338) 2:45- 2:55 (397) Conjugate gradient methods in Banach space applied to strong extremum problems in variational theory. Preliminary report. IVIE STEIN, JR., University of Toledo (816-65-352) 3:00- 3:10 (398) Two formulas for numerical indefinite integration. SEYMOUR HABER, National Bureau of Standards (816-65-421) 3:15- 3:25 (399) On a class of third order difference schemes for evolution equations with time dependent coefficients. CREPIN M. MAHOP, Howard University (816-65-472) 3:30- 3:40 (400) You can (sometimes) tell an image by its cover. RoBERT A. MELTER, Long Island University (816-68-24) 3:45- 3:55 (401) Linear problems (with extended range) have linear optimal algorithms. EDWARD W. PACKEL, Columbia University (816-68-53) (Sponsored by Joe Traub) 4:00- 4:10 (402) Infinite time computations. Preliminary report. BARRY BuRD, Drew University (816-68-287) (Sponsored by Alan Candiotti) 4:15- 4:25 (403) User-friendly software for the analysis of survival time data. Preliininary report. NazAR AzARNIA, Roswell Park Memorial Institute (816-68-331)

61 4:30- 4:40 (404) Structural investigations of push-down automata: Some algebraic tools. Preliminary report. JERALD A. KABELL, Central Michigan University (816-68-377) 4:45- 4:55 (405) On a recursive relation in computing and a two parameter difference equation. Preliminary report. S. VERMA, K. VERMA, T. S. VERMA* and R. OGAWA, University of Nevada, Las Vegas (816-68-448) (Sponsored by L. J. Simonoff) 5:00- 5:10 (406) Windowed data spaces and models of computability. ROBERT BYERLY, Texas Tech University (816-68-501)

Friday, January 11, 1985, 1:00 p.m. Session on Lattices 1:00- 1:10 (407) States on the orthomodular poset generalizations of the Greechie lattice. Preliminary report. GERALD ScHRAG, Central Missouri State University (816-06-110) 1:15- 1:25 (408) Extreme positive operators and multiplicative operators in a partially ordered linear algebra. Preliminary report. TAEN-Yu DAr, York College, City University of New York (816-06-118) 1:30- 1:40 (409) The Hahn embedding theorem for normal valued lattice ordered groups. RICHARD N. BALL, Boise State University (816-06-234) 1:45- 1:55 (410) Primary and tertiary decompositions in lattice modules. WILLIAM H. RowAN, Oakland, California (816-06-324) 2:00- 2:10 (411) Divisibility in certain lattice-ordered permutation groups. SPENCER P. HURD, The Citadel ( 816-06-240) 2:15- 2:25 (412) On the semi-Boolean algebra structure of a dominated Boolean-like ring with finite radical. Preliminary report. K. ZAK, United States Naval Academy (816-06-388) 2:30- 2:40 (413) Primary £-ideals in archimedean !-rings. Preliminary report. SuzANNE LARSON, Marquette University (816-06-395) 2:45- 2:55 (414) The Pierce-Birkhoff conjecture. Preliminary report. JAMES MADDEN, University of Kansas (816-06-452) 3:00- 3:10 (415) Archimedean simple positively ordered torsion free 1-semigroups. Preliminary report. MARLOW ANDERSON*, Colorado College, and DAVID LEGG and DouGLAS TowNSEND, Indiana University-Purdue University, Fort Wayne (816-06-473) 3:15- 3:25 (416) Semi-Heyting algebras: An abstraction from Heyting algebras. Preliminary report. H. P. SANKAPPANAVAR, State University of New York, New Paltz (816-06-502) 3:30- 3:40 (417) Clones of operations on relations. HAJNAL ANDREKA and ISTVAN NEMETI, Hungarian Academy of Sciences, Hungary, and STEPHEN D. COMER*, The Citadel (816-08-476)

Friday, January 11, 1985, 2:15 p.m. Invited Address 2:15- 3:15 (418) On Gromov's horizon for combinatorially hyperbolic groups. LAURENCE C. SIEBENMANN, Universite de Paris-Sud, France (816-54-438)

Friday, January 11, 1985, 2:15 p.m. Special Session on Finite Group Theory, I 2:15- 3:05 (419) Exceptional class functions. Preliminary report. GEORGE LuszTIG, Massachusetts Institute of Technology (816-20-77) 3:15- 3:35 (420) The Bp"property in large finite simple groups. Preliminary report. RICHARD LYONS* and DANIEL GORENSTEIN, Rutgers University, New Brunswick (816-20-62) 3:45- 4:05 (421) Simple groups with 2-components of small or even type. Preliminary report. RONALD SoLOMON, Ohio State University, Columbus (816-20-78) 4:15- 4:35 (422) The classification of weak (B, N)-pairs of rank 2. ALBERTO L. DELGADO, Kansas State University (816-20-135) 4:45- 5:35 (423) Embeddings of algebraic groups. Preliminary report. GARY M. SEITZ, University of Oregon (816-20-51)

Friday, January 11, 1985, 2:15 p.m. Session on Commutative Rings 2:15- 2:25 (425) Almost principal ideals in D[x]. Preliminary report. ELOISE HAMANN and JON L. JOHNSON*, Elmhurst College (816-13-398)

62 2:30- 2:40 (426) Two counterexamples in power series rings. ELOISE HAMANN*, Elmhurst College, and RICHARD G. SWAN, University of Chicago (816-13-245) 2:45- 2:55 (427) Power invariance of formal power series rings. Preliminary report. J. H. KIM, East Carolina University (816-13-334) 3:00- 3:10 (428) An inversion formula for two polynomials in two variables. JAMES H. McKAY*, Oakland University, and STUART S.-S. WANG, Purdue University, West Lafayette (816-13-304) 3:15- 3:25 (429) Dickson's lemma, Hilbert's basis theorem, and applications to completion in commutative Noetherian rings. GEORGE BUTLER and DALLAS LANKFORD*, Louisiana Tech University (816-13-433) 3:30- 3:40 (430) Basic sets and Vandermonde independent matrices over a finite field. JOEL BRAWLEY, Clemson University (816-15-252)

Friday, January 11, 1985, 2:15 p.m.

Special Session on Teichmuller Theory for Surfaces, Graphs and Hyperbolic Manifolds, II

2:15- 2:35 (431) Arithmetic-like properties of outer automorphisms of free groups. Preliminary report. MARC CULLER, Mathematical Sciences Research Institute, and KAREN VoGTMANN*, Cornell University (816-20-296) 2:45- 3:05 (432) Growth functions for hyperbolic surfaces. MATT GRAYSON, Mathematical Sciences Research Institute (816-51-411) 3:15- 3:35 (433) The Torelli group and Siegel space. JEFFREY MEss, University of California, Berkeley (816-57-480) 3:45- 4:05 (434) Deformation spaces associated to compact hyperbolic manifolds. JoHN MILLSON, University of California, Los Angeles (816-22-95)

Friday, January 11, 1985, 3:30 p.m. Invited Address 3:30- 4:30 (435) Recent developments in set theory. W. HUGH WooDIN, California Institute of Technology (816-04-439)

Friday, January 11, 1985, 3:30p.m.

Special Session on Differential Geometry, II 3:30- 3:50 (436) On complete minimal surfaces with finite Morse index in three manifolds. Doms FISCHER­ COLBRIE, San Diego State University (816-99-517) 4:00- 4:20 (437) Regularity of capillary surfaces over domains with comers: borderline case. LUEN-FAI TAM, Purdue University, West Lafayette (816-53-36) (Sponsored by Peter Li) 4:30- 4:50 (438) Complete embedded minimal surfaces of finite total curvature. DAVID A. HoFFMAN*, University of Massachusetts, Amherst, and WILLIAM H. MEEKS m, Rice University (816-53-81)

Friday, January 11, 1985, 3:30 p.m.

Special Session on Infinite Dimensional Topology, I 3:30- 3:50 (439) Cell-like maps onto non-compact spaces of finite cohomological dimension. LEONARD R. RuBIN*, University of Oklahoma, and PHILIP J. SCHAPIRO, University of South Carolina (816-55-04) 4:00- 4:20 (440) Extending homeomorphisms in metric linear spaces without completeness. Preliminary report. TADEUSZ DOBROWOLSKI, Texas A&M University, College Station (816-57-46) (Sponsored by James P. Henderson) 4:30- 4:50 (441) Boundary sets in hyperspaces. DouG CuRTIS, Louisiana State University, Baton Rouge (816-54-65) 5:00- 5:20 (442) Rigid sets in the Hilbert cube. JACK W. LAMOREAUX and DAVID G. WRIGHT*, Brigham Young University (816-57-59) 5:30- 5:50 (443) A peculiar boundary set in the Hilbert cube. JAN DIJKSTRA, University of Florida and Louisiana State University, Baton Rouge (816-54-89) (Sponsored by D. J. Garity)

Friday, January 11, 1985, 7:30p.m. Joint Policy Board for Mathematics National Meeting of Department Chairmen

Saturday, January 12, 1985, 1:00 p.m. Colloquium Lectures: Lecture IV 1:00- 2:00 (444) The classification of the finite simple groups. DANIEL GORENSTEIN, Rutgers University

63 Saturday, January 12, 1985, 1:00 p.m.

Special Session on Celestial Mechanics, I 1:00- 1:20 (445) A generalization of Arnold's stability theorem. K. R. MEYER* and D. S. SCHMIDT, University of Cincinnati (816-70-17) 1:30- 1:50 (446) 'Jlransition to chaos in perturbed two-body problems. RoGER BROUCKE, University of Texas, Austin (816-70-402) 2:00- 2:20 (447) Relative equilibria ofthefour-body problem. Preliminary report. RICHARD MOECKEL, University of Minnesota, Minneapolis (816-70-300) 2:30- 2:50 (448) On quasiperiodic solutions of the full three body problem. Preliminary report. MARTIN KUMMER, University of Toledo (816-70-205) 3:00- 3:20 (449) Escape manifolds for the trapezoidal 4-body problem. ERNESTO A. LACOMBA, Universidad Aut6noma Metropolitana-Iztapalapa, Mexico (816-70-321) 3:30- 3:50 (450) A new Hamiltonian formulation of particle mechanics. JoHN G. BRYANT, Universidad A'ut6noma Metropolitana-Iztapalapa, Mexico (816-70-493) (Sponsored by E. A. Lacomba) 4:00- 4:20 (451) On the Hausdorff dimension of k-fold collisions. Preliminary report. JoHN B. URENKO, Pennsylvania State University,· Schuykill Campus (816-70-223) 4:30- 4:50 (452) A note on a theorem of von Zeipel. RICHARD McGEHEE, University of Minnesota, Minneapolis (816-70-407)

Saturday, January 12, 1985, 1:00 p.m.

Special Session on Infinite Dimensional Topology, II 1:00- 1:20 (453) Examples in the setting of Hilbert space manifolds. Preliminary report. JOHN J. WALSH, University of Tennessee, Knoxville (816-57-427) 1:30- 1:50 (454) Characterizing certain incomplete infinite-dimensional absolute retracts. Preliminary report. MLADEN BESTVINA *, University of Michigan, Ann Arbor, and Mathematical Sciences Research Institute, and JERZY MOGILSKI, University of Warsaw, Poland (816-57-50) 2:00- 2:20 (455) Detecting discrete properties. Preliminary report. PHILIP L. BOWERS, Florida State University (816-57-76) 2:30- 2:50 (456) Defining sequences in Q-manifolds. TERRY L. LAY, Idaho State University (816-57-302) 3:00- 3:20 (457) The construction of homogeneous homology manifolds. Preliminary report. F. D. ANCEL*, University of Oklahoma, and L. C. SIEBENMANN, Universite de Paris-Sud, France (816-57-72) 3:30- 3:50 (458) Laminations, finitely generated perfect groups, and acyclic maps. R. J. DAVERMAN, University of Tennessee, Knoxville, and F. C. TINSLEY*, Colorado College (816-57-432)

Saturday, January 12, 1985, 1:00 p.m.

Special Session on Differential Geometry, ill 1:00- 1:20 (459) Complex manifolds with large isotropy subgroups. Preliminary report. ROBERT E. GREENE*, University of California, Los Angeles, and STEVEN G. KRANTZ, Pennsylvania State University, University Park (816-53-368) 1:30- 1:50 (460) Some remarks on the prescribed Gaussian curvature equation. Preliminary report. SHru-YuEN CHENG, University of California, Los Angeles (816-53-347) 2:00- 2:20 (461) Area and length of shortest closed geodesic. CHRISTOPHER CROKE, University of Pennsylvania and Mathematical Sciences Research Institute (816-53-466) 2:30- 2:50 (462) Some spectral properties of open Riemannian manifolds. ROBERT BROOKS, University of Southern California (816-53-37) 3:00- 3:20 (463) The local structure of Riemannian manifolds. Preliminary report. JosEPH BEMELMANS, Universitii.t des Saarlandes, Federal Republic of Germany, and ERNST A. RuH*, Indiana University, Bloomington (816-53-303) 3:30- 3:50 (464) Affine differential geometry in a Banach space. RoBERT C. REILLY, Uiliversity of California, Irvine (816-53-92) 4:00- 4:20 (465) Reduction of variables for minimal submanifolds. Preliminary report. RICHARD S. P ALAIS, Brandeis University, and CHUU-LIAN TERNG*, Northeastern University (816-53-412)

Saturday, January 12, 1985, 1:00 p.m. Session on Analysis 1:00- 1:10 (466) Non-isometric distance 1 preserving mapping E 2 -+ E 6 . BoRIS V. DEKSTER, University of Toronto, Erindale Campus (816-26-142)

64 1:15- 1:25 (467) Equipartitioning common domains of nonatomic measures. THEODORE P. HILL, University of Hawaii (816-28-115) 1:30- 1:40 (468) A note on minimal covers for sofic systems. MIKE BOYLE and BRUCE KITCHENS, IBM T. J. Watson Research Center, Yorktown Heights, and BRIAN MARcus*, IDM Research, San Jose (816-28-463) 1:45- 1:55 (469) Radon-Nikodym derivatives of incompressible transformation. Preliminary report. C. E. SILVA, Williams College (816-28-507) 2:00- 2:10 ( 470) Fine and parabolic limits for positive solutions of the heat equation on the semi-infinite slab. BERNARD MAIR, Pennsylvania State University, Mont Alto (816-31-326) (Sponsored by Gary L. Mullen) 2:15- 2:25 (471) The Newtonian capacity of a space condenser. G. D. ANDERSON*, Michigan State University, and M. K. VAMANAMURTHY, University of Auckland, New Zealand (816-31-260) 2:30- 2:40 ( 472) On certain generalized operators and their applications in special functions theory. Preliminary report. R. N. KALlA, Southwest State University (816-33-312) 2:45- 2:55 (473) Some integrals of the trace in Pn. Preliminary report. THOMAS BENGTSON, Pennsylvania State University, Delaware County Campus (816-33-209)

Saturday, January 12, 1985, 1:00 p.m.

Session on Mathematical Physics 1:00- 1:10 (474) Combinatorics and flexure. Preliminary report. D. C. RuNG, Pennsylvania State University, University Park, and S. A. 0BAID*, Pennsylvania State University, York (816-73-15) 1:15- 1:25 (475) A general form of the Betti-Castigliano theorem. VADIM KOMKOV, Winthrop College (816-73-69) 1:30- 1:40 ( 476) Hydromagnetic flow with suspension of particles in a rotating fluid system. LOKENATH DEBNATH*, University of Central Florida, and A. K. GHOSH, Jadavpur University, India (816-76-163) 1:45- 1:55 (477) Solitary waves in channels of decreasing depth. C. J. KNICKERBOCKER, St. Lawrence University (816-76-288) 2:00- 2:10 (478) Drag on a profile in a 2-D transonic flow. Preliminary report. LYNNE IPINA, University of Wyoming (816-76-365) 2:15- 2:25 (479) Stochastic quantum mechanical analysis of quantum entropy. FRANKLIN E. ScHROECK, JR., Florida Atlantic University (816-81-385) 2:30- 2:40 (480) Convective heat transfer with travelling thermal waves. KuPPALAPALLE VAJRAVELU, University of Central Florida (816-80-164) 2:45- 2:55 (481) Separation of coupled systems of differential equations. MAYER HUM!, Worcester Polytechnic Institute (816-81-497) (Sponsored by Bruce C. McQuarrie) 3:00- 3:10 (482) On some HPD inequalities. R.N. MoHAPATRA, University of Central Florida (816-40-323) 3:15- 3:25 (483) An existence-uniqueness theorem for nonmultiplying rod models subject to interior jump conditions. PAUL NELSON, Texas Tech University (816-82-145) 3:30- 3:40 (484) A new approach to Maxwell's equations via a bundle of null directions on Minkowski space. STEVEN L. KENT*, Youngstown State University, and CARLOS N. KozAMEH and E. T. NEWMAN, University of Pittsburgh (816-83-228) 3:45- 3:55 (485) Parameter esti~ation in nonlinear regression. Preliminary report. B. B. BHATTACHARYYA, North Carolina State University, and G. D. RICHARDSON*, University of Central Florida (816-62-165) (Sponsored by Lokenath Debnath)

Saturday, January 12, 1985, 2:15 p.m.

Invited Address 2:15- 3:15 ( 486) Some applications of the classification of finite simple groups. WILLIAM M. KANTOR, University of Oregon (816-20-322)

Saturday, January 12, 1985, 2:15p.m.

Session on Algebraic Number Theory 2:15- 2:25 (487) The scalar interiors of totally irregular matrix fields. J. T. B. BEARD, JR., University of Tennessee, Knoxville, and Tennessee Technological University (816-12-54) 2:30- 2:40 (488) Fields countably generated over a proper subfield. Preliminary report. JAMES K. DEVENEY and JoE YANIK*, Virginia Commonwealth University (816-12-180) 2:45- 2:55 (489) Artin root numbers, zeta functions, and Witt rings. RoBERT PERL IS, Louisiana State University, Baton Rouge (816-12-193) 3:00- 3:10 (490) Galois cohomology and Gross' p-adic regulator. Preliminary report. LESLIE JANE FEDERER, University of Michigan, Ann Arbor (816-12-247)

65 3:15- 3:25 (491) Rational and genus equivalence of forms. STAN GURAK, University of San Diego (816-12-248) (Sponsored by Lynne B. Small) 3:30- 3:40 (492) Sums of fourth powers of polynomials. BRUCE REZNICK, University of illinois, Urbana­ Champaign (816-12-189) 3:45- 3:55 ( 493) A quadratic form associated to Hopf maps. JoANN S. Tumsco, United States Naval Academy (816-12-246)

Saturday, January 12, 1985, 3:20p.m.

Special Session on Finite Group Theory, II 3:20- 3:40 (494) Finite groups and Heeke operators. GEOFFREY MASON, University of California, Santa Cruz (816-20-05) (Sponsored by Michael Aschbacher) 3:45- 4:05 ( 495) Classical groups as galois groups. JOHN H. WALTER, University of illinois, Urbana-Champaign (816-20-08) 4:10- 4:30 (496) Homology representations and geometry of simple groups. STEPHEN D. SMITH, University of Illinois, Chicago (816-20-25)

Saturday, January 12, 1985, 3:20p.m.

Special Session on Algebraic Combinatorics, II 3:20- 3:40 (498) An intrinsic explanation of semistandard Young tableaux for SLn. Preliminary report. ROBERT A. PROCTOR, California Institute of Technology (816-17-257) 3:45- 4:05 (499) !-vectors of good covers. GIL KALAl, Massachusetts Institute of Technology (816-52-91) 4:10- 4:30 (500) On lattices with Mobius function 0, ±1. JEFF KAHN, Rutgers University, New Brunswick (816-05-239)

Sunday, January 13, 1985, 8:00a.m.

Special Session on Algebraic Combinatorics, III 8:00- 8:20 (501) Partitions into odd block size. Preliminary report. PHIL HANLON*, California Institute of Technology, A. R. CALDERBANK, AT&T Bell Laboratories, and R. W. RoBINSON, University of Georgia (816-05-154) 8:30- 8:50 (502) Noncommutative rational power series and algebraic generating functions. Preliminary report. MARK HAIMAN, Massachusetts Institute of Technology (816-05-116) 9:00- 9:20 (503) Tableau symmetries and Schutzenberger operators. CuRTIS GREENE, Haverford College (816- 05-84) 9:30- 9:50 (504) Acyclic orientations of graphs and the Cartier-Foata theory of partially commutative free monoids. Preliminary report. IRA M. GESSEL, Brandeis University (816-05-71) 10:00-10:20 Discussion 10:30-10:50 (505) The homotopy type of hyperplane posets. PAUL H. EDELMAN*, University of Pennsylvania, and JAMES W. WALKER, University of South Carolina, Columbia (816-06-29) 11:00-11:20 (506) Homotopy properties of greedoids. ANDERS BJORNER*, Massachusetts Institute of Technology, BERNARD KORTE, University of Bonn, Federal Republic of Germany, and LA.szL6 LovA.sz, Ei:itvi:is University, Hungary (816-05-94) 11:30-12:00 (507) Piecewise polynomial functions on simplicial complexes. Preliminary report. Lotns J. BILLERA, Cornell University (816-05-85)

Sunday, January 13, 1985, 9:00a.m.

Special Session on Differential Geometry, IV 8:30- 8:50 (508) The variation of the de Rham zeta function. STEVEN RosENBERG, Brandeis University (816-53-27) 9:00- 9:20 (509) The Riemannian obstacle problem. STEPHANIE ALEXANDER*, I. DAVID BERG and RICHARD L. BISHOP, University of Illinois, Urbana-Champaign (816-53-101) 9:30- 9:50 (510) Group representations arising from Lorentz geometry. THOMAS P. BRANSON, Purdue University, West Lafayette (816-53-491) 10:00-10:20 (511) The classification of the curvature tensors of Kiihler manifolds. QI-KENG Lu, Institute for Advanced Study (816-53-138) 10:30-10:50 (512) Differentiable and topological structures of singular varieties. Preliminary report. STEPHEN S.-T. YAu, Yale University (816-53-401) (Sponsored by Chih-Han Sah)

66 11:00-11:20 (513) Curvature of canonical Kahler metrics and pseudoconvexity of bounded domains. E. B. LIN and B. WoNG*, University of California, Riverside (816-32-210) 11:30-11:50 (514) Maximal hypersurfaces and splitting theorems for spatially closed space-times. GREGORY J. GALLOWAY, University of Miami (816-53-58)

Sunday, January 13, 1985, 9:00a.m. Session on Statistics 9:00- 9:10 (515) Locally most powerful invariant tests. JACK TOMSKY, Lockheed Missiles and Space Company (816-62-02) 9:15- 9:25 (516) Quantitative and qualitative analysis of contributors to political, environmental and other organizations. Preliminary report. WENDY KREVISKY, Bernard M. Baruch College, City University of New York (816-62-128) 9:30- 9:40 (517) A lower bound for number of treatments in a main effect plus one plan for 25 factorials. B. C. GUPTA* and S. S. CARVAJAL, Concordia University and Universidade Federal do Rio de Janeiro, Brazil (816-62-139) (Sponsored by Harold W. Proppe) 9:45- 9:55 (518) Analysis of cyclic variation in certain time series data from medical research. Preliminary report. 0SVALDO MARRERO, Villanova University (816-62-146) 10:00-10:10 (519) The sum of squares for a sample from the "1,2,3" distribution. H. B. CooNCE, Mankato State University (816-62-166) 10:15-10:25 (520) A method for generating correlated random variables with specified marginals. RoGER B. NELSEN, Lewis and Clark College (816-62-214) (Sponsored by Robert W. Owens) 10:30-10:40 (521) The optimality of the method of key test results in series system reliability. BERNARD HARRIS, University of Wisconsin, Madison (816-62-354)

Sunday, January 13, 1985, 10:00 a.m. Special Session on Celestial Mechanics, ll 10:00-10:20 (522) Integrating the perturbations to the motion of the moon in Cartesian coordinates. DIETER ScHMIDT, University of Cincinnati (816-70-301) 10:30-10:50 (523) Bound solutions of the equal mass n-ion problem. JOSEPH L. GERVER, Rutgers University (816-70-18) 11:00-11:20 (524) Trellises formed by the stable and unstable manifolds of saddle points in the plane. RoBERT W. EASTON, University of Colorado, Boulder (816-70-286) 11:30-11:50 (525) Morse theory and central configurations. FILOMENA PACELLA, University of Napoli, Italy (816-70-403) (Sponsored by Neal Hulkower)

Hugo Rossi Salt Lake City, Utah Associate Secretary

Noncommutative Microlocal Analysis, Part I of the symbol calculus depend on the particular Michael E. Taylor representation theory of the group G. and such a theory is worked out for the Heisenberg group in (Memoirs of the AMS. Number 313) Chapter II. In Chapter Ill this theory is applied to a Pseudodifferential operators on Rn in OPS;J:0 systematic study of operator classes on contact are built out of smooth families of convolution manifolds, including parametrices for naturally operators on Rn. Similarly important classes of occurring subelliptic operators. heat asymptotics. operators can be built out of smooth families of and a study of the Szegi:i projectors. convolution operators on a noncommutative Lie 1980 Mathematics Subject Classification: group G. When the representation theory and 35H05 one ISBN 0-8218-2314-0, LC 84-18500 harmonic analysis on G are well understood. ISSN 0065··9266 can construct a noncommutative symbol calculus. iv + 182 pages (softcover), November 1984 This paper develops some aspects of the resulting List price $17, Institutional member $14, Individual member $10 noncommutative microlocal analysis. Chapter I Shipping and handling charges must be added treats operators on general Lie groups. The details To order, please specify MEM0/313N

Shipping/Handling: 1st book $2, each add'l $1, max. $25; by air, 1st book $5, each add'l $3, max. $100 Prepayment is required. Order from American Mathematical Society, P.O. Box 1571, Annex Station, Providence, Rl 02901·1571, or call toll free 800-556-777 4 to charge with Visa or MasterCard.

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

Abi-Khuzam, F. F., 65 •Cheng, S.-Y., 460 * Gerstenhaber, M., 237 Kalia, R. N., 472 Adomian, G., 172 Chin, W., 46 * Gerver, J. L., 523 Kalliongis, J., 195 Aftabizadeh, A. R., 285 •Choi, H. I., 352 •Gessel, I. M., 504 Kamowitz, H., 94 Ahn, H. J., 384 Colella, D., 257 • Ghosh, A., 371 Kannappan, P., 283 Ahuja, M., 295 Collins, C., 167 Gilbert, J., 147 •Kantor, W. M., 486 Akyildiz, E., 110 Collins, D. G., 212 Gill, T. L., 180 Karbe, M., 302 •Alexander, S., 509 Colvin, M. R., 197 Gilpin, M., 273 •Karp, L., 7 Kato, G., 55 •Alladi, K., 247 Comer, S. D., 417 *Glover, H., 320 Kaul, S. K., 15 Allday, C. J., 190 Comerford, L. P., Jr., Gael, S. K., 196 Kelingos, J. A., 63 Allen, R. W., Jr., 340 313 *Goldberg, L. R., 319 Kennedy, R. E., 29 Allison, D., 219 Comfort, W. W., 115 •Goldberg, S., 4 Kent, S. L., 484 Anastassiou, G. A., 252 • Conley, C., 86 Goldberg, V. V., 222 Keown, R., 214 •Ancel, F. D., 457 Conlon, L., 193 •Goldfeld, D., 124 •Kerckhoff, S., 298 Anderson, G. D., 471 Connor, J., 201 *Goldman, W. M., 318 Kerckhoff, S., 321 Anderson, M., 415 Coonce, H. B., 519 Goldstein, M., 227 Kertz, R. P., 153 Andrews, K. T., 96 Cooper, C. N., 30 Goldston, D. A., 243 •Keyfitz, B. L., 71 Ansari, M. A., 91 Corduneanu; C., 263 Goodman, A. W., 61 Khajeh Khalili, P., 166 Antonios, M. N., 217 *Croke, C., 461 Gordon, S. P., 294 Khavinson, D., 62 •Arveson, W., 240 *Culler, M., 78 • Gorenstein, D., 125, 348, Kim, J. H., 427 Ash, J. M., 254 Cupillari, A., 68 350, 444 Knickerbocker, C. J., 477 Komkov, V., 475 Azarian, M. K., 306 *Curtis, D., 441 *Grayson, M., 297, 432 Dai, T.-Y., 408 • Greene, C., 503 Korzeniowski, A., 156 Azarnia, N., 403 Kossowski, M., 225 Bachman, T., 204 •Darling, R. W. R., 1 Greene, J., 28 * Kranzer, H. C., 72 Ball, R. N., 409 Darling, R. W. R., 159 Greene, R. E., 459 Krevisky, S., 334 Ballotti, M., 93 •Datskovsky, B., 363 Greim, P., 109 Krevisky, W., 516 •Balser, W., 325 •Davis, B., 26 Gross, F., 59 Krishna, L. B., 390 Barton, T., 69 Day, J. M., 394 Gruendler, J. R., 388 *Kummer, M., 448 •Bass, H., 327 Debnath, L., 476 Gubbi, A. V., 17 Kuttler, J. R., 392 Bator, E., 205 Dekster, B. V., 466 Gupta, B. C., 517 * Lacomba, E. A., 449 Beard, J. T. B., Jr., 487 •Delgado, A. L., 422 Gurak, S., 491 Lambert, J. P., 393 Bechtel!, H., 310 Delzell, C. N., 113 Haber, S., 398 Lamphere, R. L., 64 Bellenot, S. F., 203 •Dijkstra, J., 443 •Haiman, M., 502 Lange, R., 181 * Ben-Artzi, M., 133 Dinculeanu, N., 157 Haimo, D. T., 260 Lankford, D., 429 Bengtson, T., 473 •Dobrowolski, T., 440 •Halberstam, H., 246 Lapidus, M. L., 182 •Dodziuk, J., 344 •Hale, J. K., 87 Larson, S., 413 Benharbit, A., 385 Laskar, R., 271 •Benson, M. L., 299 eDonagi, R., 126 Hamann, E., 426 Lax, M. D., 391 Berger, M. S., 142 Drucker, D., 52 Hamedani, G. G., 164 •Lay, T. L., 456 Bertram, E. A., 308 Duncan, J., 108 •Hanlon, P., 501 *Lee, R., 322 •Bestvina, M., 454 •Durrett, R., 2 •Harabetian, E., 135 Lee, S. J., 175 Bhaskara Rao, K. P. S., •Easton, R. W., 524 Harris, B., 521 Leela, S., 383 148 Ebanks, B., 216 •Harris, W. A., Jr., 323 * Lepowsky, J., 424 • Billera, L. J., 507 •Edelman, P. H., 505 •Hart, D., 82 _ Lesniak, L., 275 Birkenmeier, G. F., 44 Edrei, A., 56 Hart, D. R., 207 Lester, J. A., 229 •Bjorner, A., 506 •Ehrenpreis, L., 364 Hartsfield, N., 274 Levenberg, N., 67 Blanton, J. D., 194 Ehrmann, R. M., 342 * Hass, J., 351 Levine, D. S., 382 Blows, T. R., 386 •Elaydi, S., 375 Hattori, H., 7 4 Lewkowicz, R. E., 259 Bolger, E., 209 •Eloe, P., 284 Hazlewood, D. G., 35 Lewy, M. R., 314 •Bombieri, E., 127 Embry-Wardrop, M., 99 Henderson, J., 377 *Lindquist, B., 134 Bonan, S. S., 250 Hile, G. N., 173 Linton, F. E. J., 22 •Emch, G. G., 6 Lipscomb, S., 265 •Bowers, P. L., 455 Ennis, C., 341 Hill, T. P., 467 Longyear, J., 267 Brand, N., 277 •Evans, L. C., 316 Hindman, N., 266 * Lu, Q.-K., 511 ede Branges, L., 347 Fair, W., 145 Hodgson, J. P•. E., 192 •Lubotzky, A., 233 •Branson, T. P., 510 Fay, T. H., 42 •Hoffman, D. A., 438 Luecking, D. H., 60 Brant, L. J., 272 Federer, L. J., 490 Hoffman, M., 309 •Lusztig, G., 419 Brawley, J., 430 Feldman, W., 202 • Hoffstein, J., 365 *Lutz, D. A., 326 •Brio, M., 132 Fife, J. H., 189 Hoke, K. W., 270 Lutzer, D., 19 •Brooks, R., 462 •Fischer-Colbrie, D., 436 Holmes, C., 311 Lyon, B. C., 41 •Broucke, R., 446 Fitzpatrick, B., Jr., 13 •Hsieh, P.-F., 83 *Lyons, R., 420 •Bryant, J. G., 450 Fjelstad, P., 339 Humi, M., 481 MacDonnell, J., 119 Bucki, A., 228 •Floyd, W. J., 80 Hupert, L. E. P., 49 Maceli, J. C., 208 Bulman-Fleming, S., 303 Foged, L., 16 Hurd, S. P., 411 Madden, J., 414 Burd, B., 402 Foote, R., 497 Ipina, L., 478 *Magid, A., 232 Mahfoud, W. E., 281 Burke, D. K., 10 Foote, R. L., 218 •Isaacson, E. L., 329 Mahop, C. M., 399 Byerly, R., 406 Frantz, D. A., 290 Jeter, M. W., 146 Mair, B., 470 Cahill, R., 338 •Fredricks, G. A., 221 Johnson, J. L., 425 *Malek-Madani, R., 75 Campbell, J. T., 185 •Freiman, G., 367 • Johnson, R., 138 * Mallet-Paret, J., 84 Cannon, J. W., 301 Fridy, J., 289 Jones, J., Jr., 374 Malone, J. J., 43 *Chacon, R. V., 345 * Friedberg, S., 128 *Joseph, D. D., 332 •March, P., 3 Chaney, R. W., 210 Galambos, J., 160 * Jurkat, W. B., 141 * Marchesin, D., 331 Chang, C., 213 •Gallagher, P., 244 Kabel!, J. A., 404 Marcus, B., 468 • Charney, R. M., 70 *Galloway, G. J., 514 •Kahn, J., 500 *Markus, L., 136 * Chavel, I., 8 Gaudefroy, A. L., 120 •Kalai, G., 499 Marrero, 0., 518

68 •Martelli, M. U., 373 Peyrovian, M. R., 117 Shiue, J.-S., 32 Tsangaris, P., 40 Mashburn, J., 18 •Phillips, R., 129 Shivaji, R., 171 •Tubbs, R., 27 •Mason, G., 494 Piacenza, R., 188 Shulberg, G. W., 89 Turett, B., 106 Matchett, A., 150 * Piatetski-Shapiro, I., 368 * Sibuya, Y., 328 Turisco, J. S., 493 Mate, A., 256 *Piech, M. A., 5 eSiebenmann, L. C., 418 Unger, F. R., 249 Mazumdar, T., 165 Piotrowski, Z., 23 Silva, C. E., 469 * Urenko, J. B., 451 McCartney, P. W., 337 Proctor, R. A., 498 Silverman, H., 58 * Vaaler, J. D., 370 McDowell, K., 304 Puttaswamy, T. K., 379 Simms, J., 121 Vajravelu, K., 480 •McGehee, R., 452 Quine, J. R., 57 *Simon, B., 140 Vanden Eynden, C., 37 251 McKay, J. H., 428 Quinn, D., 48 Singh, B., 282 Varma, A. K., Vatsala, A. S., 170 •Meeks, W. H., 231 •Rabin, M. 0., 236 Sirisaengtaksin, 0., 380 Vaughan, T. P., 36 Meerschaert, M. M., 162 Rajalakshmi, S. G., 381 Siskakis, A. G., 198 Verde-Star, L., 269 Melter, R. A., 400 Sitaramachandrarao, R., Raphael, M., 187 Verma, R. U., 88 Mess, J., 433 33 Rawlings, D., 268 Verma, T. S., 405 Slattery, M. C., 305 Mett, C., 336 Reed, G. M., 12 * Vogtmann, K., 431 •Meyer, K. R., 85, 445 Reich, J. I., 155 * Slemrod, M., 333 *Wachs, M., 358 Michaelis, W., 47 •Reilly, R. C., 464 Smith, H. F., 51 Wagon, S., 38 Migliore, J., 112 Reznick, B., 492 •Smith, S.D., 496 * Wagreich, P ., 79 Mignone, R., 122 Rhaly, C., 95 *Smythe, N., 300 *Walker, J. W., 357 Miller, S. S., 66 Richardson, G. D., 485 Snader, J. C., 184 Walker, R., 389 Millett, K. C., 191 Richert, N., 39 Snow, D. R., 287 *Walsh, J. J., 453 •Millson, J., 434 Richman, D. R., 143 Snyder, A. K., 107 Walsh, S., 179 •Moeckel, R., 447 •Robbins, D.P., 362 Solian, A., 54 *Walter, J. H., 495 Mohapatra, R.N., 482 Robinson, C. E., Jr., 144 *Solomon, R., 421 Warchall, H. A., 174 •Mooney, J. B., Jr., 349 •Rochberg, R., 241 *Sperber, S., 324 Ward, J. D., 92 Moore, L. C., Jr., 200 Rose, D. A., 11 Spigler, R., 152 Washburn, S., 25 Morales, C. H., 183 •Rosenberg, S., 508 *Stanley, R. P., 360 Watro, R. J., 123 Motte, D., 90 Rosinski, J., 163 *Stanton, D., 359 Watson, S., 101 •Myerson, G., 248 Ross, J. A., 151 *Stark, H. M., 130 Wei, S. W., 223, 353 Nagle, R. K., 168 Rotman, J., 280 * Stasheff, J., 238 Weinberg, D., 111 Nelsen, R. B., 520 Rowan, W. H., 410 Stein, I., Jr., 397 *Weintraub, S. H., 317 Nelson, P., 483 •Rubin, L. R., 439 Stevens, T. C., 116 Weis, L., 104 •Neumann, W. D., 77 Ruckle, W. H., 103 Stewart, J., 258 Wenjen, C., 31 •Ng, E. K. S., 242 •Ruh, E. A., 463 Stout, L. N., 276 Weston, K. W., 312 293 Nymann, J. E., 288 Saccoman, J. J., 100 Strauss, M., 335 Wetzel, J. E., *White, D., 356 Obaid, S. A., 474 Sachs, D., 291 •Stroock, D. W., 343 * Odlyzko, A. M., 245 *Sullivan, D., 81, 346 *Wilkerson, C. W., 239 * Sagan, B., 361 Wilkinson, S., 220 * O'Halloran, J., 235 Sung, C. H., 206 Salingaros, N., 118 Williamson, R., 230 Okada, S., 105 Sankappanavar, H. P., Swaminathan, S., 199 Wiseman, J., 315 416 *Osher, S., 131 Swart, J., 14 Wollman, S., 169 Szpunar-Lojasiewicz, W., Outlaw, C., 395 * Santanilla, J., 376 *Wong, B., 513 Owens, R. W., 211 Sarafyan, D., 396 177 • Woodin, W. H., 435 •Pacella, F., 525 *Saxton, R. A., 76 Tall, F. D., 21 *Worley, D. R., 355 Packel, E. W., 401 *Schack, S. D., 234 •Tam, L.-F., 437 *Wright, D. G., 442 Papadopol, P., 224 Schaffer, M., 102 * Tatsuoka, K., 296 *Wright, D. J., 369 Parish, A. E., Jr., 215 Schay, G., 176 *Temple, B., 330 Yang, J. S., 114 Park, C., 154 Schein, B. M., 279 * Terng, C.-L., 465 Yanik, J., 488 Parker, P. E., 226 *Schmidt, D., 522 •Terras, A., 366 Yaqub, A., 45 Passell, N., 278 Schrag, G., 407 Testerman, D. M., 307 * Yau, S. S.-T., 512 Passty, G. B., 97 Schroeck, F. E., Jr., 479 Tian, J.-H., 372 Yerion, K. A., 186 Pedersen, P. S., 34 Schwarz, F., 24 Tikoo, M., 9 Young, E. C., 264 Perko, L. M., 387 Schwarz, T. J. E., 50 •Tinsley, F. C., 458 Zachariah, T. M., 286 Perlis, R., 489 *Seitz, G. M., 423 Tollis, T., 149 Zak, K., 412 •Perry, D., 139 *Sell, G. R., 137 Tomsky, J., 515 Zalik, R. A., 253 Peters, J., 262 Serfling, R. J., 158 Torrejon, R., 98 Zamfirescu, T., 292 Peters, J. V., 261 *Shearer, M., 73 Treiman, J., 178 •Zaslavsky, T., 354 Peters, T. J., 20 Shields, P., 161 Trench, W. F., 378 Zielinski, M. F., 255

