Notices of the American Mathematical Society 0817643052, 0817636048, 0817634088, 0817633731, 0817635262, 081763777X, 0817632573

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ISSN 0002-9920

of the American Mathematical Society january 2004

Volume 51, Number 1

Cantor and Sierpinski, Julia and Fatou: Complex Topology Meets Complex Dynamics page 9

Donald C. Spencer (19 12-2 001 ) page 17

Tallahassee Meeting page 87

Athens Meeting p age 89

Phoenix Program p age 10 5

-, t

Plain Bob (see p age 3)

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International Mathematics Research Notices Editors

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FORTHCOMING ARTICLES • Chen Lie Algebras, Stefan Papadima and Alexander I. Suciu • Defining Equations of Subspace Arrangements Embedded in Reflection Arrangements, Jessica Sidman • Double Affine Heeke Algebras of Rank 1 and Affine Cubic Surfaces, Alexei Oblomkov • Equations of Shimura Curves of Genus 2, Josep Gonzalez and Victor Rotger • Free Analysis Questions 1: Duality Transform for the Co algebra of Clx:B, Dan Voiculescu • Potential Theory of Signed Riesz Kernels: Capacity and Hausdorff Measure, Laura Prat • Representation Theory and the Quantum Inverse Scattering Method: The Open Toda Chain and the Hyperbolic Sutherland Model, A . Gerasimov, S. Kharchev, and D. Lebedev • Representations of Wreath Products on Cohomology of De Concini-Procesi Compactifications, Anthony Henderson • The Chord Problem and a New Method of Filling by Pseudoholomorphic Curves, CasimAbbas

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NEW f0 NOTEWORTHY Mathematical Olympiad Treasures

Momentum Maps and Hamiltonian Reduction

T. ANDREESCU, American Mathematics Competitions, University of Nebraska, Lincoln, NE; and B. ENESCU, B.P Hasdeu National College, Buzau, Romania

J.P. ORTEGA, CNRS, Universite de Franche-Comte, Besanron, France; and T. S. RATIU, Ecole Poly technique Federate de Lausanne, Switzerland

Mathematical Olympiad Treasures aims at building a bridge between ordinary high school examples and exercises and more sophisticated, intricate and abstract concepts and problems in undergraduate mathematics. The book contains a stimulating collection of problems in algebra, geometry, trigonometry, number theory, and combinatorics. While it may be considered a sequel to Mathematical Olympiad Challenges (ISBN 0-8176-41556), the focus of Treasures is on engaging a wider audience of undergraduates to think creatively in applying techniques and strategies to problems in the real world. The problems are clustered by topic into self-contained sections. Unlike Challenges, however, Treasures begins with elementary facts, followed by a number of carefully selected problems and an extensive discussion of their solutions. This discussion then leads to more complicated and more intellectually challenging problems, as well as their solutions. Throughout the book students are encouraged to express their ideas, conjectures, and conclusions in writing. The goal is to help readers develop a host of new mathematical tools and strategies that will be useful beyond the classroom and in a number of disciplines.

The use of symmetries and conservation laws in the qualitative description of dynamics has a long history going back to the founders of classical mechanics. The focus of this work is a comprehensive and selfcontained presentation of the intimate connection between symmetries, conservation laws, and reduction, treating the singular case in detail. This Ferran Sunyer i Balaguer Prize-winning monograph is the first selfcontained and thorough presentation of the theory of Hamiltonian reduction in the presence of singularities. It can serve as a resource for graduate courses and seminars in symplectic and Poisson geometry, mechanics, Lie theory, mathematical physics, and as a comprehensive reference resource for researchers.

2003/APPROX. 264 PP., 60 ILLUS./SOFTCOVER/$29.95 ISBN 0-8176-4305-2

Mathematical Theory of Diffraction R. J. NAGEM and G. SANDRI, both, Boston University, MA; and M. ZAMPOLLI, NATO SACLANT Undersea Research Centre, LaSpezia, Italy (Translators) A Sommerfeld's Mathematische Theorie der Diffraction

marks a milestone in optical theory, full of insights that are still relevant today. In a stunning tour de force, Sommerfeld derives the first mathematically rigorous solution of an optical diffraction problem. Indeed, his diffraction analysis is a surprisingly rich and complex mix of pure and applied mathematics, and his often-cited diffraction solution is presented only as an application of a much more general set of mathematical results. This complete translation, reflecting substantial scholarship, is the first publication in English of Sommerfeld's original work. The extensive notes by the translators are rich in historical background and provide many technical details for the reader. 2003/APPROX. 200 PP., 38JLLUS./HARDCOVER/$54.95 ISBN 0-8176-3604-8 PROGRESS IN MATHEMATICAL PHYSICS, VOL. 35