69 Chicago, March 22-23, 1985, University of Illinois at Chicago Second Announcement of the 817th meeting

The eight hundred and seventeenth meeting of the Henri Gillet, D. Grayson, J. Jardine, M. Stein, R. American Mathematical Society will be held at the Thomason, and C. Weibel. University of Illinois, Chicago, Illinois, on Friday and Mathematical computer science, WoLFGANG Saturday, March 22 and 23, 1985. All sessions will be MAASS, University of Illinois, Chicago. The tentative held in the Lecture Center on the University campus. speakers include Andreas R. Blass, Allan B. Borodin, John W. Case, Steven Cook, Harvey Friedman, Yuri Invited Address Gurevich, Kenneth Kunen, Jeffery S. Leon, Angus Macintyre, Vera Pless, Franco P. Preparata, Georg By invitation of the Committee to Select Hour Schnitger, and Saharon Shelah. Speakers for Central Sectional Meetings, there will be Stochastic analysis and related topics, PHILIP four invited one-hour addresses. The speakers, their PROTTER, Purdue University. The tentative affiliations, the titles of their talks, and the scheduled speakers include K. Bichteler, D. Burkholder, E. times of presentation are as follows: Cinlar, R. DeBlassie, A. Gut, W. Klieman, J. Mitro, GRAHAM HIGMAN, University of Oxford, P. Ney, S. Orey, M. Pinsky, P. Protter, T. Salisbury, England, and the University of Illinois, Urbana­ and D. Stroock. Champaign, Inflexions in characteristic 3, 11:00 Borel structures and classical measure theory, a.m. Saturday. K. P. S. BHASKARA RAO and RAE MICHAEL MICHAEL MARCUS, Texas A&M University, SHORTT, Michigan Technological University. The College Station, Random Fourier series, 1:30 p.m. tentative speakers include T. Armstrong, Jack Brown, Friday. R. B. Darst, N. Dinculeanu, Gerald A. Edgar, Thomas Jech, Roy A. Johnson, R. Daniel Mauldin, J. MARSHALL OsBORN, University of Wisconsin, Arnold Miller, John C. Morgan II, Karel Prikry, D. Madison, What are nonassociative algebras?, 1:30 Ramachandran, Cesar Silva, Arthur H. Stone, and p.m. Saturday. Dorothy Stone. ROGER PENROSE, University of Oxford, England, Groups and , MARK A. RoNAN and and Rice University, Title to be announced, 11:00 STEPHEN D. SMITH, University of Illinois, Chicago. a.m. Friday. The tentative speakers include M. A~chbacher, J. Hall, R. Liebler, G. Mason, 8. Rees, anl! E. Shult. Special Sessions Most of the papers to be presented at these special By invitation of the same committee, there will sessions will be by invitation. However, anyone be eight special sessions of selected twenty-minute submitting an abstract for the meeting who feels that his or her paper would be particularly appropriate papers. The topics of these special sessions, the for one of these special sessions should indicate names and affiliations of the organizers, and partial this clearly on the abstract form and submit it by lists of speakers, are as follows: January 2, 1985, three weeks before the deadline for Plethysms, JOSEPH BRENNAN, Michigan State contributed papers, in order that it may be considered University, The tentative speakers include Joseph for inclusion. All abstracts must be accompanied by Brennan, Y. M. Chen, Peter Hoffman, J. Patera, R. payment of $15 to cover a portion of the processing C. Read, Frank J. Servedio, and Hiroshi Uehara. costs. Participants are reminded that a charge of $12 Periodic and almost periodic solutions of is also imposed for retyping abstracts that are not in differential equations, T. A. BuRTON, Southern Il­ camera-ready form. linois University, Carbondale. The tentative speakers include 0. Arino, M. Bardi, Stephen Bernfeld, C. Contributed Papers Corduneanu, A. M. Fink, John Graef, John Haddock, There will also be sessions for contributed ten­ M. Islam, R. Kannan, G. S. Ladde, V. Lakshmikan­ minute papers. Abstracts should be prepared tham, Carl E. Langenhop, William Layton, Warren S. on the standard AMS form available from the Loud, W. Mahfoud, Stephen J. Merrill, Allan Peter­ AMS office in Providence or in Departments of son, Jane Cronin Scanlon, George Seifert, Alfredo Mathematics. Abstracts should be sent to the Somolinos, Lian Wang, and Mu-Qiu Wang .. American Mathematical Society, P. 0. Box 6248, History of logic, THOMAS L. DRUCKER, Univer­ Providence, RI 02940, so as to arrive before the January 23, 1985, abstract deadline. All abstracts sity of Wisconsin Extension, Madison. The list of must be accompanied by payment of the $15 tentative speakers includes Irving Anellis, William processing charge. Participants are reminded that a Aspray, Joseph Dauben, Martin Davis, John Dawson, charge of $12 is also imposed for retyping abstracts Steven C. Kleene, , Jan Mycielski, that are not in camera-ready form. Ani! Nerode, Daniel O'Leary, J. Barkley Rosser, Dirk Siefkes, Craig Smorynski, and Robert Soare. Registration K-theory, HENRI GILLET, University of Illinois, The meeting registration desk will be located in Chicago. The tentative speakers include W. Dwyer, Room 120 Science and Engineering Offices Building.

70 The desk will be open from 8:00 a.m. to 3:30 p.m. on Comfort Inn (formerly Ramada Inn) is five blocks Friday, and from 8:00a.m. to 11:00 a.m. on Saturday. east of campus and just south of the Eisenhower The registration fees are $10 for members, $16 for Expressway. nonmembers, and $5 for students or unemployed Quality Inn mathematicians. 1 S. Halsted Street, Chicago 60606 Petition Table Telephone: 312-829-5000 A petition table will be set up in the registration Single $32 Double $38 area. Additional information can be found in a box Quality Inn (formerly Holiday Inn) is six blocks in the Anaheim meeting announcement in this issue north of campus and just west of the Kennedy of the Notices. Expressway. Accommodations University of lllinois Housing Office A block of rooms is being held at the following 1933 West Polk Street, Chicago 60612 location for participants attending the meeting. Telephone: 312-996-8100 These rooms will be held until February 21, after Single $36-40 Double $42-46 which reservations will be accepted on a space Reservations for University Housing Service guest available basis. Participants should make their rooms are handled by the Housing Office; both are own arrangements directly with the hotel and be located on the west end of the campus (Health sure to mention the AMS meeting at UIC when Sciences Center), a mile west of the University Center making reservations. A daily buffet breakfast is end of campus where the scientific sessions will take complimentary for hotel guests; however, individuals place. Shuttle buses run a continuous circuit between are expected to pay the appropriate tax and gratuity. the east and west campus about every 20 minutes. Hyde Park Hilton Food Service 4900 S. Lake Shore Drive, Chicago 60615 The cafeteria in the Chicago Circle Center will Telephone: 312-288-5800 be open on Friday from 7:30 a.m. until 2:00 p.m., Single $40 Double $46 but will not be open on Saturday. A few blocks The Hilton is several miles from the campus; north of the campus (on Halsted Street) is Greek however, complimentary limousine service is provided Town, where several Greek restaurants are located. to and from McCormick Place as well as to and from Immediately to the west of the campus are numerous the UIC campus. Parking is complimentary for hotel Italian restaurants. Participants who wish to go into guests. the Loop to eat should note that bus and subway Rooms have not been blocked at any of the transfers (10 cents in addition to the base 90 cents following locations, and they are listed here for fare) are good for one hour and can be used for the information purposes. Participants should make their return trip from the Loop. own arrangements directly with the hotel or motel of their choice and identify themselves as attending Travel the AMS meeting at the University of Illinois when The University of Illinois at Chicago University making reservations. Center is located just west and south of the junction Americana Congress of the three major expressways: the Kennedy (I-90), 520 S. Michigan Avenue, Chicago 60605 Eisenhower (I-294}, and Dan Ryan (I-94). Arriving by Telephone: 312-427-3800 car from the north take I-90 to I-294 westbound and keep to the right. Take the first exit (Morgan Street) Single $40 Double $50 from I-294 and go one block south to the campus. The Americana Congress is a mile and a half east From the south take the Dan Ryan (I-94) and exit at of the campus. 1200 South (Roosevelt Road) or 1000 South (Taylor Bismark Hotel Street); go west one block on either Roosevelt or 171 West Randolph, Chicago 60601 Taylor to the campus. From the west take the Telephone: 312-236-0123 Eisenhower Expressway (I-294) to the Racine Avenue Single $32 Double $40 exit; go one-half block south to Harrison Street, then The Bismark is on the north side of the Loop, east one block to the campus. From the east take about two miles from campus. Harrison Street west to the campus. Blackstone Hotel If coming to the campus by bus, participants 636 S. Michigan Avenue, Chicago 60605 should use any of the following: No. 60 Blue Island- Telephone: 312-427-4300 26th St.; No. 8 Halsted Street; No. 7 Harrison St.; No. 12 Roosevelt Road; or No. 37 Taylor Street. Single $42 Double $47 The Halsted/University of Illinois stop on the route The Blackstone Hotel is about a mile and a half of the Douglas-Milwaukee-Congress elevated-subway east of the campus. trains is at the north edge of the campus in the Comfort Inn middle of the Eisenhower Expressway. Both the A 506 W. Harrison Street, Chicago 60607 and B trains stop at Halsted, which is the first stop Telephone: 312-427-6969 above ground after the line leaves the subway heading Single $35 Double $45 west from the Loop. This line provides service all

71 the way to O'Hare Airport; the trip from O'Hare to Taxicabs charge about $20 for the trip from O'Hare Halsted takes about 45 minutes. Information about to the Loop, and airport buses charge $6.75 for the the Chicago Transit Authority buses and trains can same trip. C & W Limousine Service from O'Hare to be obtained by calling 312-836-7000. the Hilton at Hyde Park is $7.50. Trains of the Burlington Northern, Penn Central, Parking Milwaukee Road and the Illinois Central Gulf Visitors to the University may park in any one of railroads arrive at Chicago's Union Station, one the following cash lots; the fee is $3. mile north and east of the campus. Northwestern trains arrive at the Northwestern Station two blocks Lot 4: Garage on Halsted with entrances on Polk north of Union Station. From there take the No. 60 and Taylor Streets. bus (Blue Island-26th Street) at Clinton and Madison, Lot 5C: Lot on Morgan Street near Roosevelt Adams or Jackson Streets. Some Illinois Central, and Road. all South Shore trains, arrive at the IC Station at Lot 7: Garage between Morgan Street and Racine Randolph Street and Michigan Avenue. From the Avenue, with visitor's entrance on Harrison. station walk three blocks west to Dearborn Street Participants driving to the campus should be aware and take a westbound A or B train on the Douglas­ that street parking in the residental area just west of Congress- Milwaukee subway to the Halsted/UIC the campus is restricted to area residents by special station. Rock Island trains arrive at the LaSalle permit only. Street Station; take westbound subway at LaSalle and Congress to Halsted (second stop). Robert M. Fossum Elevated-subway trains run every 10 minutes from Urbana, Illinois Associate Secretary O'Hare Airport to the Loop, and the fare is 90 cents.

AMS SHORT COURSE LECTURE NOTES Introductory Survey Lectures (Proceedings of Symposia in Applied Mathematics)

Population Biology Simon A. Levin, Editor

The lecture notes contained in this volume were tion to ordinary and partial differential equations, presented at the AMS Short Course on Population and linear algebra will make the book accessible. Biology, held August 6-7, 1983 in Albany, New All of the papers included have high research York in conjunction with the eighty-seventh summer value. They are meeting of the American Mathematical Society. Simon Levin, Mathematical population biology Population biology is probably the oldest area in James Frauenthal, Population dynamics and demog- mathematical biology, but remains a constant source raphy of new mathematical problems and the area of biol­ Thomas Nagylaki, Some mathematical problems in ogy best integrated with mathematical theory. The population genetics need for mathematical approaches has never been Ethan Akin, Evolution: game theory and economics greater, as evolutionary theory is challenged by new Wayne Getz, Optimal control and principles in popu­ interpretations of the paleontological record and lation management new discoveries at the molecular level, as world re­ George Sugihara, Graph theory, homology and food sources for feeding populations become limiting, as webs the problems of pollution increase, and as both animal and plant epidemiological problems receive 1980 Mathematics Subject Classifications: 92A 15, 92A 10, closer scrutiny. 92A17 The purpose of this course was to acquaint the Proceedings of Symposia in Applied Mathematics Volume 30, x + 102 pages participant with the mathematical ideas that pervade Soft cover prices: List $21, institutional member $17, almost every level of thinking in population biology individual member $13 and to provide an introduction to the many applica­ Hard cover prices: List $27, institutional member $22, tions of mathematics in the field. Research mathe­ individual member $16 maticians, college teachers of mathematics, and ISBN 0-8218-0083·3; LC 83-21389 Publication date: March 1984 graduate students should all find this book of inter­ To order, please specify PSAPM/30N (hard cover) est A background of advanced calculus, introduc- PSA PMS/30N (soft cover)

Shipping/Handling: 1st book $2, each add'l $1, max. $25; by air, 1st book $5, each add'l $3, max. $100 Prepayment is required. Order from American Mathematical Society, P.O. Box 1571, Annex Station, Providence, Rl 02901-1571, or call toll free 800-556-7114 to charge with Visa or MasterCard.

72 Tucson, April 12-13, 1985, University of Arizona Second Announcement of the 818th meeting

The eight hundred eighteenth meeting of the a charge of $12 is also imposed for retyping abstracts American Mathematical Society will be held at that are not in camera-ready form. the University of Arizona, Tucson, on Friday and Contributed Papers Saturday, April 12 and 13, 1985. This meeting will be held in conjunction with meetings of the There will also be sessions for contributed ten­ minute papers. Abstracts should be prepared on the Mathematical Association of America (MAA) and the Sociedad Matematica Mexicana (SMM). standard AMS form available from the AMS office in Providence or in Departments of Mathematics. They Invited Addresses should be sent to the Editorial Department, American By invitation of the Committee to Select Hour Mathematical Society, P. 0. Box 6248, Providence, Speakers for Far Western Sectional Meetings, there RI 02940, so as to arrive prior to the January 25, will be two invited one-hour addresses. The speakers 1985, abstract deadline. These abstracts must also and the titles of their talks are: be accompanied by payment of the $15 processing GEORGE M. BERGMAN, University of California, charge. Participants are reminded that a charge of Berkeley, Representable functors among categories $12 is also imposed for retyping abstracts that are not of algebras. in camera-ready form. Late papers will be accepted for presentation at the meeting, but will not appear GREGORY BRUMFIEL, Stanford University, in the printed program. Modern real algebra. MAAProgram Special Sessions The MAA Program will include two invited By invitation of the same committee, there will be speakers. IvAN NIVEN of the University of Oregon four special sessions of selected twenty-minute papers. will deliver an address titled Some observations on The topics of these special sessions and names of the mathematics and mathematicians. CoNSTANCE organizers are as follows: REID, San Francisco, will also deliver an address; Abelian group theory, Ross BEAUMONT, Univer­ the title is not yet available. A panel discussion on sity of Washington. The history of the mathematical relations between The arithmetic of algebraic function fields of Mexico and the United States will also take place, one variable, DANIEL J. MADDEN, University of and a banquet will be held on Friday evening. Arizona. Registration Galois module structure of algebraic number The meeting registration desk will be located in fields, ALBRECHT FROHLICH, King's College, the main lobby of the Mathematics Building, and University of London, England, and the University of will be open from 1:00 p.m. to 4:30 p.m. on Friday, Arizona. The list of tentative speakers includes Steve and from 8:30 a.m. until noon on Saturday. The Chase, Lindsay Childs, Ten Chinburg, Gary Cornell, registration fees are $6 for members of the AMS, MAA, Kurt Foster, Albrecht Frolich, Benedict Gross, Uwe or SMM, $8 for nonmembers, and $2 for students or Jansen, Donald Maurer, Leon McCulloh, Shankar unemployed mathematicians. Sen, Olga Taussky-Todd, Martin Taylor, Stephen Ullom, and Steve Watt. Petition Table New ideas in nonlinear science, ALAN C. A petition table will be set up in the registration NEWELL, University of Arizona. area. Additional information about the petition table Most of the papers to be presented at these special can be found in a box in the Anaheim meeting sessions will be by invitation. However, anyone announcement in this issue of the Notices. submitting an abstract for the meeting who feels that Accommodations his or her paper would be particularly appropriate The following motels are located five miles or less for one of these sessions should indicate this clearly from the campus. Participants should make their on the abstract form and submit it by January 4, own reservations directly with the motel of their 1985, three weeks before the deadline for contributed choice. Rates are subject to possible change, and do papers, in order that it may be considered for not include any applicable local taxes. inclusion. Abstracts should be prepared on the standard AMS form available from the AMS office Arizona Inn (One mile from campus) in Providence or in Departments of Mathematics. 2200 East Elm Street 85719 Abstracts should be sent to the Editorial Department, Telephone: 602-325-1541 American Mathematical Society, P. 0. Box 6248, Toll free in Arizona: 800-421-1093 Providence, RI 02940. Each abstract must be Single $75 and up Double $80 and up accompanied by payment of $15 to cover a portion of Limousine fare from the airport to hotel is $5 per the process;ng costs. Participants are reminded that person.

73 74 Motel6 (Five miles from campus) Transportation 960 South Freeway 857 45 Tucson is served by Greyhound and Trailways Telephone: 602-624-6345 bus lines. The air carriers serving the Tucson Single $16.95 Double $20.95 Airport include Aero Mexico, Airways of New Limousine fare from the airport to motel IS Mexico, American, American West, Eastern, Frontier, approximately $5.25 per person. Northwest, PSA, Republic, Sun World, TWA, Santa Rita Hotel and Conference Center USAir, United, and Western Airlines. Arizona (Two miles from campus) Stagecoach Limousine Service provides transportation 88 East Broadway 85701 between the airport and the university; the fare is Telephone: 602-791-7581 or toll free 800-528-3444 approximately $5.25 per person. By reservation, Toll free in Arizona: 800-362-3470 Arizona Stagecoach will also transport participants from hotels to the university or back to the Tucson Single $34 Double $38 Airport. These reservations are required 24 hours Complimentary limousine service from airport to the in advance; the telephone number to call is 602-889- hotel. Limousine service also provided between hotel 9681. and campus; the fare is $1.50 per person. A welcome The University of Arizona campus is situated to reception with complimentary margarita cocktails the east of Interstate Route {I-10), which runs and dry snacks will be provided for hotel guests at #10 from north to south. Drivers entering Tucson from poolside from 8:30 to 9:30 p.m. on Thursday, April either direction should take the Speedway Boulevard 11. Exit and travel east for a distance of approximately Western 6 {Five miles from campus) two miles until reaching Euclid Avenue. Make a 1338 West Grant Road 857 45 right turn onto Euclid A venue; at the second traffic Telephone: 602-622-4784 light turn left onto Sixth Street and proceed four Single $21.95 Double $25.95 blocks until reaching Santa Rita Avenue. A left Limousine fare from airport to motel is $6.25 per turn at Santa Rita Avenue will lead directly to the person. Limousine service also available between Mathematics Building, a right turn will lead to the motel and campus. on-street parking, or drivers can continue on Sixth Food Service Street and make a left turn onto Highland Avenue. The latter will lead directly to the pay parking lot Restaurants in the Student Union will be open adjacent to the Science Library. during both days of the meeting. In addition, there are several restaurants within three blocks of the Parking Mathematics Department. Free parking is available in the pay parking lots Social adjacent to the Science Library, or off Second Street north of the Administration Building. In order to A banquet will be held at p.in. on Friday 6:00 obtain free parking, drivers must identify themselves in the Fiesta Room at the Santa Rita Hotel and to the attendants as participants at the AMS meeting. Conference Center. The cost for the prime rib dinner On-street parking is also available approximately will be $13 per person. Preceding the banquet there three to four blocks directly south of the Mathematics will be a no-host cash bar, also at the Santa Rita Building. Hotel. Reservations and payment for the banquet should be sent by March 15 to William Y. Velez, Hugo Rossi Department of Mathematics, University of Arizona, Salt Lake City, Utah Associate Secretary Tucson, Arizona 85721.

Measurable Selectors of PCA universally measurable selector with the property M ultifunctions with of Baire whenever the graph of F is a C-set of Applications Selivanovskii (or a Borel-programmable set of Blackwell. or an R-set of Kolmogorov. or a Marian Srebrny Borel-game set of Vaught) and whose value of F is (Memoirs of the AMS. Number 311) either nonmeager or nonnull with respect to a In this Memoir, measurable selection theory is given Borel probability measure distribution. investigated from the modern descriptive set 1980 Mathematics Subject Classifications: theory point of view. This approach leads to a 28A05, 04A15, 03E15 ISBN 0-8218-2299-3, LC 84-18464 general measurable selection theorem-scheme. A ISSN 0065-9266 necessary and sufficient condition is given for the iv + 50 pages ( softcover), November 1984 existence of a measurable selector. In the case of a List price S9 1 Institutional member $7, Individual member $5 multifunction F from X to subsets of Y. both Shipping and handling charges must be added Polish spaces. it is shown that F admits a To order, please specify MEM0/311N Shipping/Handling: 1st book $2, each add'l $1, max. $25; by air, 1st book $5, each add'l $3, max. $100 Prepayment is required. Order from American Mathematical Society, P.O. Box 1571, Annex Station, Providence, Rl 02901-1571, or call toll free 800-556-7774 to charge with Visa or MasterCard.

75 Worcester, April 20-21, 1985, College of the Holy Cross Second announcement of the 819th meeting

The eight hundred and nineteenth meeting of Gilbert Labelle, Pierre Leroux, Bruce Sagan, Louis the American Mathematical Society will be held Shapiro, Richard Stanley, Dennis Stanton, and at the College of the Holy Cross in Worcester, Dennis White. Massachusetts, on Saturday and Sunday, April 20 Fractal geometry, BENOIT B. MANDELBROT, and 21, 1985. All scientific sessions will be held IBM T. J. Watson Research Center and Harvard in Haberlin Hall in the science and mathematics University. The list of anticipated speakers includes complex at the College. M. Barnsley, M. Benedicks, M. Bessis, R. L. Dezaney, Invited Addresses A. Douady, S. Dubuc, J. Hubbard, C. Itzykson, Benoit Mandelbrot, , Dennis Sullivan, By invitation of the Committee to Select Hour M. Taqqu, S. J. Taylor, and C. Tricot. Speakers for Central Sectional Meetings, there will be four invited one-hour addresses. The speakers, their Methods of K-theory, RoBERT W. THOMASON. affiliations, the titles of their talks, and the scheduled The tentative speakers include T. Fischer, H. Gillet, times of presentation are as follows: H. Hiller, R. Joshua, D. Ramakrishnan, K. Vogtmann, and C. Weibel. WILLIAM ABIKOFF, University of Connecticut, Storrs, Kleinian groups-an invitation to mathe­ Most of the papers to be presented at these matics, 1:30 p.m. Saturday. special sessions will be by invitation. However, IRA M. GESSEL, Brandeis University, Recent anyone submitting an abstract for the meeting who work in enumerative combinatorics, 11:00 a.m. feels that his or her paper would be particularly Sunday. appropriate for one of these special sessions should indicate this clearly on the abstract form and submit ROBERT W. THOMASON, Johns Hopkins Univer­ it by January 7, 1985, three weeks before the sity Algebraic and topological K-theory, 1:30 p.m. deadline for contributed papers, in order that it may Sunday. be considered for inclusion. Abstracts should be STEPHEN S.-T. YAu, University of Illinois at prepared on the standard AMS form available from Chicago and Yale University, Isolated singularities the AMS office in Providence or in Departments and finite dimensional solvable Lie algebras, 11:00 of Mathematics. Abstracts should be sent to a.m. Saturday. ~he Editorial Department, American Mathematical Special Sessions Society, P. 0. Box 6248, Providence, RI 02940. Each By invitation of the same committee, there will be abstract must be accompanied by payment of $15 to six special sessions of selected twenty-minute papers. cover a portion of the processing costs. Participants The topics of these special sessions, the names and are reminded that a charge of $12 is also imposed affiliations of the organizers, and some partial lists of for retyping abstracts that are not in camera-ready tentative speakers, are as follows: form. Geometric function theory, WILLIAM ABIKOFF Contributed Papers and IRWIN KRA, SUNY at Stony Brook. The There will also be sessions for contributed ten­ tentative speakers include William Abikoff, Lipman minute papers. Abstracts should be prepared on the Bers, Clifford Earle, Frederick Gardiner, Fred standard AMS form available from the AMS office Gehring, Jane Gilman, Andrew Haas, Linda Keen, in Providence or in Departments of Mathematics. Irwin Kra, Albert Marden, Bernard Maskit, Howard Abstracts should be sent to the Editorial Department, Masur, Caroline Series, and Scott Wolpert. American Mathematical Society, P. 0. Box 6248, Differential geometry of submanifolds, THOMAS Providence, RI 02940, so as to arrive before the E. CECIL, College of the Holy Cross and STEPHEN January 28, 1985, abstract deadline. These abstracts S.-T. YAu. The tentative speakers include must also be accompanied by payment of the $15 Kinetsu Abe, Thomas Banchoff, David Blair, Carol processing charge. Participants are reminded that a Blomstrom, B.-Y. Chen, Richard Escobales, Michael charge of $12 is also imposed for retyping abstracts Gage, Detlef Gromoll, Gerald Ludden, Martin Magid, that are not in camera-ready form. Katsumi Nomizu, Patrick Ryan, and Wolfgang Ziller. It appears unlikely that late papers can be Singularities and complex geometry, THOMAS accommodated. E. CECIL and STEPHEN S.-T. YAu. The tentative speakers include Max Benson, Alan Durfee, Y.-N. Registration Gau, Anatoly Libgober, T.-T. Moh, Peter Orlik, The registration desk will also be located in Mark Spivakovsky, and Bun Wong. Haberlin Hall, and will be open from 8:15 a.m. Enumerative combinatorics, IRA M. GESSEL. until 1:45 p.m. on both Saturday and Sunday. The list of tentative speakers includes George The registration fees are $10 for members, $16 for Andrews, Anders Bjorner, David Bressoud, Ian nonmembers, and $5 for students or unemployed Goulden, Curtis Greene, Andre Joyal, Gil Kalai, mathematicians.

76 Petition Table Worcester, MA 01610 A petition table will be set up in the registration Telephone: 617-852-5800 area. Additional information about the petition table Single $26.96 Double $30.94 can be found in the Anaheim meeting announcement Yankee Drummer Inn in this issue of the Notices. 624 Southbridge Street Accommodations Auburn, MA 01501 Rooms have been blocked at the Howard Johnson's Telephone: 617-832-3221 Motor Lodge adjacent to the campus, and at the Single $49.90 Double $52.90 Quality Inn which is about a mile from the campus Food Service in downtown Worcester. Participants should make A variety of options their own reservations directly with the motel of will be available for luncheon in Hogan Center on Saturday and Sunday. A special their choice and identify themselves as attending the section in the Center will be designated as the dining meeting of the American Mathematical Society at area for meeting the College of the Holy Cross. The cutoff date for participants, where meal service is cafeteria-style. reservations at these two locations is February 15, Those who prefer to do so may wish to eat 1985. The rates listed below are subject to change at Kimball Hall instead. Information and do not include applicable taxes. about various restaurants in the Worcester area will be available at the meeting registration desk. Howard Johnson's Motor Lodge 800 Southbridge Street Social Event Worcester, MA 01610 The Local Arrangements Committee is planning a Telephone: 617-791-5501 beer and pizza party at the Hogan Center on Saturday Single $41 Double $51 evening. Although tickets may be purchased at the door, the Committee requests that those who can Quality Inn conveniently do so should purchase their tickets m 70 Southbridge Street advance at the meeting registration desk. Worcester, MA 01610 Telephone: 617-791-2291 Travel Single $42 Double $48 The Worcester Airport is located about five miles from the Holy Cross campus. Airline service to The following motels are located between two and Worcester is provided by Bar Harbor Airlines, with five miles from campus. Although rooms have not flights from Logan Airport in Boston and Laguardia been blocked at any of these locations, they are Airport in New York. Tri State Airlines also provides included here for information purposes. service from Newark Airport, however, service on Best Western Centrum Inn both of these carriers is very limited or nonexistent 110 Summer Street on Saturday and Sunday. Participants who fly to Worcester, MA 01610 Logan Airport should make use of the Worcester Telephone: 617-757-0400 Limousine Service, which will transport passengers Single $45 Double $51 directly to the campus or elsewhere in Worcester. Days Lodge of Worcester The cost is $17 one way, but reduced rates usually 50 Oriol Drive apply when two or more passengers are transported to Worcester, MA 01610 the same destination in Worcester. Reservations are Telephone: 617-852-2800 necessary and may be obtained by calling 617-756- 4834; at the s~:me time information will be provided Single $42.88 Double $47.88 concerning passenger pickup at Logan. Howard Johnson's Motor Lodge Worcester is also served by both Greyhound and West Boylston Street Trailways bus lines. The bus station is about one West Boylston, MA 01583 mile from the campus. Taxicab service is available Telephone: 617-835-4456 from the bus station, and the cost for transportation Single $47 Double $54 to the campus is approximately $3. Sheraton-Lincoln Inn Participants driving to the meeting should use 500 Lincoln Street Auburn Exit No. 10 from the Massachusetts Turnpike, Worcester, MA 01610 then take Route 290 East to Worcester. The College TeJ.ephone: 617-852-4000 Square Exit from Route 290 is a block from the Single $67-$73 Double $76-$81 campus. Worcester Marriott Parking 10 Lincoln Square Free parking is available at several lots located on Worcester, MA 01610 the Holy Cross campus. Telephone: 617-791-1600 Single $77 Double $89 W. Wistar Comfort Yankee Budget Motor Lodge Middletown, Connecticut Associate Secretary 531 Lincoln Street

77 Mobile, May 3-4, 1985, University of South Alabama Second Announcement of the 820th meeting

The eight hundred twentieth meeting of the accompanied by payment of $15 to cover a portion of American Mathematical Society will be held at the the processing costs. Participants are reminded that University of South Alabama Brookley Center in a charge of $12 is also imposed for retyping abstracts Mobile, Alabama, on Friday and Saturday, May 3 that are not in camera-ready form. and 4, 1985. Sessions will be held at the Brookley Contributed Papers Center, which also has guest rooms. There will also be sessions for contributed ten­ fuvited Addresses minute papers. Abstracts should be prepared on the By invitation of the Committee to Select Hour standard AMS form available from the AMS office Speakers for Southeastern Sectional meetings, there in Providence or in Departments of Mathematics. will be four invited one-hour addresses. The speakers, Abstracts should be sent to the Editorial Department, their affiliations, and the titles of their talks are as American Mathematical Society, P. 0. Box 6248, follows: Providence, RI 02940, so as to arrive before the FRED CoHEN, University of Kentucky, Classical January 30, 1985, abstract deadline. These abstracts homotopy theory and loop spaces. must also be accompanied by payment of the $15 DENNIS DETURCK, University of Pennsylvania, processing charge. Participants are reminded that a Can you hear the shape of a manifold?. charge of $12 is also imposed for retyping abstracts JoHN GILBERT, University of Texas, Austin, In­ that are not in camera-ready form. variant differential operators in harmonic analysis. Registration JEFFERY LAG ARIAS, AT & T Bell Laboratories, The meeting registration desk will be located in Short vectors in lattices and public key cryptog­ the lobby of Building 2002, and will be open from raphy. 8:00 a.m. to 5:00 p.m. on Friday, and from 8:00 a.m. Special Sessions until noon on Saturday. The registration fees are $10 for members, $16 for nonmembers, and $5 for By invitation of the same committee, there will be students or unemployed mathematicians. six special sessions of selected twenty-minute papers. The topics of these special sessions and names of the Petition Table organizers are as follows: A petition table will be set up in the registration Combinatorics and graph theory, THOMAS area. Additional information about the petition table BRYLAWSKI, University of North Carolina, Chapel can be found in the Anaheim meeting announcement Hill. in this issue of the Notices. Nonlinear problems in geometry, DENNIS Accommodations DETURCK, Rooms will be available for participants at Oak Analysis on homogeneous spaces, RAY KuNZE, Tree Lodge, Pine Tree Lodge, and Building 2002 University of Georgia, Athens. at Brookley Center. All are centrally located and Number theory and its applications, JEFFERY within easy walking distance of the meeting activities. LAG ARIAS. Private units at the lodges include one or two bedroom Algebraic topology, JOEL NEISENDORFER, Ohio suites with living area, small kitchenette, and State University. bath, while Building 2002 contains standard motel­ Symbolic dynamics and , SusAN style rooms. All accommodations have individually WILLIAMS, University of South Alabama, and controlled heating and air conditioning, as well as BRUCE KITCHENS, IBM T. J. Watson Research closed circuit color television. Accommodations are Center. available the nights of May 3 and 4; however, only a Most of the papers to be presented at these special limited number of rooms will be available on May 2. sessions will be by invitation. However, anyone The daily rates are $25, $30, $36, and $40 for single, submitting an abstract for the meeting who feels that double, triple, or quadruple occupancy, respectively, his or her paper would be particularly appropriate and are tax free. Participants should make their for one of these sessions should indicate this clearly own reservations by writing to Ms. Sharon Davis, on the abstract form and submit it by January 9, University of South Alabama Brookley Center, 2002 1985, three weeks before the deadline for contributed Old Bay Front Road, Mobile, AL 36615, or by papers, in order that it may be considered for telephoning her at 205-431-6410 (or 205-433-4966) inclusion. Abstracts should be prepared on the between the hours of 8:00 a.m. and 4:00 p.m. Monday standard AMS form available from the AMS office through Friday. The deadline for reservations is in Providence or in Departments of Mathematics. April15. Abstracts should be sent to the Editorial Department, The following accommodations are also available American Mathematical Society, P. 0. Box 6248, in the area of Brookley Center. The Ramada and Providence, RI 02940. Each abstract must be Rodeway Inns are within two miles, while the Malaga

78 a: Q Cl) a: ""Q z o( :IE :IE 0u

UNIVERSITY OF SOUTH ALABAMA BROCKLEY CENTER

0 RAMADA INN 0 RODEWAY INN .a.. @ LODGING CHECK-IN N

79 Inn and Stouffer's Riverview Plaza are five miles or cheese trays, and mini sandwiches, as well as beer less from the Center. Rates quoted are subject to and iced tea. Participants not residing at the change, and do not include the additional 8 percent Center should make their checks payable to the tax. University of South Alabama Brookley Center and Malaga Inn send them by April 15 to Ms. Sharon Davis. The 359 Church Street, Mobile 36602 mailing address is included in the section above titled Telephone: 205-438-4701 Accommodations. Participants who will be lodging at Brookley Center can arrange to attend the beer Single $38 or $44 Double $44 or $52 party when making their room reservations. Ramada Inn 1705 Dauphin Island Parkway, Mobile 36605 Parking Telephone: 205-471-6114 There is ample free parking in lots at the Brookley Center, including the residence areas. Single $32 Double $40 Rodewaylnn Travel 1724 Michigan Avenue, Mobile 36605 Mobile is served by several of the major airlines, Telephone: 205-478-3014 including American, Delta, Eastern, and Republic. Single $25 Double $30 Bates Field, the Mobile municipal airport, is approximately sixteen miles from Brookley Center. Stouft'er's Riverview Plaza Taxi and limousine service is available from the 64 South Water Street, Mobile 36602 airport to Brookley Center. Car rental agencies also Telephone: 205-438-4000 located at the airport include Avis, Budget, Dollar, Single $49 Double $49 Hertz, National, and Thrifty. Participants driving Food Service from Bates Field to the Center should take Airport Boulevard east for approximately eight miles until The Brookley Center cafeteria will be serving reaching Interstate 65 (1-65), then turn south on I- breakfast from 7:00 a.m.-9:00a.m., and lunch from 65 for approximately three miles to Interstate 10 11:00 a.m.-1:30 p.m. on Thursday, Friday, and (I-10). Take I-10 East toward Pensacola, Florida Saturday. The cafeteria is not open for dinner and for approximately four miles and exit on Michigan is closed on Sunday. Many restaurants are located Avenue. Go south on Michigan Avenue and take within five miles of the Center, and a restaurant the first possible left turn, which will be onto Broad guide will be available at the registration desk. Street. Stay on Broad Street for approximately 6/10 Soeial of a mile until the road veers to the left and intersects A beer party will be held at the Conference Center Old Bay Front Road. Turn right onto Old Bay Front (Building 254) on Friday evening. The cost for Road and continue to Brookley Center. the party is $11.50 per person, and includes as hors d'oeuvres boiled shrimp, oysters on the half Frank T. Birtel shell, chicken nuggets, creole meatballs, relish and New Orleans, Louisiana Associate Secretary

80 On Some Mathematical Questions in Biology Plant Biology 1985 Symposium, Los Angeles, California, May 1985

The nineteenth annual Symposium on Some The program has been arranged by an Organizing Mathematical Questions in Biology will be held during Committee consisting of H. Thomas Banks (Brown the annual meeting of the American Association for University); Gail A. Carpenter, (Northeastern Univer­ the Advancement of Science, May 26-31, in Los sity); Joel E. Cohen (Rockefeller University); Joseph Angeles, California. The date and location of the B. Keller (Stanford University); Robert M. Miura symposium will be announced in the March issue (University of British Columbia), chairman; Garrett of the Notices. The symposium is sponsored by M. Odell (Rensselaer Polytechnic Institute); Charles the American Mathematical Society, the Society for S. Peskin (Courant Institute, New York University); Industrial and Applied Mathematics, and Section A and John Rinzel (National Institutes of Health). (Mathematics) of the American Association for the The theme of the symposium is Plant Biology. Advancement of Science. Cosponsors: Sections G There will be two half-day sessions, each including (Biological Sciences) and 0 (Agriculture). three one-hour lectures.

PROGRAM Chairman: Robert M. Miura morning Some Mathematical Questions in Biology-Plant Biology Presiding: LOUIS J. GRoss, University of Tennessee, Knoxville Computer simulations of branching-patterns and their implications on the evolution of plants. KARL J. NIKLAS, Cornell University Dynamics of stomate fields in leaves. RICHARD H. RAND, Cornell University Modelling plant processes and crop growth. JoHN H. M. THORNLEY, Grassland Research Institute

afternoon Some Mathematical Questions in Biology-Plant Biology Presiding: RICHARD H. RAND, Cornell University Photosynthetic dynamics and plant adaptation to environmental variability. Loms J. GRoss, University of Tennessee, Knoxville Life cycle models for plants. HAL CASWELL, Woods Hole Oceanographic Institution Models of population processes for plants. JoNATHAN RouGHGARDEN, Stanford University

81 1985 Summer Seminar In Applied Mathematics, June 30-July 13 Reacting Flows: Combustion and Chemical Reactors

The seventeenth AMS-SIAM Summer Seminar in served at breaks and for social events. There will Applied Mathematics will be held June 30-July 13, also be a meeting registration fee. A copy of the 1985, at Cornell University, Ithaca, New York. The proceedings will be available to registered participants seminar will be sponsored jointly by the American as a privilege of participation in.the seminar. Mathematical Society and the Society for Industrial Application blanks for admission and/or financial and Applied Mathematics. It is anticipated that it assistance can be obtained from the Meetings will be supported by a grant from a federal agency. Department, American Mathematical Society, P. 0. The topic Reacting Flows: Combustion and Chemical Box 6248, Providence, Rhode Island 02940. An Reactors was selected by the AMS-SIAM Committee applicant should have completed at least one year on Applied Mathematics whose members at the time of graduate school and will be asked to indicate were Roger W. Brockett, C. K. Chu, A. K. Konheim, his or her scientific background and interest. A Alari C. Newell (chairman), George C. Papanicolaou, graduate student's application must be accompanied and Robert F. Warming. The proceedings of the by a letter from his or her faculty advisor concerning seminar will be published by the Society in the series the applicant's ability and promise. Those who Lectures in Applied Mathematics. wish to apply for a grant-in-aid should so indicate; The seminar is the culmination of the Special Year however, funds available for the seminar are limited 1984-85 on the same subject held at the Center and individuals who can obtain support from other for Applied Mathematics of Cornell University. The sources should do so. theory of reacting flows has finally blossomed as a mathematical science in the last decade, and an attempt will be made to synthesize it into a firm Topics for AMS/SIAM Summer Seminar foundation for future large-scale computing. The (Reviews preferred) seminar will not, however, be aimed at computational Laminar Combustion fluid mechanics as a whole, but only those parts Diffusion flame structure, extinction and spread peculiar to reacting flows. Deflagration structure, stability and extinction A series of five lectures each will be given by Ruther­ Ignition and explosion development ford Aris (University of Minnesota, Minneapolis), G. Detonation structure, initiation and failure S. S. Ludford (Cornell University), and Andrew Deflagration-to-detonation transition Majda (University of California, Berkeley); shorter Multiple-step kinetics series will be presented by Harry Dwyer (University of Fluid-dynamical effects California, Davis), and A. F. Ghoniem (Massachusetts Turbulent Combustion Institute of Technology). There will also be lec­ tures by John D. Buckmaster (University of illinois, Reactors (stirred tank, tubular, countercurrent, Urbana), Donald Cohen (California Institute of Tech­ two-phase) nology), John Guckenheimer (University of California, Fluidized and packed beds Santa Cruz), Ingo Miiller (Berlin), Basil Nicolaenko Control, multiplicity of states, oscillations, (Los Alamos National Laboratory), Herschel Rabitz stability (Princeton University), and Forman A. Williams Pyrolysis and Gasification (Princeton University). Together, these lectures will Gas-solid reactions, autocatalysis, summarize the Cornell Special Year and sharpen the catalyst preparation focus onto computational questions. Polymerization, mass-action kinetics The remaining speakers will be selected by Mathematical Questions the Organizing and Advisory Committees on the Existence, uniqueness and stability of basis of abstracts submitted and commitments combustion structures to a timely written version. The Organizing Ignition modeling Committee consists of Donald Cohen, G. S. S. Analysis of complex reactions Ludford, (chairman), , and Forman A. Governing equations of reacting flows Williams; the members of the Advisory Committee Sensitivity analysis are Rutherford Aris, John D. Buckmaster, H. Dwyer, Qualitative methods and transition to chaos in John Guckenheimer, Ingo Miiller, Basil Nicolaenko, reactive systems and Herschel Rabitz. A list of topics at which Computational Questions abstracts should be aimed can be obtained from: Professor G. S. S. Ludford, Theoretical & Applied Laminar-flame structure Mechanics, Thurston Hall, Cornell University, Ithaca, Detonation-wave structure New York 14853. Transition to detonation Statistical calculations of turbulent flames In the early spring a brochure will be available from Large-eddy simulations (vortex dynamics) the AMS office which will include a description of the Adaptive-mesh techniques scientific program, information on the residence and Elliptic free-boundary problems dining hall facilities, firm room and board rates, local Numerical bifurcation and instability in reactors information, and a reservation form to be used to and combustion obtain accommodations on campus. Each participant Sensitivity analysis will pay a social fee to cover the cost of refreshments

82 1985 Summer Research Institute, July 8-26 Algebraic Geometry

The thirty-third Summer Research Institute spon­ It is anticipated that there will be a number of sored by the American Mathematical Society will lecture series presenting topics from classical algebraic be devoted to algebraic geometry, and will take geometry such as enumerative geometry, moduli of place at Bowdoin College in Brunswick, Maine, from curves, classification of varieties, and arithmetic July 8 to 26, 1985. Members of the Organizing theory, which have undergone very extensive recent Committee include Spencer Bloch, David Eisenbud development. There will also be a number of research (chairman), William Fulton, David Gieseker, Joe level seminars on these and other topics which seem Harris, Robin Hartshorne, and Shigefumi Mori. It likely to play a major role in the subject in the years is anticipated that the institute will be partially ahead. supported by a grant from the National Science Housing accommodations will be available in the Foundation. Proceedings of the institute will be pub­ campus residence halls for participants and their lished in the AMS series Proceedings of Symposia in families, and cafeteria-style meals will be served daily Pure Mathematics. in the adjacent dining hall. Residence and dining The topic was selected by the 1983 Committee facilities, as well as rooms used for the scientific on Summer Institutes, whose members were Michael sessions at Bowdoin College, are accessible to the Artin, Thomas H. Brylawski, Robert Osserman handicapped. (chairman), George C. Papanicolaou, Harold M. In the spring a brochure will be sent to all Stark, and Stephen Wainger. who are invited to attend the institute. It will The field of algebraic geometry has undergone very include information about the scientific program, intense development since the AMS Summer Research the residence and dining facilities, room and board Institute took place in 1974. Since that time there rates, travel and local information, and a reservation has been a very substantial return to the hard form for on-campus housing accommodations. Each special problems at the base of algebraic geometry participant will pay a social fee of $25 to cover and a corresponding wealth of special results and the cost of social events and refreshments served at examples. It is anticipated that the institute will have breaks. There will also be a meeting registration a broad enough scope to encompass the important fee. A copy of the proceedings will be available to developments in recent years in what might be registered participants as a privilege of participation called "classical" algebraic geometry, centered around in the institute. Unfortunately, funds for financial projective varieties in characteristic 0, allowing leeway assistance will be limited and, therefore, it will be for the representation of the most exciting new results necessary for many participants to obtain their own from the whole field. Algebraic geometry has changed funds. Anyone who wishes to receive an invitation considerably in its emphasis and practices in the to participate in the institute and/or be considered last ten years, and an amazing number of classical for financial assistance should write to Mrs. Dorothy conjectures have been settled. The demography Smith, American Mathematical Society, P. 0. Box of the field has also changed substantially; many 6248, Providence, Rhode Island 02940 prior to more algebraic geometers now work outside the great April 12, 1985. The Organizing Committee will centers. For these reasons, an institute in which subsequently consider those requests and applicants at least the classical side of algebraic geometry is will be informed at a later date if funds are granted "pulled together" is extremely desirable at this time. to provide support.

83 Call For Topics For 1987 Conferences

Suggestions are invited from mathematicians, sectional meeting at a site that has not yet been either singly or in groups, for topics of the various selected. Topics in recent years have been Inverse conferences that will be organized by the Society in Problems (1983); Mathematical Psychology and 1987. The deadlines for receipt of these suggestions, Psychophysiology (1980); Mathematical problems as well as some relevant information about each of in fracture mechanics (1978); and Computational the conferences are outlined below. An application fluid dynamics (1977). Proceedings are published form to be used when submitting suggested topic(s) by the Society as volumes in the series SIAM-AMS for any of these conferences (except the Short Course Proceedings. Series) may be obtained by writing to the Meetings Deadline For Suggestions: August 15, 1985 Department, American Mathematical Society, P. 0. Box 6248, Providence, Rhode Island 02940, or telephoning 401-272-9500, extension 296. 1987 AMS Summer Institute Individuals willing to serve as organizers should Summer institutes are intended to provide an be aware that the professional meeting staff in the understandable presentation of the state of the art Society's Providence office will provide full support in an active field of research in pure mathematics, and assistance, before, during, and after each of these and usually extend over a three-week period. Dates conferences. Organizers should also note that for all for a summer institute must not overlap those of conferences except Summer Research Conferences, it the Society's summer meeting (not known at this is required that the proceedings be published by the printing, but sometime in August) and, in fact, there Society, and that SRC's are frequently published. A should be a period of at least one week between them. member of the Organizing Committee must be willing The topic for the 1985 summer institute is Algebraic to serve as editor of the proceedings. geometry, and in 1986 it will be Representations All suggestions must include (1) the names and of finite groups and related topics. Other recent affiliations of proposed members and chairman of topics have been Geometric measure theory and the the Organizing Committee; (2) a two- or three­ calculus of variations (1984); Nonlinear functional page detailed outline of the subject(s) to be covered, analysis and its applications (1983); Recursion including the importance, timeliness of the topic, theory (1982); and Singularities (1981). Proceedings and estimated attendance; (3) a list of the recent are published by the Society as volumes in the series conferences in the same or closely related areas; (4) a Proceedings of Symposia in Pure Mathematics. tentative list of names and affiliations of the proposed Deadline For Suggestions: August 15, 1985 principal speakers; (5) a list of likely candidates who would be invited to participate and their current affiliations; and (6) any other observations which may 1987 AMS~SIAM Symposium affect the size of the conference and the amount of Some Mathematical Questions in Biology support required. Any suggestions as to sites and dates should be made as early as possible in order to This one-day symposium is usually held in allow adequate time for planning. By action of the conjunction with the Annual Meeting of the AAAS in AMS Board of Trustees, the Meetings Department of May. the Society is responsible for the final selection of Some recent topics in these annual symposia the site for each conference, and for all negotiations have been Biomechanics and mathematical models with the host institution. Individuals submitting in developmental biology (1981), Neurobiology, suggestions for the conferences listed below are the study of the nervous systems of organisms requested to recommend sites or geographic areas (1982), Muscle physiology (1983), DNA Sequence which would assist the Meetings Department in their Analysis (1984), and Plant biology (1985). The search for an appropriate site. In the case of Joint 1986 Symposium will be on Modeling of circadian Summer Research Conferences in the Mathematical rhythms in Philadelphia, Pennsylvania. Papers from Sciences, a one-, two-, or three-week conference may the symposia are published by the Society as volumes be proposed. in the series Lectures on Mathematics in the Lif~ Sciences. 1987 AMS-SIAM Symposium In Deadline For Suggestions: April1, 1985 Applied Mathematics 1987 AMS-SIAM Summer Seminar This two-day symposium in applied mathematics will henceforth take place in every odd-numbered The goal of the summer seminar is to provide an year, alternating with a symposium in pure mathe­ environment and program in applied mathematics matics in even-numbered years. The next regularly in which experts can exchange the latest ideas and scheduled symposium is scheduled to be held dur­ newcomers can learn about the field. Recent topics ing the two days preceding the 1987 spring AMS are Mathematical aspects of physiology (1980),

84 Fluid dynamical problems in astrophysics and geophysics (1981), Applications of group theory in Call for Topics for physics and mathematical physics (1982), Large­ 1987 AMS Short Course Series scale computations in fluid mechanics (1983), Nonlinear systems of partial differential equations The AMS Short Courses consist of a series of introductory survey lectures and discussions in applied mathematics (1984), and Reacting ordinarily extending over a period of one and Flows: Combustion and Chemical Reactors (1985). one-half days immediately prior to the Joint Proceedings are published by the Society as volumes Mathematics Meetings held in January and August in the series Lectures in Applied Mathematics. each year. Each of the courses is devoted Deadline For Suggestions: August 15, 1985 to a specific area of applied mathematics or to areas of mathematics used in the study 1987 Joint AMS-IMS-SIAM Summer of a specific subject or collection of problems Research Conferences in the in one of the physical, biological, or social Mathematical Sciences. sciences. Topics in recent years have been Fair Allocation (January 1985), Environmental These conferences are similar in structure to those and Natural Resource Mathematics (August held at Oberwolfach, and represent diverse areas of 1984), Mathematics of Information Processing mathematical activity, with emphasis on areas cur­ (January 1984), Population Biology (August 1983), rently especially active. Careful attention is paid to and Computer Communications (January 1983). subjects in which there is important interdisciplinary Proceedings are published by the Society as volumes activity at present. Topics for the fourth series of in the series Proceedings of Symposia in Applied one-week conferences, being held in 1985, are Brown­ Mathematics, with the approval of the Editorial Gitler spectra and applications, Applications of Committee. Lie groups in differential geometry, Numerical Deadline for Suggestions: July 1, 1985 for simulations of fluid flow, Multiparameter bifurca­ January 1987 course, and December 1, 1985 for tion theory, Harmonic analysis in Rn, Function August 1987 course. estimates, Applications of mathematical logic to Submit suggestions to: Professor Stefan A. finite combinatorics, Combinatorics and ordered Burr, Chairman, AMS Short Course Subcommittee, sets, Current trends in arithmetical algebraic Department of Computer Sciences, CUNY, City geometry, and Computational number theory. If College, New York, New York 10031. proceedings are published by the Society, they will appear as volumes in the series Contemporary Mathematics. Deadline For Suggestions: August 15, 1985

Quasilinear Degenerate and Nonuniformly Elliptic and Parabolic Equations of Second Order A. V. Ivanov translated by J. R. Schulenberger parabolic equations of nondivergence form. Parts II This monograph is devoted to the study of and Ill are devoted to the construction of a theory questions of solvability of main boundary value of solvability of the main boundary value problems problems for degenerate and nonuniformly elliptic for large classes of quasilinear equations with a and parabolic equations of second order and to the nonnegative characteristic form. Part IV is devoted investigation of differential and certain qualitative to the study of properties of generalized solutions properties of the solutions of such equations. The of quasilinear, weakly degenerate parabolic study of various questions of variational calculus. equations. differential geometry. and the mechanics of Proceedings of the Steklov Institute continuous media leads to quasilinear degenerate Number 160, xii + 292 pages (softcover) 1980 Mathematics Subject Classifications: or nonuniformly elliptic and parabolic equations. 35J65, 35J70, 35K60, 35K65, 35005 The monograph consists of four parts. In Part I ISBN 0-8218-3080-5; LC 84-12386 the principal object of investigation is the question Publication date: September 1984 List price $75, institutional member $60, of classical solvability of the first boundary value individual member $45 problem for quasilinear, nonuniformly elliptic and To order, please specify STEKLO /160N Shipping/Handling: 1st book $2, each add'l $1, max. $25; by air, 1st book $5, each add'l $3, max. $100 Prepayment is required. Order from American Mathematical Society, P.O. Box 1571, Annex Station, Providence, Rl 02901-1571, or call toll free 800-556-7774 to charge with Visa or MasterCard.

85 K.P.S. Bhaskara Rao and Rae Michael Shortt, Invited Speakers Borel structures and classical measure theory and Special Sessions Mark A. Ronan and Stephen D. Smith, Groups and geometries Invited Speakers at AMS Meetings April 1985 Meeting in Tucson The individuals listed below have accepted invita­ Far Western Section tions to address the Society at the times and places Deadline for organizers: Expired indicated. For some meetings, the list of speakers is Deadline for consideration: January 4 incomplete. Ross Beaumont, Abelian group theory Daniel J. Madden, The arithmetic of algebraic Chicago, March 1985 function fields of one variable Graham Higman J. Marshall Osborn Albrecht Frohlich, Galois module structure of Michael Marcus Roger Penrose algebraic number fields Alan C. Newell, New ideas in nonlinear science Tucson, April 1985 April1985 Meeting in Worcester George M. Bergman Gregory Brumfiel Eastern Section Worcester, April 1985 Deadline for organizers: Expired William Abikoff Robert W. Thomason Deadline for consideration: January 7 William Abikoff and Irwin Kra, Geometric Ira M. Gessel Stephen S.-T. Yau function theory Mobile, May 1985 Thomas E. Cecil and Stephen S.-T. Yau, Differential geometry of submanifolds Fred Cohen John Gilbert Thomas E. Cecil and Stephen S.-T. Yau, Sin- Dennis deTurck Jeffery Lagarias gularities and complex geometry Laramie, August 1985 Ira M. Gessel, Enumerative combinatorics Stuart S. Antman Ronald J. Stern Benoit B. Mandelbrot, Fractal geometry Robert W. Thomason, Methods of K-theory Richard E. Block Jerrold Tunnell Robert L. Bryant Karen K. Uhlenbeck May 1985 Meeting in Mobile David B. MacQueen (Colloquium Lecturer) Southeastern Section David E. Rohrlich Lai-Sang Young Deadline for organizers: Expired Dennis Stanton Deadline for consideration: January 9 Thomas Brylawski, Combinatorics and graph Amherst, October 1985 theory Vaughan F. R. Jones Ngaiming Mok Dennis deTurck, Nonlinear problems in geometry Andre Joyal Robert T. Seeley Ray Kunze, Analysis on homogeneous spaces Jeffery Lagarias, Number theory and its applica- Columbia, November 1985 tions Eric Friedlander M. Talagrand Joseph Neisendorfer, Algebraic topology Carlos Kenig Susan Williams and Bruce Kitchens, Symbolic dynamics and ergodic theory Organizers and Topics August 1985 Meeting in Laramie of Special Sessions Associate Secretary: Robert M. Fossum The list below contains all the information about Deadline for organizers: February 15, 1985 Special Sessions at meetings of the Society available Deadline for consideration: To be announced at the time this issue of the Notices went to the Fall1985 Meeting in Amherst printer. The section below entitled Information for Eastern Section Organizers describes the timetable for announcing Deadline for organizers: April15, 1985 the existence of Special Sessions. Deadline for consideration: To be announced March 1985 Meeting in Chicago Fall 1985 Meeting in Columbia Central Section Central Section Deadline for organizers: Expired Deadline for organizers: April15, 1985 Deadline for consideration: January 2 Deadline for consideration: To be announced Joseph Brennan, Plethysms Fall1985 Meeting T. A. Burton, Periodic and almost periodic Far Western Section solutions of differential equations Deadline for organizers: April15, 1985 Thomas L. Drucker, History of logic Deadline for consideration: To be announced Henri Gillet, K-theory Fall1985 Meeting Wolfgang Maass, Mathematical computer science Southeastern Section Philip Protter, Stochastic analysis and related Deadline for organizers: April15, 1985 topics Deadline for consideration: To be announced

86 January 1986 Meeting in New Orleans Information for Speakers Associate Secretary: Frank T. Birtel A great many of the papers presented in Special Deadline for organizers: April15, 1985 Sessions at meetings of the Society are invited papers, Deadline for consideration: To be announced but any member of the Society who wishes to do so may submit an abstract for consideration for Information for Organizers presentation in a Special Session, provided it is received in Providence prior to the special early Special Sessions at Annual and Summer meetings deadline announced above and in the announcements are held under the general supervision of the Program of the meeting at which the Special Session has been Committee. They are administered by the Associate scheduled. Secretary in charge of the meeting with staff assistance Abstracts of papers submitted for consideration for from the Society office in Providence. presentation at a Special Session must be received Some Special Sessions arise from an invitation to by the Providence office (Editorial Department, a proposed organizer issued through the Associate American Mathematical Society, Post Office Box Secretary. Others are spontaneously proposed by 6248, Providence, Rl 02940) by the special deadline interested organizers or participants. Such proposals for Special Sessions, which is usually three weeks are welcomed by the Associate Secretaries. earlier than the deadline for contributed papers for The number of Special Sessions at a Summer or the same meeting. The Council has decreed that no Annual Meeting is limited to twelve. Proposals, paper, whether invited or contributed, may be listed invited or offered, which are received at least in the program of a meeting of the Society unless an nine months prior to the meeting are screened for abstract of the paper has been received in Providence suitability of the topic and of the proposed list prior to the deadline. of speakers, and for pos§ible overlap or conflict with other proposals (specific deadlines for requesting Send Proposals for Special Sessions to the approval for Special Sessions at national meetings are Associate Secretaries given above). If necessary, the numerical limitation is enforced. The programs of sectional meetings are arranged by Proposals for Special Sessions should be submitted the Associate Secretary for the section in question: directly to the Associate Secretary in charge of the Far Western Section (Pacific and Mountain) meeting (at the address given in the accompanying Hugo Rossi, Associate Secretary box). If such proposals are sent to the Providence Department of Mathematics office, addressed to the Notices, or directed to anyone University of Utah other than the Associate Secretary, they will have Salt Lake City, UT 84112 to be forwarded and may not be received before the (Telephone 801-581-8159) quota is filled. Central Section In accordance with an action of the Executive Robert M. Fossum, Associate Secretary Committee of the Council, no Special Session may Department of Mathematics be arranged so late that it may not be announced in University of lllinois the Notices early enough to allow any member of the 1409 West Green Street Society, who wishes to do so, to submit an abstract for Urbana, IL 61801 (Telephone 217-333-3975) consideration for presentation in the Special Session before the deadline for such consideration. Eastern Section Special Sessions are effective at Sectional Meetings W. Wistar Comfort, Associate Secretary and can usually be accommodated. They are arranged Department of Mathematics Wesleyan University by the Associate Secretary under the supervision of Middletown, CT 06457 the Committee to Select Hour Speakers for the (Telephone 203-347-9411) section. The limitation on the number of sessions depends on the space and time available. The same Southeastern Section restriction as for national meetings applies to the Frank T. Birtel, Associate Secretary deadline for announcing Special Sessions at sectional Department of Mathematics Tulane University meetings: no Special Session may be approved too New Orleans, LA 70118 late for its announcement to appear in time to (Telephone 504-865-5646) allow a reasonable interval for members to prepare As a general rule, members who anticipate organizing and submit their abstracts prior to the special early Special Sessions at AMS meetings are advised to seek deadline set for consideration of papers for Special approval at least nine months prior to the scheduled date Sessions. of the meeting. No Special Sessions can be approved The Society reserves the right of first refusal too late to provide adequate advance notice to members for the publication of proceedings of any special who wish to participate. session. These proceedings appear in the book series Contemporary Mathematics.

87 Joint Summer Research Conferences in the Mathematical Sciences Humboldt State University, Arcata, California, June 23 to August 31, 1985

The 1985 Joint Summer Research Conferences in these conferences are limited and so individuals who the Mathematical Sciences will be held at Humboldt can obtain support from other sources should do so. State University, Arcata, California, between June 23 The Joint Summer Research Conferences in the and August 31, 1985. It is anticipated that the series Mathematical Sciences are under the direction of of week-long conferences will be supported by a grant the AMS-IMS-SIAM Committee on Joint Summer from the National Science Foundation. Research Conferences in the Mathematical Sciences There will be ten one-week conferences in ten which includes: Ronald L. Graham, Benedict H. different areas of mathematics. Each week par­ Gross, Malcolm R. Leadbetter, Angus J. Macintyre, ticipants will arrive on Sunday and leave the following Jerrold E. Marsden, John R. Martin, James McKenna, Saturday. Lectures will begin on Monday morning Tilla Klotz Milnor, Evelyn Nelson, Katsumi Nomizu, and end Friday afternoon. The topics and organizers and R. 0. Wells, Jr. (chairman). for the ten conferences were selected by the AMS­ Descriptions of the subject matter of each of the IMS-SIAM Commmittee on Joint Summer Research 1985 Conferences appeared in the October Notices, Conferences in the Mathematical Sciences. The pages 686 to 688; they were accompanied by lists of selections were based on suggestions made by the members of the respective organizing committees. members of the committee and others. The committee considered it important that the conferences represent June 23 to June 29 diverse areas of mathematical activity, with emphasis Brown-Gitler spectra and applications on areas currently especially active, and paid careful R. JAMES MILGRAM (Stanford University), Chair­ attention to subjects in which there is important man interdisciplinary activity at present. The conferences will be similiar in structure to June 30 to July 6 those held throughout the year at Oberwolfach. These Applications of Lie groups in differential geometry conferences are intended to complement the Society's WoLFGANG ZILLER (University of Pennsylvania), program of annual Summer Institutes and Summer Chairman Seminars, which have a larger attendance and are July 7 to July 13 substantially broader in scope. The conferences are Numerical simulations of fluid flow research conferences, and are not intended to provide GREGORY BAKER (University of Arizona), Chair­ an entree to a field in which a participant has not man already worked. It is expected that funding will be available for July 14 to July 20 a limited number of participants in each conference. Multiparameter bifurcation theory Others, in addition to those funded, will be welcome, MARTIN GOLUBITSKY (University of Houston), Co­ within the limitations of the facilities of the campus. Chairman Up to about 100 participants can be accommodated JOHN M. GucKENHEIMER (University of Califor­ at each conference. Housing accommodations will nia, Santa Cruz), Co-Chairman be available on campus for those attending the conferences, and daily meals will be served in the July 21 to July 27 Jolly Giant Conference Center near the dormitories. Harmonic analysis in Rn A brochure describing the facilities available at ELIAS M. STEIN (Princeton University), Chairman Humboldt State University will be available from the AMS office in March 1985. The brochure will include July 28 to August 3 information on firm room rates, the residence and Jilunction estimates dining hall facilities, as well as local information (University of California, and a reservation form to be used for requesting San Diego), Chairman accommodations on campus. Each participant will pay a registration fee and a social fee to cover the August 4 to August 10 cost of refreshments served at breaks and for social Applications of mathematical logic to finite combinatorics events. STEPHEN G. SIMPSON (Pennsylvania State Univer­ Those interested in attending one of the conferences sity), Chairman should request an application form from Carole August 11 to August 17 Kohanski, Summer Research Conference Coordinator, Combinatorics and ordered sets American Mathematical Society, Post Office Box IVAN RIVAL (University of Calgary), Chairman 6248, Providence, RI 02940 (401-272-9500, extension 286), specifying which conference they wish to August 18 to August 24 attend. Selection of the participants and approval of Current trends in arithmetical algebraic geometry participant support will be made by the Organizing KENNETH A. RIBET (University of California, Committee for each conference. Women and members Berkeley), Chairman of minority groups are encouraged to apply and to participate in these conferences. The deadline for August 25 to August 31 receipt of applications is January 27, 1985. Those who Computational number theory wish to apply for a grant-in-aid should so indicate ANDREW M. 0DLYZKO (AT&T Bell Laboratories), on the application form; however, funds available for Chairman

88 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), deadlines for abstracts or contributed papers, and source of further information. Meetings held outside the North American area may carry more detailed information. All communications on special meetings should be sent to the Editor of the Notices, care of the American Mathematical Society in Providence. DEADLINES for entries in this section are listed on the inside front cover of each issue. In order to allow participants to arrange their travel plans, organizers of meetings are urged to submit information for these listings early enough to allow them to appear in more than one issue of the Notices prior to the meeting in question. To achieve this, listings should be received in Providence SIX MONTHS prior to the scheduled date of the meeting.

October 7, 1984--December 14, 1985. Mathematisches JANUARY 1985 Forschungsinstitut Oberwolfach (Weekly Conferences), 7-9. Scientific Computing and Mathematical Modelling, Federal Republic of Germany. (October 1984, p. 689) Stockholm, Sweden. Information: Swedish Institute of Applied Mathematics, 1985. European Mechanics Colloquia, Various locations. Gustaf Soderlind, P. 0. Box 56073, S-102 42 Stockholm, (October 1984, p. 690) Sweden. August 21, 1984-May 20, 1985. Special Year in Logie, 7-11. NSF-CBMS Regional Conference on Multivariate University of Illinois, Urbana, lllinois. (August 1984, Estimation, University of Florida, Gainesville, Florida. p. 521) (June 1984, p. 398) 9-19. Workshop on Three-Manifolds, Berkeley, California. September 1, 1984--August 31, 1985. Program on (August 1984, p. 524) Continuum Physics and Partial Differential Equations, 10-19. Conference on Solitons and Coherent Structures, Institute for Mathematics and its Applications, University The Institute for Theoretical Physics, University of of Minnesota, Minneapolis, Minnesota. (August 1984, California, Santa Barbara, California. (August 1984, p. 521) p. 524) 1984--1985. Special Year Devoted to Minimal Surfaces 12-13. Association for Symbolic Logie Annual Meeting, and their Applications to Low-Dimensional Topology, Anaheim, California. (November 1984, p. 800) Department of Mathematics, University of California, 14-February 1. Twenty-fifth Summer Research Institute Santa Barbara, California. (October 1984, p. 690) of the Australian Mathematical Society, Auckland, New Zealand. (October 1984, p. 691) 1984--1985. Academic Year Devoted to Nonlinear 21-24. SEG-SIAM-SPE Conference on Mathematical and Dift'erential Equations, The Mittag-Leffier Institute, Computational Methods in Seismic Exploration and Djursholm, Sweden. (February 1984, p. 194) Reservoir Modeling, Houston, Texas. (August 1984, p. 524) 1984-1985. Special Year Devoted to Reacting Flows: 21-25. Workshop on Liquid Crystals and Liquid Crystal Combustion and Chemical Reactors, Center for Applied Polymers, University of Minnesota, Minneapolis, Min­ Mathematics, Cornell University, Ithaca, New York. (April nesota. (November 1984, p. 801) 1984, p. 333) 28-30. Meeting of Industrial Statisticians, Marseille­ Luminy, France. Spring 1985. Special Semester in the Theory of Sin­ Information: C. Deniau, Journees Statistique-Industrie, gularities, Banach Center, Warsaw, Poland. (August 1984, CIRM, Case 916, 70, Route Leon Lachamp, 13288 p. 521) Marseille Cedex 09.