Table of Contents: Manifolds and smooth structures • Lie group actions • Pseudogroups and groupoids • The standard momentum map • Generalizations of the momentum map • Regular symplectic reduction theory • The Symplectic Slice Theorem • Singular reduction and the stratification theorem • Optimal reduction • Poisson reduction • Dual Pairs • Bibliography • Index 2003/APPROX. 588 PP., 10 ILLUS./HAROCOVER/$69.95 ISBN 0-817 6-4307-9 PROGRESS IN MATHEMATICS, VOL. 222

Introduction to Vertex Operator Algebras and Their Representations J. LEPOWSKY, Rutgers University, Piscataway, NJ; and H. LI,

University, Piscataway, NJ and Harbin Normal University, China

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The field of vertex operator algebras is an active area of research and plays an integral role in infinitedimensional Lie theory, string theory, and conformal field theory, and other subdisciplines of mathematics and physics. This book begins with a careful presentation of the theoretical foundations of vertex operator algebras and their modules, and then proceeds to a range of applications. The text features new, original results and a fresh perspective on the important works of many researchers; in particular, it provides a detailed treatment of the concept of a "representation" of a vertex (operator) algebra. Requiring only a familiarity with basic algebra, this broad, self-contained treatment of the core topics in vertex algebras will appeal to graduate students and researchers in both mathematics and physics. 2003/APPROX. 328 PP./HARDCOVER/$89.95 ISBN 0-8176-3408-8 PROGRESS IN MATHEMATICS, VOL. 227

from Birkhiiuser lie Theory J.P. ANKER, Universite d'Orleans, Orleans, France; and B. ORSTED, University ofSouthern Denmark, Odense, Denmark {Eds.}

Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, number theory, and mathematical physics. Three volumes, under the general title Lie Theory, feature survey work and original results by well-established researchers in key areas of semisimple Lie theory. Awide spectrum of topics is treated, with emphasis on the interplay between representation theory and the geometry of adjoint orbits for Lie algebras over fields of possibly finite characteristic, as well as for infinitedimensional Lie algebras. Also covered is unitary representation theory and branching Jaws for reductive subgroups, an active part of modern representation theory. Finally, there is a thorough discussion of compactifications of symmetric spaces, number theory via Selberg's trace formula, and harmonic analysis through a far-reaching generalization of Harish-Chandra's Plancherel formula for semisimple Lie groups.

Lie Theory: Lie Algebras and Representations Contains work by J.C. JANTZEN and K.H. NEEB. 2003/APPROX 336 PP., 10 ILLUS./HARDCOVER/$69.95 ISBN 0-8176-3373-1/PROGRESS IN MATHEMATICS, VOL 228

Lie Theory: Unitary Representations and Compactifications Contains work by A. BOREL, L. Jl, and T. KOBAYASHI. 2004/APPROX 352 PP., 10 ILLUS./HARDCOVER/$69.95 (TENT.) ISBN 0-8176-3526-2/PROGRESS IN MATHEMATICS

Lie Theory: Harmonic Analysis on Symmetric Spaces Contains work by E. VAN DEN BAN, P. DELORME, and H. SCHLICHTKRULL. 2005/APPROX 350 PP., 10 ILLUS./HARDCOVER/$69.95 (TENT.) ISBN 0-8176-3777-X/PROGRESS IN MATHEMATICS

lectures on Clifford (Geometric) Algebras and Applications R. ABtAMOWTCZ, Tennessee Technological University, Cookeville, TN; and G. SOBCZVK, Universidad de las Americas, Pueblo, Mexico (Eds.)

This text, written by established mathematicians and physicists, provides a systematic, unified exposition of Clifford geometric algebras. Beginning with an introductory chapter, the book covers the mathematical structure of Clifford algebras and the basic concepts of Clifford analysis, and then provides a detailed examination of the many applications of Clifford algebras to differential geometry, physics, computer vision and robotics. No prior knowledge of the subject is assumed. 2003/240 PP., 251LLUS./SOFTCOVER/$29.95 ISBN 0-8176-3257-3

CALL: 1-800-777-4643 • FAX: (201) 348-4505 E-MAIL: [email protected] • VISIT: www.birkhauser.com Please mention promotion #Y9650 when ordering. Prices are valid in the Americas only and are subject to change without notice. For price and ordering information outside the Americas, please contact Birkhauser Verlag AG by E-mail: [email protected]

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N ot ic es

January 2004

Featu re Artic les 7

Cantor and Sierpinski, Julia and Fatou: Complex Topology Meets Complex Dynamics Robert L. Devane y This article demonstrates the interesting topological and metric properties of some of the well-known julia sets that occur in complex dynamics.

17

Donald C. Spencer (1912-2 001) joseph ]. Kohn, Phillip A. Griffiths , Hubert Goldschmidt, Enrico Bombier i, Bohous Cenkl, Paul Garabed ian, Louis Nirenbe rg The authors recall the mathemati cal legacy and life of an influential American mathematician.