1985-1986. Academic Year Devoted to Nonlinear FEBRUARY 1985 Ditrerential Equations, Mittag-Leffier Institute, Djursholm, 3-7. i985 Applied Mathematics Conference, Australian Sweden. Maritime College, Launceston, Tasmania. (October 1984, Program: The program tentatively includes variational p. 692) and optimization problems and the study of nonlinear 11-15. Sixteenth Southeastem Intemational Conference systems such as harmonic maps, minimal surfaces and on Combinatories, Graph Theory and Computing, Florida the equations of elasticity. Atlantic University, Boca Raton, Florida. (October 1984, Deadline for Application: April 1, 1985. Limited funds are p. 692) available for grants. 18-21. Conference on Mathematical Analysis and its Information: Lars Hormander, Institut Mittag-Leffier, The Applications, Kuwait University, Kuwait. (August 1984, Royal Swedish Academy of Sciences, Auraviigen 17, 182 p. 524) 62 Djursholm, Sweden; or Luis A. Caffarelli, Department 28-March 1. Reasoning and Higher Education: A Multidis­ of Mathematics, University of Chicago, Chicago, lllinois ciplinary Experiential Conference, Boise, Idaho. (November 60637. 1984, p. 801)

89 MARCH 1985 12-13. Workshop on Numerical Fluid Dynamics, Georgia Institute of Technology, Atlanta, Georgia. (October 1984, 11-15. Symposium on the Occasion of the Proof of p. 692) the Bieberbach Conjecture, Purdue University, West 17-19. Symposium on Complexity of Approximately Lafayette, Indiana. Solved Problems, Columbia University, New York, New Program: The conference will consider the recent solution York. (August 1984, p. 524) of the Bieberbach conjecture, and future perspectives in classical analysis and geometric function theory. Several 18-20. Applications of Harmonic Measure: Annual Lec­ addresses will be given. ture Series in the Mathematical Sciences, Fayetteville, Arkansas. (November 1984, p. 801) Invited Participants: A. L. Ahlfors, E. Bombieri, L. de Branges, P. R. Garabedian, W. K. Hayman, Ch. 25-26. Sixteenth Annual Pittsburgh Conference on Pommerenke, and M. Schiffer. Modeling and Simulation, University of Pittsburgh, Support: It is hoped that support can be provided to most Pittsburgh, Pennsylvania. (October 1984, p. 692) participants. 25-27. Geometric Topology ·Conference Honoring the Deadline: January 25, 1985. Sixty-fifth Birthday of Professor C. E. Burgess, Brigham Information: D. Drasin, Department of Mathematics, Young University, Provo, Utah. (November 1984, p. 801) Purdue University, West Lafayette, Indiana 47907. 26-27. Association for Symbolic Logic Spring Meeting, 18-22. Short Course on Numerical Methods for Partial Palmer House, Chicago, Illinois. (November 1984, p. 801) Differential Equations, University of Tennessee Space 29-May 2. Second SIAM Conference on Applied Linear Institute, Tullahoma, Tennessee. (October 1984, p. 692) Algebra, Mission Valley Inn, Raleigh, North Carolina. 18-22. NSF-CBMS Regional Conference on Mathematical Sponsor: SIAM Activity Group on Linear Algebra. Ecology, University of California, Davis, California. Program: The conference will focus on recent developments (October 1984, p. 692) in linear algebra with respect to their applications and 20-22. GI-Fachtagung "Datenbanksysteme in Biiro, Tech­ some of the needs of the future. The following specific nik und Wissenschaft", Karlsruhe, Federal Republic of themes will be highlighted: numerical methods in linear Germany. (October 1984, p. 692) algebra; parallelism in linear algebra; matrix methods in partial differential equations; perturbation theory 22-24. Conference on Automorphic Forms and L­ of operators; matrix polynomials; exact computations; Functions, Purdue University, West Lafayette, Indiana. applications of linear algebra in discrete mathematics (October 1984, p. 692) and statistics, engineering, control and systems theory, 25-29. Conference on Chaotic Dynamics, Georgia Institute cryptography, coding theory, population biology. of Technology, Atlanta, Georgia. (October 1984, p. 692) Speakers: J. H. Wilkinson (National Physical Laboratory, ), I. Olkin (Stanford University), R. 25-29. Everett Pitcher Lecture Series, Lehigh University, Voigt (NASA Langley Research Center), C. Davis Bethlehem, Pennsylvania. (University of Toronto), P. Lancaster (University of Program: Jiirgen K. Moser (Eidgenossische Technische Calgary), J. Cohen (Rockefeller University), R. W. Hochschule Zurich) will deliver the 1984-1985 lectures; Brockett (Harvard University), S. V. Parter (University the general topic will be the stability of hamiltonian of Wisconsin), R. L. Graham (AT&T Bell Laboratories), systems. W. M. Kahan (Stanford University), 0. T. Todd Information: Department of Mathematics, Christmas­ (California Institute of Technology). Saucon Hall 14, Lehigh University, Bethlehem, Pennsyl­ Minisymposia Organizers: A. Erisman (Boeing Computer vania 18015. Services), B. D. Saunders (Rensselaer Polytechnic 26-28. M. C. Escher: An Interdisciplinary Congress, Institute). University of Rome, Rome, Italy. (August 1984, p. 524) Registration: Advance registration material will be available in February 1985. 27-29. Conference on Information Sciences and Systems, Information: Conference Coordinator, SIAM, 117 South The Johns Hopkins University, Baltimore, Maryland. 17th 'Street, Suite 1405, Philadelphia, Pennsylvania (October 1984, p. 692) 19103, 215-564-2929. 28-31. Sixteenth Annual Iranian Mathematics Conference, Zahedan, Iran. (October 1984, p. 692) MAY 1985

APRIL 1985 1-3. Alaska Statistics Conference, Juneau, Alaska. (August 1984, p. 524) 1-3. EUROCAL '85: European Conference on Computer 2-4. John H. Barrett Memorial Lectures, University of Algebra {Symbolic and Algebraic Computation), Linz, Tennessee, Knoxville, Tennessee. Austria. (October 1984, p. 692) Program: Lectures will be given by Richard K. Miller (Iowa 8-13. Third Easter Conference on Model Theory, Berlin, State University). In addition there will be sessions for German Democratic Republic. (November 1984, p. 801) contributed papers. Information: Don Hinton or Suzanne Lenhart, Department 8-19. International Seminar on Algebraic and Topological of Mathematics, University of Tennessee, Knoxville, Graph Theory, Dubrovnik, Yugoslavia. (November 1984, Tennessee 37996-1300. p. 801) 3-4. )mnual Regional Meeting on Group Theory, Univer­ 12-13. lllinois Number Theory Conference, Illinois State sity of Pittsburgh, Pittsburgh, Pennsylvania. University, Normal, Illinois. Information: W. E. Deskins, Department of Mathematics Program: David Masser and will each give and Statistics, University of Pittsburgh, Pittsburgh, two 1-hour talks. There will also be 20-minute talks on Pennsylvania 15260. current or proposed research, and informal discussions. Call for papers: Title and a one- or two-sentence abstract 5-11. Third International Conference on Complex Analysis Bulgaria. (November 1984, p. 802) should be sent to the address below by March 25, 1985. and Applications, Varna, Information: Lawrence C. Eggan, Applied Computer 6-8. Seventeenth Annual ACM Symposium on Theory Science Department, Illinois State University, Normal, of Computing, Providence, Rhode Island. (October 1984, Illinois 61761. p. 692)

90 13-17. Australasian Mathematics Convention, University 3-7. Program Design and Pascal, Salisbury State College, of New South Wales, Kensington, Australia. Salisbury, Maryland. Program: All areas of mathematics will be represented. Principal Lecturer: William J. Collins, Salisbury State Invited Speakers: G. Baker, M. Barber, D. Bertrand, D. College. Boyd, D. Brownawell, V. Dlab, B. Dwok, J. Ford, A. Sponsor: MD-DC-VA Section of the MAA. Gleason, U. Haagerub, R. Hersh, H. Hubbert, V. Jones, Purpose: To give college teachers an opportunity to learn R. Leadbetter, M. Longuet Higgens, W. Luxemburg, A. an algorithm approach to problem-solving for practical Mees, H. Pollak, T. Rockafellar, W. Schmidt, K. Shah, use in the classroom. A. Sinclair, T. Speed, R. Tijdeman, G. Weiss. Information: B. A. Fusaro, Department of Mathematical Deadline for Papers: April 15, 1985. Sciences, Salisbury State College, Salisbury, Maryland Information: J. F. Price, School of Mathematics, University 21801; 301-543-6470. of New South Wales, P.O. Box 1, Kensington, N.S.W. 2033, Australia. 5-8. International Conference on Computational Geometry and Computer Aided Design, New Orleans, Louisiana. 16-17. European Conferenee on 'lEX For Scientific Topics: The mathematical aspects of computational Documentation, Varenna, Italy. (November 1984, p. 802) geometry including spline curves and surfaces, Bezier 16-21. Workshop on Differential Geometry, Berkeley, and B-spline approaches, surface patch procedures, California. (August 1984, p. 524) blending methods and underlying geometric principles, splines under tension, rational approximations, varia­ 17-19. Conferenee on the History and Philosophy of tional geometry, contouring, intrinsic curve definitions, Modem Mathematics, Minneapolis, Minnesota. (November and newer approaches to surfaces. 1984, p. 802) Invited Speakers: Robert A. Barnhill (University of 20-23. International Conferenee on Theory and Applica­ Utah), Wolfgang Boehm (Technische Universitat tions of Dilferential Equations, Pan American University, Braunschweig), James D. Emery (Bendix Corporation), Edinburg, Texas. Michael J. Pratt (Cranfield Institute of Technology), Program: The conference will feature survey lectures and Malcolm Sabin (Cambridge University). talks on topics of current interest by invited speakers Sponsors: The National Aeronautics and Space Administra­ from the United States and abroad. A balance between tion, Langley Research Center; the University of theory and applications will be maintained. There Southern Mississippi. will be sessions for contributed papers and a session Deadline for Abstracts: Persons interested in presenting a to discuss open problems and new directions. This 20-minute talk should submit five copies of an extended conference will stress the following areas: ordinary abstract (not to exceed three pages) by January 31, differential equations in the real and complex domain, 1985. functional differential equations, partial differential Information: Temple Fay, Conference Organizer, Depart­ equations, numerical methods, and applications. ment of Mathematics, S. S. Box 5045, University of Organizing Committee: Joseph Wiener, Chairman (Pan Southern Mississippi, Hattiesburg, Mississippi 39406. American University); Reza Aftabizadeh (Pan American University); K. L. Cooke (Pomona College); C. 5-14. Conferenee on Geometry and Operator Algebras, Corduneanu (University of Texas, Arlington); S. M. Berkeley, California. (August 1984, p. 525) Shah (University of Kentucky). 10-14. Computer Solutions to Differential Equations, Information and Abstracts: Reza Aftabizadeh or Joseph Salisbury State College, Salisbury, Maryland. Wiener, Department of Mathematics and Computer Principal Lecturer: Herbert S. Wilf (University of Pennsyl­ Science, Pan American University, Edinburg, Texas vania). 78539. Sponsor: MD-DC-VA Section of the MAA. 20-24. Fifth Annual Conferenee on Evolution, Games and Purpose: To give college teachers an opportunity to learn Leaming: Models for Adaptation in Machines and Nature, computational mathematics for practical use in the Los Alamos, New Mexico. (November 1984, p. 802) classroom. 20-24. Pacific Statistical Congress, Auckland, New Information: B. A. Fusaro, Department of Mathematical Zealand. Sciences, Salisbury State College, Salisbury, Maryland 21801, 301-543-6470. Information: The Committee Secretary, Pacific Statistical Congress, Department of Mathematics, University of 10-14. Third Intemational Conferenee on Combinatorial Otago, P. 0. Box 56, Dunedin, New Zealand. Mathematics, New York, New York. (November 1984, p. 802) 23-June 1. Workshop on Four-Manifolds and Geometry, Berkeley, California. (August 1984, p. 524) 10-14. Seventh International Symposium on the Mathe­ matical Theory of Networks and Systems, Royal Institute 26-June 2. lntemational Conferenee on Functional­ of Technology, Stockholm, Sweden. (October 1984, p. 693) Differential Systems and Related Topics IV, Jachranka, Poland. (August 1984, p. 524) 10-15. Conferenee on Topology, National University of Singapore. (November 1984, p. 802) 28-June 1. Colloque de Combinatoire Enumerative, Montreal, Quebec, Canada. (October 1984, p. 693) 19-21. Fourth International Conference on the Numerical Analysis of Semiconductor Deviees and Integrated Circuits, Dublin, Ireland. (June 1984, p. 398) JUNE 1985 20-July 5. Third Workshop on Nonlinear Evolution 3-7. CIT-CNNAA Joint Dilferential Equations Seminar, Equations and Dynamical Systems, Leece, Italy. (October Taiwan, Republic of China. 1984, p. 693) Topics: Analytical and numerical aspects of differential 24-26. SIAM 1985 Spring Meeting, Pittsburgh Hyatt equations. House, Pittsburgh, Pennsylvania. Invited Speakers: Paul Garabedian, , Paul Program: Invited presentations, minisymposia, contributed Rabinowitz, Daniel Strook, and S. S. Yau. papers and poster presentations will feature the fol­ Support: Possible local support for United States scientists. lowing topics: robotics, including geometric modeling; Information and Abstracts: Tai-Ping Liu, Department of supercomputers/supercomputing, including architecture Mathematics, University of Maryland, College Park, and algorithms; numerical methods in control; applica­ Maryland 20742. tions of finite element methods in fluid dynamics and

91 material science, including composite materials; varia­ 22-25. SLU-GTE Conference on Sequence Spaces, St. tional methods in engineering and science; optimal Lawrence University, Canton, New York. design of large systems; numerical methods in non­ Program: Invited addresses and contributed papers. linear algebra systems; pattern selection in the physical Principal Speakers: G. Bennett (Indiana University), sciences; nonlinear reaction-diffusion systems. A. Jakimovski (Tel Aviv, Israel), A. Peyerimhoff Speakers: C. M. Dafermos (Brown University), J. Smoller (Universitiit Ulm, West Germany), W. Ruckle (Clemson (University of Michigan), S. A. Orszag (Princeton University), D. Russell (York University, Canada), University), P. A. Raviart (University of Paris), D. Berg D. Snyder (Lehigh University), A. Wilansky (Lehigh (Rensselaer Polytechnic Institute), R. Reddy (Carnegie­ University), K. Zeller (Mathematisches Institut der Mellon University), W. G. Strang (Massachusetts Universitat, West Germany). Institute of Technology), H. F. Weinberger (University Deadline for Abstracts: April 1, 1985. of Minnesota). Information and Abstracts: J. DeFranza or D. J. Fleming, MiniBymposia Organizers: C. Irwin (West Virginia Univer- Mathematics Department, St. Lawrence University, sity), T. Hallam (University of Tennessee). Canton, New York 13617, 315-379-5227. Deadline for Abstracts: February 14, 1985. 22-26. Tenth British Combinatorial Conference, Glasgow, Deadline for Minisymposia Proposals: January 15, 1985. , United Kingdom. (October 1984, p. 693) Information: Society for Industrial and Applied Mathe- 27-August 10. Groups-St. Andrews 1985, St. Andrews, matics, 117 South 17th Street, Suite 1405, Philadelphia, Scotland. Pennsylvania 19103, 215-564-2929. Sponsors: The Mathematical Society; the London Mathematical Society. 24-28. Aspects of Positivity in Functional Analysis, Program: During the first week a course of lectures Institut der Universitat Tiibingen, Federal Mathematisches will be given by the following speakers: S. Bachmuth of Germany. (August 1984, p. 525) Republic (California), G. Baumslag (New York), P.M. Neumann (Oxford), J. E. Roseblade (Cambridge) and J. Tits (Paris). The second week will consist of seminars and JULY 1985 invited lectures by other conference participants. Information and Applications: C. M. Campbell and E. F. 1-5. International Conference on Classical and Categorical Robertson, Mathematical Institute, University of St. Algebra, University of Natal, Durban, Republic of South Andrews, North Haugh, St. Andrews, KY16 9SS, Fife, Africa. (October 1984, p. 693) Scotland. 1-6. First International Fuooy Systems Association Con­ 28-August 10. Conference on Banach Spaces and Classical gress, Palma de Mallorca, Balearic Islands, Spain. (October Analysis, Kent State University, Kent, Ohio. (November 1984, p. 693) 1984, p. 802) 29-August 16. NATO Advanced Study Institute: Non­ 2-6. Fifteenth Conference on Stochastic Processes and linear Dynamical Systems; Integrability and Qualitative their Applications, Nagoya, Japan. (October 1984, p. 693) Behavior, Universite de Montreal, Montreal, Canada. 5-6. International Colloquium on Applications of Mathe­ Sponsors/Support: NATO Advanced Study Institutes Pro- matics, Hamburg, Federal Republic of Germany. (October gramme, Ministry of Education of Quebec, Natural 1984, p. 693) Sciences and Engineering Research Council of Canada, Universite de Montreal, National Science Foundation. 7-13. Logie Colloquium 85: European Summer Meeting of Topics: Inverse spectral transforms and solitons; differential the Association for Symbolic Logie, University of Paris XI, geometric, group theoretical and Lie algebraic methods, Orsay, France. (October 1984, p. 693) infinite dimensional Lie algebras, chaos and integrability; applications of algebraic geometry. 8-20. Conference on Logie, Language and Computation, Principal Speakers: M. J. Ablowitz (Clarkson), F. Calogero University, Stanford, California. (November 1984, Stanford (Rome), M. Flato (Dijon), J. Hamad (Advanced Study p. 802) Institute), N. Hitchin (Oxford), V. Kac (MIT), B. 9-12. Fourth International Conference on Numerical Kostant (MIT), M. b. Kruskal (Princeton), J. E. Methods in Laminar and Turbulent Flow, Swansea, United Marsden (Berkeley), A. C. Newell (Arizona), T. S. Kingdom. Ratiu (Arizona), S. Shnider (McGill), P. van Moerbeke (Louvain), P. Winternitz (Montreal). Information: C. Taylor, Department of Civil Engineering, University College, Swansea, SA2 8PP, United Kingdom. Information: G. David, Departement de mathematiques et de statistique, Universite de Montreal, C. P. 6128, 15-18. SIAM Conference on Mathematics of CAD/CAM, Montreal H3C 3J7, Canada. Rensselaer Polytechnic Institute, Troy, New York. 31-August 8. Symposium on the Transmission of Mathe­ Information: Society for Industrial and Applied Mathe- matical Science, Berkeley, California. (June 1984, p. 398) matics, 117 South 17th Street, Suite 1405, Philadelphia, Pennsylvania 19103, 215-564-2929. AUGUST 1985 15-18. Numerical Methods in Thermal Problems, Swansea, and Near-fields, Tiibingen, United Kingdom. 4--10. Conference on Near-rings Federal Republic of Germany. Information: R. W. Lewis, Department of Civil Engineer­ Information: Gerhard Betsch, Mathematisches Institut der ing, University College, Swansea, SA2 8PP, United Universitat, D-7400 Tiibingen 1, Federal Republic of Kingdom. Germany. 15-19. Conference on Algorithms for the Approximation 5-9. Second Seminar on Random Graphs and Probabilistic of Function and Data, Shrivenham, United Kingdom. Methods in Combinatoric•, Poznan, Poland. (October Information: Institute of Mathematics and its Applications, 1984, p. 694) Maitland House, Warrior Square, Southend-on-Sea, 5-16. Georgia Topology Conference, University of Georgia, Essex, SS1 2JY, United Kingdom. Athens, Georgia. (October 1984, p. 694) 16-19. Second International Conference on the Teaching 12-16. Workshop/Conference on Hydroeodes and Other of Mathematical Modelling, University of Exeter, Exeter, Codes on Parallel Processors, Michigan Technological England. (August 1984, p. 525) University, Houghton, Michigan. (October 1984, p. 694)

92 16-23. International Conferenee on Radieals; Theory and OCTOBER 1985 Applications, KremsfDonau, Austria. Information: Rainer Mlitz, Institut fiir Angewandte und 22-24. Seventeenth National SAMPE Teehnical Con­ Numerische Mathematik, TU Wien, A-1040 Wien, ferenee, Kiamesha Lake, New York. (October 1984, p. 694) Gu:6hausstra.f.le 27-29, Austria. 28-30. SIAM 1985 Fall Meeting, Arizona State University, 26-30. Colloquium on Ordered Sets, Szeged, Hungary. Tempe, Arizona. (November 1984, p. 803) Information: Society for Industrial and Applied Mathe­ matics, 117 South 17th Street, Suite 1405, Philadelphia, 26-31. International Symposium on Operator Theory, Pennsylvania 19103, 215-564-2929. Athens, Greece. Topics: Functional Analysis and Linear Algebra. Invited Speakers: H. Amann, H. Bart, L. Berg, P. Hess, NOVEMBER 1985 H. Konig, T. Laffey, P. Lancaster, H. Peitgen, H. Schneider, C. Stegall, V. Ptak, J. Webb. 18-20. Second SIAM Conferenee on Parallel Proeessing and Scientifle Computing, Omni International Hotel, Norfolk, Deadline for Abstracts: June 10, 1985. Virginia. Information: S. Rokou, Department of Mathematics, National Technical University, Zografou Campus, 157 Information: Society for Industrial and Applied Mathe­ matics, 117 South 17th Street, Suite 1405, Philadelphia, 73 Athens, Greece. Pennsylvania 19103, 215-564-2929. SEPTEMBER 1985 2-12. NATO Advaneed Study Institute: Advanees in ****** Mieroloeal Analysis, ll Ciocco, Castelvecchio-Pascoli, Italy. (August 1984, p. 525) MAY 1986 9-12. International Symposium on Computational Fluid Dynamies, Tokyo, Japan. 18-21. International Symposium on Flood Frequency and Information: Koichi Oshima, Institute of Space and Risk Analyses, Louisiana State University, Baton Rouge, Astronautical Science, 6-1, Komada 4-chome, Meguro­ Louisiana. (October 1984, p. 694) ku, Tokyo 153, Japan. 16-21. Eleventh International Congress of the AUGUST 1986 Osterreiehisehe Mathematisehe Gesellsehaft, Graz, Austria. (October 1984, p. 694) 3-11. International Congress of Mathematicians, Berkeley, California. (February 1984, p. 159) 17-19. Conferenee on Mathematies and Signal Proeessing, University of Bath, United Kingdom. 11-16. Second International Conferenee on Teaehing Statisties, University of Victoria, Victoria, British Colum­ Information: Institute of Mathematics and its Applications, bia, Canada. Maitland House, Warrior Square, Southend-on-Sea, Essex, SS1 2JY, United Kingdom. Sponsors: International Statistical Institute; University of Victoria. 17-19. International Symposium on Numerieal Analysis, Program: The conference will cover the teaching of Madrid, Spain. (August 1984, p. 525) statistics from the school to the university level, as 30-0ctober 5. Fourth International Conferenee on Topol­ well as teaching statistics in government, business ogy and its Applications, Dubrovnik, Yogoslavia. and industry. Key goals include fostering international Organizer: The Union of Mathematicians, Physicists and cooperation among teachers of statistics, and promoting Astronomers of Yugoslavia. The organizing committee the exchange of ideas about teaching materials, methods, consists of Sibe Marde§ic (Chairman), Du§an Adnadevic and content. Opportunities will be provided to see and (Vice-chairman), Mila Mr§evic (Secretary), Joi!e Vrabec, experiment with the latest in computer hardware and Ivan Ivan§ic. software for statistical work. Program: The conference will be divided into five Chairman of Program Committee: Robert V. Hogg sections: general topology, geometric topology, algebraic (University of Iowa). topology, differential topology, and applications. Information: Tom Lietaer, University Extension Conference Deadline for Registration: January 31, 1985. Office, University of Victoria, P. 0. Box 1700, Victoria, Information: M. Mr§evic, Dru§tvo Matematicara SR Srbije, British Columbia, Canada V8W 2Y2. Knez Mihailova 35/N, p.p. 791, 11001 Beograd, Yugoslavia.

93 New AMS Publications

Applications of Group Theory George W. Mackey. Quantum mechanics from in Physics and the point of view of the theory of group representations Mathematical Physics Daniel Siernheimer. Phase-space representations Moshe Flato, Paul Sally and Gregg David A. Vogan, Jr .. Classifying representations Zuckerman, Editors by lowest K -type Joseph A. Wolf. Indefinite harmonic theory and (Lectures in Applied Mathematics. Volume 21) unitary representations The past decade has seen a renewal in the close Gregg J. Zuckerman. Induced representations ties between mathematics and physics. Completely and quantum fields integrable systems. classical and quantum field L. Dolan. Why Kac-Moody subalgebras are theories. in particular. gauge theories. interesting in physics supersymmetry and supergravity. and grand unified I. B. Frenkel. Representations of Kac-Moody theories were developed with the aid of. and. in algebras and dual resonance models turn. brought new developments into. several Bernard Julia. Kac-Moody symmetry of diverse areas of mathematics. The Chicago gravitation and supergravity theories Summer Seminar on Applications of Group Theory J. Lepowsky. Some constructions of the affine Lie in Physics and Mathematical Physics. held in July. algebra APl 1982. was organized to bring together a broad Jacques C. H. Simon. Nonlinear representations spectrum of scientists from theoretical physics. and the affine group of the complex plane mathematical physics. and various branches of 1980 Mathematics Subject Classifications: pure and applied mathematics in order to promote 16A58, 17B65, 20G45, 22-06, 22EXX, and interaction and an exchange of ideas and results in others ISBN 0-8218-1121-5, LC 84-24191 areas of common interest. ISSN 0075-8485 This volume contains the papers submitted by Approx. 430 pages (hardcover), February 1985 speakers at the Seminar. The reader will find List price $70, Institutional member $56, Individual member $42 several groups of articles varying from the most Shipping and handling charges must be added abstract aspects of mathematics to a concrete To order, please specify LAM/21N phenomenological description of some models applicable to particle physics. The papers have Combinatorics and Algebra been divided into four categories corresponding t~ the principal topics covered at the Seminar. This is Curtis Greene, Editor only a rough division. and some papers overlap two (Contemporary Mathematics. Volume 34) or more of these categories. This volume contains the Proceedings of the AMS-NSF Joint Summer Research Conference on Combinatorics and Algebra held at the University Contents of Colorado during June 1983. V. Nambu. Topological excitations in physics Although combinatorial techniques have I. Bars. Supergroups and their representations pervaded the study of algebra throughout its Peter G. 0. Freund. Topics in dimensional history. it is only in recent years that any kind of reduction systematic attempt has been made to understand Mary K. Gaillard. Bound state spectra in the connections between algebra and extended supergravity theories combinatorics. This Conference drew together John H. Schwarz. Mathematical issues in specialists in both algebra and combinatorics. and superstring theory provided an invaluable opportunity for them to P. van Nieuwenhuizen. Gauging of groups and collaborate. supergroups The topic most discussed was representation C. Fronsdal. Semisimple gauge theories and theory of the symmetric group and complex conformal gravity general linear group. The close connections with Roger Howe. Dual pairs in physics: harmonic combinatorics. especially the theory of Young oscillators. photons. electrons. and singletons tableaux. was evident from the pioneering work of A. W. Knapp. Langlands' classification and G. Frobenius. I. Schur. A. Young. H. Weyl. and unitary dual of SU(2.2) D. E. Littlewood. Phil Hanlon gave an introductory

To order use the order form in this issue or call 800-556-7774 to use VISA or MasterCard

94 survey of this subject. whose inclusion in this The basis of this book was a special course volume should make many of the remaining papers given by the author at the Mechanics-Mathematics more accessible to a reader with little background Faculty of Moscow University. The material in representation theory. presumes almost no previous knowledge and is Ten of the papers impinge on representation completely understandable to a reader who is in theory in various ways. Some are directly command of a standard course of mathematical concerned with the groups, Lie algebras. etc .. analysis. themselves. while others deal with purely Contents combinatorial topics which arose from 1. Normal algorithms and enumerable sets representation theory and suggest the possibility of 2. Constructive real numbers a deeper connection between the combinatorics 3. Constructive convergence. Effective and the algebra. uncountability of the constructive continuum The remaining papers are concerned with a wide variety of topics. There are valuable surveys on the 4. The impossibility of certain algorithms classical subject of hyperplane arrangements and connected with constructive real numbers its recently discovered connections with lattice 5. Constructive functions theory and differential forms. and on the surprising 6. Differentiation of constructive functions connections between algebra. topology, and the 7. Riemann integration of constructive functions counting of faces of convex polytopes and related 8. Singular coverings and some of their applications complexes. There also appears an instructive 9. Constructive metric spaces example of the interplay between combinatorial and algebraic properties of finite lattices. and an There are an extensive bibliography and indexes interesting illustration of combinatorial reasoning which will be helpful to students. to prove a fundamental algebraic identity. 1980 Mathematics Subject Classification: In addition. a highly successful problem session 03F50 ISBN 0-8218-4513-6, LC 84-18459 was held during the conference: a list of the ISSN 0065-9282 problems presented appears at the end of the vi + 346 pages (hardcover), December 1984 List price $95, Institutional member $76, volume. Individual member $57 Papers are included by the following: Shipping and handling charges must be added To order, please specify MMON0/60N Eiichi Bannai N. Metropolis Margaret M. Bayer Peter Orlik Louis J. Billera Amitai Regev Fifteen Papers on Functional Anders Bjorner J. Remmel Analysis Gian Carlo Rota Jeffrey B. Remmel (American Mathematical Society Translations. V. M. Chen Louis Solomon Series 2. Volume 124) Paul Edelman Richard P. Stanley A.M. Garsia Dennis Stanton The papers in this book are translated from the Ira M. Gessel Hiroaki Terao Russian. Curtis Greene Michelle Wachs Contents Phil Hanlon Dennis E. White S. D. Sinanyan, On the quasianalyticity generated by the metric of the space Lp 1980 Mathematics Subject Classifications: 05A15, 05A17, 05A19, 20C30, 22E46 I. E. Verbitskii. An estimate of the norm of a ISBN 0-8218-5029-6, LC 84-18608 function in a Hardy space in terms of the norms ISSN 0271-4132 of its real and imaginary parts x + 318 pages (softcover), December 1984 List price $30, Institutional member $24, G. E. Tkebuchava, On unconditional bases in Individual member $18 nonreflexive function spaces Shipping and handling charges must be added To order, please specify CONM/34N L. I. Klenina, Nontriviality of some classes of periodic functions of the type of infinite-order Sobolev spaces Lectures on V. G. Maz'ya and T. 0. Shaposhnikova. Constructive Mathematical Multipliers of Sobolev spaces in a domain V. G. Maz'ya and T. 0. Shaposhnikova. Analysis Multipliers in pairs of spaces of potentials 8. A. Kushner V. G. Maz'ya and T. 0. Shaposhnikova, On (Translations of Mathematical Monographs, sufficient conditions for functions to belong to Volume 60) classes of multipliers

To order use the order form in this issue or call 800-556-7774 to use VISA or MasterCard

95 A. Ya. Khelemskii. Smallest values assumed by SOCIETE MATHEMATIQUE DE FRANCE. the global homological dimension of Banach ASTERISQUE function algebras N. K. Nikol'skii. The present state of the spectral The AMS distributes Asterisque in the U.S .. analysis-synthesis problem. I Canada. and Mexico. Orders from other countries V. A. Zolotarev. On the structure and triangular should be sent to the SMF. B.P. 126-05. 75226 models of systems of a class of commutative Paris Cedex 05. France. or to OFFILIB. 48 rue operators Gay-Lussac. 75240 Paris Cedex 05. France. A. N. Kochubel. On extensions of a Individual members of either AMS or SMF are positive-definite symmetric operator entitled to the member price. F. G. Maksudov and B. P. Allakhverdiev. Multiple expansion in generalized eigenvectors and associated vectors of a class of Cohomologie p-adique operator-valued functions in the presence of a (Asterisque. Volume 119-120) continuous spectrum Ce volume. dedie a B. DWORK. contient A. V. Zafievskii. New classes of semigroups differentes applications des methodes A. S. Fa'inshte'in. Stability of Fredholm complexes cohomologiques p-adiques de Dwork. Les sujets relative to perturbations that of Banach spaces etudies sont: sommes de caracteres sur les corps q-norm are small in finis. action de Frobenius. equations differentielles M. Ya. Antonovskii. Existence and properties of p-adiques. fonctions theta p-adiques. On y trouve the degree of almost strongly Fredholm des contributions de A. Adolphson. F. Baldassarri. mappings P. Berthelot. M. Boyarsky. G. Christo!. 1980 Mathematics Subject Classifications: V. Cristante. J. Fresnel. N. Katz. P. Robba. 30060, 42B30, 46-XX, 47-XX, 58615 ISBN 0-8218-3085-6, LC 84-21678 S. Sperber. ISSN 0065-9290 viii + 184 pages (hardcover), December 1984 List price $60, Institutional member $48, ISSN 0303-1179 Individual member $36 List price $23, Individual member $16 Shipping and handling charges must be added Shipping and handling charges must be added To order, please specify TRANS2/124N To order, please specify AST /119/120N

To order use the order form in this issue or call 800-556-7774 to use VISA or MasterCard

96 Miscellaneous

Personal Items Visiting Mathematicians (Supplementary List) Zbigniew Piotrowski of Auburn University has been appointed to an assistant professorship at Mathematicians visiting other institutions during Youngstown State University. the 1984-1985 academic year have been listed in Gian-Carlo Rota of M.I. T. was awarded a Doctor's recent issues of the Notices: June 1984, pages 403- degree honoris causa by the University of Strasbourg 405; August 1984, pages 536-537; October 1984, on December 10, 1984. pages 708-709; and November 1984, page 806. The list below gives the name and home country, the host Barry Simon of Caltech has been named the IBM institution, period of visit, and field of special interest Professor of Mathematics and Theoretical Physics at of additional visiting mathematicians. the California Institute of Technology. Robert Burton (U.S.A.), University of Giittingen, Ellen Torrance, formerly a freelance consultant, West Germany, September 1984 to June 1985, ergodic is now an Actuary with M&R Services, Inc., the theory, probability, dynamical systems. actuarial data processing affiliate of Milliman and Robertson, consulting actuaries. Rastislav Telgarsky (Poland), Virginia Polytech­ nic Institute and State University, September 1984 to theory. Deaths August 1985, topology and game

Opris Gheorghe of the Polytechnic Institute of Cluj-Napoca, died on September 23, 1984. He was a member of the Society for 3 years. Mark Kac of the University of Southern California, died on October 26, 1984, at the age of 70. He was a member of the Society for 45 years. For more information see the News and Announcements section of this issue of the Notices. K. Nageswara Rao of North Dakota State University, died on August 28, 1984, at the age of 50. Professor Rao was a member of the Society for 18 years.

Applied Cryptology, Cryptographic Protocols, and Computer Security Models Richard A. DeMilio, George I. Davida, David P. Dobkin, Michael A. Harrison, and Richard J. Lipton

"Applied Cryptology, Cryptographic Protocols, and Computer Security Models is an excellent treat­ ment of a subject that has attracted substantial attention in both the technical and popular literature. it is a pleasure to read a book that combines an intuitive feel for its subject with mathematical rigor. The book should have broad appeal. New-comers to the field will appreciate its clear motivation of the material and exposition of the mechanics of the various schemes. Researchers and serious students will be aided by its wide scope that pulls together many topics that are generally dealt with separately, condensed proofs, and rationales for the validity and usefulness of the various approaches taken. It is quite comprehensive, with the exception of the exclusion of work in statistical data bases that have been innoculated with errors to prevent compromise." - David L. Wells Southern Methodist University Proceedings of Symposium in Applied Mathematics, 1983, 204 pages, softcover; List price $23, Institutional member $18, Individual member $14. Order code PSAPM/29N Shipping/Handling: 1st book $2, each add'l $1, max. $25; by air, 1st book $5, each add'l $3, max.~ 1llO Prepayment is required. Order from American Mathematical Society, P.O. Box 1571, Annex Station, Providence, Rl 02901-1571, or call toll free 800-556-7774 to charge with Visa or MasterCard.

97 AMS Reports and Communications

Recent Appointments Speakers for Central Sectional Meetings. Other members of the committee are Eric Bedford (1985), Committee members' terms of office on standing Robert M. Fossum (ex officio), and Bhama Srinivasan committees expire on December 31 of the year (1985). given in parentheses following their names, unless President-Elect Irving Kaplansky has appointed otherwise specified. Clifford J. Earle, Jr., (1986) and Srinivasa S. R. Varadhan (1986) to the Committee to Select Hour Peter J. Weinberger (1987) has been appointed to Speakers for Eastern Sectional Meetings. Floyd the Visiting Committee on Computer Operations L. Williams (1985) has been appointed chairman. and Facilities by Chairman of the Board of Trustees, Continuing members of the committee are W. Wistar Cathleen S. Morawetz. Other members of the Comfort (exoffficio), and George R. Kempf (1985). committee are Lee P. Neuwirth (1985), and S. Tucker Adriano M. Garsia (1986) has been appointed Taft (1986). to the Committee to Select Hour Speakers for Steve Armentrout (1986) has been appointed and Far Western Sectional Meetings by President-Elect Murray Gerstenhaber (1985) has been reappointed Irving Kaplansky and Ramesh A. Gangolli (1985) has been appointed chairman. Continuing members by Chairman of the Board of Trustees, Cathlee~ S. Morawetz, to the Committee on the Publication are Hugo Rossi (ex officio), and Masamichi Takesaki Program. Continuing members of the committee (1985). are Barbara Janson, consultant, William E. Kirwan Kevin M. McCrimmon (1986) and James R. II (1985), William J. LeVeque (ex officio), Everett Retherford (1986) have been appointed by President­ Pitcher (ex officio), Hugo Rossi (1985) and Elias M. Elect Irving Kaplansky to the Committee to Select Stein (1985). Professor Gerstenhaber has also been Hour Speakers for Southeastern Sectional Meetings reappointed chairman. and Leonard L. Scott, Jr., (1985) has been appointed chairman. Other members of the committee are Harold M. Stark has been appointed chairman of Frank T. Birtel (ex officio), and ·Michael Schlessinger the Nominating Committee by President Julia B. (1985). Robinson. Continuing members of the committee are Heini Halberstam (1985), Robert P. Langlands Marian B. Pour-El (1985), David A. Sanchez (1985), (1985), Barry Simon (1985). and Guido L. Weiss (1985), have been reappointed to the Committee on Agenda for Business Meetings by Robert W. Bartle, Edwin Hewitt, Paul R. Halmos, President-Elect Irving Kaplansky. The other member and Hans F. Weinberger have been appointed of the committee is Everett Pitcher, chairman. by President-Elect Irving Kaplansky to an ad hoc Advisory Committee on a Russian-English President-Elect Irving Kaplansky has appointed Dictionary. Professor Weinberger will serve as Shoshichi Kobayashi (1987) and Vera S. Pless (1987) chairman. to the Committee on Academic Freedom, Tenure, and Employment Security. Continuing members Michael A. Buchner and Roger C. Entringer were of the committee are Edward George Effros (1986), appointed by President-Elect Irving Kaplansky to be Charlotte Lin (1986), Robert R. Phelps (1986), and the Tellers for the election of 1984. Halsey L. Royden (1985), who has been appointed Steven W. Weintraub has been elected, Ralph P. chairman. Boas (1988), and Mary Ellen Rudin (1988) have been Philip C. Curtis, Jr., has been appointed and reelected by the Council to the Notices Editorial Donald C. Rung (1987) has been reappointed to Committee. Continuing members of the committee the Committee on Employment and Educational are Paul F. Baum (1986), Raymond L. Johnson Policy by President-Elect Irving Kaplansky. Other (1986), Everett Pitcher (ex officio), chairman, and members of the committee are Lida K. Barrett (1985), Daniel Zelinsky (1986). Stefan A. Burr (1986), Lis! Novak Gaal (1985), and F. Reese Harvey (1987) and Neil J. Sloane Gerald J. Janusz (1986). Professor Rung has also have been appointed to the Program Committee been reappointed chairman. for National Meetings by President-Elect Irving President-Elect Irving Kaplansky has appointed Kaplansky. (1985) has been Charles Herbert Clemens (1987) and Seymour appointed chairman. Other members of the Schuster (1987) to the Committee on Human Rights committee are Kenneth J. Barwise (1986), Barry of Mathematicians. Continuing members of the Mazur (1985), Everett Pitcher (ex officio), and committee are Lenore Blum (1986), Chandler Davis, William P. Ziemer (1986). chairman (1986, Leon A. Henkin (1985), Joshua A. Peter P. Orlik (1986) and Jeffrey B. Rauch Leslie (1986), and John Nohel (1985). (1986) have been appointed by President-Elect Irving William G. Chinn (1987), Amassa C. Fauntleroy Kaplansky to the Committee to Select Hour (1987), and Tepper L. Gill (1987) have been

98 appointed by President-Elect Irving Kaplansky to by President-Elect Irving Kaplansky to the joint AMS­ the Committee on Opportunities in Mathematics IMS-SIAM Committee on Scientific Collaboration for Disadvantaged Groups. Other members of the with Latin American Countries. Other members committee are Manuel P. Berriozabal (1985), and of the committee are Richard J. Griego (AMS), Gloria F. Gilmer (1985) who has been appointed chairman, Juan Jorge Schaffer (AMS), and Cesareo chairman. Villegas (IMS). J. William Helton (1986), Peter J. Kahn (1986), Donald C. Rung (AMS, 1987) has been reap­ Neal I. Koblitz (1986), and Ivar Stakgold (1986) pointed to the joint AMS-MAA-SIAM Committee have been appointed to the Committee on Research on Employment Opportunities by President-Elect Fellowships by President-Elect Irving Kaplansky. Irving Kaplansky. Continuing members of the com­ Continuing members of the committee are George E. mittee are Wilfred E. Barnes (MAA, 1984), Richard Andrews (1985), chairman, H. Jerome Keisler (1985), E. Ewing (siAM, 1986), Patrick Hagan (siAM, 1985), and Alan D. Weinstein (1985). Terms expire on June Calvin T. Long (MAA, 1986), and John W. Petro 30. (AMS, 1985). Frederick W. Gehring (1987) has been appointed, President-Elect Irving Kaplansky has appointed Hyman Bass (1987) and Felix E. Browder (1987) have Melvin Henriksen to the American Mathematical been reappointed by President-Elect Irving Kaplansky Society-MAA-SIAM Joint Committee on the Status to the Committee on Science Policy. Continuing of the Profession. Other members of the committee members of the committee are Ronald G. Douglas (1986), Louis N. Howard (1986), Irving Kaplansky (ex are Lida K. Barrett (MAA), Wendell H. Fleming officio), Joseph J. Kohn (1985), William J. LeVeque (SIAM), Louise Hay (AMS), Irwin Kra, member-at­ (ex officio), Cathleen S. Morawetz (1985), Julia B. large, Bernard L. Madison (MAA), Robert McKelvey Robinson (ex officio), Hugo Rossi (1985), and Guido (SIAM), chairman. L. Weiss (1985). Professor Browder has also been President-Elect Irving Kaplansky has appointed reappointed chairman. James M. Hyman (1987) and reappointed Robert F. The Committee on Prizes has been discharged Warming (1987) to the joint AMS-SIAM Committee with thanks. on Applied Mathematics. Continuing members of the committee are C. K. Chu (1985), Constantine Thomas H. Brylawski (1985) has been appointed M. Dafermos (1986), Alan G. Konheim (1985), and chairman of the Committee on Summer Institutes by President-Elect Irving Kaplansky. Continuing George C. Papanicolaou (1986), chairman. members of the committee are Michael Artin (1985), Richard E. Plant (1988), and Hans G. Othmer Albert Baernstein II (1987), Hui-Hsiung Kuo (1986), (1988) have been appointed by President-Elect Irving H. Blaine Lawson, Jr., (1987), and Judith D. Sally Kaplansky to the joint AMS-SIAM Committee on (1986). Mathematics in the Life Sciences. Other members Michael Brin (1987), Igor Dolgachev (1987), of the committee are Gail A. Carpenter (1986), Richard Ericson (1987), and Dmitry Khavinson (1987) Kenneth L. Lange (1987), Alan S. Perelson (1987) have been appointed to the AMS-ASL-IMS Committee and John Rinzel (1986). on Translations from Russian and Other Foreign Languages by President Julia B. Robinson. Boris Reports of Past Meetings M. Schein (1985) has been appointed chairman. Continuing members of AMS subcommittee are Frank B. Cannonito (1985), David V. Chudnovsky (1986), 1984 Symposium on Some Mathematical Jack K. Hale (1986), Marian B. Pour-El (1985), Questions in Biology Marina Ratner (1985), Donald E. Sarason (1985), DNA Sequence Analysis Boris M. Schein (1985), chairman, and (1986). The ASL subcommittee members are Gregory The eighteenth annual symposium on Some L. Cherlin (1986), James P. Jones (1984), Vladimir Mathematical Questions in Biology was held on Lifschitz (1987), Gregory Mine (1987). The IMS May 28, 1984, in the Beekman Room of the New subcommittee members are A. T. Bharucha-Reid, York Hilton, in New York, New York. Miklos Csorgo, Eugene M. Klimko, Eugene Lukacs, The symposium was held in conjunction with chairman, and Lajos F. Takacs. the annual meeting of the American Association for The name of the AMS-IMS-SIAM Ad Hoc Oversight the Advancement of Science. The symposium was Committee of the Evaluation Panel for NSF sponsored by the American Mathematical Society, Postdoctoral Fellowships in the Mathematical the Society for Industrial and Applied Mathematics, Sciences has been changed to AMS-IMS-SIAM Ad Hoc and Section G (Biological Sciences) and U (Statistics) Executive Committee of the Evaluation Panel for of the American Association for the Advancement NSF Postdoctoral Fellowships in the Mathematical of Science. The program was arranged by an Sciences. Members of the committee are Mark organizing committee consisting of H. Thomas Banks Ablowitz (siAM), Johan H. B. Kemperman (IMS), (Brown University); Gail A. Carpenter, (Northeastern chairman, and David A. Sanchez (AMS). University); Joel E. Cohen (Rockefeller University); On the recommendation of President Hirsh Cohen Joseph 8. Keller (Stanford University); Robert M. (SIAM), Richard A. Tapia (siAM) has been appointed Miura (University of British Columbia), chairman;

99 Garrett M. Odell (Rensselaer Polytechnic Institute); There were were sixty-six invited addresses and Charles S. Peskin (Courant Institute of Mathematical ten informal seminars. A seminar syllabus helped Sciences, New York University); and John Rinzel to inter-relate the various topics and facilitate (National Institutes of Health). intercommunication. The theme of the symposium was DNA Sequence There were 140 mathematicians who registered for Analysis. There were two half-day sessions, each the institute, 12 of whom were accompanied by some including three one-hour lectures. Eighty people member(s) of their families for at least part of the registered for the symposium. time which included 12 spouses and 16 children. Support was provided by a grant from the National According to the registration cards, of those who Science Foundation. attended 21 stayed only during the first week, 22 only during the second week and 97 for up to two weeks. 1984 AMS-SIAM Summer Seminar Seven countries not in North America were Nonlinear Systems of Partial Differential represented by the following numbers of participants: Equations in Applied Mathematics Austria (1), Belgium (1), China (2), France (13), Germany (1), Israel (1), and Norway (2). The American Mathematical Society and the As with previous summer seminars, the Society Society for Industrial and Applied Mathematics will publish formal proceedings in the series Lectures cosponsored the 1984 AMS-SIAM Summer Seminar at in Applied Mathematics, which will include papers the College of Santa Fe, Santa Fe, New Mexico, from by most of the speakers. July 22-August 3, 1984. The seminar was supported The topic of this seminar was selected by the AMS­ by the Air Force Office of Scientific Research; Army SIAM Committee on Applied Mathematics, whose Research Office; Center for Nonlinear Studies, Los members at the time were Roger W. Brockett, J. E. Alamos National Laboratory (through a grant from Dennis, Jr., Norman R. Lebovitz, Alan C. Newell the Department of Energy); and the National Science (chairman), George C. Papanicolaou, and Robert S. Foundation. Warming. The purpose of the seminar was to crystallize a The Advisory Committee for the seminar included number of interwoven trends in nonlinear systems Peter D. Lax, Pierre L. Lions, Jerrold E. Marsden, of Partial Differential Equations, and to lead David W. McLaughlin, Louis Nirenberg, and Isadore to cross-fertilization between such sub-categories M. Singer. The Organizing Committee included as Hyperbolic Systems, Integrable and Dispersive Darryl D. Holm, James M. Hyman, and Basil Systems, Nonlinear Diffusion Systems, and Dynamical Nicolaenko (chairman). Systems.