Comm u nicati ons 31 A Tribute to Boris Weisfeiler Alexander Lubotzky, Neal Koblitz

43 Demaine Receives MacArthu r Fellowship 44 Engle and Granger Receive Nobel Prize in Economic Sciences

Comm entary 7 Opinion 8 Letters to the Editor

3 5 The Mathema tics ofjuggling -A Book Review Reviewed by Allen Knutson

39 Beyond the Limit: The Dream of Sofya Kovalevs kaya-A Book Review Reviewed by Ann Hibner Koblitz

Notices of the American Mathematical Sodcl\

EDITOR: Andy Magid ASSOCIATE EDITORS: Susanne C. Brenner, Bill Casselman (Covers Editor), Robert j. Daverman, Nathaniel Dean, Rick Durrett, Susan Friedlander, Robion Kirby, Steven G. Krantz, Elliott H. Ueb, Mark Saul, Karen E. Smith, Audrey Terras, Usa Traynor SENIOR WRITER and DEPUTY EDITOR: Allyn jackson MANAGING EDITOR: Sandra Frost CONTRIBUTING WRITER: Elaine Kehoe PRODUCTION ASSISTANT: Muriel Toupin PRODUCTION: Marcia Almeida, Kyle Antonevich, Stephen Moye, Lori Nero, Karen Ouellette, Donna Salter, Deborah Smith, Peter Sykes ADVERTISING SALES: Anne Newcomb SUBSCRIPTION INFORMATION: Subscription prices for Volume 51 (2004) are $40llist; $321 institutional member; $241 individual member. (The subscription price for members is included in the annual dues.) A late charge of 10% of the subscription price will be imposed upon orders received from nonmembers after January 1 of the subscription year. Add for postage: Surface delivery outside the United States and India-$20; in India-$40; expedited delivery to destinations in North America-$35; elsewhere-$87. Subscriptions and orders for AMS publications should be addressed to the American Mathematical Society, P.O. Box 845904, Boston, MA 02284-5904 USA. All orders must be prepaid. ADVERTISING: Notices publishes situations wanted and classified advertising, and display advertising for publishers and academic or scientific organizations. Advenising material or questions may be faxed to 401-331-3842 (indicate "Notices advertising" on fax cover sheet).

Departments Mathematics People ..... . ... . . . ............. ... ........... . ... 45 Lindenstrauss and Soundararajan Awarded 2003 Salem Prize, Prizes of the Mathematical Society of japan, Kuo Wins Information-Based Complexity Young Researcher Award, NSF CAREER Awards for 2002 and 2003, Trjitzinsky Memorial Awards Presented. Mathematics Opportunities .. ..... ... .. ...... . ........... .. .. .. 48 Deadlines and Target Dates at the OMS, ONR Young Investigator Program, Collaborations in Mathematical Geosciences, News from AIM, News from the MBI, News from the SAMSI, Departments Coordinate job Offer Deadlines. Inside the AMS .......... .. .. . ... . .... .... . ............ . .. ... .. 51 Experimental "Current Events" Session at joint Meetings, Fan and Caldwell Scholarships Awarded, AMS Participates in Celebration of von Neumann's Birth, Deaths of AMS Members. Reference and Book List . .. .. ... . .. .. .. ........ ... .. .. . .. .... . . 53 Mathematics Calendar ......................... . .. . .. .. .. . . . . . . 61 New Publications Offered by the AMS .. . .. . . . . . .. .. ... . .. ...... 65 Classifieds . .. .. ...... ..... .. .. ..... . ............... . ... . .. . ... 72 General Information Regarding Meetings & Conferences of the AMS . . .... . ....... .. . .. .... .. .. . ...... .. .. . ... .......... 84 Presenters of Papers, joint Meetings in Phoenix . . ....... ..... .. 99 Program of the Sessions, joint Meetings in Phoenix . ..... . .... 105 Meetings and Conferences Table of Contents .. . .. .. ...... .. .. 1 76

SUBMISSIONS: Articles and letters may be sent to the editor by email at [email protected], by fax at 979-845-6028, or by postal mail at Department of Mathematics, 601 Elm, PHSC 423, University of Oklahoma, Norman, OK 73019-0001. Email is preferred. Correspondence with the managing editor may be sent to noti ces@ams. org. For more information, see the section "Reference and Book Ust". NOTICES ON THE AMS WEBSITE: Most of this publication is available electronically through the AMS website, the Society's resource for delivering electronic products and services. Use the URL http: I /www. ams . org/notices/ to access the Notices on the website. [NortcesoftheAmericanMathemartca/ Society is published monthly except bimonthly in june/July by the American Mathematical Society at 201 Charles Street, Providence, Rl 02904-2294 USA, GSTNo. 12189 2046 RT****. Periodicals postage paid at Providence, Rl, and additional mailing offices. POSTMASTER: Send address change notices to Notices of the American Mathematical Society, P.O. Box 6248, Providence, Rl 02940-6248 USA.) 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. Tel:401-455-4000,email: noti ces@ams. org. ©Copyright 2004 by the American Mathematical Society. All rights reserved. Printed in the United States of America. The paper used in this journal is acid-free and falls within the guidelines established to ensure permanence and durability.