Elliptic Boundary Value Problems AMS TRANSLATIONS, SERIES 2

This volume contains seven papers translated from the Russian on the topic of elliptic boundary V. G. Maz'ya. B. A. PlamenevskiT and N. F. value problems. Morozov, On nonlinear bending of a plate with a crack Contents V. G. Maz'ya and B. A. PlamenevskiT, Schauder V. G. Maz'ya and B. A. PlamenevskiT, Estimates in estimates of solutions of elliptic boundary value Lp and in Holder classes and the problems in domains with edges on the Miranda-Agmon maximum principle for boundary solutions of elliptic boundary value problems in V. G. Maz'ya, B. A. PlamenevskiT and L. Stupyaus domains with singular points on the boundary [Stupeus]. The three-dimensional problem of ---· On the coefficients in the asymptotics of steady-state motion of a fluid with a free solutions of elliptic boundary value problems in boundary domains with conical points AMS Translations, Series 2 ---· Weight spaces with inhomogeneous norms Volume 123, approx. 270 pages (hardcover) and boundary value problems in domains with 1980 Mathematics Subject Classifications: 35840, 35845, 46E35, 73C10, 76005 and conical points others ___, On properties of solutions of ISBN 0-8218-3082-1; LC 84-15750 three-dimensional problems of elasticity theory Publication date: December 1984 List price $75, institutional member $60, and hydrodynamics in domains with isolated individual member $45 singular points To order, please specify TRANS2/123N

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.

100 Classified Advertisements

SUGGESTED USES for classified advertising are books or lecture notes for sale, books being sought, positions available. exchange or rental of houses. and typing services. THE RATE IS $.55 per word with a minimum of $5.00. The same ad in 6 consecutive issues is $3.00 per word. Type will be set solid unless centering and spacing are requested. A centered line of any length or the equivalent in white space is $5.00. A word is defined as a group of characters with space at each end. Prepayment is required of individuals but not of institutions. For an additional $10.00 charge, announcements can be placed anonymously. Correspondence will be forwarded. DEADLINES are listed on the inside front cover. U. S. LAWS PROHIBIT discrimination in employment on the basis of color, age, sex. race, religion or national origin. "Positions Available" advertisements from institutions outside the U. S. cannot be published unless they are accompanied by a statement that the institution does not discriminate on these grounds whether or not it is subject to U. S. laws. Details and specific wording may be found following the Classified Advertisements in the January and August issues of the Notices. SITUATIONS WANTED ADVERTISEMENTS from involuntarily unemployed mathematicians are accepted under certain conditions for free publication. Call toll-free 800-556-7774 and speak to Wahlene Siconio for further information. SEND AD AND CHECK TO: Advertising Department. AMS. P. 0. Box 6248, Providence, Rhode Island 02940. Individuals are requested to pay in advance. institutions are not required to do so.

POSITIONS AVAILABLE LOYOLA COllEGE DEPARTMENT OF MATHEMATICAL SCIENCES WEST VIRGINIA UNIVERSITY 4501 N. Charles Street Anticipated Asst./Assoc. Prof. tenure track positions, Fall Baltimore, Maryland 21210-2699 1985. Full Prof. appt. may be possible. A demonstrated A possible tenure track Assistant Professorship will be avail­ commitment to research in num. anal., applied math. or able for Fall '85. Candidate should have a Ph.D. in Statistics computational, discrete math and to teaching is expected. or some related Mathematical Science with the ability to Preference at the junior level will be given applicants who teach basic and upper level Statistics courses. The Department can participate in the depart. 's research program to main­ offers a strong undergraduate program in the Mathematical tain or establish interdisciplinary ties. At the senior level Sciences with concentrations including Statistics and Opera· strong consideration will be given applicants who will aug­ tions Research. Teaching duty is 3 courses/semester. Excel· ment the research of present faculty in applied analysis, lence in teaching and a moderate amount of research is re· applied math, or num. anal. Send vita to: Interim Chair, quired. Applicants should submit a current vita, three letters Dept. of Math, WVU, Morgantown, WV 26506. Applica­ of recommendation and transcripts of all college and graduate tions will be reviewed beginning Feb. 15, 1985. WVU is an level work to Dr. john Hennessey, Chairman. Resumes re· AA/EOE. ceived after February 20, 1985, may not be considered. Affirmative Action Employer LOYOLA COllEGE DEPARTMENT OF MATHEMATICAL SCIENCES YORK UNIVERSITY 4501 N. Charles Street Department of Mathematics Baltimore, Maryland 21210-2699 A permanent full-time position is available at the Instructor The Department of Mathematics at York University invites level. Candidate should have a Masters degree in a mathemat­ applications for tenure-track positions at the Assistant Pro· ical science and a desire to teach basic undergraduate mathe· fessor or higher level, and limited term (one, two, or three­ matics to qualify for this non-tenure track position. The year) positions, commencing July 85 (subject to academic college offers a strong undergraduate program in Math Sci­ and budgetary approval). Special consideration will be given ences. Teaching duty is 4 courses/semester. Applicants should to applicants in statistics, operations research, applied analy­ send vita, three letters of recommendation, and transcripts sis, and discrete mathematics. Cross appointments with other of all college and graduate level work to Dr. john Hennessey, departments are possible. Vita and three letters of reference Chairman. Applications received after january 18, 1985 may should be sent to Chairman, Mathematics, York University, North York (in Toronto), Ontario M3J 1 P3. In accordance not be considered. Affirmative Action Employer with Canadian Immigration requirements, this ad is directed to Canadian citizens and permanent residents of Canada. MATHEMATICS DEPARTMENT UNITED STATES NAVAL ACADEMY DEPARTMENT OF MATHEMATICS ANNAPOLIS, MARYLAND 21402-1385 UNIVERSITY OF CALIFORNIA RIVERSIDE, CALIFORNIA Applications are invited for a three year tenure-track appoint­ ment as Assistant Professor commencing August 1985. Ten Applications are invited for a faculty position in Mathematics month salary $21,000-$30,000, commensurate with experi­ beginning September 1985. This position is unrestricted as to ence and qualifications. Research opportunities exist for level of appointment and area of specialization. Candidates augmenting salary during summer. Specialization in combina· must have demonstrated research ability and a commitment torics or applied mathematics preferred. Applicants must to excellence in teaching at the undergraduate and graduate possess Ph.D., have a commitment to excellence in teaching, levels. Candidates should send a vita and arrange for at be capable of pursuing independent research, and have U.S. least three letters of recommendation to be sent to: Professor Citizenship. Send inquiries and applications not later than James D. Stafney, Chair, Search Committee, Department of February 1, 1985 to Prof. F. I. Davis, Chairman. Required Mathematics, University of California, Riverside, California of each applicant are a resume, transcripts, and three letters 92521. of recommendation discussing applicant's teaching and re­ The University of California is an Equal Opportunity/Affirma· search. The Naval Academy is an EO/AA employer. tive Action Employer.

101 POSITIONS AVAILABLE THE UNIVERSITY OF ADELAIDE invites applications from both men and women for the Baylor University following positions: Storm Chair of Mathematics LECTURER IN PURE MATHEMATICS The Mathematics Department is accepting applications (Tenurable) for the Storm Chair of Mathematics. We are seeking an (Ref: A 1525) in the Department of Pure Mathematics. established mathematician for a research-teaching position. Applicants should be effective undergraduate teachers and The Department offers the BA, BS, and MS degrees. The have proven research capability in mathematics. Applicants Department has an enrollment of 2500 students and the would normally be expected to be holders of a Ph.D. de· University has 11,000 students. Baylor is located in Waco, gree. Texas, which is 100 miles from Dallas and 100 miles from Austin. It is a private University affiliated with the Baptist The Department of Pure Mathematics is engaged in teaching denomination. Send applications to Howard Rolf, Mathe­ to the Honours degree level, and maintains an active Ph.D. matics Department, Baylor University, Waco, TX 76798. programme, its main research interests being in algebra, Baylor is an equal opportunity, affirmative action analysis, geometry, combinatorics and number theory. employer. The position is available from August 26, 1985. A later commencement date may be negotiated. HEAD, DEPARTMENT OF MATHEMATICAL SCIENCES Detailed information about the Department can be obtained COLLEGE OF LIBERAL ARTS AND SCIENCES from the Chairman, Department of Pure Mathematics, Pro­ BUTLER UNIVERSITY fessor W. Moran, telephone (618) 228-5415. Applications are invited for the position of Head of the Holders of full-time tenured or tenurable academic appoint­ Department of Mathematical Sciences. The department of ments have the opportunity to take leave without pay on a twelve full·time faculty offers undergraduate programs in half·time basis for a specific period of up to ten years where mathematics, computer science, and actuarial science. Aca· this is necessary for the care of children. demic computing facilities include a VAX-11 /780 and micro­ It is University policy to encourage women to apply for computers. Butler University is an independent, non-sectarian, consideration for appointment to, in particular tenurable coeducational institution located on a scenic three-hundred· academic appointments. acre campus in a residential section of Indianapolis. There FURTHER INFORMATION about the general conditions are approximately 3,000 full-time-equivalent undergraduate of all appointments may be obtained from the Senior and graduate students in colleges of liberal arts and sciences, Assistant Registrar (Personnel) at the University. business administration, pharmacy, fine arts, and education. Qualifications for the position include an earned doctorate SALARY per annum: A$24,353 x 7 - A$31 ,994 (salary in mathematical sciences, successful college teaching experience, under review). documented evidence of continuing research and scholarly APPLICATIONS, IN DUPLICATE, quoting reference num­ activity consistent with appointment to senior faculty rank, ber and giving full personal particulars (including residential evidence of leadership ability and effective communication status), details of academic qualifications and names and skills. Salary for this August 1985 appointment is commen· addresses of three referees should reach the Senior Assistant surate with qualifications and experience. Fringe benefits Registrar (Personnel) at the University of Adelaide, GPO include TIAA/CREF. Box 498, Adelaide, South Australia, 5001, Telex UNIVAD Applications should include a comprehensive curriculum AA 89141 not later than February 28, 1985. vitae and the names, addresses, and phone numbers of at The University reserves the right not to make an appoint­ least three references. Please apply by March 1, 1985, to: ment or to appoint by invitation. Paul R. Quinney, Ph.D. Chairman, Search Committee College of Liberal Arts and Sciences NICHOLLS STATE UNIVERSITY Butler University DEPARTMENT OF MATHEMATICS 4600 Sunset Avenue THIBODAUX, LOUISIANA Indianapolis, IN 46208 Tenure-track position available beginning fall semester 1985. Butler University is an equal opportunity/affirmative action Rank and salary open. Applicants should have a Ph.D. in employer. mathematical computing, applied statistics, operations re· search, or numerical analysis. Duties include teaching in KENT STATE UNIVERSITY undergraduate and M.S. graduate programs in applied DEPARTMENT OF MATHEMATICAL SCIENCES mathematics, recruiting, and continued research efforts. Good communications skills a must. For further information Applications are invited for a tenure-track faculty position write: Donald Bardwell, Head, Department of Mathematics, in numerical analysis and computational mathematics at the Nicholls State University, Thibodaux, LA 70310. NSU is an assistant or associate professor level beginning Fall, 1985. Affirmative Action/Equal Opportunity Employer. Applicants should have a degree in Mathematics. Duties in· elude undergraduate and graduate teaching, and research. The Institute for Computational Mathematics, with Richard PRINCETON UNIVERSITY S. Varga as Director, is housed in the Department, and focuses on research in numerical analysis as well as compu­ FACULTY POSITIONS IN MATHEMATICS tational mathematics. Departmental computing equipment AND MATHEMATICAL PHYSICS includes a VAX 11/780 running MACSYMA and REDUCE, Applications are invited from persons with an established for research; a VAX 11/750 under UNIX for upper level record of research accomplishment in algebraic number instructional purposes, a Chromatics raster graphics display, theory, complex analysis, topology, or mathematical phy­ and a laser printer. The Department has access to Goodyear sics; for senior faculty positions in the mathematics depart­ Aerospace Corporation parallel SIMD machines. The De­ ment, or, for mathematical physics, jointly in the mathe­ partment is on CSNET. Salary is competitive. Send resume matics and physics departments. Inquiries, accompanied by and three letters of recommendation to: vitae and publication record, should be addressed promptly Olaf P. Stackelberg, Chairman to Wu·chung Hsiang, Chairman, Department of Mathematics, Department of Mathematical Sciences Fine Hall, Washington Road, Princeton, NJ 08544. Princeton Kent State University University is an equal opportunity, affirmative action em­ Kent, Ohio 44242 ployer.

102 POSITIONS AVAILABLE DEPARTMENT OF MATHEMATICS AND STATISTICS Case Western Reserve University THE UNIVERSITY OF CALGARY Tenure track position in the area of numerical methods RESEARCH PROFESSORSHIPS AND POSTDOCTORAL for partial differential equations to begin August 15, 1985. MATHEMATICS FELLOWSHIPS IN APPLIED Outstanding research record and/or proven research poten­ Applications are invited by the Division of Applied Mathe­ tial, and teaching excellence required. Rank open. Possibility matics at The University of Calgary for research positions of a joint appointment with the Department of Mechanical in areas of Mathematical Biology having application to medi­ and Aerospace Engineering. The successful candidate will be cal science. Selected applicants will be nominated to the expected to cooperate with computational fluid dynamics Alberta Heritage Foundation for Medical Research. Appli­ groups on campus and in NASA-Lewis Research Center cants with more than five years of research experience be­ (CRAY-1 accessibility). Send vita plus three letters of rec­ yond a Ph.D. degree will be nominated for five year appoint­ ommendation to Professor W. A. Woyczynski, Chairman, ments as Research Scholars and applicants who recently Department of Mathematics & Statistics, Case Western Re­ obtained the Ph.D. degree will be nominated for one year serve University, Cleveland, Ohio 44106. as Research Fellows. appointments (three times renewable) Possible regular and/or visiting positions in other areas be based on the Remuneration for Research Scholars will represented in the department. academic salary scales of the University. Remuneration for action, equal opportunity employer. Research Fellows is set by the Foundation and will be in An affirmative excess of $21,800 per annum depending on experience. UNIVERSITY In accordance with Canadian immigration requirements, PAN AMERICAN priority will be given to Canadian citizens and permanent DEPARTMENT CHAIR residents; however, others are encouraged to apply. MATHEMATICS AND COMPUTER SCIENCE Interested applicants should send their curriculum vitae Pan American University, a state-supported, regional insti­ by February 28, 1985 to: Chairman, Division of Applied tution in the Lower Rio Grande Valley of Texas with an Mathematics, The University of Calgary, Calgary, Alberta, enrollment of 10,000 students, seeks a chair for a depart­ Canada, T2N 1 N4. ment of 27 faculty members. Position is at the associate or full professor rank, depending on qualifications, and the SOUTHWEST TEXAS STATE UNIV., DEPT. OF MATH/CS, salary is negotiable. Applicants must have an earned doc­ SAN MARCOS, TX 78666. One or more assist. or assoc. torate in one of the disciplines of the department-mathe­ professorships expected for fall 1985. Possibility of tenure­ matics, mathematics education, computer science, or for excel­ track appointments. Ph.D. {or equiv.) and potential statistics-and experience in higher education. The depart­ Prefer those in lence in research and teaching required. ment seeks a person with a record of scholarship, demon­ diff. eq. {o.d.e. math. ed., applied math., computer science, strated leadership, and a willingness to coordinate all aspects or p.d.e.), dynamical systems, number theory and topology. of a diverse department. The position begins August, 1985. San Contact Chairman, Southwest Texas State University, Applicants should send a vita and three (3) letters of ref­ Marcos, TX 78666. Application deadline: 2/1/85, late erence to: Dr. Gerald Brazier, Chairman, Department Chair an equal applications considered if openings exist. SWTSU is Search, Department of Mathematics and Computer Science, opportunity /affirmative action employer. Pan American University, Edinburg, Texas 78539. The deadline for applications is February 1, 1985. Pan American OREGON STATE UNIVERSITY University is an AA/EOE. Visiting appointments in mathematics for 1985 -86. Ph.D. or equivalent training and experience. All ranks con­ Department of Mathematics and Computer Science sidered. Preference to applicants who augment research University of Maryland Baltimore County areas in the department, or who meet instructional needs. Full or part-time appointments. Renewals may be possible. Applications are invited for the position of Chairperson, Closing date March 1, 1985. at the rank of Full Professor with tenure, from individuals Write to: Dr. P. M. Anselone, Chairman with strong records of research and national prominence, Department of Mathematics capable of providing leadership to this vital and expanding Oregon State University department as it strives toward academic and scientific ex­ Corvallis, OR 97331-4605 cellence. Located in the Baltimore-Washington corridor, to numerous con­ Attn: Staff Selection Committee with easy access to federal agencies and sulting and industrial firms in the area, the department is Oregon State University is an Affirmative Action/Equal experiencing particularly rapid growth in both applied Opportunity Employer and complies with Section 504 of mathematics and computer science. Currently comprising the Rehabilitation Act of 1973. 30 full-time faculty lines, with a number of new positions scheduled to be filled in the immediate future, the depart­ OREGON STATE UNIVERSITY ment offers degree programs from the baccalaureate through Associate Professor of Mathematics in numerical analysis and the doctoral levels. Particularly needed during this critical applications with preference for interaction with applied period of rapid growth is leadership capable of providing research groups. direction in the development of one or more research·con­ Assistant Professor{s) of Mathematics; all areas considered. centrations which will contribute to the deparment's the diverse interests and Salary negotiable, depending on qualifications. Start national stature while balancing including a cur­ September 1985. Closing date january 15, 1985. Write to: concerns of the department. Applications, riculum vitae and the names of five referees, as well as Professor P. M. Anselone, Chairman requests for further information, should be directed to Department of Mathematics Professor Leon H. Levy, Chairperson, Search Committee Oregon State University for Chairperson of Department of Mathematics and Com­ Corvallis, OR 97331 puter Science, University of Maryland Baltimore County, Attn: Staff Selection Committee Catonsville, Maryland 21228. Inquiries may also be made Oregon State University is an Affirmative Action/Equal by phone at {301) 455-2415. Initial inquiries and applica­ Opportunity Employer and complies with Section 504 of tions will be treated as confidential. The University of Mary­ the Rehabilitation Act of 1973. land is an equal opportunity, affirmative action employer.

103 POSITIONS AVAILABLE UNIVERSITY OF CALIFORNIA RIVERSIDE STATE UNIVERSITY OF NEW YORK Faculty Position in Computer Science COLLEGE AT POTSDAM Applications are invited for a tenure-track pQsition in Com­ The Department of Mathematics invites applications for two puter Science beginning with the 1985-86 academic year. full-time tenure-track positions commencing August 1985 to Applicants must have a Ph.D. in Computer Science and a teach undergraduate and beginning graduate courses. Rank demonstrated commitment to teaching and research. Candi­ and salary: open. Potsdam College enrollment exceeds 4500 dates from all areas of specialization in Computer Science students of whom, more than 400 major in Mathematics. will be considered. More than 130 majors are Pi Mu Epsilon members. The Department seeks applicants with a Ph.D. in any area of Rank and salary are open; candidates for senior rank must Mathematics and would prefer a background in the areas of have leadership ability and a proven research record. statistics and Applied Mathematics. Excellent teaching skills The Computer Science program at Riverside is housed in the are required. Direct inquiries to: H. B. Foisy, Chairman of well-established Department of Mathematics, which offers Search Committee, Department of Mathematics, State Uni­ bachelor's, master's, and doctoral degrees in Mathematics as versity College of Arts and Science, Potsdam, New York well as the B.S. and M.S. in Computer Science. The Depart· 13676. Women and Minorities are encouraged to apply. An ment owns four VAX 11 /750s and various microcomputers. Equal Opportunity /Affirmative Action Employer. General campus facilities include an IBM 4341-2, a. PRIME 750, and two VAXs. UNIVERSITY OF BRIDGEPORT To apply, send resume with names of three references to: CHAIRPERSON, DEPARTMENT OF MATHEMATICS Professor Theodore J. Barth, Chair Tenure-track appointment beginning Fall 1985. Candidates Computer Science Search Committee must have a Ph.D. in Mathematics/Mathematical Sciences. Department of Mathematics and Computer Science Applicants should have evidence of leadership ability and University of California excellence in teaching. Research interests in Applied Mathe­ Riverside, CA 92521 matics/Statistics preferred, but outstanding candidates in any The University of California is an Equal Opportunity I field will be considered. Some expertise in Computer Science Affirmative Action Employer. is desirable. The Department offers degree programs in Math­ ematics and Computer Science, and graduate programs are UNIVERSITY OF MASSACHUSETTS AT AMHERST, under development. Send resume and names of four refer­ CENTER FOR APPLIED MATHEMATICS AND MATHE­ ences to Dr. Grace Ho, Mathematics Department, University MATICAL SCIENCE of Bridgeport, Bridgeport, CT 06601. UB is an Equal Oppor­ Subject to budgetary limitations, the Center, in conjunc­ tunity/Affirmative Action Employer. tion with the Department of Mathematics and Statistics, Skidmore College expects to have tenure-track positions in Numerical Analysis/ Department of Mathematics and Computer Science Scientific Computation/Analysis beginning Fall 1985, rank Saratoga Springs, NY 12866-0851 to be determined by qualifications. Candidates with a prom­ ising research record and a keen interest in pursuing re­ Director of Computational Skills Laboratory open for Sep­ search and teaching in applied math in an expanding scien­ tember 1985. Responsibilities will include teaching, develop­ tific environment should apply by February 15, 1985, to ment of curriculum, (involving traditional, self-paced, and Georgette Healy, Coordinator, Center for Applied Mathe­ computer-based approaches to teaching) and management matics and Mathematical Science, 1521B Lederle GRC, of departmental involvement in a new college-wide quanti­ University of Massachusetts, Amherst, MA 01003. tative reasoning program. Knowledge of computing, commit­ The University of Massachusetts is an Affirmative Action/ ment to excellence in planning and in teaching of mathemat­ Equal Opportunity Employer. ics required. Applications are invited from candidates with M.S. or Ph.D. in mathematics or in computer science. Send THE DEPARTMENT OF MATHEMATICS, UNIVERSITY vita and letters of reference by February 15, 1985 to Robert OF CALIFORNIA, SANTA BARBARA invites applications P. DeSieno, above address. Skidmore is an Affirmative Action/ for the KY FAN ASSISTANT PROFESSORSHIP. The KY Equal Opportunity Employer. FAN Assistant Professorship is a special two-year position UNIVERSITY OF SOUTH FLORIDA which carries a research stipend. Candidates should possess a recent Ph.D. degree in mathematics or expect to receive Department of Mathematics one prior to September 1985. Selection will be based pri­ Tenure-track teaching and research positions are anticipated marily on demonstrated research achievement. Teaching beginning August, 1985. Applicants must possess a Ph.D. experience is desirable. Teaching load will consist of four degree. Applicants specializing in Approximation Theory, to five quarter courses per year including graduate seminars Computer Science, Numerical Analysis, Probability, or in candidate's field of interest. To apply, have at least three Statistics are preferred. Rank and salary will depend on ex­ letters of reference, vita and publications sent to the "Fac­ perience. To apply send resume to Kenneth Pothoven, ulty Search Committee", Department of Mathematics, Chairman, Tampa, FL 33620. The University of South University of California, Santa Barbara, CA 93106. We ex­ Florida is an equal opportunity employer. pect the candidate to have referees write to us directly. All applications received by January 15, 1985 will be given ST. JOHN'S UNIVERSITY, NEW YORK thorough consideration. UCSB is an Equal Opportunity/ STATEN ISLAND CAMPUS Affirmative Action Employer. The Division of Mathematics and Science invites applications for a tenure-track position at the assistant professor level POSITIONS IN MATHEMATICS beginning September 1985. Ph.D. in mathematics or com· Applications are invited for faculty positions in mathematics, puter science is required; some experience with computers applied mathematics and statistics. Rank and salary depend is desirable. Duties include undergraduate teaching in mathe­ on experience and qualifications. A strong research record matics and computer science; research potential is expected. or potential and a dedication to teaching are required. Send nlsume and three letters of recommendation to: Resume and four letters of recommendation should be sent Dr. David Patterson, Chairman of the Division of Mathemat­ to: ics and Science, St. John's University, 300 Howard Ave., Dr. William T. Trotter, Jr., Chairman New York, N.Y. 10301. Department of Mathematics and Statistics An Equal Opportunity Emp/oyer-M/F University of South Carolina, Columbia, SC 29208 AA/EOE

104 POSITIONS AVAILABLE HOBART AND WILLIAM SMITH COLLEGES Department of Mathematics and Computer Science Ander Applications are invited for two tenure-track positions, be· UNIVERSITAT TUBINGEN ginning September 1985. wird das Fach lnformatik ausgebaut. Hierflir werden u.a. die Position 1: Assistant or Associate Professor; Ph.D. in Mathe­ folgenden zwei Professorenstellen fur Praktische lnformatik matics with strong background (preferably a Master's) in ausgeschrieben, von denen je eine in der Mathematischen Computer Science required; teach all levels of undergrad· Fakultat (Stelle noch im Genehmigungsverfahren; Genehmi­ uate mathematics and computer science and participate gung ist zu erwarten) und in der Fakultat fUr Physik einge­ in the General Curriculum. richtet wird. Position 2: Assistant Professor; Ph.D. in Mathematics with Von den Stelleninhabern wird enwartet, dass sie sich an some background and strong interest in Computer Sci­ allen Ausbildungsangeboten der lnformatik beteiligen und ence required; teach all levels of undergraduate mathe­ gemeinsam am weiteren Ausbau des Faches mitwirken. matics and some computer science, and participate in Neben der Vertretung des Faches in Forschung und Lehre the General Curriculum. wird ferner erwartet: Aufgeschlossenheit fUr Methoden For both positions, candidates should have strong commit­ benachbarter Wissenschaften sowie die Bereitschaft zur ment to excellence in teaching and promise of continued Zusammenarbeit mit Physikern und Mathematikern. Es ist scholarly activity. Teaching load two courses per trimester. beabsichtigt, die lnformatik in einem gemeinsamen und Salary negotiable and competitive. Mathematikern. Es ist beabsichtigt, die lnformatik in einem Applicants should send detailed n\sume, three letters of gemeinsamen lnstitut der beteiligten Fakultaten zusammen­ recommendation (at least one including comments on zufassen. teaching ability), and undergraduate and graduate transcripts Fakultat fiir Physik (photocopies) to: Professur (C4) fiir Praktische lnformatik Professor Irving Bentsen, Chairman Der Stelleninhaber soli sich in Forschung und Lehre auf Department of Mathematics and Computer Science dem Gebiet der Software-Technologic oder der Systempro· Hobart and William Smith Colleges grammierung wissenschaftlich ausgewiesen haven. Schwer­ Geneva, New York 14456 punkte konnen sein: Programmiermethodik, Software-Kon­ An Equal Opportunity Employer. struktion, Betriebssysteme oder Verteilte Systeme. Einstellungsvoraussetzungen sind: Habilitation oder gleich· Columbia University wertige wissenschaftliche Leitstungen. Department of Computer Science Mathematische Fakultat Lectureships Professur (C4) fiir Praktische lnformatik Positions as Lecturer or Senior Lecturer will be offered Der Stelleninhaber soli das Fach Praktische lnformatik in to excellent teachers with superior research and academic Forschung und Lehre vertreten. Schwerpunkte Konnen sein: backgrounds. Faculty of all ranks in other mathematical Rechnergraphik, Verteilte Systeme, Kiinstliche lntelligenz disciplines, as well as computer science, are encouraged to oder Computerarchitektur. apply for these non-tenured term appointments, whose be three to six years. Pay is com­ Einstellungsvoraussetzungen sind: Habilitation oder gleich­ duration will typically wertige wissenschaftliche Leistungen. parable to professorial levels. These lectureships provide an opportunity for teacher/ 31.12.1984* zu richten an: Bewerbungen sind bis zum scholars with some substantial prior computing experience Dekan der Fakultat fiir Physik to make a transition to computer science. Columbia Univer­ der Universitat Tiibingen sity has an outstanding young research faculty and facilities, Keplerstrasse 17 now working in a five-million dollar office and research­ D-7400 Tiibingen 1 laboratory building. Lecturers will be encouraged to partic­ bzw. ipate fully in departmental activities. Dekan der Mathematischen Fakultat Lecturers will teach two undergraduate courses each der Universitat Tiibingen semester. They must be able to make highly effective pre­ Auf der Morgenstelle 10 sentations to large classes. The University has several DEC D-7400 Tiibingen 1 2060 computer systems dedicated to instructional use. * Bewerbungen, die sich auf diese Anzeige beziehen, werden Many terminals for students are in dormitories and other auch noch nachtraglich berucksichtigt. convenient locations. Knowledge of innovative uses of tech· nology for teaching is desirable. Send resume and names of three references by February to Professor Jonathan Gross, Vice­ UNIVERSITY OF CENTRAL FLORIDA 15, 1985, if possible, Chairman, Department of Computer Science, Columbia Department of Mathematics University, New York, New York 10027. Please write Applications are invited for several tenure-track and visiting "Re Lectureship" on the envelope of your letter of inquiry positions at the Associate or Assistant professor, or Instruc­ or application. tor level, beginning August, 1985. Ph.D. degree with strong COLUMBIA UNIVERSITY IS AN EQUAL OPPOR­ dedication to teaching research potential or experience, and TUNITY/AFFIRMATIVE ACTION EMPLOYER. WE ARE required for appointment at associate or assistant level. INTERESTED IN RECEIVING APPLICATIONS FROM Candidates with substantial completion of Ph.D. require· MINORITIES. ments will be considered for assistant or instructor level. QUALIFIED WOMEN AND Preferred research areas include applied mathematics, ordi­ UNIVERSITY OF CALIFORNIA, LOS ANGELES nary or partial differential equations, applicable mathemat­ ics, continuum mechanics, and applied analysis. The visiting DEPARTMENT OF MATHEMATICS positions are unrestricted as to area of specialization within Subject to administrative approval, a few adjunct assis· mathematical sciences. Candidate should send a detailed tant professorships; two year appointment only; strong resume and arrange to have at least three letters of recom­ research and teaching background; no restriction as to field. mendation and a transcript sent to: Professor Lokenath Salary $26,600 for academic year. Teaching load: Five Debnath, Chairman, Department of Mathematics, University quarter courses per year. To apply, write to Yiannis N. of Central Florida, Orlando, Florida 32816, postmarked by Moschovakis, Chair, Los Angeles, CA 90024. January 15,1985. The University is an equal opportunity/ UCLA is an equal opportunity affirmative action em­ affirmative action employer. ployer.

105 POSITIONS AVAILABLE SYRACUSE UNIVERSITY Department of Mathematics LAWRENCE UNIVERSITY Syracuse University invites applications for a tenure­ DEPARTMENT OF MATHEMATICS track position with rank and salary to be determined by Tenure-track position at the assistant professor level qualifications of appointee. Outstanding candidates having starting fall 1985. The Department seeks candidates special­ potential for strengthening any existing research area will izing in graph theory or combinatorics, but will consider be seriously considered, but preference will be given to can­ especially strong candidates in any area. Lawrence is a lib· didates in the broad area of analysis. Potential for excel­ eral arts college with a national reputation, small classes, lence in research and teaching is required. For a senior level and excellent students. Teaching load two courses each ten appointment proven excellence in research and teaching is week term. Salary competitive. Send resume, transcripts, expected. Send vita and arrange for three reference letters and three or four supporting letters to Bruce Pourciau, (also a transcript if recent Ph.D.) to be sent to L. j. Lardy, Chairman, Department of Mathematics, Lawrence University, Chairman, Department of Mathematics, Syracuse University, Appleton, WI 54912. These letters should provide specific Syracuse, NY 13210. Syracuse University is an AA/EEO evidence on the candidate's potential for outstanding under­ Employer. graduate teaching and continued research. Deadline january 20 but application by December 20 makes possible an inter­ TRW INCORPORATED view at the january AMS meeting. Equal Opportunity ADVANCED TECHNOLOGY RESEARCH Employer. Applications are invited for a position in Mathematics/ Computer Science for an individual with at least eight ARIZONA STATE UNIVERSITY years of industry experience (or a more junior individual Department of Mathematics with exceptional academic preparation) for research and Applications are invited for anticipated positions at ranks of project work in multi-level computer security. Special Assistant and Associate Professor. There is a possibility of technology experience of relevance includes: guards/down­ appointments at Professor rank. Visiting positions are also graders, security kernels, communications security, automatic expected. Send vita and direct three letters of recommenda­ theorem proving, cryptography, artificial intelligence, for- tion to J. Bustoz, Chair, Department of Mathematics, Arizona mal verification, fault tolerant computing, networking, and State University, Tempe, AZ 85287. A.S.U. is an equal data base management. Individual should have a balance opportunity employer. of hardware and software skills. Individual will have the opportunity to work in a new, well-equipped MLS labora· STATE UNIVERSITY OF NEW YORK, COLLEGE AT tory in Redondo Beach, California. Activities have a prod­ NEW PALTZ has a tenure-track position beginning Sept. uct orientation within an overall M LS architecture frame· 1985 for a person capable of making a substantial contribu­ work. TRW, a recognized industry leader in advanced sys­ tion in teaching math. at the undergrad. and beginning grad tems development, is an equal opportunity /affirmative levels, as well as major research contributions in his/her area action employer offering competitive benefits and salary of specialization. The salary is competitive. Applicants should structure. Send resume to: Dr. B. K. Richard, Advanced have a Ph. D. by Sept. 1985. The College is in the beautiful Technology Manager, TRW-DSG, 02/1305, Redondo Beach, Catskill region, 75 miles north of NY City. It is surrounded CA 90278. (213) 536-8564. U.S. Citizenship Required. by major high technology corporations. Send letter describ­ ing professional referees to: Prof. H. P. Sankappanavar, UNIVERSITY OF CALIFORNIA, SANTA BARBARA Dept. of Math. & Camp. Sci., Box 10, SUNY, New Paltz, DEPARTMENT OF MATHEMATICS NY 12561. Review of candidates will begin December 1, UCSB Department of Mathematics has designated 1985-1986 1984. An AA/EOE. as a special year in minimal surfaces and their applications to low-dimensional topology. The department anticipates Department of Mathematics making up to four visiting faculty appointments of candi· North Carolina State University dates possessing a Ph.D. in mathematics, a commitment to A tenure-track position at the assistant or associate level excellence in teaching, and research expertise in minimal is available in algebra, Lie groups and related areas. surfaces or low-dimensional topology. A number of dis­ Applicants must have a Ph.D. degree in mathematics and tinguished visitors are expected to be in residence for vari­ have a strong record or potential in both research and in­ ous time periods during the year. Applicants should send struction. Send a resume, relevant reprints, thesis abstract vitae and publication list, and should arrange for three and three letters of reference to Professor ). Luh, Search letters of recommendation to be sent to: Committee Chairman, Department of Mathematics, Box Professor james Robertson, Chairman 8205, North Carolina State University, Raleigh, North Department of Mathematics Carolina 27695-8205. University of California North Carolina State University is an Affirmative Action Santa Barbara, CA 93106 and Equal Opportunity Employer. Applications will be accepted until january 15, 1985, or until the positions are filled. UCSB is an affirmative action/ UNIVERSITY OF NORTH FLORIDA equal opportunity employer. The Department of Mathematical Sciences anticipates at UNIVERSITY OF CALIFORNIA, LOS ANGELES least two (2) tenure-track assistant professorships beginning August, 1985. Visiting positions may also be available. Can­ DEPARTMENT OF MATHEMATICS didates should have a Ph. D. in mathematics or statistics, Subject to administrative approval, a few assistant profes­ strong teaching ability, and continuing scholarly activity. sorships, with special attention given to candidates in Duties include teaching major, graduate and service courses. applied mathematics, algebraic number theory/modular The Department offers the B.A. and B. S. degrees in math· forms, several complex variables and topology. Strong re­ ematics and statistics and the M.A. degree with tracks in search and teaching background required. Sufficiently out­ mathematics, statistics and computer science. The University standing candidates in other fields and/or at higher levels is a growing institution in the State University System of will also be considered. Salary $26,600 for academic year. Florida. Send resume and three letters of recommendation Teaching load: Five quarter courses per year. Also several by February 15, 1985, to: Leonard J. Lipkin, Chairperson, positions for visitors and lecturers. To apply, write to Department of Mathematical Sciences, University of North Yiannis N. Moschovakis, Chair, Los Angeles, CA 90024. Florida, 4567 St. John's Bluff Road, jacksonville, Florida UCLA is an equal opportunity affirmative action em­ 32216. An AA/EOE employer. ployer.

106 POSITIONS AVAILABLE ROCHESTER INSTITUTE OF TECHNOLOGY Department of Mathematics QUEENS COLLEGE OF THE Rochester, NY 14623 CITY UNIVERSITY OF NEW YORK At least one asst/assoc prof., tenure-track position antici­ The Department of Mathematics invites applications for a pated for Sept., 1985. Ph.D. in math or statistics preferred, tenure track position beginning with the Fall Semester 1985. MS with extensive applied experience considered. Preferred Applicants must have a Ph.D. or its equivalent and a strong specialties: Applied prob/stat, or, computational math, graph commitment to research and undergraduate teaching. Prefer­ theory, discrete math. Applicant must have primary interest ence will be given to applicants with a specialty in discrete in teaching undergrad math, as well as doing some research mathematics and its applications. or consulting. Salary: Competitive, negotiable. Contact: Applicants should send a curriculum vita and three letters Prof. james Glasenapp, Chairman, Faculty Recruiting Com­ of recommendation to Professor Gerald Roskes, Chairman, mittee. RIT is affirmative action/equal opportunity employer. Department of Mathematics, Queens College, Flushing, New York 11367. Deadline March 1, 1985. THE UNIVERSITY OF ALABAMA IN BIRMINGHAM Queens College is an Affirmative Action/Equal Opportunity DEPARTMENT OF MATHEMATICS Employer. Applications are invited for tenure track positions in the Applications are invited for two tenure-track positions, pend­ Department of Mathematics. Applicants with research in any ing budgetary approval, in applied mathematics at the Assistant area are welcome, but mathematicians with major research Professor level or higher and one visiting one year Assistant interests in the areas of dynamical systems, mathematical Professor position commencing August 1985. Areas of special physics, nonlinear analysis on Riemannian manifolds, differ­ interest include ordinary and partial differential equations, ential topology-geometry and nonlinear differential equa­ numerical analysis and stochastic processes. Responsibilities: tions are particularly encouraged to apply. Successful appli­ teach courses in applied mathematics and actively pursue re­ cants will be expected to be strong or promising researchers, search. Teaching experience desirable. Send resume and mini­ good teachers, and to significantly interact with other mem­ mum three letters of recommendation by February 2, 1985 to: bers of the department. Rank and salary are open. The David A. Sanchez, Chairman, Mathematics and Statistics, Uni­ teaching load for research faculty normally does not exceed versity of New Mexico, Albuquerque, NM 87131. AA/EOE. two courses per term. Fringe benefits are excellent. Appli­ cants should send resume and three letters of recommenda­ WILKES COLLEGE tion to Roger T. Lewis, Department of Mathematics, Univer­ in Birmingham, Birmingham, AL 35294. Faculty Position sity of Alabama This information should be received by january 1, 1985, The Department of Mathematics and Computer Science but will be considered until position is filled. UAB is an invites applications for a tenure-track position beginning fall, Affirmative Action/Equal Opportunity Employer. 1985. Ph.D. or ABD in computer science or a Ph.D. in math­ ematics and substantial training in computer science is re­ MACALESTER COLLEGE quired. Wilkes College has 1800 undergraduates; the depart­ ment has 13 faculty members and 175 majors. Send resume The Department of Mathematics and Computer Science is and three letters of recommendation to Richard E. Sours, inviting applications for a full-time position, beginning Chairman, Department of Mathematics and Computer Science, September 1985. Applicants should have a degree (prefer­ Wilkes College, Wilkes-Barre, PA 18766. ably Ph.D.) in mathematics or computer science. Initial ap­ pointment is for one year, position may become tenure DEPARTMENT OF MATHEMATICS track. Salary is competitive. Applications, including resume AND COMPUTER SCIENCE and three references, should be addressed to john Schue, CALIFORNIA STATE UNIVERSITY Chair, Department of Mathematics and Computer Science, LOS ANGELES, CALIFORNIA 90032 St. Paul, MN, 55105, prior to March 15, 1985. Phone (612) 696-6335. Macalester is an affirmative action, equal Assistant or Associate Professor, tenure-track position. Ph.D. opportunity employer. in Mathematics or Ph.D. in Computer Science with a back­ ground in Mathematics required. Strong computer science background desirable. Starting date: September 1985. Salary: MATHEMATICAL SCIENCES $24200 -- $35200 with additional summer employment pos­ CENTRE COLLEGE sibilities. Evaluation of applicants will begin February 1, 1985. Tenure-track position beginning january or September Send inquiries to Wayne Bishop, Chair, at the above address. 1985 for assistant or associate professor, Ph.D. in mathe­ An Equal Opportunity, Affirmative-Action, Handicapped matics, to teach in undergraduate mathematics program. Title I X Em pi oyer. Ability to teach computer programming and/or statistics courses desirable. Teaching experience preferred. Salary THE CITADEL commensurate with background and experience. Excellent Applications are invited for tenure-track positions at the fringe benefits. Centre seeks faculty members with a strong assistant or associate level. Teaching responsibilities at all commitment to the liberal arts and to undergraduate teach­ undergraduate levels of Computer Science and Mathematics. ing. E.O.E. Applications, resumes, transcripts, and references Qualifications include a Ph.D. in Mathematics, Statistics, or should be sent to Leonard M. DiLillo, Vice President and Computer Science with a capacity for research and a dedica­ Dean, Centre College, Danville, Kentucky 40422. tion to undergraduate teaching. At least one position will be filled with someone who has a strong background in com­ Applications are invited for two tenure-track positions, pend­ puting. Salary negotiable. Liberal benefits include possible ing budgetary approval, at Assistant Professor level or higher resources for assistance to pursue advanced computer sci­ beginning August 1985. One position is for mathematician ence degrees. with research interests in analysis, preferably harmonic analysis. The Citadel is a state-supported, liberal arts, military col­ Candidates for second position should have research interests lege offering undergraduate degrees in the Arts, Sciences, in at least one of following areas: algebra, geometry, topology Engineering, Education and Business Administration. or global analysis. Responsibilities: teach courses in pure math­ Please send resume and three letters of reference to ematics and actively pursue research. Teaching experience de­ Charles E. Cleaver, Head, Department of Mathematics and sirable. Send resume and minimum three letters of recom­ Computer Science, The Citadel, Charleston, South Carolina mendation by February 2, 1985 to: David A. Sanchez, Chair­ 29409. Applications should be received by February 15, man, Mathematics and Statistics, University of New Mexico, 1985, to insure consideration. Albuquerque, NM 87131. AA/EOE.

107 POSITIONS AVAILABLE LAMAR UNIVERSITY Department of Mathematics DEPARTMENT OF Three tenure track positions and one Visiting Professor· MATHEMATICS HEADSHIP ships available in 1985: two in January; two, August. The & TENURE-TRACK POSITIONS Department seeks faculty in applied mathematics, statistics, Eastern Michigan University's Department of Mathematics and mathematics computer-aided instruction. Salary and and Computer Science is dividing into two departments, rank commensurate with qualifications. Expected: Teaching effective Fall 1985, and invites applications for the follow­ excellence and commitment to creative, scholarly activities. ing positions: Visiting Professor will teach two courses each semester and HEADSHIP/FULL PROFESSOR RANK interact with research faculty. Application deadlines: Decem­ ber 1, 1984, for january positions; February 15, 1985, for Applicants must have a Doctorate in a mathematical science, August. Send resume and three letters of recommendation a minimum of seven years of teaching experience, and be to Dr. George Poole, Head, Department of Mathematics, willing to teach at least one course per academic year. The P.O. Box 10047, Lamar University, Beaumont, TX 77710. successful candidate will have proven managerial skills, high Lamar University is an Equal Opportunity/Affirmative teaching recommendations, proven research competence in Action Employer. mathematics, and will be an articulate advocate for the mathematics and mathematics education programs in the department. The University of Illinois at Urbana-Champaign hopes to fill TENURE-TRACK FACULTY POSITIONS one or more positions at junior level for the academic year 1985-86. Minimum salary of $24,000. Applicants must pre­ Several tenure-track Assistant Professorship positions are sent evidence of excellence in teaching and research. Ph.D. anticipated for Fall 1985. All areas of specialization will be required. Send letter of application and credentials and have considered. A Doctorate in a mathematical science is re· at least three letters of reference sent to: qui red. Heini Halberstam, Head The Department has well established undergraduate and Department of Mathematics graduate programs with about 120 majors in mathematics University of Illinois at Urbana-Champaign and mathematics education. An evening Master's Program is also offered in these disciplines. These programs are aug­ 273 Altgeld 1409 W. Green umented by a large number of courses serving the College of­ Urbana, IL 61801 tel. (217) 333-3352 Technology, the College of Business, the College of Educa· tion and other departments within the College of Arts and To ensure full consideration applications should be received Sciences. The University with its 15,000 undergraduate and by january 31, 1985. The University of Illinois is an Equal 5,000 graduate students is the fourth largest in the state. Opportunity /Affirmative Action Employer. Eastern Michigan University offers a competitive salary and excellent fringe benefits. It is thirty miles from metropolitan UNIVERSITY OF CONNECTICUT, Department of Mathe· Detroit and adjacent to Ann Arbor. Its location in Ypsilanti matics, Storrs, CT 06268. Assistant/Associate/Full Professor· provides ready access to a broad spectrum of cultural and tenure track or visiting positions expected to be available academic events supported in the region. fall 1985. Qualified candidates must submit resume, transcripts, letters Teach courses in mathematics at graduate and under-graduate of recommendation and a standard application package by levels. Participate in Department research effort in areas of March 1, 1985. Application is available by contacting: expertise. Ph.D. in mathematics required. Demonstrated com· Search Committee, Headship Mathematics or Mathematics mitments to research and to teaching. Preference given to Faculty, {whichever position applying for), Eastern Michigan an applicant with ability and background to contribute to University, Personnel Department, 310 King Hall, Ypsilanti, the development of Department's program in Applied and Ml 48197, {313) 487-3430. Computational Mathematics. Preferred areas of research are For further information regarding these positions, please numerical analysis, combinatorics, coding theory, dynamical contact Professor H. Hoft, Acting Department Head, systems, probability, algorithms or complexity theory. Salary (313) 487-1444. negotiable. Screening begins February 15, 1985. An Equal Opportunity /Affirmative Action Employer Contact Howard Roberts, Acting Department Head. Univer· sity of Connecticut is an equal opportunity /affirmative action employer. THE UNIVERSITY OF TENNESSEE AT MARTIN Applications are invited for two tenure-track assistant or Eminent Scholar in Science: Applications and nominations associate professor level positions in mathematics, beginning are invited for the Glenwood and Martha Creech Eminent September 1985. Ph.D. in math or a closely related area is Scholar Chair in Science at Florida Atlantic University. This required. Teaching experience is desirable. Duties will in· position is supported by a one million dollar endowment elude teaching 12 hours of undergraduate courses. Salary and will be filled at the senior level in the College of Sci· competitive, excellent fringe benefits. UTM has an enroll· ence, which consists of Departments of Physics, Mathemat· ment of approximately 5000 and emphasizes quality under· ics, Chemistry, Psychology, Biology, and Geology. Individu­ graduate education. The department has 21 full-time and als with broad interdisciplinary research interests among the several part-time faculty. UTM is a primary campus of The traditional science areas as well as computer science are University of Tennessee system and is located 120 miles encouraged to apply. northeast of Memphis. Martin is a very friendly town with Applicants and nominees should have a distinguished a population of 9000. academic and research reputation that includes a successful Candidates should send a letter of application, transcripts, record in obtaining contract and grant support. The primary and names of three references to responsibilities of the successful candidate will be to signif­ Bill Austin, Chairman icantly contribute to the expansion of the research program Department of Mathematics in the College of Science and to provide graduate level and Computer Science training in his or her field of expertise. The University of Tennessee at Martin Completed applications must be received by january 31, Martin, Tennessee 38238·5049 1985. Closing date-February 15, 1985 or until filled. UTM is an Florida Atlantic University is an affirmative action/equal equal opportunity/affirmative action employer. opportunity employer.

108 POSITIONS AVAILABLE RUTGERS, THE STATE UNIVERSITY OF NEW JERSEY, Department of Mathematics, New Brunswick, Nj, anticipates MEMPHIS STATE UNIVERSITY the following open positions beginning September 1985: The Department of MATHEMATICAL SCIENCES invites (1) TENURE-TRACK AND TENURE POSITIONS. The De­ applications for (anticipated) tenure-track positions at all partment anticipates 2-3 appointments to tenure-track ranks in all areas of the mathematical sciences (including assistant professorships, depending on the qualifications of mathematics, computer science and applied statistics) for the applicants, one may be at the tenure (associate or full Fall 1985. Applicants must have a Ph.D. by September 1, professor) level. Candidates must have Ph.D., outstanding 1985 and strong potential for excellence in teaching and research ability in pure or applied mathematics, and con­ research. cern for teaching. Normal course load approx. 7 hours. Preference given to applicants working in classical analysis, The Department is committed to continued growth and differential geometry, logic, nonlinear functional analysis, development of its pure and applied programs. A Ph.D. is numerical analysis, operations research, or theoretical com­ offered in mathematics and applied statistics. puter science. Closing date is Feb. 15, 1985 or until all positions are (2) HILL ASSISTANT PROFESSORSHIPS. These are three­ filled. Applicants should submit resume (include at least year non-renewable positions. Candidates should have re­ 3 references) to: cently received the Ph.D., show outstanding promise in Ralph F audree, Chairman research ability in pure or applied mathematics, and have Department of Mathematical Sciences concern for teaching. Normal course load approx. 7 hours. Memphis State University Memphis, Tennessee 38152 (3) LECTURESHIPS (Assistant Professor level). Normal An Equal Opportunity/Affirmative Action Employer. course load approx. 7 hours. Candidates must have Ph.D., show outstanding promise in research ability in pure or TENNESSEE TECHNOLOGICAL UNIVERSITY applied mathematics, and have concern for teaching. These are one or two year non-tenure-track positions. Department of Mathematics and Computer Science (4) LECTURESHIPS (Instructor level). Primary responsi­ The Tennessee Tech Department of Mathematics and bility for teaching. Normal course load 9-10 hours. Candi· Computer Science anticipates having three open tenure· dates must have Ph.D., teaching experience at the college track positions beginning September 1985. level, and some interest in research. These are one or two ASSISTANT PROFESSOR OF MATHEMATICS year non-tenure-track positions. Candidates for this position should have a Ph.D. in Math­ (5) INSTRUCTORSHIPS. Responsibility for teaching mainly ematics or Statistics, a strong commitment to teaching at at the level of precalculus and below. Normal course load both the undergraduate and the graduate levels, and a 12 hours. Candidates must have masters degree or equiva­ genuine interest in research and scholarly activity. lent related experience and provide evidence of teaching INSTRUCTOR OF MATHEMATICS (2) ability. These are one or two year non-tenure-track positions. Candidates for these positions should have at least a (6) VISITING POSITIONS. Normal course load approx. master's degree in Mathematics or Statistics, and a dedication 7 hours. These positions are intended to permit individuals to teaching undergraduate mathematics. Preference in filling with regular appointments elsewhere to visit Rutgers for the one of these positions will be given to applicants with spec· purpose of engaging in joint research with members of the ialization in Applied Mathematics or Statistics. faculty. Candidates must have Ph.D., proven record of out­ To apply, send a letter stating which position is being standing research accomplishments in pure or applied math· sought, a transcript and a detailed resume, and arrange to ematics, and concern for teaching. These are one or two have three letters of recommendation sent to: year non-renewable positons. Dr. Leland L. Long, Chairman Send resume and 3 letters of recommendation to: CHAIR, Department of Mathematics & CSC SEARCH COMMITTEE, Dept. of Math., Rutgers University, Box 5054, TTU New Brunswick, Nj 08903 by February 1, 1985. Indicate Cookeville, TN 38505 position desired. RUTGERS UNIVERSITY IS AN EQUAL Evaluation of Applicants will begin on February 1, 1985. OPPORTUNITY/AFFIRMATIVE ACTION EMPLOYER. TTU is an Affirmative Action/Equal Opportunity Employer. MATHEMATICS: The Virginia Military Institute, a state EMORY UNIVERSITY supported undergraduate college, anticipates an opening in Department of Mathematics and Computer Science the Department of Mathematics in August 1985. Preference will be given an applicant with a Ph.D. Salary and rank will Applications are invited for a position as (tenure track) be dependent on degree, qualifications, and experience. The assistant professor with interests in numerical analysis/scien­ applicant should have a strong interest in teaching under­ tific computation beginning August 1985. Requirements are graduate mathematics and participating in the development a Ph.D. in mathematics or computer science and a strong research commitment. of a quality computer science program. Send your resume by March 1, 1985 to the Department of Mathematics, The EMORY UNIVERSITY, located in suburban Atlanta, is en· Virginia Military Institute, Lexington, Virginia 24450. larging the faculty of the Department of Mathematics and AA/EOE Employer. Computer Science in response to the growth of both the graduate and undergraduate programs. The teaching environ· UNIVERSITY OF CALIFORNIA, LOS ANGELES ment (small classes, able students, no remedial programs) is unusually good. All applications should include a vita, a DEPARTMENT OF MATHEMATICS publication list, and at least three letters of reference. These Three or four E. R. Hedrick Assistant Professors. Appli­ should be submitted to: cants must show strong promise in research and must have Paul Waltman, Chairman received the Ph.D. after 1 january 1984 (but may be of Department of Mathematics and Computer Science any age); no restrictions as to field; salary $30,800. Three Emory University year appointment; research supplement of $3,400 first Atlanta, GA 30322 summer. Teaching load: Four quarter courses per year, in­ cluding one advanced course in candidates field. Deadline Applications will be reviewed beginning january 1, 1985. for applications is january 15, 1985. To apply, write to EMORY UNIVERSITY is an affirmative action/equal oppor­ Yiannis N. Moschovakis, Chair, Los Angeles, CA 90024. tunity employer. Applications from members of minority UCLA is an equal opportunity affirmative action em­ groups and women are particularly encouraged. ployer.

109 POSITIONS AVAILABLE UNIVERSITY OF HAWAII DEPARTMENT OF MATHEMATICS TEXAS A&M UNIVERSITY junior position in mathematics-assistant or associate pro­ DEPARTMENT OF MATHEMATICS fessor-to begin approximately August 15, 1985. Tenure Applications are invited for several openings. All areas track. Ph.D. or equivalent required. Strong research and and ranks are considered, but tenure·track requires perman· teaching background required. There is no restriction as to ent residence or U.S. citizenship. The Department has active field; however, preference will be given to those whose re­ research groups in Algebra, Approximation Theory, Func· search is of interest to some of Hawaii's permanent staff. tional Analysis, Geometry and Non-linear Analysis, Number The salary range for assistant professors is $17,724-$26,568, Theory and Partial Differential Equations and Combinatorics, and for associate professors it is $22,380-$34,044. The Applied Mathematics, Probability, and Topology. teaching load is two courses per semester. To apply write to Interested individuals should send a vita and arrange for Professor William A. Lampe, Chairman, Department of letters to be sent to: Mathematics, University of Hawaii at Manoa, 2565 The Mall, Dr. H. E. Lacey, Head Keller 401 A, Honolulu, Hawaii, 96822. Send a curriculum Department of Mathematics vitae. Have three references write directly. To be guaranteed Texas A&M University full consideration an application should be completed by College Station, Texas 77843 January 15, 1985. Equal Opportunity Through Affirmative Action. The University of Hawaii is an equal opportunity affirm­ ative action employer. DEPARTMENT OF MATHEMATICS COLLEGE OF CHARLESTON Applications are invited for three tenure-track positions COMPUTER SCIENCE AT PROVIDENCE COLLEGE at the junior or senior level available Fall, 1985. Candidates The Department of Mathematics and Computer Science at must have a Ph.D. in one of the mathematical sciences, a Providence College invites applications for two positions in commitment to undergraduate teaching, and potential for Computer Science. These positions become available in continuing research. The normal teaching load is 12 hrs/wk September 1985. Applicants should possess the Ph.D. or its with course reductions for those engaged in research. The equivalent in Computer Science. Candidates with a M.S. in minimum salary is $25,000. Internal grants for release time Computer Science will also be considered for non-tenure or financial support for research projects are available as is track appointments. Providence College is a four year, co­ travel support. Applicants should send a vita and have three education, very selective liberal arts college conducted under letters of recommendation sent to William L. Golightly, the auspices of the Dominican Fathers. It enrolls 3500 stu­ Chairman, Department of Mathematics, College of Charleston, dents of which approximately 200 are mathematical science Charleston, SC 29424. The College of Charleston is an majors. Affirmative Action/Equal Opportunity Employer. The duties of this position include 9-12 hours of teaching in Computer Science, the pursuit of research interests and Applications are invited for a limited term assistant profes­ participation in the growth of our rapidly expanding de­ sorship beginning July 1st, 1985 for a term of 3 years. partment. Salary and rank are commensurate with qualifi­ Duties consist of research and teaching and candidates must cations. Applications will be considered until the position is demonstrate clear strength in both. Erindale College is filled. Please send vita, transcripts and the names of three located on the Mississauga campus of the University of references to: Toronto. Search Committee Applications should be sent to Professor T. Bloom, Chairman, Department of Mathematics/Computer Science Department of Mathematics, University of Toronto, Toronto, Providence College Ontario, Canada, M5S 1 A1, and should include a complete Providence, Rhode Island 02918 curriculum vitae and the names of at least three referees. Providence College is an equal opportunity affirmation The deadline is February 15, 1985. action employer. In accordance with the Canadian Immigration requirements this advertisement is directed to Canadian citizens and per· manent residents. CHAIRPERSON DEPARTMENT OF MATHEMATICS WEST VIRGINIA UNIVERSITY The department of Mathematics at Smith College seeks a statistician or a mathematician with a strong background in Applications and nominations are invited for the position statistics, Ph.D. in statistics or Ph.D. in mathematics with of Chairperson of the Department of Mathematics at West research area in statistics, is required. The position is for Virginia University. The Chair is the chief administrative 3-year term, tenure track, assistant professor level. Please officer of the department. The search is for a person who has submit resume and 3 letters of reference (include at least a strong research record, a commitment to excellence in in­ one letter evaluating your teaching) to Kathy Bartus, struction, and the ability to provide scientific and adminis­ Secretary, Department of Mathematics, Smith College, North­ trative leadership of the 35-member department, which hampton, MA 01063. An equal opportunity employer. offers B.S. and M.S. degrees. West Virginia University is the state's sole comprehensive, land-grant, doctoral institution with an enrollment of 20,000 Tenure-track and visiting positions in mathematics, sta­ students. The Department of Mathematics is part of the tistics and computer science are available beginning Septem­ College of Arts and Sciences. ber 1985. Excellent teaching and a commitment to research A complete application consists of a vita and the names are required. Some three-year instructorships may be open. and addresses of at least four references. Applications will The department offers B.S. and M.S. degrees in mathematics be received until the position is filled but should arrive by and computer science. MTU is a state supported university February 1, 1985, to insure consideration. emphasizing science and engineering. To apply, write: Applications and nominations should be addressed to Dr. Deborah Frank Lockhart, Acting Head, Mathematical Dr. Emory Kemp, Chair, Mathematics Department Chair and Computer Sciences, Michigan Technological University, Search Committee, 201 Woodburn Hall, West Virginia Uni­ Houghton, Ml 49931. versity, Morgantown, West Virginia 26506. Michigan Technological University is an equal opportunity West Virginia University is an Affirmative Action/Equal educational institution/equal opportunity employer. Opportunity Employer.

110 POSITIONS AVAILABLE SOUTHWEST TEXAS STATE UNIV., DEPT. OF MATH/CS, SAN MARCOS, TX 78666. One or more non-tenure track UNIVERSITY OF SOUTH ALABAMA instructorships expected for fall 1985. Master's degree in Department of Mathematics and Statistics mathematics or computer science and potential for excel­ Applications are being accepted for at least one tenure-track lence in teaching required. Contact Chairman, Department position at the rank of Assistant Professor. A successful of Mathematics and Computer Science, Southwest Texas applicant must possess a Ph.D. in Mathematics. Preferred State University, San Marcos, TX 78666. Application dead­ specialties include differential equations, dynamical systems, line: 2/1/85. Late applications considered if openings exist. ergodic theory, functional analysis, geometric topology, Southwest Texas State University is an equal opportunity/ number theory, and numerical analysis. The duties include affirmative action employer. teaching undergraduate and graduate mathematics courses, and carrying out research or other creative activity. The SUNY College at Brockport appointment will begin September, 1985. Applicants should Tenure-track position in Computer Science available Sep­ send a detailed resume, transcripts, and three letters of tember 1985. Candidates should have strong commitment recommendation to Dr. S. Gene Crossley, Chairman, De­ to Computer Science education. Ph.D. in Computer Science partment of Mathematics and Statistics, University of South or related area required. Masters' level expertise in Compu­ Alabama, Mobile, AL 36688. Screening will begin on ter Science necessary. Specialization should be in one of: February 1, 1985. USA is an equal opportunity /affirmative action employer. Database Management, Microprocessors, Networking. For particulars contact: Dr. K. Nakano, Chairperson, Department The Department of Mathematics and Statistics at Mississippi of Mathematics/Computer Science (phone: 716-395-2194). State University anticipates two or more tenure track posi· To apply, send a letter of application and resume, and have tions at the Assistant Professor level for the 1985-86 aca­ three letters of reference sent by February 15 to the Office demic year. A Ph.D. is preferred. Responsibilities include of Faculty/Staff Relations, SUNY College at Brockport, NY 14420. EO/AAE. teaching and research. Candidates should submit a vita and Brockport, three letters of recommendation to Professor Roger C. McCann, Chairman Screening Committee, Department of SUNY College at Brockport Mathematics and Statistics, Mississippi State, MS 39762. Tenure-track assistant professorship in Mathematics antici­ Screening will begin on December 15, 1984, and continue pated September 1985. Applicants should have a Ph.D. in until positions are filled. Mississippi State University is an Mathematics with expertise in discrete mathematics, prob­ equal opportunity/affirmative action employer. ability, or applied mathematics, and a strong commitment to the teaching of Mathematics at the Undergraduate and THE UNIVERSITY OF FLORIDA Masters' level. For more information, contact Dr. K. Nakano, DEPARTMENT OF MATHEMATICS Chairperson, Department of Mathematics/Computer Science announces the opening of two new tenure-track assistant (phone: 716-395-2194). To apply, send a letter of applica­ professorships beginning August, 1985. Those applying for tion and resume, and have three letters of reference sent by these positions should have demonstrable research potential. February 15 to the Office of Faculty/Staff Relations, In particular the search committee encourages applications SUNY College at Brockport, Brockport, NY 14420. from mathematicians with postdoctoral experience and from EO/AAE. those whose research interests are compatible with the inter­ ests of current department members. Priority areas include DEPARTMENT OF MATHEMATICS algebra/combinatorics, analysis, differential equations, logic, AND COMPUTER SCIENCE and numerical analysis/approximation theory. The salaries PAN AMERICAN UNIVERSITY will be highly competitive. Applicants should provide a EDINBURG, TEXAS 78539 resume (including a list of publications) and should arrange Positions pending budget approval. for at least three letters of reference to be sent to: Applications are invited for a number of tenure-track assis­ David A. Drake tant professor positions in mathematics beginning August Chair, Search and Screen Committee 1985. Ph.D. degree in mathematics, with research potential Department of Mathematics and dedication to teaching at undergraduate level required. University of Florida Outstanding applications in any area of mathematics will Gainesville, Florida 32611 be seriously considered but preferred research areas include Differential Equations (o.d.e., or p.d.e.) and Applied Mathe­ EMORY UNIVERSITY matics. Send vita, transcripts, three letters of recommenda­ Department of Mathematics and Computer Science tion, and letter of application to Dr. Reza Aftabizadeh, Tenure-track·assistant professor in applied mathematics Chairman Search Committee by February 15, 1985. An (beginning August 1985 ). A strong background in analysis Affirmative Action/Equal Opportunity Employer. and good computer skills are required. EMORY UNIVERSITY, located in suburban Atlanta, is en­ FACULTY POSITION IN MATHEMATICS larging the faculty of the Department of Mathematics and FLORIDA INTERNATIONAL UNIVERSITY Computer Science in response to the growth of both the The Department of Mathematical Sciences at Florida Inter­ graduate and undergraduate programs. The teaching environ· national University announces tenure-track positions at all ment (small classes, able students, no remedial programs) is levels beginning in unusually good. All applications should include a vita, a january and/or August, 1985. Candi­ publication list, and at least three letters of reference. These dates must have a Ph.D. in Mathematics, research poten­ should be submitted to: tial, and demonstrated teaching ability. Teaching load is fifteen semester-hours per academic year; summer teaching Paul Waltman, Chairman available. Preferred areas of specialization include harmonic Department of Mathematics and Computer Science analysis, algebra, and mathematical logic; qualified candi­ Emory University dates in other areas will be considered. Send resume and Atlanta, GA 30322 three letters of reference to Dr. David Barton, Mathemat­ Applications will be reviewed beginning December 1, 1984. ics Recruitment, Department of Mathematical Sciences. EMORY UNIVERSITY is an affirmative action/equal oppor­ Florida International University, Miami, FL33199. F.I.U. tunity employer. Applications from members of minority is a member of the State University System of Florida groups and women are particularly encouraged. and an equal opportunity/affirmative action employer.

111 POSITIONS AVAILABLE FAIRFIELD UNIVERSITY Assistant/Associate Professor of Computer Science UNIVERSITY OF HOUSTON - CLEAR LAKE Assistant Professor Fairfield University is a jesuit school located near Long Island Sound, about 70 miles from and The University of Houston-Clear Lake invites applications 30 miles from New Haven. This is a tenure-track position for a tenure-track position in Mathematics at the assistant requiring an average of 10 hours teaching and continued professor level. Available Sept. 1, 1985. Salary commensurate research. Rank and salary are competitive and will depend with background and experience. Responsibilities will include on qualifications. Preferred qualifications include a Ph.D. in upper division and MS level courses in mathematics with Computer Science or a Ph.D. in a related area with a some preference for applied areas. A relevant Ph.D. and Master's in Computer Science. Applications will be accepted strong teaching ability is required. Relevant academic or until the position is filled and full consideration is assured industrial researcoh experience is strongly desired. The recip­ those received prior to February 1, 1985. Starting date is ient will be expected to develop long term research produc­ September 1985. To apply, please send a curriculum vitae tivity. Interested persons should submit a letter of interest, with salary requirements including the names and phone current vitae, and three letters of reference by March 1, 1985 numbers of three references to: to: Search Committee - Mathematical Science, Dr. Michael j. Mezzino, Jr., Chairman, University of Houston-Clear Lake, George E. Lang, j r., Chair 2700 Bay Area Blvd., Houston, TX 77058. An AA/EO/MF/ Department of Mathematics & Computer Science HNDCP employer. Fairfield University Fairfield, CT 06430 DEAN, SCHOOL OF MATHEMATICAL SCIENCES AND Equal Opportunity /Affirmative Action Employer TECHNOLOGY, Eastern Washington University. Applications are invited for Dean of the new School of Mathematical Sci­ ences and Technology comprising the Departments of Mathe­ FAIRFIELD UNIVERSITY matics, Computer Science, Physics, and Technology. Com­ Assistant Professor of Mathematics plementing existing graduate and undergraduate programs, Fairfield University is a jesuit school located near Long these departments are actively developing new programs to Island Sound about 70 miles from New York City and serve the growing educational and technological needs of 30 miles from New Haven. This is a tenure-track position Spokane and the Pacific Northwest. The Dean is the chief requiring an" a'le[age"of lO_h"o"urs teaching and continued administrative officer of the School ana reports to the research. Applicants should have a Ph.D. in Mathematics Provost for Academic Affairs. This person will provide aca­ and the ability to teach Numerical Analysis. Full consid­ demic leadership; establish and strengthen contacts with eration will be given to applications received prior to business, industry and government; represent the School February 1, 1985. The position starts September 1985. within the University; and be responsible for developing and Please send a curriculum vitae, a letter of application in­ implementing policies and budgets for the School. Qualifica­ cluding salary requirements, and the name and phone num­ tions sought include an earned doctorate. Applicants should ber of three references to: have a record of significant accomplishments in mathematics, computer science, physics, engineering or technology as George E. Lang, Lr., Chair well as university teaching experience. Administrative experi­ Department of Mathematics & Computer Science ence demonstrating superior leadership is expected. Business, Fairfield University Fairfield, CT 06430 industrial or governmental experience is desirable. Salary is competitive, with liberal fringe benefits. Eastern Washington An equal opportunity /affirmative action employer University serves the Spokane, metropolitan area and Eastern Washington from a main campus in Cheney and a Spokane Center. The Spokane area offers many opportunities for STATE UNIVERSITY OF NEW YORK AT BINGHAMTON outdoor recreation and cultural activities. A letter of appli­ The Department of Mathematical Sciences expects to have cation or nomination along with a current resume, a separate tenure track junior positions open in Fall1985. A senior or statement of philosophy arid professional objectives, and the visiting appointment is also a possibility. Applications are names and telephone numbers of at least three references invited from candidates having excellent research records or should be forwarded to: Search Committee, Dean of the potential. All areas of pure and applied mathematics, in· School of Mathematical Sciences and Technology, Office cluding computer science, will be considered. The department of the Provost for Academic Affairs, Eastern Washington has considerable computer science responsibilities, so appli­ University, Cheney, WA 99004. Review of applications will cants with computer science experience, at whatever level, begin in january, 1985 and will continue until a qualified are asked to describe it. Send vita and letters of recommenda· candidate is selected. An Equal Opportunity Employer. tion to: David L. Hanson, Chairman MICHIGAN TECHNOLOGICAL UNIVERSITY Department of Mathematical Sciences HEAD- DEPARTMENT OF MATHEMATICAL State University of New York at Binghamton AND COMPUTER SCIENCES Binghamton, NY 13901 We invite applications and nominations for the position of An Equal Opportunity/Affirmative Action Employer department head. Candidates should have a well-established reputation in research and scholarship and a special interest THE UNIVERSITY OF PITTSBURGH in applied mathematics, statistics or computer science. A PITTSBURGH, PENNSYLVANIA 15260 commitment to active research and effective teaching is necessary. The department has 40 faculty members and Applications invited for two junior-level tenure-track offers B.S. and M.S. degrees in mathematics and computer faculty positions anticipated in 1985. Preferred areas: POE's, science. MTU is a state-supported university (enrollment analysis, applied mathematics. Present teaching loads: two 7000) emphasizing science and engineering. Applicants classes per term, 2-term 8-month academic year. Ph.D., pub­ should send a resume and arrange to have at least three licati.ons, effective teaching ability required. C. V., four letters of recommendation sent to: MACS Search Committee, letters of recommendation, reprints, preprints should be sent cfo Department of Mathematical and Computer Sciences, to W. E. Deskins, Chairman, Departmetlt of Mathematics Michigan Technological University, Houghton, Ml 49931. and Statistics, University of Pittsburgh, Pittsburgh, Pennsyl­ Michigan Technological University is an equal opportunity vania 15260. educational institution/equal opportunity employer. U. P. is an Equal Opportunity/Affirmative Action Employer.