From the AMS Se~tetary AMs standard ~over

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Letter from the Editor

Reflections of a New Editor "The report was condemned in Parliament for being 'Unhelpful to a nonspecialist audience'. Opposition leaders called for resignations" (emphasis added). This reporting from the BBC newsreader, and especially the highlighted phrase, certainly caught my attention. Our central Oklahoma classical music station carries BBC World Service bulletins several times a day; I was half-listening to this 7 a.m. one on a morning last September. The disposition of the report was (and remains at this writing) a serious matter, but it was the characterization "unhelpful to a nonspecialist audience" that made me put down my morning paper and start speculating. How many times do we find ourselves in departmental colloquia or at invited addresses at meetings or starting to read survey or expository articles in journals or conference proceedings only to discover that they are "unhelpful to a nonspecialist audience"? Or what about the times that curiosity or research needs draw us to topics beyond our own specialities only to discover that the available articles and monographs expect prerequisites from their readers only a specialist is likely to have? Conversely, and positively, consider the pleasure and satisfaction of hearing a great talk or reading a great article that gives you a sense of what's happening in a field you thought would always b e closed to you. And, of course, let's not overlook the pleasure and satisfaction, if one can do it, of giving such a talk or writing such an article. I begin with this issue a term as editor of these Notices. In all the range of material the Notices carries, from mathematics feature articles to reviews of mathematically connected film and fiction, to memorial articles, history (including personal history), and in all its aspects as the journal of record of the American Mathematical Society, it is my hope that the Notices remains interesting and satisfying to read and, above all, helpful to a nonspecialist audience. It has been my honor and pleasure to serve on the editorial board of the Notices since the AMS launched the current "enhanced" Notices in January 1995. One of the honors and pleasures has been to be able to observe and admire the efforts and achievements of the editors: Hugo Rossi, Tony Knapp, and Harold Boas. All are owed a debt of gratitude by the American Mathematical Society and indeed by the mathematics community in general. I want to especially thank Harold Boas for his personal assistance in this latest transition. Many of the articles you will enjoy in this and future issues are the fruits of Harold's editorial efforts. The Society and community should also b e grateful that the Notices continues to benefit from the services of managing editor Sandra Frost and deputy editor Allyn Jackson, as it has since its 1995 launch. jANUARY

2004

The Notices, like many of the Society's successful efforts, relies heavily on mathematician volunteers. All mathematical articles that appear in the Notices have been through an editorial process in which they are edited both for mathematical content (by an expert in the field) as well as for expository style. Both content and style readers are volunteers, often drawn from our editorial board of associate editors. The editorial board also nominates andrecruits authors. And many in the mathematical community have also helped advise the Notices about mathematical developments that the Notices should cover, as well as suggesting possible authors of articles. But of course ultimately the success of the Notices depends on its authors. While one way to become a Notices author is to accept a solicitation from the editor or an editorial board member (and many mathematicians have kindly done so), the Notices welcomes contributions. I would hope that all mathematicians in a position to write articles helpful to a nonspecialist audience will consider doing so for the Notices. For example, an author of a monograph may find that the book's introduction is easily adapted to be a Notices article, as are many colloquium talks or seminars aimed at graduate student audiences. Information for authors is published regularly in the Notices, most recently in the June/ July 2003 issue (page 706). Suggestions for articles and author inquiries can also be sent to Noti ces@math. ou. edu.

NOTICES OF lHE AMS

-Andy Magid

7

Letters to the Editor Parallelizable Manifolds It has recently come to the attention of one of us (AW) that an old result due to Cartan and Schouten [1] and the other of us [3] is frequently misquoted in the mathematics and physics literature (on the sci. physics. research newsgroup as well as in published books and papers). We hope that this letter will help to prevent further misquotations. The "theorem" is frequently stated in a form like: "Every compact, simply connected, parallelizable manifold is (diffeomorphic to) a product of 7-spheres and Lie groups." In fact, the theorem requires a strong geometric hypothesis, namely, that among the pseudo-riemannian metrics which are invariant under the flat connection naturally associated to a parallelization, there is at least one whose geodesics are the same as those of the connection. (Without this hypothesis, the Poincare conjecture would be an easy corollary.) It is not hard to find counterexamples when the geometric hypothesis is dropped. For instance, Kervaire [2] proved that a product of spheres is parallelizable as long as at least one of them has odd dimension; most such products are not diffeomorphic to products of Lie groups, since a compact, simply connected Lie group has nontrivial third cohomology. We would like to thank Robert Bryant, Rob Kirby, and Jack Lee for some interesting discussion of this matter.