112 POSITIONS AVAILABLE CARNEGIE-MELLON UNIVERSITY Department of Mathematics THE UNIVERSITY OF SUSSEX Applied Stochastic Analysis Position CHAIR OF MATHEMATICS The Mathematics Department expects to have one tenure­ Applications are invited for the post of Professor of Mathe­ track position at the Assistant Professor level available in the matics from 1st October 1985. The person appointed will Fall of 1985. Preference will be in the general area of sto­ have research interests within one or more of the fields chastic processes. Candidates for this position should have a encompassed by the term 'Applied Mathematics' interpreted strong mathematical background and research interests in in the broadest sense, and will be expected to provide aca­ one or more of the following areas: stochastic control, demic leadership especially in research and post-graduate queueing, reliability, mathematical statistics, diffusion activity. The salary will be not less than £17,275 (under processes. In exceptional circumstances, an appointment at a review), (approximately $21 ,500) with Universities Super­ higher level will be considered. Interested candidates should annuation Scheme benefits. send r~sumt!s, a copy of their transcript, and three reference Further particulars and application forms (closing date 31st letters to Professor George j. Fix, Head, Department of january 1985) from Mrs. S. Cory-Wright, Personnel Office, Mathematics, Carnegie-Mellon University, Schenley Park, Sussex House, University of Sussex, Falmer, Brighton, East Pittsburgh, PA 15213. Carnegie-Mellon University is an Sussex BNl 9RH. Affirmative Action/Equal Opportunity Employer.

CREIGHTON UNIVERSITY MELLON FELLOWSHIP PROGRAM 1985 DEPARTMENT OF MATHEMATICS The Program in Science, Technology, and Society at Applications are invited for a tenure-track faculty position MIT invites proposals from scientists, engineers, and physi­ in the Mathematics Department beginning Fall Semester cians for several one year study fellowships on the relation­ 1985. All specialities will be considered. Selection will be ships of science, technology, or medicine with society. Ph.D. based on potential for research and quality teaching. Salary or equivalent in science or engineering is desirable. Partial and rank will depend on the qualifications of the applicant. or full stipend. Deadline: February 1, 1985. For more Duties will include teaching both graduate and under-Dos­ information, write: Leon Trilling, Chairman, Mellon Fellow­ siers from candidates should include a detailed curriculum ship Committee, E51-128 MIT, Cambridge, MA 02139. vitae and at least three reference letters. Please send dossiers MIT is an equal opportunity/affirmative action employer. by jan. 15, 1985 to Dr. john Mordeson, Department of Mathematics, Creighton University, Omaha, Nebraska 68178. UNIVERSITY OF NORTHERN IOWA Creighton University is an equal opportunity/affirmative Tenure track position at Assistant Professor level. Salary and action employer. benefits competitive. Preferred specialty of algebra. Doctorate in mathematical specialty, demonstrated teaching ability, and UNIVERSITY OF LOWELL, Lowell, Mass. MATHEMATICS. scholarly productivity/promise required. Closing date of Several tenure-track positions at all levels anticipated for March 20. For complete announcement, contact Dr. David academic year 1985-86. All areas considered but statistics Duncan, Head, Department of Mathematics and Computer and applied mathematics preferred. Requirements are: Ph.D., Science, University of Northern Iowa, Cedar Falls, Iowa strong research credentials, evidence of active interest in 50614. An Equal Opportunity/Affirmative Employer. quality teaching and U.S. Citizenship or permanent resident status. Rank and salary commensurate with experience. WABASH COLLEGE, CRAWFORDSVILLE, IN. 47933, an Applicants should send vita, statement of current research undergraduate liberal arts college for men, seeks a recent or activities and three letters of recommendation to: Professor june '85 Ph.D. in mathematics beginning August '85. The Alan Doerr, Personnel Committee, Department of Mathe­ first two years will be as a Byron K. Trippet Assistant Pro­ matics, University of Lowell, Lowell, Mass. 01854. Positions fessor. The appointment includes a 9-month salary and a contigent upon funding. The University of Lowell is an summer research stipend. Funds for travel and other research equal opportunity/affirmative action, Title IX, 504 em­ support are also available. The position involves nine hours ployer. teaching per week. A background in applied math, statistics, or computer science is desirable, but more important is a APPLIED MATHEMATICS strong commitment to teaching at a liberal arts college and continuing interest in research. Please send rt!sum~ and at University of Wyoming least three letters of recommendation (at least one of which One or more tenure-track positions are anticipated in should discuss teaching) by February 15, 1985, to Professor applied mathematics. Emphasis on energy-related research, Bonnie Gold, Acting Chairman, Mathematics Department. interaction with the scientific and engineering communities, Applications from minorities and women are particularly and leadership within the Mathematics Department. Excel­ welcome. lent research opportunities. Inquiries or applications should be sent to Professor UNIVERSITY OF SOUTHERN CALIFORNIA Richard E. Ewing, Personnel Committee, Department of DEPARTMENT OF MATHEMATICS Mathematics, The University of Wyoming, Laramie, Wyo­ ming 82071. LOS ANGELES, CA 90089-1113 The University of Wyoming is an Equal Opportunity I Applications are invited for several tenure track Assistant Affirmative Action Employer. Professorships, available for September 1985, and for some senior level positions at the ranks of Professor and Associate University of Toledo Professor. Recent Ph.D.'s are expected to teach two courses Department of Mathematics per semester, and must show strong research promise. Ap­ Toledo, Ohio 43606 plicants for senior level positions should have an outstanding The Department of Mathematics expects one or more record of research and scholastic achievements. Persons tenure-track positions to be available beginning in September specializing in Statistics, Partial Differential Equations, 1985. Applicants should have a Ph.D. (or have completed Combinatorial Analysis and areas of Applied Mathematics the Ph.D. by September 1985), and be committed to excel­ such as Numerical Analysis are especially encouraged to lence in both teaching and research. Send a r~sum~ and apply. Applications should be addressed to Chairman, three letters of reference to Harvey Wolff, Chairman, Depart­ Search Committee, University of Southern California, De­ ment of Mathematics. The University of Toledo is an equal partment of Mathematics, ORB 306, Los Angeles, California opportunity, affirmative action employer. 90089-1113.

113 POSITIONS AVAILABLE FOR SALE

THE UNIVERSITY OF MISSISSIPPI INTRODUCTION TO MATHEMATICAL MODELS IN ECONOMIC DYNAMICS by David Clements: $18.95. The Department of Mathematics invites applications for one of several tenure-track positions beginning Fall 1985. The MODERN COURSE ON THE THEORY OF EQUATIONS department is especially interested in filling one of these by Dobbs and Hanks: $15. positions with a statistician. Candidates must have a Ph.D. MR. MATRIX (matrix manipulation software for IBM PCs): and commitment to research. Rank, teaching load and salary $20. competitive. Persons with a specialty in any area may apply. Our catalog: free, of course. Polygonal Publishing House, Special consideration might be given to numerical analysis, 210 Broad Street, Washington, NJ 07882. graph theory, stochastic processes or linear models, func· tiona( analysis, ordinary or partial differential equations, or certain additional areas supporting applied research. Appli­ MATH SCI PRESS, 53 Jordan Rd., Brookline MA 02146, 617-738-Q307. Just published: Proceedings of the Berkeley­ c~nts sh?uld submit resume, graduate transcript, reprints, dassertataon abstract, and three reference letters. Applica· Ames Conference on Nonlinear Problems In Control and tions should be postmarked by February 15. Apply to: Fluid Dynamics, L. R. Hunt and C. F. Martin, (Eds.), 450 Dr. James F. Porter, Chairman, Department of Mathematics, pages, $50. (Lie Groups; Systems Information and Control, University of Mississippi, University, MS 38677. Telephone: vol. II). Topics in the Geometric Theory of Linear Systems, 601-232-7071. EQUAL OPPORTUNITY EMPLOYER by Robert Hermann, $50. (Interdisciplinary Mathematics, vol. 22). In press: Topics in the Geometric Theory of Inte­ grable Systems, by Robert Hermann. Special Sale: Develop­ UNIVERSITY OF COLORADO, BOULDER ment of Mathematics in the 19th Century, by Felix Klein, Department of Mathematics $20. Write or call for other special prices on back list. The Department of Mathematics of the University of Colorado invites applications for faculty positions beginning in the fall of 1985. Although these positions are primarily at the assistant professor level, we also welcome strong applications at the associate professor level. Preference will be given to those whose research would complement the interests of our current faculty. Salary range- $24,000 to $35,000. Applications should be completed by January 1, 1985, or by March 1, 1985 for any positions not filled from the initial group of applicants. The University of Colorado is an Affirmative Action/ Equal Opportunity Employer. Inquiries should be addressed to: New Appointments, Department of Mathematics, Box 426, University of Colorado, Boulder, CO 80309.

114 TECHNICAL TYPING ON THE IBM PC Ease the burden of technical typing with Quick-Edit/Quick-Form - a powerful, affordable system designed to meet the needs of students, faculty, secretaries, and professionals. It's easy to learn, fast, and convenient to use. Full word processing capabilities include: form letters, footnotes, headers and footers, page numbering, and unlimited document length. Plus: special symbols (math, Greek, script, oversize, lines, boxes, and user-defined characters), multi-level subscripts and superscripts within An text (e.g. ~~), and displayed equations:

=I r k (iAX)j + . liAxlk+l I {1) j 1 l; {k+l) !J~ dFn{x). ~l j=OL .

Minimum Configuration: DOS 2.0 and 128K, one double-sided disk drive, so­ column monitor, and one of the following printers: EPSON MX+GraphtraxPlus-, RX- or FX-80, NEC Pinwriter P2, HP LaserJet (user-adaptable to others).

Price: $149; demo version (EPSON printers only) and manual $39 (applicable to purchase price); volume discounts and site licenses available. NY residents add sales tax.

Heath and Jackson, P.O. Box 4646, Ithaca, NY 14852 florida Atlantic University LOIICIDICO ..UTD Department of Mathematics, Boca Raton, Fl. MATHEMATICS AND COMPUTER SCIENCE. Applica­ ICIIrrriiT tions are invited for anticipated positions The MITRE Corporation seeks mathematicians with a back­ at all levels, including visiting positions ground in logic and computer science. A Ph.D. is preferred at the senior level, beginning August 1985. with knowledge ofprogtam verification and artificial intelli­ An applicant for a senior position should gence. U.S. Citizenship is required. have a recognized record of sponsored re­ In connection with the development of a verification system. search as well as d·irecting doctoral stu­ opportunities are available in the following areas: formal specification of mathematical models of program behaviOr, dents and will be expected to p1 ay a key development of a transformational approach to program ver­ rol& in developing a new Ph.D. program. An ification, and creation and use of software tools to execute applicant for a junior position must have a verification algorithms. Ph.D. in computer or mathematical sciences, Opportunities are also available in related work evaluating demonstrated research potential, and the and monitoring the development of existing verification willingness to teach introductory ca.puter systems. science courses. Preference will be given Applicants should submit resumes to: J.G. Williams, to applicants whose research is algebraic Specification & Verification Group, The MITRE Corpo­ geometry, commutative algebra, automata and ration, Bedford, MA 01730. Deadline for applications is 15 March 1985. If interested in similar positions in the formal languages, artificial intelligence, Washington DC area, please forward a resume to M.X. combinatorics and graph theory, number the­ Mason, The MITRE Corporation, 1820 Dolley Madison ory, mathematical physics, partial differ­ Blvd., McLean, VA 22102. ential equations or probability. Send MITRE is an equal opportunity employer actil'ely seeking vitae and the names of three references to applications under its affirmatil'e action program. Professor Frank 0. Hadlock, Chainnan, Department of Mathematics, Florida Atlantic University, Boca Raton, Florida 33431. Closing date for applications for permanent positions is March 1, 1985. AA/EO MITRE

115 F 1( Pitman Research Notes in Mathematics~ Two recent additions to our range of up-to-date, low cost research notes for mathematicians who want to keep abreast of new work and results in their field. Research Note Number 113 Differential Equations, Flow Invariance and Applications A H Pavel, Universitatea 'AI I Cuza', Romania An original and simplified presentation of the basic properties of nonlinear operators (of dissipative type) and semigroups, studying the differential equations associated with such operators and indicating applications to ordinary differential equations, partial differential equations and flight mechanics. 264 pages/ISBN 0 273 08651 0/$18.95 Publication November 1984

Research Note Number 99 Stochastic Functional Differential Equations SEA Mohammed, University of Khartoum, Studies the dynamical theory of stochastic functional differential equations on Euclidean space, bringing together the hitherto disjoint fields of stochastic differential equations and deterministic functional differential equations. The unified treatment lends itself to a range of applications in science, engineering and stochastic control. 250 pages/ISBN 0 273 08593 X/$21.95 Publication July 1984 Order via your local bookseller or direct from Cashpost, Pitman Publishing Ltd, Slaidburn Crescent, Southport PR9 9YF Available in the USA from Pitman Publishing Inc., 1020 Plain Street, Marshfield, Massachusetts Pitman iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiil JOrMath"' a text-formatter for mathematical C*·Bundles and papers, books and theses Compact Transformation Groups Bruce D. Evans This paper is concerned with the strU

116 Can you print this? a(x,y,z) r--- m f(x,y,z) 9(p,.,9) dpd.de - ~ax-1 n

TECH/PRINT™ CAN! TECH/PRINTTM orovides enhanced printing of documents. Use: -Up to four custom type fonts. -All features of IBM Graphics* and Epson printers. -Variable line heights. -Double width and compressed type sizes. -Subscripts and superscripts. -Print scientific and technical text, graphics, foreign languages. TECH/PRINT™ includes: -The TECH/PRINTn• printer driver. -Three custom fonts: mathematics/scientific, IBM* graphics characters, italics. -The TECH/FONTTM custom font editor. A must Only $69.95 plus shipping. Write or call Requirements GOLDSTEIN SOFTWARE -IBM PC, PC/XT, PCjr or 2 Redgate Court 100% compatible Silver Spring, MD 20904 -1 disk drive (single or 301-384-5565 double sided) -96k RAM Printers supported: IBM GRAPHICS, IBM COLOR, EPSON RX, MX, or FX, OKIDATA 84 1 92, 93, TI SSO, SSS, GEMINI STAR, DIABLO 630 ECS, C.ITOH PROWRITER, HP LASERJET

• Registered trademark International Business Machines Corp. •• Registered trademark Epson America, Inc. PROGRAM MANAGER MATHEMATICIAN

The Air Force Office of Scientific Research, Air ($36,327- $47,226 per yeax) or GM-14 ($42,928 Force Systems Command, located at Bolling Air $55,807 per year) depending on qualifications. No Force Base, Washington, DC, invites applications prior Government service is required. Send Office from U.S. citizens qualified to manage an estab­ of Personnel Management Standard Form 171, lished program of basic research in applied mathe­ "Personal Qualifications Statement," and/or resume matics. The successful applicant will manage the and list of publications to: United States Air Force program of basic research grants and contracts in areas that involve applied anal­ Civilian Personnel Office ysis, mathematical optimization, and finite mathe­ 1776 ABW/DPCS matics. The Program Manager will have multi-disci­ ATIN: Mrs. Hittinger plinary interactions with the program areas of mathe­ AndrewsAFB, MD 20331 matical research in signal processing and communi­ Include Announcement #800-84 on your application. cation, dynamics and control, and computer science. Applications must be received by January 21, 1985. The ability to communicate effectively with leading scientists and senior Government officials is crucial. For further information, contact Dr. D. W. Fox, A PhD or equivalent in mathematics is desired, Director of Mathematical and Information Sciences, along with a solid record of research and publica­ AFOSR, (202) 767-5025 or AUTOVON 297-5025. tions. The position is career civil service GM -13 AN EQUAL OPPORTUNITY EMPLOYER

CHAIRPERSON UNIVERSITY OF VIRGINIA THE DEPARTMENT OF MATHEMATICS UNIVERSITY OF OKLAHOMA The Department of Mathematics wishes to fill the Nominations and applications are invited for the McConnell-Bernard Chair of Mathematics. position of Chairperson, Department of Mathemat-­ ics, effective Fall 1985. Applications are sought from can­ Candidates should possess a substantial record of didates who have made outstanding research achievement, a commitment to excellence in teaching, and leadership and administrative abili­ research contributions in some area or ties appropriate to a growing department dedicated areas of the mathematical sciences. to a balanced program of qualitY research and teaching. The starting date is negotiable. For a The Department has a faculty of fortY actively in­ volved in research, offers programs for bachelors, full application, send a curriculum masters, and Ph.D. degrees, and supports an exten­ vitae, including the names of at least sive program of scientific activity supplemented by a substantial endowment for discretionary funds. three references to: Candidates should send a vita and names of four references ( includin_g at least one concerning admin­ Chairman, Department of Mathematics istrative abilities) to Mathematics/Astronomy Building Prof. Andy Magid, Chairperson Search University of Virginia Dep-artment of Mathematics University of Oklahoma Charlottesville, Virginia 22903 Norman, Oklahoma 73019 Tentative applications or enquiries Initial closing date for applications is FEB. 1, 1985 are also welcome, and will be treated and every two weeks thereafter. EQUAL OPPORTUNITY/ in confidence. An affirmative action/ AFFIRMATIVE ACTION EMPLOYER equal opportunity employer.

118 A New Year For Academic Press 1985 otti01'1 An Introduction to tl8..,.,~ Stochastic Modeling Introduction to Probability Howard Taylor, Cornell University Models, Third Edition University Samuel Karlin, Stanford Sheldon M. Ross, University of California, Berkeley authors features: This new title by distinguished Professor Ross continues to take an intuitive Markov chains that covers first a discussion of approach to teaching probability models in this as long-run behavior passage problems, as well new edition. Statistical material is now covered approach to Poisson processes •the point process throughout the text, Chapter 8 now contains a variety of current interest and spatial processes· a section on network of queues, and more computer forms. models covered in queueing science examples are presented.

Linear Algebra and hs di'tiol'ls tl8..,., ~ Continued Success with McKeague. Applications, Second Edition Gilbert Strang, Massachusetts Institute of Beginning Algebra: A Text/ Technology 1980 The second edition, a leader in its field, has been Workbook, Second Edition adopted and re-adopted at a wide range of colleges Intermediate Algebra: A Text/ and universities for its clear presentation of linear algebra and its many applications. Workbook, Second Edition Charles P. McKeague, Cuesta College McKeague brings in the new year with new edi­ tions that continue his friendly, informal style and New Edition from Kolman and Shapiro straightforward, step-by-step presentation of College Algebra, Second Edition new concepts. Bernard Kolman, Drexel University Both text/workbooks are again supplemented by Arnold Shapiro, Temple University the popular and class-tested videotape program. This new edition covers all traditional college An Instructor's Manual with Tests and a algebra topics and has an extensive pedagogical microcomputer testbank are also available. program. It emphasizes graphs and graphing techniques. Instructor's Manual and Test Bank available. Trigonometry Charles P. McKeague 1984 McKeague uses the right triangle approach to the study of trigonometry, with special emphasis on Precalculus: Functions identities, graphing, vectors, and circular motion. and Graphs Bernard Kolman and Arnold Shapiro 1984 Widely adopted for Fall1984, Precalculus stresses Calculus, Third Edition the concept of a function, function notation, and Stanley I. Grossman 1984 graphs of functions along with discussions of A wealth of problems and examples from a variety analytic geometry, matrices, and linear of disciplines continues to set Grossman apart from programming. the rest. The author presents an early introduction to the derivative and a simplified introduction to the integral. Instructor's Manual, Student Solutions Manual, and Computer Software available.

Academic Press College Division Orlando, FL 32887

119 !BIOBIIS AD MI!BODSIIf MA!BIMA!ICS FBOM JOBR WILEY & SOBS. MODULAB FOBMS COMBINATORIAL Edited by Robert A. Rankin, OPTIMIZATION University of Glasgow Annotated Bibliographies (0-10099-S) approx. liS pp. Edited by M. O'hEigeartaigb., National Institute December 1984 $84.98 for Higher Education, Ireland, J.K. Lenstra, Ill:t"B.ODUCTION TO Centre for Mathematics and Computer Science, CONVERGENCE The Netherlands and A.H.G. Rinnooy Kan, S.C. Malik, S.G.T.B. Khalsa College, Econometric Institute, Erasmus University University of Delhi (1-90490-1) approx. 100 pp. (0-10070-7) 166 pp. 1984 $14.98 October 1984 $18.98 lVIA.THElVIA.TICAL .ANALYSIS MULTIPLE GAUSSIAN S.C. Malik, S.G.T.B. Khalsa College, ~ERGEOMETBICSEBXES University of Delhi H.M. Srivastava, The University of Victoria, (0-10018-1) 898 pp. 1984 $19.98 and P.W. Karlsson, The Technical University of Denmark BEAL .ANALYSIS Modern Techniques and Their Applications (0-10100-1) approx. 370 pp. Gerald B. Folland, University of Washington December 1984 $69.98 (1-80988-8) 380 pp. 1984 $34.98 AB Dl"l"B.ODUCTION TO .AlVIENABLE LOCALLY THE THEORY OF SMOOTH COMPACT GROUPS DYN.AlVIICAL SYSTEMS Jean-Paul Pier, Centre Universitaire de W. Szlenk, University of Warsaw Luxembourg (1-90117-1) approx. 400 pp. (1-89390-0) 418 pp. 1984 $44.98 November 1984 $84.98 GB.APHS.AND APPLICATIONS GLOBAL BXElVl.Al.\TNIAN Proceedings of the First Colorado Symposium on GEOMETRY Graph Theory (Ellis Horwood Series on Mathematics and Edited by Frank Harary, University of Michigan its Applications) and John Maybee, University of Colorado T.J. Willmore, University of Durham and (1-88771-1) 368 pp. N.J. Hitchin, St. Catherine's College, Oxford November 1984 $44.98 (0-10017-0) 113 pp. 1984 $84.98 APPLIED EXTEBJ:OR A TBE.A.TISE ON CALCULUS GENERATING FUNCTIONS Dominic G.B. Edelen, Lehigh University (Ellis Horwood Series on Mathematics and (1-80773-7) approz. BOO pp. its Applications) January 1988 $44.98 H.M. Srivastava, The University of Victoria, and Dl'l'ERVAL OB.DE:BS AND H.L. Manocha, Indian Institute of Technology Dl'l'ERVAL GRAPHS (0-10010-3) 889 pp. 1984 $89.98 A Study of Partially Ordered Sets Peter C. Fishburn, AT & T Bell Laboratories, New Jersey (1-81184-8) approz. 180 pp. To order, write to Julie Harrington, Dept. 5-1587 December 1984 $33.80 illJOBIT WILEY & SOilS, IITC. 605 THIRD AVENUE, NEW YORK, N.Y. 10158 \'::!:) In Canada: 22 Worcester Road, Rexdale, Ontario M9.W lLl For faster service call toll free: 1 800-816-8868 In New Jersey call collect: { 101) 841-6707 Order Code# 5-1587. Visa, MasterCard, American Express accepted on phone orders. Prices subject to change and higher in Canada. 092-5-1687

120 DON'T MAKE A

Give your students the best math texts available. From Benjamin/Cummings: fyou want to include not all. There are over I both the basics of 30 vignettes to help you linear algebra and its convince your students applications in your there really are applica- course, we've got the tions fur linear algebra. ideal book fur you: Noncomputational prob- Roberts' Elementary lems have been added Linear Algebra, Second to the problem sets, and Edition. Not only will greater emphasis is you enjoy teaching from given to Determinants, this book, your students Gaussain Elimination, will enjoy learning from Vectors in R,n and Span- it. The writing style is ning Sets. Thoroughly clear and infurmal, so it's easy to fullow checked for errors, this new edition and non-intimidating for your non- is unmistakablY. the right choice for math majors. But that's your class. Other excellent books: ALGEBRA, Second Edition New Fourth Editions of Serge Lang BASIC TECHNICAL MATHEMATICS and A PROBLEM SOLVING BASIC TECHNICAL MATHEMATICS APPROACH TO MATHEMATICS WffB CALCULUS FOR ELEMENTARY SCHOOL Allyn]. Washington TEACHERS, Second Edition TECHNICAL CALCULUS WITH Rick Billstein, Shlomo Libeskind, and ANALmC GEOMETRY, Johnny W. Lott Second Edition ELEMENTS OF ALGEBRAIC Allyn]. Washington TOPOWGY HARMONIC ANALYSIS James R. Munkres Henry Helson See all of these books and more at our booth, or call us toll-free at: (800) 227-1936 (USA) ..~"'<=-0"~.,. The Benjamin/Cummings (800) 982-6140 (CA) ~ Publishing Company, Inc~ 2727 Sand Hill Road -liM'" Menlo Park, CA94025 Collection «Chaire Aisenstadt» Pllysical Aspects of U. GIOf$ Tlteolr Sur quelques questions cranalyse, de ROBERT HERMANN- 272 p. 16$ mecaniQue at de contr61e optimal a.....,.. proltiHiea mat"'matlques en JACQUESLOUISLIONS-212p. 18$ ..... statlatique La Th8orie des aoua-gradlents et ses MAAKl

DELES L'UMYERSITf: PRESSES .a. Le livre DEMONTRhL C.P. 6128, Succ. •A• Montreal (Quebec), Canada H3C 3.17 T61. : (5 343-6321·25 universitaire

122 Scott, Foresman and Company We've got you covered, whatever the course! From Lial & Miller Three new editions for your math for management courses with complete computer application program: Mathematics and Finite Calculus with Calculus with Mathematics Applications Applications Third Edition Third Edition Second Edition Available Now Available Now Available Now ©1985, 512 pages, ©1985, 640 pages, ©1985, 864 pages, hardbound hardbound hardbound

All three texts above with Instructor's Guide including Testbank, Student Solutions Manual, and Manual with Computer Diskette (by Donald R. Coscia and Thomas Hasiotis) for student use on Apple If's or an IBM PC.

New Computer-Generated Testing Program for use with Lial & Miller's Beginning Intermediate Algebra Algebra Fourth Edition Fourth Edition ©1984, 416 pages, ©1984, 560 pages, hardbound hardbound Each text with Instructor's Guide, Study Guide, Instructor's Solutions Manual, Student Solutions Manual, Videotape and Audiotape Cassettes, and Supplementary Exercises. New from Saltz A Short Calculus Visit the Scott, Foresman An Applied Approach Booth or write Fourth Edition Meredith Hellestrae, Available Now Department SA-NAMS ©1985, 624 pages, hardbound, 1900 East Lake Avenue Instructor's Guide Glenview, Illinois 60025 r. Scott, Foresman and Company

123 Academic Press Continues to ~IJ/l>,~ 4c ~ Publish Outstanding Books in ~": Motivation and chapter provide complements to, and extensions of, Perspective. Fundamentals and Formalism. Multi­ results in the main text. component Models. Multifacetted System Modelling. Multifacetted System Architectures. 10015

Academic Press, Inc. (Harcourt Brace Jovanovich, Publishers) Orlando, Florida 32887, U.S.A. 24/28 Oval Road, London NW1 7DX, U.K.

Orlando San Diego New York London Toronto Montreal Sydney Tokyo

For Fastest Service CALL TOLL FREE 1-800·321·5068. To Place An Order From Florida, Hawaii, Or Alaska CALL 1-305-345-4100. In The U.K. CALL (01J 3Q0.0155. Credit Card Orders Only. Send payment with order and sava postage and handling. Prices are In U.S. dollars and ara aubjact to change without notice.

124 CountonWikTtextbooks for aUfields ofmathematics.

COLLEGE ALGEBRA (Best seller) 2nd Edition CALCULUS WITH ANALYTIC GEOMETRY John R. Durbin, University of Texas at Austin 2nd Edition (0-471-81714-7) January 1985 500 pp. Howard Anton, Drexel University MODERN ALGEBRA (0-471-08271-6) 1984 1264 pp. John R. Durbin, University of Texas at Austin Supplements: Solutions Manual, Students (0-471-88487-1) January 1985 407 pp. Solutions (even numbered exercises), Answers, ELEMENTARY PLANE GEOMETRY Sampler, Linear Algebra Supplement, DE 2nd Edition Supplement, Testing Disks, Test Bank (printed). R. David Gustafson, Rock Valley College THE CALCULUS COMPANION TO ACCOMPANY Peter D. Frisk, Rock Valley College CALCULUS WITH ANALYTIC GEOMETRY, (0-471-89047-2) 1984 225 pp. Second Edition, Vols, 1 and 2. APPLICATIONS OF ABSTRACT ALGEBRA William H. Barker and James E. Ward, both George Mackiw, Loyola College of Bowdoin College. (0-471-81078-9) January 1985 200 pp. A FIRST COURSE IN (Best seller) APPLIED COMPLEX VARIABLES Lester A. Rubenfeld, Rensselaer Polytechnic ELEMENTARY LINEAR ALGEBRA Institute 4th Edition (0-471-09843-4) January 1985 525 pp. Howard Anton, Drexel University PREPARATION FOR CALCULUS (0-471-04840-6) 1984 464 pp. 3rd Edition Supplements: Solutions Manual A.L. Salas C. G. Salas (Best seller) (0-471-87386-1) January 1985 480 pp. APPLIED COMBINATORICS APPLICATIONS OF LINEAR ALGEBRA 2nd Edition 3rd Edition Alan Tucker, Stanford University Howard Anton and Chris Rorres, both of (0-471-86371-8) 1984 464 pp. Drexel University ALGEBRA AND TRIGONOMETRY: (0-471-86800-0) 1984 250 pp. A STRAIGHTFORWARD APPROACH ELEMENTARY NUMERICAL ANALYSIS 2nd Edition Kendall E. Atkinson, University of Iowa Martin M. Zuckerman, City College of the City (0-471-897'33-7) January 1985 480 pp. University of New York APPLIED CALCULUS (0-471-09789-6) January 1985 576 pp. Alan M. Baum, General Motors Research COLLEGE ALGEBRA: Laboratories A STRAIGHTFORWARD APPROACH Stephen J. Milles, University of Michigan Martin M. Zuckerman, City College of the City Henry J. Schultz, Lockheed Aircraft Corp. University of New York (0-471-80306-5) January 1985 480 pp. (0-471-09619-6) January 1985 450 pp.

To be considered for complimentary copies of any of the listed titles, write to LeRoy Davis, Dept. JW-4157. Please include course name, approxi­ mate enrollment, title of current text, and texts desired. Wlle,- leading the wayfor over150 years.

JOHN WILEY & SONS, Inc. 605 Third Avenue New York, N.Y. 10158 In Canada: 22 Worcester Road Rexdale, Ontario M9W 1L 1

12S "'"L.O~UL.II~ WITH ANALYTIC GEOMETRY 2nd Edition Howard Anton, Drexel University (0-471-08271-6) 1984 1264 pp. Supplements: Solutions Manual, Students Solutions (even numbered exercises), Answers, Sampler, Linear Algebra Supplement, DE Supplement, Testing Disks, Test Bank (printed). Wlley­ The Calculus Companion to Accompany Calculus With Analytic Geometry, Second Edition, Vols. 1 and 2. William H. Barker and James E. Ward, both of Bow­ leadingthe doin College. ELEMENTARY LINEAR ALGEBRA war for over Edition •Hc1wa1rd Anton, Drexel University (0-471-04840-6) 1984 464 pp. 150rears Supplements: Solutions Manual. APPLICATIONS OF LINEAR ALGEBRA in all 3rd Edition IHc1wa1rd Anton and Chris Rorres, both of Drexel fields of 1984 250 pp.

mathematics. ELEMENTARY NUMERICAL ANALYSIS Kendall E. Atkinson, University of Iowa (0-471-89733-7) January 1985 480 pp. APPLIED CALCULUS To be considered for compli­ Alan M. Baum, General Motors Research Laboratories mentary copies of any of the Stephen J. Milles, University of Michigan listed titles, write to LeRoy Henry J. Schultz, Lockheed Aircraft Corp. Davis, Dept. JW-4159. Please (0-471-80306-5) January 1985 480 pp. include course name, approx­ COLLEGE ALGEBRA imate enrollment, title of cur­ 2nd Edition John A. Durbin, University of Texas at Austin rent text, and texts desired. (0-471-81714-7) January 1985 500 pp. MODERN ALGEBRA John A. Durbin, University of Texas at Austin (0-471-88487-1) January 1985 407 pp. ELEMENTARY PLANE GEOMETRY Wlley... 2nd Edition A. David Gustafson, Rock Valley College Peter D. Frisk, Rock Valley College come (0-471-89047-2) 1984 225 pp. APPLICATIONS OF ABSTRACT ALGEBRA see us George Mackiw, Loyola College (0-471-81078-9) January 1985 200 pp. A FIRST COURSE IN APPLIED COMPLEX VARIABLES at our Lester A. Rubenfeld, Rensselaer Polytechnic Institute (0-471-09843-4) January 1985 525 pp. PREPARATION FOR CALCULUS booth... 3rd Edition A. L. Salas, C. G. Salas (0-471-87386-1) January 1985 480 pp. APPLIED COMBINATORICS @) 2nd Edition Alan Tucker, Stanford University JOHN WILEY & SONS, Inc. (0-471-86371-8) 1984 464 pp. 605 Third Avenue ALGEBRA AND TRIGONOMETRY: A STRAIGHTFORWARD APPROACH New York, N.Y. 10158 2nd Edition In Canada: 22 Worcester Road Martin M. Zuckerman, City College of the City University Rexdale, Ontario of New York M9W 1L1 (D-471-09789-6) January 1985 576 pp. COLLEGE ALGEBRA: A STRAIGHTFORWARD APPROACH Martin M. Zuckerman, City College of the City University of New York 9-6) January 1985 450 pp.

126 Multiply student interest with Harper &Row texts. lust released! Mary Kay Beavers Ignacio Bello BASIC MATHEMATICS CONTEMPORARY WITH ALGEBRA AND INTRODUCTORY GEOMETRY ALGEBRA Paper. 720 pages/tent. Instructor's Manual. Paper. 512 pages/tent. Instructor's Manual. Test Bank Computerized Study Aid. Louis Leithold James A. Mason BEFORE CALCULUS Functions, Graphs, and Analytical LEARNING APL Geometry An Array Processing Approach 700 pages/tent. Instructor's Manual. Paper. 228 pages. Now available Mary Kay Beavers Ignacio Bello ESSENTIAL CONTEMPORARY BASIC MATHEMATICS MATHEMATICS SKIUS Secdnd Edition Paper. 611 pages. Instructor's Manual. Test Bank Paper. 402 pages. Instructor's Manual.

And don~t forget the Computer-Assisted Instructional Courseware o..ff!!f'ed b_r Harp_er & Row and CONDUIT-- Richard C. Detmer John C. Kelly Clinton W Smullen DISCOVERY LEARNING ALGEBRA DRIU AND IN TRIGONOMETRY PRACTICE SecondEdition Austin R. Brown, Jr. These three programs are offered for the Apple II or the Apple II+ , and include printed ARB PLOT instructor's manuals or student guides. A Computer Graphics Utility for Calculus

i!6l!!fJ . To request examination copies, write Suite 3D, Harper & Row, 10 East 53d Street, ,______-r- 'lbj;~Q'qc;;ru=<=

127 SAUNDERS COLLEGE PUBLISHING ...

CALCULUS DENNIS BERKEY, Boston University 1984 • 1200 pages • hardcover •ISBN 0-03-059522-3 Instructor's Solutions Manual • Student Solutions Manual • Computer Test Bank (with computer graphics) ** also available: T.A.'S HANDBOOK, by WILLIAM PERRY and DOUGLAS JEWETT, both of Texas A&M University HERE'S WHAT YOUR COLLEAGUES ARE SAYING ABOUT THIS OUTSTANDING NEW TEXTBOOK. .. "The major strengths of Berkey Calculus are its clearness, good examples, readability for students, problems, and illustrations." -Paul W. Haggard, East Carolina University "The text was very readable and the illustrations excellent; the text was written at a level appropriate to a beginning calculus class." -Ellen Ferrell, Pima Community College "The number and variety of exercises are outstanding." -Louie Huffman, Midwestern State University

SUPPLEMENTS ... MICRO-CALCULUS: A GRAPHING AND TUTORIAL PROGRAM By TECHNICAL EDUCATIONAL CONSULTANTS

This two-diskette package for the Apple from differential and integral calculus that II + and lie features graphic routines that can be used in a classroom or individually are selected by the user. It contains illus­ as a tutorial. trative problems and examples drawn 1984 •ISBN 0-03-062821-0

INTERFACE: CALCULUS AND THE COMPUTER, Second Edition By DAVID A. SMITH, Duke University

Designed for use in· computer labs, this gramming are included. An instructor's computer enrichment text for beginning disk, which contains the computer pro­ calculus introduces students to the appli­ grams, is available for the Apple II, 1/e, the cations of calculus to numerical compu­ IBM PC, or the TRS-80. tations. Most of the text is language inde­ 1984 • 250 pages • paper • pendent; some elements of BASIC pro- ISBN 0-03-070663-7 • Instructor's Disk

• SAUNDERS COLLEGE PUBLISHING

128 A COMMITMENT TO EXCELLENCE

PRESENTING SAUNDERS 1985 MATHEMATICS LIST... NEW! AN INTRODUCTION NEW! MATHEMATICS WITH TO LINEAR ALGEBRA WITH APPLICATIONS TO BUSINESS, APPLICATIONS ECONOMICS, AND SOCIAL STEVE ROMAN, California State Uni­ SCIENCES versity at Fullerton RICHARD BOULDIN, University of Georgia Emphasizes motivation and contains 1985 • 784 pages • Hardcover abundant examples. • ISBN 0-03-062164-X 1985 • 528 pages • Hardcover • Instructor's Manual • Test Bank • Com­ • ISBN 0-03-064017-2 puterized Test Bank • Student Solutions Manual NEW! STATISTICS AND NEW! CALCULUS WITH PROBABILITY AND THEIR APPLICATIONS TO BUSINESS, APPLICATIONS ECONOMICS, AND SOCIAL PATRICK BROCKETT, University of SCIENCES Texas at Austin and ARNOLD LEVINE, RICHARD BOULDIN, University of Georgia Tulane University 1985 • 544 pages • Hardcover Covers sampling theory and surveys. • ISBN 0-03-069764-6 1985 • 624 pages • Hardcover • Instructor's Manual • Test Bank • Com­ • ISBN 0-03-053406-2 puterized Test Bank • Instructor's Manual • Study Guide • Test Bank • Computerized Test Bank AND DON'T FORGET THESE NEW! BASIC MATHEMATICS, OUTSTANDING TEXTS ... A REVIEW Second Edition ELEMENTARY LINEAR JACK BARKER, JAMES ROGERS, and ALGEBRA JAMES VAN DYKE, a// of Portland Com­ J.A. THORPE and P.G. KUMPEL, both of munity College SUNY, Stony Brook Designed for students in need of review, 1983 • 512 pages • Hardcover this worktext covers arithmetic and ele­ • ISBN 0-03-061249-7 mentary algebra in one course. • Instructor's Manual 1985 • 656 pages • Paper • Student Solutions Manual •ISBN 0-03-071588-1 • Instructor's Manual • Test Bank DIFFERENTIAL EQUATIONS: A FIRST COURSE NEW! PRECALCULUS MARTIN GUTERMAN and ZBIGNIEW Second Edition MATHEMATICS NITECKI, both of Tufts University THOMAS HUNGERFORD, Cleveland W. 1983 • 650 pages • Hardcover • ISBN State University and RICHARD 0-03-062502-5 • Student Solutions Manual MERCER, Wright State University 1985 • 624 pages • H'ardcover HOW TO ORDER: • ISBN 0-03-00843-3 For examination copies, please contact your • Computerized Test Bank • Test Bank • local Saunders College Publishing sales repre­ Instructor's Manual sentative or write on your college letterhead to: Karen S. Misler, S11, Saunders College Pub­ lishing, P.O. Box 36, Lavalette, NJ, 08735. Include your course title, enrollment, and text A division of CBS Educational and Professional Publishing currently in use. To expedite shipping, please 383 MADISON AVENUE • NEW YORK, include the ISBN (International Standard Book NY 10017 Number) for each item requested.

S11-AMN5

129 !U

Better than anyone else, you know that the study of things mathematical is on the rise. Students across the country are enrolling in math courses in record numbers. At Wadsworth, we have been committed to the discipline for the past 25 years. And we continue to honor this commitment by publishing pedagogically sound, innovative textbooks and supplements. A look below will give you an idea of the kinds of services we can offer you this year. Because today, math matters more than ever before. - AN EXCEPTIONAL SALES FORCE The spirit of our commitment to mathematics is reflected in our staff of sales representatives. We hope you've seen them visiting your math departments to help you with your book selections, answer your questions, and obtain for you desk copies and supplemental materials. Since math is their #1 discipline, you can be sure they will be around to help you out. Math matters to them. AN EXCELLENT NEW TESTING SERVICE It's called MICRO-PAC®, and it's one of the most innovative and efficient testing systems around. MICRO-PAC is simple-to-use software from Wadsworth that is compatible with your department's IBM PC, Apple 11/lle, TRS-80, or IBM- or Apple-compatible computer. Available for use upon adoption of many of our math texts, MICRO-PAC will help you turn your microcomputer into an outstanding test-authoring and test-generating system that will cut in half (at least!) the time you now spend preparing tests. MATH MATTERS AT BOOTH 17 Stop by the Wadsworth booth and meet our math editors and members of our sales staff. Test out MICRO-PAC yourself. Pick up a complimentary poster depicting the lives of some of today's most creative and interesting mathematicians. And, take a look at our textbook offerings for the coming year.

For more information about these and other Wadsworth mathematics texts, stop by Booth 17 or write: Heather Bennett/Jim Harrison, Mathematics Editors Box AMS-1-85 '\\\17 WADSWORTH PUBLISHING COMPANY U~ Ten Davis Drive, Belmont, California 94002

130 Princeton Mathematics

c Cohomology of Quotients in Sympledic and Algebraic Geometry Frances Clare Kirwan Mathematical Notes, 31 $17.50

Arithmetic Moduli of Elliptic Curves Nicholas Katz and Annals of Mathematics Studies, 108 P: $22.50. C: $60.00

Functional Integration and Partial Differential Equations Mark Freid/in Annals of Mathematics Studies, 109 P: $19.95. C: $60.00

A History of Mathematics Carl B. Boyer P: $12.50

Write for our new Math Catalog. Please Visit Us at Booth #14 in Anaheim

Princeton University Press 41 William Street Princeton NJ 08540

131 HISTORY OF ALGEBRAIC GEOMETRY Jean Dieudonne This book consists of a translation of Chapters I through VIII of Volume 1 of the 1974 edition of Cours de geometrie algebrique and a new Chapter IX by Dr. Dieudonne, which covers the period 1975-1984. Contents: I. Introduction; II. The First Epoch-Prehistory ( 400 B.c.-1630 A.D.); III. The Second Epoch-Exploration (1630-1795); IV. The Third Epoch-The Golden Age of Projective Geometry (1795-1850); V. The Fourth Epoch-Riemann and Birational Geometry (1850-1866); VI. The Fifth Epoch-Development and Chaos (1866-1920); VII. The Sixth Epoch-New Structures in Algebraic Geometry (1920-1950); VIII. The Seventh Epoch-Sheaves and Schemes (1950- ); IX. Recent Results and Open Problems. January 1985, 256 pp., cloth, ISBN 0-534-03723-2, $32.95.

BROWNIAN MOTION AND MARTINGALES IN ANALYSIS Richard Durrett In the last forty years it has been shown that Brownian motion can be used to prove many results in classical analysis, primarily concerning the behavior of harmonic and analytic functions and the solutions of certain partial differential equations. This book provides a self-contained survey of this area beginning with the definition of Brownian motion and then develops the theory needed for the applications. For analysts there is an appendix that describes, without proof, the facts needed from probability theory. Contents: 1. Brownian Motion; 2. Stochastic Integration; 3. Conditioned Brownian Motions; 4. Boundary Limits of Harmonic Functions; 5. Complex Brownian Motion and Analytic Functions; 6. Hardy Spaces and Related Spaces of Martingales; 7. H1 and BMO, m1 and BMO; 8. P.D.E:s Which Can Be Solved by Running a Brownian Motion; 9. Stochastic Differential Equations. 1984, 328pp., cloth, ISBN 0-534-03065-3,$34.95.

MATHEMATICS: PEOPLE, PROBLEMS, RESULTS Douglas M. Campbell and John C. Higgins, editors This three-volume collection of entertaining articles about mathematics, statistics, and computer science will be of interest to both the specialist and the general reader. The ninety selections include articles by Courant, Dieudonne, Knuth, Le Corbusier, P6lya, Ulam, von Neumann, Hilbert, Russell, Wiener, Mosteller, and many others. "Immensely interesting" (Washington Post). 1984, 871 pp., three-volume set, paper ISBN 0-534-03202-8, $29.95; cloth ISBN 0-534- 03199-4,$44.95.

COMPLEX ANALYSIS AND APPLICATIONS, Second Edition William R. Derrick The new edition of this introductory text for mathematics, engineering, and physics students features an early introduction to complex integration and a wide choice of applications, including optics, jet flows, and wakes as well as the traditional applications. Contents: 1. Analytic Functions; 2. Complex Integration; 3. Infinite Series; 4. Contour Integration; 5. Conformal Mappings; 6. Boundary Value and Initial Value Problems. 1984,347 pp., cloth, ISBN0-534-02853-5, $33.95.

132 ,---MACMILLAN~ MATI-IEMATICS ARITHMETIC By JACQUELINE C. AUSTIN and MARGARITA IS ERN, both Miami Dade Community College FUNDAMENTAL MATHEMATICS FOR BUSINESS By RUDOLPH MAGLIO, Oakton Community College, and JACQUELINE PORTNEY DLATT, University ofChicago at Chicago Circle ELEMENTARY ALGEBRA By ANDREW DEMETROPOULOS and KENNETH C. WOLFF, both Montclair State College INTERMEDIATE ALGEBRA By ANDREW DEMETROPOULOS and KENNETH C. WOLFF, both Montclair State College INTRODUCTORY liNEAR ALGEBRA WITH APPLICATIONS ThirdEdition By BERNARD KOLMAN, Drexel University DISCRETE MATHEMATICS By RICHARD JOHNSONBAUGH, DePaul University

STATISTICS PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS second Edition By RONALD E. WALPOLE, Roanoke College, and RAYMOND H. MYERS, Virginia Polytechnic Institute

A FIRST COURSE IN PROBABILITY secondEdition By SHELDON M. ROSS, University ofCalifornia-Berkeley PROBABiliTY AND STOCHASTIC PROCESSES FOR ENGINEERS By CARL W HELSTROM, University ofCalifornia, San Diego PROBABiliTY AND STATISTICAL INFERENCE Second Edition By ROBERT V HOGG, University ofIowa, and ELLIOT A. TANIS, Hope College

fi" For more information call our TOU-FREE number (800) 223-3215, or write: MACMILLAN PUBLISHING COMPANY COLLEGE DMSION • 866 THIRD AVENUE • NEW YORK, NY 10022

133 Harley Flanders believes that the main objective of a calculus text is to help students learn to use calculus-how to set up and solve problems. And he never loses sight of that goal. Efficient, economic organization Flanders organizes each major section by developing a small amount of introductory material on theory (leaving detailed proofs and unusual topics for optional sections), work­ ing out examples to illustrate techniques and applications, and then providing numerous and varied exercises. Careful, informal explanation and motivation of topics Major topics are introduced with informal explanations, examples, and many graphics before the mathematical details of the theory or technique are presented. Attention to problem solving Keeping the student in mind at all times, Flanders fills the text with hints and suggestions for setting up and solving problems. He even provides a unique section on problem solving to help students develop problem-solving skills early in the course. Avoidance of unnecessary mathematical detail By focusing on what is important and not being distracted by lengthy, time-consuming details, Flanders is able to develop the transcendental functions prior to integration, so that students can see some applications of integration during the first semester. An assurance of accuracy Instructors and students expect their calculus text to be accurate and error-free. The publisher has had each calculation and answer checked independently at several stages of production. We invite you to examine Flander's new Calculus for yourself. To obtain your copy, simply address your request on school letterhead to: W. H. Freeman and Company Be sure to include your course name, current rn 41 Madison Avenue text, and anticipated enrollment. New York, N.Y. 10010

134 Science... ~23Q5Blaqo~23Q5Blaqo~23Q5Bl *PASCAL PLUS DATA STRUCTURES, ALGORITHMS, AND ADVANCED PROGRAMMING Nell Dale, University of Texas at Austin Susan C. Lilly 1985 Paper 400 pages est. I Instructor's Guide Designed to follow the popular Introduction to Pascal and Structured Design, this second­ course text reviews basic concepts while stressing good programming practice and problem solving. An effective follow-up to any introductory text, Pascal Plus features careful, logical explanations of advanced programming techniques, standard algorithms, and elementary data structures. Larger sample programs of real-life applications illustrate, for this level, such modern computer science theory and methods as data abstraction and encapsulation. *STRUCTURED COBOL Gary Haggard, University of Maine at Orono Wendell Jones, United States Military Academy 1985 Paper 576 pages est. I Instructor's Guide A clear introduction to problem solving using the COBOL language, this text uses modern design methodology and structured programming techniques. This text features complete, concise programs and a predefined block of code for the ENVIRONMENT DIVISION. In addition, sections of the DATA DIVISION are designed to simulate common computing practices, allowing students to concentrate immediately on problem solving. The text offers step-by-step presentation of new concepts and numerous real applications based on files listed in the Appendices. Now Available! HEATH COMPUTER LANGUAGE WHEELS Peter M. Ginter and Andrew C. Rucks • Pascal • Applesoft BASIC • FORTRAN 77 • TRS-80® 11114 BASIC • COBOL • IBM PC BASIC • Apple® Pascal These handy computer language wheels save valuable time and minimize frustration for both new and experienced programmers. Designed as quick references or refreshers for key commands, summary tables and charts, and examples, these easy-to-use computer language guides put vital information at the users' fingertips simply by the turn of a wheel. INTRODUCTION TO PASCAL AND STRUCTURED DESIGN Nell Dale and David Orshalick, both of the University of Texas at Austin 1983 Paper 470 pages I Instructor's Guide This comprehensive text is a successful introduction to computer science using the Pascal language. The text emphasizes problem solving, good programming habits, and design techniques using top-down methodology. Rich in sample programs and program segments, the authors methodically present and demonstrate all of standard Pascal in precise, jargon-free detail. An extensive Instructor's Guide offers helpful support. Visit D.C. Heath Booths 6&7!

135 For 1bp17otch texts 1234567890123456789 DEVELOPMENTAL STUDIES •BASIC ALGEBRA FOR INTRODUCTORY ALGEBRA Novak COLLEGE STUDENTS 1983 Paper 586 pages Second Edition Instructor's Guide with Tests/Student Lawrence G. Gilligan, University of Guide to Margin Exercises/Answer Key/ Cincinnati Computerized Testing Package/Video Robert B. Nenno, Monroe Community Tapes College Anthony S. Pruchnicki, Jr., Mattatuck INTERMEDIATE ALGEBRA Community College Novak 1985 Paper 398 pages 1983 Paper 668 pages Instructor's Guide with Tests Instructor's Guide with Tests/Student Guide to Margin Exercises/Answer Key/ INTERMEDIATE ALGEBRA Computerized Testing Package/Video FOR Tapes COLLEGE STUDENTS Second Edition ARITHMETIC FOR COLLEGE Gilligan/Nenno STUDENTS 1984 Paper 484 pages Fourth Edition Text with Apple® Disk/Instructor's Guide Wright 1983 Cloth 386 pages *INTERMEDIATE ALGEBRA Instructor's Guide/Student Workbook Marcus M. McWaters and You-Feng Lin, both of the University of South Florida 1985 Cloth 450 pages est. Instructor's Guide with Tests/Student Study Guide/Student Solutions Guide/ Solutions to Even-Numbered Exercises ARITHMETIC David Novak, Simmons College 1983 PaP.er 514 pages Instructors Guide with Tests/Student Guide to Margin Exercises/Answer Key/ Computerized Testing Package/Video Tapes

For details or sample copies, call us toll free: 800-225-1388. In Massachusetts, call collect: 8 617-863-1948. HEATH D. C. HEATH AND COMPANY/College Division

136 0123456788012345678 APPLIED PRECALCULUS MATHEMATICS *MATHEMATICAL *ALGEBRA AND APPLICATIONS TRIGONOMETRY Roland E. Larson and Robert P. For Management, Life, and Hostetler, Social Sciences both of The Pennsylvania State Second Edition University, Ronald J. Harshbarger and The Behrend College James J. Reynolds, 1985 Cloth 638 pages est. both of The Pennsylvania State Study and Solutions Guide/ University, Beaver Campus Instructor's Guide 1985 Cloth 752 pages est. Solutions Guide/Answer Key *COLLEGE ALGEBRA Larson/Hostetler APPLICATIONS OF COLLEGE 1983 Cloth 438 pages est. MATHEMATICS Instructor's Guide/Study and Solutions Management, Life, and Social Guide Sciences * PRECALCULUS Stanci/Stancl Larson/Hostetler 1983 Cloth 720 pages 1985 Cloth 638 pages est. Instructor's Guide/Computer Problem-Solving Instructor's Guide Guide *TRIGONOMETRY UNDERSTANDABLE STATISTICS Larson/Hostetler Concepts and Methods 1985 Cloth 332 pages est. Second Edition Instructor's Guide Brase/Brase 1983 Cloth 489 pages BRIEF CALCULUS WITH APPLICATIONS Larson/Hostetler 1983 Cloth 621 pages Answer Key/Student Solutions Manual BRIEF CALCULUS WITH APPLICATIONS Alternate Edition Larson/Hostetler 1983 Cloth 433 pages Answer Key/Student Solutions Manual

125 Spring StreeVLexington, MA 02173/BOOTHS 6 & 7

137 Quantum Space and Time­ Classical General Relativity The Quest Continues W. B. BONNOR, J. N.ISLAM and Studies and Essays in Honour of M.A. H. MacCALLUM, Editors $44.50 Louis de Broglie, Paul Dirac, and Symplectic Techniques in ASIM 0. BARUT, ALWYN VAN DER Physics MERWE and JEAN-PAUL VIGIER, VICTOR GUILLEMIN and Editors SHLOMO STERNBERG Cambridge·Monographs on Physics $49.50 $49.50 A Concise Introduction to the The Geometry of Fractal Sets Theory of Numbers KENNETH FALCONER ALAN BAKER Cambridge Tracts in Mathematics 85 Forthcoming Forthcoming Games Programming Future Directions in Finite ERIC SOLOMON Group Theory $14.95 MICHAEL ASCHBACHER, DANIEL GORENSTEIN, R. LYONS, M. O'NAN FPF Ring Theory and C. SIMS, Editors Faithful Modules and $39.50 Generators of mod-R Supermanifolds CARL FAITH and STANLEY PAGE London Mathematical Society Lecture Note BRYCE S. DE WITI Series88 Cambridge Monographs on Mathematical Physics Paper$19.95 $59.50 General Irreducible Markov Classgroups of Group Rings MARTIN TAYLOR Chains and Non-Linear London Mathematical Society Lecture Note Operators Series91 ESA NUMMELIN Paper $17.95 Cambridge Tracts in Mathematics 83 $37.50 Representations of General Linear Groups Recursion via Pascal G. D. JAMES J. S. ROHL London Mathematical Society Lecture Note Cambridge Computer Science Texts 19 Series94 Cloth $39.50 Paper $17.95 Paper $19.95 Ninth Colloquium on Trees in Martingales and Stochastic Algebra and Programming Integrals B. COURCELLE, Editor EKKEHARD KOPP $39.50 $29.95 A Topological Tribute Diophantine Equations over I. M. JAMES and Function Fields E. H. KRONHEIMER, Editors R. C. MASON London Mathematical Society Lecture Note London Mathematical Society Lecture Note Series94 Series96 Paper $21 .95 Paper$15.95

138 SOFTWARE ENGINEERS New products in Hughes Radar Systems' Tactical Software technical disciplines is preferred. Real-time software experience Departments have created several openings for Software is a plus. Engineers at various experience levels. A number of challenging assignments are available in developing real-time scientific ap­ Hughes offers a highly competitive salary, excellent benefits plication software for airborne radar signal and data processors. including medical and dental coverage, tuition reimbursement and a tax-deferred savings plan. A variety of software processing is utilized including the following: You are invited to call David Johnson-collect at (213) 648•2913 • Forming digital filters for bandpass signal filtering. for more information or send your resume to Ed Smith, Hughes • Extracting spectral information from the radar signal Aircraft Company Radar Systems Group, Employment Depart­ using Fast Fourier Transforms. ment MAN- 1 , R8/4400, P.O. Box 92426, Los Angeles, • Target range and velocity resolving. California 90009. Proof of U.S. Citizenship Required. Equal • Target detection and thresholding. Opportunity Employer. • Closed loop target tracking using Kalman filtering. • Forming two dimensional high resolution maps. Principals only, please. • Detection and tracking of ground moving targets. Join us and grow professionally in a rewarding career while working on radar systems for the F-14, F-15, F/A-18 aircraft and other advanced applications. HUGHES A Bachelor or advanced degree in Mathematics or related AIRCRAFT COMPANY RADAR SYSTEMS GROUP

THE UNIVERSITY OF FLORIDA Department of Mathematics DEPARTMENT OF MATHEMATICS UNIVERSITY OF HOUSTON announces the opening of two new tenure-track UNIVERSITY PARK assistant professorships beginning August, 1985. The Department of Mathematics will have both Those applying for these positions should have permanent and visiting positions available for the demonstrable research potential. In particular the 1985-86 academic year. Openings for permanent appointments are at all search committee encourages applications from levels, and strong <'lpplicants in all fields are encour­ mathematicians with postdoctoral experience and aged to apply. Applicants in numerical analysis, from those whose research interests are compat­ analysis, probability, statistics and applied mathe­ ible with the interests of current department matics are especially encouraged. Vitae and three letters of reference should be sent to Professor members. Priority areas include algebra/combina­ G. J. Etgen, Chairman, Department of Mathematics, torics, analysis, differential equations, logic, and University of Houston, University Park, Houston, numerical analysis/approximation theory. The Texas 77004. Tel. 713-749-4827. salaries will be highly competitive. Applicants The Department will also have two visiting faculty positions, and these will be available for should provide a resume (including a list of pub­ visits of either one or two semesters. The visiting lications) and should arrange for at least three faculty members will be named letters of reference to be sent to: D. G. Bourgin Visiting Scholars. David A. Drake Some teaching duties will be required, but the Chair, Search and Screen Committee main purpose of the visit is to collaborate with Department of Mathematics the permanent faculty on research centered in the areas of algebra, analysis, or University of Florida topology_ Interested persons should apply by February 15, 1985, to Gainesville, Florida 32611 Professor A. Lelek at the address indicated above. Applications must be received by January The University of Houston is an equal opportunity/ 21, 1985. affirmative action employer The University of Florida is an equal oppor­ tunity employer. sssssssssssssssss

139 The West Math Collection '85 COLLEGE ALGEBRA Jose Barros-Neto, Rutgers University • Instructor's Manual with Test Bank/Student Solutions Manual • 1985/500 pp.(t)/Hardcover COLLEGE ALGEBRA AND TRIGONOMETRY Jose Barros-Neto, Rutgers University • Instructor's Manual with Test Bank/Student Solutions Manual • 1985/600 pp.(t)/Hardcover ARITHMETIC: A PROBLEM SOLVING APPROACH Joseph F. Cleary, Jr., Massasoit Junior College Walter Gleason, Bridgewater State College • Instructor's Manual with Test Bank and Transparency Masters • 1985/500 pp.(t)/Softcover INTRODUCTORY ALGEBRA Michael Gallo, Monroe Comm. College Charles Kiehl, SUNY-Brockport • Instructor's Manual/Study Guide • 1985/575 pp.(t)/Hardcover FINITE MATHEMATICS George J. Kertz, University of Toledo • Solutions/Instructor's Manual • 1985/530 pp.(t)/Hardcover FINITE MATHEMATICS WITH CALCULUS George J. Kertz, University of Toledo • SolutionS/Instructor's Manual • 1985/750 pp.(t)/Hardcover BASIC STATISTICS WITH APPLICATIONS John W. McGhee, California State Univ.- Northridge • Instructor's Manual/Study Guide/Diskette • 1985/650 pp.(t)/Hardcover INTERMEDIATE ALGEBRA Michael N. Payne, College of Alameda, California • Instructor's Manual/Study Guide • 1985/544 pp.(t)/Hardcover TRIGONOMETRY Ralph C. Steinlage, University of Dayton • InstructorS/Solutions Manual • 1985/375 pp.(t)/Hardcover

Need more information? Call or write to: II. WEST PUBLISHING COMPANY, College Dept 6F, 50 W. Kellogg Blvd., P.O. Box 64526, St. Paul, MN 55164. Toll-free 800-328-9424.

140 AMERICAN MATHEMATICAL SOCIETY

AMS SHORT COURSE LECTURE NOTES Introductory Survey Lectures PROCEEDINGS OF SYMPOSIA IN APPLIED MATHEMATICS

COMPUTED TOMOGRAPHY Applied Cryptology, Lawrence A. Shepp, Editor Cryptographic Protocols, Volume 27, 1983, x + 86 pages Softcover: List $15, institutional member $12, and Computer Security Models individual member $9 Richard A. DeMilio, George I. Davida, David To order, please specify PSAPM/27 N P. Dobkin, Michael A. Harrison, and THE MATHEMATICS OF NETWORKS Richard J. Lipton Stefan A. Burr, Editor Volume 26, 1982, viii + 142 pages This survey of cryptology and computer Softcover: List $17, institutional member $14, security is an edited and expanded version of individual member $10 To order, please specify PSAPM/26 N the notes which the Society distributed to accompany the short course on Cryptology in OPERATIONS RESEARCH: MATHEMATICS AND MODELS Revolution: Mathematics and Models. Some Saul I. Gass, Editor friction exists and has existed between certain Volume 25, 1981, reprinted 1983, viii + 198 pages US Government agencies. academic researchers. Softcover: List $12, institutional member $10, and professional individual member $7 societies. and a brief account of To order, please specify PSAPM/25 N the issues which have led to this controversy is given in Chapter 1. This is followed by a survey GAME THEORY AND ITS APPLICATIONS William F. Lucas, Editor of cryptographic theory which emphasizes the Volume 24, 1981, viii + 128 pages two major developments of contemporary Softcover: List $14, institutional member $11, cryptography (the federal data encryption individual member $8 standard and public-key cryptography). The To order, please specify PSAPM/24 N third chapter presents a survey of security MODERN STATISTICS: METHODS AND APPLICATIONS problems which arise in the use of time-shared Robert V. Hogg, Editor and networked digital computers. Finally. a Volume 23, 1980, vi + 110 pages number of protocols which are used to achieve Softcover: List $15, institutional member $12, levels of security in computer systems and the individual member $9 To order, please specify PSAPM/23 N emerging theory surrounding cryptographic protocols are presented. NUMERICAL ANALYSIS Gene H. Golub and Joseph Oliger, Editors Volume 29, 1983, reprinted 1984, xii + 204 pages Softcover: List $24, institutional member $19, Volume 22, 1978, viii + 135 pages individual member $14 Softcover: List $13, institutional member $10, To order, please specify PSAPM/29 individual member $8 To order, please specify PSAPM/22 N

MATHEMATICAL ASPECTS OF PRODUCTION POPULATION BIOLOGY AND DISTRIBUTION OF ENERGY Simon A. Levin, Editor Peter D. Lax, Editor Volume 30, 1984, x + 102 pages Volume 21, 1977, 137 pages Softcover: List $21, institutional member $17, Softcover: List $18, institutional member $14, individual member $13 individual member $11 To order, please specify PSAPMS/30N To order, please specify PSAPM/21N Hardcover: List $27, institutional member $22, individual member $16 Shipping and handling charges: surface To order, please specify PSAPM/30 N delivery - $2 first book, $1 each additional, maximum $25; air delivery - $5 first book, $3 each additional, STATISTICAL DATA ANALYSIS maximum $100. Prepayment Is required. Order Ram Gnanadesikan, Editor from American Mathematical Society, PO Box 1571. Volume 28, 1983, 142 pages Annex Station, Providence, Rl 02901-1571 USA. Softcover: List $17, institutional member $14, individual member $10 Other correspondence should be addressed to To order, please specify PSAPM/28N PO Box 6248, Providence, Rl 02940 USA.

141 Conference on Modern Analysis and Probability (1982, Yale University) Richard Beals, Anatole Beck, and Arshag Hajian, Editors

The Conference in Modern Analysis and Probability William B. johnson and Joram Lindenstrauss, Exten­ in honor of Professor Shizuo Kakutani was held on sions of Lipschitz mappings into a Hilbert space june 8-11, 1982, at Yale University on the occasion Robert R. Kallman, A uniqueness result for a class of his retirement In these Proceedings the papers of compact connected groups that were submitted for this Conference are presented. L. A. Karlovitz, Two extremal properties of functions Initial funding was provided by the National Science Robert Kaufman, On Bernoulli convolutions Foundation. Harvey B. Keynes and Mahesh G. Nerurkar, Generic The three major areas of mathematics on which theorems for lifting dynamical properties by con­ the Conference focused were functional analysis, prob· tinuous affine cocyc/es ability theory, and ergodic theo.ry. Most of the ar­ Bruce Kitchens, Linear algebra and subshifts of ticles presented were works by the respective authors finite type on problems that were pioneered by Professor Kaku­ Anthony Lo Bello, The etymology of the word tani in the past. Questions in Brownian motion, in­ ergodic duced transformations, representation of M-spaces, Peter A. Loeb, A functional approach to nonstandard and fixed point theorems were discussed. measure theory Contents Dorothy Maharam, On positive operators Roy L. Adler and Leopold Flatto, Cross section map Brian Marcus, Karl Petersen and Susan Williams, for the geodesic flow on the modular surface Transmission rates and factors of Markov chains M. A. Akcoglu and L. Sucheston, On identification I. Namioka, Ellis groups and compact right topolog­ of superadditive ergodic limits ical groups j. R. Baxter and R. V. Chacon, The equivalence of William Parry and Klaus Schmidt, Invariants of diffusions on networks to Brownian motion finitary isomorphisms with finite expected code­ A. Bellow and V. Losert, On sequences of density lengths zero in ergodic theory Marina Ratner, Ergodic theory in hyperbolic space 1 1 j. van den Berg and M. Keane, On the continuity of Haskell P. Rosenthal, Embedding of L in L the percolation probability function Daniel j. Rudolph, Inner and barely linear time Felix E. Browder, Coincidence theorems, minimax changes of ergodic Rk·actions theorems, and variational inequalities M. j. Sharpe, Processes evolving from the Indefinite j. R. Choksi, Recent developments arising out of past Kakutani's work on completion regularity of Erik G. F. Thomas, An infinitesimal characterization measure of Gelfand pairs j. R. Choksi and S. j. Eigen, An automorphism of Nils Tongring, Multiple points of Brownian motion a homogeneous measure algebra which does not Benjamin Weiss, Measurable dynamics factorize into a direct product K6saku Yosida and Shigetake Matsuura, A note on Daniel I. A. Cohen, Another generalization of the Mikusit1ski's proof of the Titchmarsh convolution l)rQuwer fixed point theorem theorem Yaet'Naim Dowker, An ergodic theorem Robert J. Zimmer, Ergodic actions of arithmetic groups Nathaniel A. Friedman, Higher order partial mixing and the Kakutani-Markov fixed point theorem , IP-systems In ergodic theory Arshag Hajian and Yuji Ito, Induced transformations on a section 1980 Mathematics Subject Classifications: 46Bxx, 60Gxx, Edwin Hewitt, Conjugate Fourier series on the charac­ 28Dxx ter group of the additive rationals Contemporary Mathematics Volume 26, xii + 432 pages (soft cover) Kiyosi Ito, A stochastic differential equation in List price $34, institutional member $27, infinite dimensions individual member $20 Kinrad jacobs, Ergodic theory and combinatorics ISBN 0-8218-5030-X; LC 84-484 Publication date: May 1984 To order, please specify CONM/26N

Shipping/Handling: 1st book $2, each add'l $1; max. $25; by air, 1st book $5, each add'l $3, max. $100 Prepayment is required. Order from American Mathematical Society, P.O. Box 1571, Annex Station, Providence, Rl 02901-1571, or call toll free 800-556-7774 to charge with Visa or MasterCard.

142 Order Form (Use your peel-ofT label from the Notices)

Ordered by: ______Mail to (if different): ______

QTY CODE AUTHOR and TITLE PRICE $

Shipping and Handling D Surface D Air

Total due (All orders must be prepaid) $

To order using VISA or MasterCard (for book orders only) fill out the following or call 800-556-7774 D VISA D MasterCard. Account Number------Expiration Date ______Signature ______

Shipping and Handling Books are sent via surface mail (UPS to U.S. Journal back numbers. Mathematical Reviews addresses and printed matter elsewhere) unless air indexes. and review volumes are sent via surface delivery is requested. The shipping and handling mail to any destination unless air delivery is re­ charges for book orders are shown below. quested. Postage for surface mail is paid by the AMS. Air delivery rates. which will be quoted upon request. must be paid by the purchaser. First Each Book Additional Maximum Surface $2 $1 $ 25 Air $5 $3 $100

A reminder: the individual member rate applies to the purchase of one copy of any book for personal use. and is not an alternative means of lowering costs for libraries. Staple here

Fold here

NO POSTAGE 111111 NECESSARY IF MAILED IN THE UNITED STATES BUSINESS REPLY MAIL FIRST CLASS PERMIT NO. 554B PROVIDENCE, RI

POSTAGE WlLL BE PAID BY ADDRESSEE

AMERICAN MATHEMATICAL SOCIETY P.O. Box 1571 Annex Station Providence, RI 02901-1571

Fold here

Fasten PAYMENT securely Mathematical Social Sciences Managing Editor: Scope: Kl HANG KIM, The international, interdisciplinary journal MATHEMATICAL Mathematics Research Group, SOCIAL SCIENCES publishes original research, as well as Alabama State University, survey papers, short notes, news items, calendar of Montgomery, AL 36195, U.S.A. meetings and book reviews, which are of broad interest in the mathematical social sciences. The following topics are Advisory Editors: covered: analysis of human ecosystems, analysis of quality of life, analysis of structures and adaptive systems, automata HEINO FASSBENDER, theory, cluster analysis, decision theory, game theory, kinship Dusseldorf, Fed. Rep. Germany, systems, scaling, social welfare theory, the theory of informa­ PETER FISHBURN, tion processes and systems, theory of teams, voting theory, Murray Hill, NJ, U.S.A., KARLA. FOX, and other interdisciplinary topics. Ames, lA, U.S.A., MICHAEL D.INTRILIGATOR, Selection of important papers published in the Los Angeles, CA, U.S.A., Journal: WILHELM KRELLE, Bonn, Fed. Rep. Germany, P .S. Albin, Structure and complexity in economic and social systems. FRED S. ROBERTS, E. Bennatt, Characterization results for aspirations in games with New Brunswick, NJ, U.S.A. sidepayments. B. Dutta, Individual strategy and manipulation of issues. P.C. Fishburn, SSB utility theory: an economic perspective. C. Fla­ ment, On incomplete preference structures. W.V. Gahrlaln and P.C. Editorial Board: Fishburn, Constant scoring rule and majority agreements for large elec­ torates with arbitrary preferences. J.C. Harsanyl, Solutions for some Peter S. Albin (U.S.A.) bargaining games under the Harsanyi-Selten solution theory. E. Kalal, Martin J. Beckmann (W. Germany) Preplay negotiations and the prisoner's dilemma. M. Kaneko, The op­ Steven J. Brams (U.S.A.) timal progessive income tax-the existence and the limit tax rates. M.C. Zoltan Domotor (U.S.A.) Kemp and Y .-K. Ng, Individualistic social welfare functions under or­ Claude Flament (France) dinalism: a reply to Mayston. K.H. Kim and F. W. Roush, Social systems analysis. I. Llpnowskland Y. Shllony, The design of a tort law to control Rebecca M. Frumklna (U.S.S.R.) accidents. B.-C. Llu and C.-T. Hsieh, An integrated model for earth­ Hana W. Gottlnger (W. Germany) quake risk and damage assessment. D.J. Mayston, The generation of a David F. Greenberg (U.S.A.) social welfare function under ordinal preferences. K. Menger, On social Frank Harary (U.S.A.) groups and relations. G. de Maur and P. Jorlon, A possible genealogy John C. Harsanyl (U.S.A.) of Australian marriage systems. H. Moulin, Non-cooperative implemen­ Melvin F. Janowitz (U.S.A.) tation: a survey of recent results. S. Muto, Sequential auctions on Ehud Kalal (U.S.A.) Bohm-Bawerk's horse market. M. Nakayama, Truthful revelation of Ben-Chleh Llu (U.S.A.) preferences for a public good. S. V. Ovchlnnlkov, Convex geometry and group choice. R. Seltan, Evolutionary stability in extensive two-person David Mayston (England) games. P.P. Shenoy, The Banzhaf index for political games. M. Shublk Bernard Monjardet (France) and M.H. Wooders, Approximate cores of replica games and Herv6 Moulin (France) economies. M. Shublk and M.H. Woodars, Replica games exter­ Marla Nowakowska (Poland) nalities, and approximate cores. W. Thomson and T. Lansbarg, Yew-Kwang Ng (Australia) Guarantee structures for problems of fair division. John Rhodes (U.S.A.) Fred W. Roush (U.S.A.) Boris M. Schein (U.S.A.) Reinhard Selten (W. Germany) Coupon for a free copy of Amartya Sen (England) MATHEMATICAL SOCIAL SCIENCES Mltauhlko Toda (Japan) A.L. Toom (U.S.S.R.) Please send to: Tamotau Yokoyama (Japan) Elsevier Science Publishers Attn.: H. de Brouwer Subscription Information: P.O. Box 1991, 1000 BZ Amsterdam, The Netherlands. 1985: Vols. 9 & 10 in 6 issues In the U.S.A. and Canada: Subscription Price: Elsevier Science Publishing Co., Inc. US $151.75/Dfl. 410.00 Journal Information Center (add US$ 16.25/Dfl. 44.00 for 52 Vanderbilt Avenue, New York, NY 10017 postage/handling) Name ______Total Price: US $168.00/Dfl. 454.00 ISSN: 0165-4896 Professional Address ------NORTH-HOLLAND

Tile Dulch ~price II dellnltlve. US $ prices ara sub/eCIIO eiiChange rate lluctuarlom. NH-I&BIOA·SS/JAU6053f Visit our display at the AMS National Meeting and see these and other significant contributions to the field of mathematics ... Geometry of Algebraic Curves Entropy, Large Deviations, and Volume I (of 2) Statistical Mechanics E. Arbarello, M. Cornalba, P.A. Griffiths, Richard S. Ellis and J. Harris 1984/ approx. 300 pp./8 ill us. 1Hardcover Presents the advanced theory of algebraic $39.00 curves, based on a systematic and u p-to-