- Alan Weinstein University of California, Berkeley [email protected] joseph Wolf University of California, Berkeley [email protected] References [1] £. CARTAN and ]. A. S CHOUTEN, On riemannian geometries admitting an absolute parallelism, Nederl. Akad. Weten· sch. Proc. Ser. A 29 (1926), 933-946.

8

[2] M. KERvAIRE, Courbure integrale generalis e et homotopie, Math. Ann. 131 (1956), 219-252. [3]]. A. WOLF, On the geometry and classification of absolute parallelisms. I, II, ]. Differential Geom. 6 (1971 / 72), 317-342; 7(1972), 19-44.

(Received October 2003) Shtuka and Stuka Dear Readers, Recently the Notices received from a reader a message about the term "shtuka", which was the subject of a "WHAT IS ... ?" column in the January 2003 issue. The reader conjectured that the term comes from the German word "Stuka", the abbreviated name for "Sturzkampfflugzeug," a World War 11-era dive bomber. Our curiosity piqued, we wrote to the originator of the term, Vladimir Drinfeld. He kindly agreed to let us publish his reply, which appears below.

-Allyn jackson The Russian noun "shtuka" has the following translations: 1. piece, item, unit 2. (colloquial) thing 3. trick It stems from the German noun "Stiick", which means "piece, item, unit". In my Russian letter to David Kazhdan (1976), in which I described my proof of the Langlands conjecture for GL(2) over a functional field, I used "shtuka" in the second sense ("thing") as a temporary name. Later I suggested the names "FH-sheaf" or "F-sheaf", because the definition of these objects involves the Frobenius morphism and the Heeke correspondences (F=Frobenius, H=Hecke). But the authors who wrote in English or French preferred "shtuka" (probably because "shtuka" has no meaning for them, just like "quark"). In Russian "shtuka" sounds funny, and in German it is probably quite misleading, because according to my dictionary the German "Stuck" cannot mean "thing".

NOTICES OF THE

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I know nothing about "stuka" as short for "Sturzkampfflugzeug". -Vladimir Drinfeld University of Chicago (Received October 15, 2003) About the Cover

Plain Bob The topic for this month's cover was taken from the book The Mathematics of juggling, written by Burkard Polster and reviewed in this issue by Allen Knutson. Chapter 6 in the bookis about bell ringing. The object of this principally English pastime is to cycle though all the permutations of a certain number of bells, following strict rules that effectively force the ringers to trace a Hamiltonian cycle in a Cayley graph associated to the permutation group §n. For 4 bells the Cayley graph can be drawn on the edges of a truncated octahedron. The figure at the right is the score of the method, telling each of the bell ringers what his timing is in each change. I have left out the last change, which is the same as the first. The names of sequences of changes are extremely attractive, I suppose going back for centuries. In doing the cover, I was torn between 'Plain Bob', 'Canterbury', 'St. Nicholas', or 'Single Court'. The version of Plain Bob illustrated on the cover is more correctly known as Plain Bob Minimus, to distinguish it from analgous sequences with more bells. For more on the mathematics of bell ringing, look at the article 'Ringing the changes' (Math. Proc. Cambridge Phil. Soc. 94, 1983) by Arthur T. White and also http: I I www. ringing. info. My thanks to Alexander Holroyd for expert help. -Bill Casselman, Covers Editor ([email protected])

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Cantor and Sierpinski, Julia and Fatou:

Complex Topology Meets Complex Dynamics Robert L. Devaney

Introduction Topologists have enjoyed pondering the exotic properties of fascinating objects such as indecomposable continua, Sierpinski curves, and Cantor bouquets for almost one hundred years, while complex dynamicists have only recently begun to enjoy the beauty and intricacy of fractal objects known as the Julia sets. Recent developments, however, have brought both of these fields closer together, as many of the extraordinary spaces from planar topology have now been shown to arise as Julia sets. In this article we describe a few of these topological incursions into complex dynamics. Julia Sets Let F : ( ~ ( be a complex analytic function, and let P denote F composed with itself n times, the nth iterate of F. For a point z E (, the orbit of z is the sequence z, F(z), F 2 (z), .... Of interest in dynamics is the fate of these orbits: Is this fate predictable or is it not? In complex dynamics the predictable set is the Fatou set; points in this set have the property that all nearby orbits b ehave "similarly". Thanks to work of Julia ana Fatou in the years 1910- 19 and Sullivan in the 1980s, the dynamics of F on the Fatou set is completely understood. There are only a few types of b ehaviors associated with such points: Most often, points in the Fatou set simply tend to an attracting periodic orbit, although there are several other well-understood, though less commonly encountered, p ossibilities. Robert L. Devaney is professor of mathematics at Boston University, Boston. His email address is bob@bu. edu. }ANUARY

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The julia set is the complement of the Fatou set: It consists of points for which nearby orbits behave

in vastly different manners. This is the "chaotic" set for such maps. By a classical theorem of Mantel, if z is a point in the Julia set of F and U is any neighborhood of z, then the union of the forward images of U contains the entire plane (with the exception of at most one point). So F depends quite sensitively on initial conditions on its Julia set in the sense that a small error in specifying the initial point can lead to huge changes in the fate of the orbit. There are other equivalent definitions of the Julia set. For example, the Julia set is also the closure of the set of repelling periodic points for F. From a dynamical systems point of view, all of the interesting behavior of a complex analytic function occurs on its Julia set, and it is this set that contains the interesting topology. As a simple example, consider the function F(z) = z 2 • The behavior of all orbits of this function is easy to describe. If 0 < lzl < 1, then IF(z)i < izl, and so all orbits that begin inside the unit circle simply tend to 0, which is an attracting fixed point. If Iz I > 1, then all orbits increase in magnitude and tend to oo . Finally, if z lies on the unit circle, then the images of any small neighborhood of this point under P eventually cover the entire plane, except (possibly) the origin. As a consequence, the Julia set of z 2 is the unit circle, and the Fatou set contains all other points in C The reader should be forewarned that very few other Julia sets are as simple to understand. Often, these Julia sets are extremely complicated fractal sets with equally complicated topology, as we shall see.

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Figure 1. The Sierpinski carpet.

Sierpinski Curves A Sierpinski curve is a planar set that is homeomorphic to the well-known Sierpinski carpet fractal C (see Figure 1). The Sierpinski carpet is constructed as follows. Start with the unit square in the plane and divide it into nine equal sub squares. Then remove the open middle square, leaving eight closed subsquares. Now repeat this process, removing the open middle third from each of the eight sub squares, leaving 64 smaller squares. When this process is repeated ad infinitum, the resulting set is the Sierpinski carpet. While this set may at first look rather tame, in fact its topology is quite rich: The Sierpinski carpet contains a homeomorphic copy of any compact, connected one (topological) dimensional planar set, no matter how complicated that set is. In this sense the Sierpinski curve is a "universal" planar set. Note that all of the open squares removed during the construction of C have boundaries that are pairwise disjoint simple closed curves. Indeed, the lines x = 112 andy= 112 meet C in a Cantor middle-thirds set, with the endpoints of this Cantor set providing the intersections of the boundaries of removed squares. In addition, it is easy to check that the carpet is compact, connected, locally connected, and nowhere dense in the plane. In fact, these properties characterize Sierpinski curves, for any planar set that shares all of these properties is homeomorphic to the Sierpinski carpet [11] and hence is also a universal planar set. Sierpinski Curve Julia Sets Sierpinski curves arise as Julia sets of certain rational functions. The first example of this was given by .Milnor and Tan Lei [10]. A more accessible collection 10

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z

A +2 z

where A * 0 is a complex parameter. It is known [2] that, for this family, there are infinitely many open sets in the A-plane in any neighborhood of A = 0 that have the property that the Julia set of Fil is a Sierpinski curve whenever A lies in one of these sets. Hence all of these Julia sets are homeomorphic, so that, from a topological point of view, all of these Julia sets are the same. However, from the point of view of dynamical systems, the dynamics on these Julia sets are quite different: Dynamicists say that two maps whose parameters lie in different open sets are not topologically conjugate. For a rough idea of the construction of these Julia sets, note that if I z I is sufficiently large, then I AI z 2 1 is small, so Fil is essentially given by z ..... z 2 • As a consequence, any orbit sufficiently far from the origin simply tends to oo. The open set about the point at oo consisting of all points whose orbits tend to oo is called the basin of attraction of oo. As in the case of z 2 , provided that IAI is small, the boundary of this basin is a simple closed curve surrounding the origin. Inside this curve the dynamical behavior is much more complicated. For definiteness, let us fix A = -1 I 16 and denote the corresponding map by F. Clearly, F has a pole at 0. There are four pre-poles for this function, at the points ±1 12 and ±i l 2, and there are also four critical points for F at points of the form w I 2, where w is any fourth root of -1. Note that F(w 12) = ±i l 2, so that P(w 12) = 0, and so all four critical points are mapped to the pole after two iterations. This is what makes the case A = -1 I 16 so special. The Julia setofF is shown in Figure 2. Let B denote the basin of attraction of oo. As above, B is bounded by a simple closed curve. There is an open set T about the pole at 0 that is mapped in two-to-one fashion onto B; we call T the trap door, since any orbit that enters it "falls through" it and ends up in the basin of oo. The only preimages of a point in the basin lie either in B or in T, since the rational map F has degree four. One checks easily that the boundaries of T and B are disjoint. Now consider the preimages ofT. The preimage of the real axis under F is just the real and imaginary axes. Thus the four preimages of Tare open sets surrounding the prepoles on these axes, and the boundaries of each of these sets are disjoint from one another as well as from the boundaries of T and B. These are the four large red regions surrounding T that intersect the axes. Next consider the preimages of these sets. The four critical points fall into the trap door at iteration two, and they are surrounded by open sets that have the

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same property. These are the largest red regions intersecting the rays e = ± TT I 4 and e = ± 3TT I 4. There are eight other smaller open sets that are mapped onto the trap door by F 2 , and each of these preimages is bounded by a simple closed curve which is disjoint from those previously constructed. Continuing in this manner yields the set of points whose orbits eventually enter B. These are the analogues of the removed open squares in the Sierpinski carpet. It is known that the union of these sets forms the Fatou set for F; the Julia set is its complement. See [2] for more details. The Sierpinski curve Julia sets of several other members of the family F;~. are shown in Figure 3. Each is homeomorphic to the Julia set for .\ = - 1116, but the dynamical behavior on each set is quite different. The well-known fractal called the Sierpinski triangle (or gasket) also arises as a Julia set, this time for the related function G(z) = z 2 +.\I z where .\ "' -0.593. See Figure 4. Though this set shares the same first name as the Sierpinski curve, it is both topologically and dynamically quite different. For example, note that the boundaries of B, T, and the preimages of T are not pairwise disjoint in this case. Cantor Bouquets and the Complex Exponential Another type of interesting Julia set is a Cantor bouquet. Roughly speaking, a Cantor bouquet is an uncountable collection of disjoint continuous curves tending to oo in a certain direction in the plane, each of which has a distinguished endpoint. More precisely, following Aarts and Oversteegen [1], a Cantor bouquet is any planar set that is homeomorphic to a straight brush. To define this set, let 'B be a subset of [0, oo) x 1 where 1 is a dense subset of the irrational numbers. The set 'B is a straight brush if it has the following three properties: 1. Hairiness. For each point (x, oc) E 'B, there is a t 01 E [0, oo) such that {t I (t, oc) E 'B} = [t 01 , oo). The point (t 01 , oc) is the endpoint of the hair given by [t 01 , oo) X {oc}. 2. Endpoint density. For each (x, oc) E 'B, there exists a pair of sequences Wn} and LYn} in 1 converging to oc from both · above and below and such that the corresponding sequences of endpoints tfln and t r n converge to x. 3. Closed. The set 'B is a closed subset of ~ 2 • To see a Cantor bouquet in complex dynamics, consider the complex exponential function E;~.(z) = .\exp(z) where 0 < .\ < 11e. For such a value of.\, the graph of the real exponential.\ exp(x) meets the diagonal line y = x at two points, an attracting fixed point at q" and a repelling fixed point at P.Jo..· Note that E.\(- log.\) = 1, so that q" < - log.\ < PJo... See Figure 5. jANUARY

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Figure 2. The julia set for F(z) = z 2 - 1116z 2 • Colors indicate the number of iterations to enter a neighborhood of oo, with shades of red indicating fastest entrance, followed by yellow, green, and blue. The boundary of the colored region is the julia set.

In C, consider the vertical line Re z = - log .\. The exponential wraps this line around a circle centered at the origin and lying to the left of x =- log.\, since £"(-log.\)= 1 1 I e, this orbit now tends to oo. When this occurs, it is known that ](Ell)=([.

Figure 5. The graphs of Ell 1 for A1 < 1 I e, A2 = 1 I e, and ,\3 > 1 I e.

the graph of Ell is tangent to the diagonal line at x = 1, so that the two fixed points q;~. and p;~. coalesce to become one neutral fixed point. For ,\ > 1 I e the fixed points disappear from the real line. Dynamicists call this simple transition a saddle-node bifurcation (although in this low-dimensional setting there is no saddle point apparent anywhere). In the plane, however, this change is much more dramatic. Suddenly, for ,\ > 1 I e, the Julia set be-

Indecomposable Continua One reason that the Julia set of E;~. explodes for ,\ > 1 1e is the fact that the set of repelling periodic points suddenly becomes dense in C A second, more topological reason is that, as ,\ increases through 11e, infinitely many of the hairs suddenly become another kind of interesting topological object, namely indecomposable continua. An indecomposable continuum is a compact, connected set that carmot be written as the union of two compact, connected, proper subsets. This union is not a disjoint union, by the way. For readers not familiar with these sets, try for just a moment to think of such an indecomposable set. The closed unit interval is not indecomposable, since it may be written, for example, as [0, 213] u [113, 1]. The unit circle is not indecomposable, for it is the

Figure 6. The tip ofthe Cantor bouquet for Ell with,\ < 11e and the ensuing explosion when ,\ > 11e. Note the remnants of the bouquet. jANUARY

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nected. If we consider a closed subset that contains the curve starting at 0, then we find that this curve passes through, in succession, the points in the Cantor set lying at x = 1, 213, 113, 219, 719, .. . , and ultimately all of the endpoints of the Cantor set. Hence the closure of this curve is the entire Knaster continuum, and so this subset is not proper. Topologically, this set contains much more. There are infinitely many disjoint curves in this set, and each of them is dense. Only the aforementioned curve through 0 has an endpoint, however, and this is the only curve that is "accessible" from the exterior.

Figure 7. The barest outline of the Knaster continuum.

union of its upper and lower (closed) semicircles. Neither is a sphere or a torus or even the Sierpinski carpet or the Cantor bouquet (with the point at oo added to make it connected) described earlier. The simplest example of an indecomposable continuum is the Knaster continuum. This set is constructed as follows. Start with the Cantor middle-thirds set on the real line in !Rt 2 • This set is symmetric about x = 1 I 2, so we can join any symmetric pair of points in the Cantor set by a semicircle in the upper half plane centered at x = 1 I 2. Now look in the lower half plane. Points in the right-hand portion of the Cantor set between 213 and 1 may be connected by semicircles lying in the lower half plane, this time centered about 516. This leaves the left half of the Cantor set. This portion may also be cut in half, and symmetric pairs of points in the right portion may now be joined by semicircles. Continuing in this fashion, in the limit we get a set that is known to be indecomposable. See Figure 7. To get a feeling for why this set is indecomposable, suppose we try to break this set into its left and right halves as we did with the unit interval. Then the resulting sets are clearly no longer connected. Similarly, dividing the set into its upper and lower portions also causes the resulting sets to be discon-

Figure 8. The hair in the region 0 ~ Im z ~ rr.

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Back to the julia Set To see how indecomposable continua arise for the complex exponential, consider what happens on the real line. For .\ ~ 1 I e, there is a hair in the Julia set given by the interval [p", oo) lying along the real line. When .\ exceeds 1 I e, this hair suddenly fills the entire real line. But there is more. Consider the line y = rr (or y = -rr). This line is mapped to the real axis, and so, by adjoining the point at -oo (the preimage of 0) to these lines, we get a hair that is even longer. But there is a preimage of the line y = rr contained in the strip 0 < y < rr; this is another "C"-shaped curve that tends to oo tangentially toy = rr andy = 0. And this curve has a preimage in the strip, and this preimage has a preimage, and so forth. See Figure 8. If we compactify the picture by compressing everything into the strip -1 ~ x ~ 1, say, and then adjoining the endpoints as we travel around the hair, we obtain a curve that can be shown to accumulate everywhere on itself, just as in the case of the Knaster continuum. The closure of this set is then known to be an indecomposable continuum. Open problems abound in this setting. The above construction gives an indecomposable continuum in the Julia set for each value of .\ > 1 I e. Are each of these sets homeomorphic? Probably not. It is entirely possible to have a "continuum" of topologically different indecomposable continua. Beyond the hair that lies on the real axis, uncountably many other hairs also explode in a similar manner as we pass through the bifurcation. See [3]. Again, what is the topology of these sets? How does this topology depend on .\? These too are open questions. Acknowledgements It is a pleasure to thank many colleagues for illuminating conversations regarding both the topology and the dynamics of the above examples. This list includes Paul Blanchard, Adrien Douady, Tan Lei, John Mayer, John Milnor, Carsten Petersen, Monica Moreno Rocha, Pascale Roesch, James Rogers, and Mitsuhiro Shishikura. java applets written by Yakov Shapiro that can be used to explore these maps

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are available at the author's website, http: I I math.bu.edulpeoplelbob. References [1]]. AARTS and L. 0VERSTEEGEN, The geometry of Julia sets, Trans. Amer. Math. Soc. 338 (1993), 897-918. [2] P. BLANCHARD, R. L. DEVANEY, D. M. LOOK, P. SEAL, and Y. SHAPIRO, Sierpinski curve Julia sets and singular perturbations of complex polynomials, to appear. Available at:math.bu.edu/people/bob/ papers.html. [3] R. L. DEVANEY and X. JARQUE, Indecomposable continua in exponential dynamics, Conform. Geom. Dyn. 6

,.Get your copy of this new book at the Joint Mathematics Meetings and have it signed by the author!

Math~matical Puzzl~ '(I Connoi~~~ur'~ Cotl~ction

(2002), 1-12. [4] R. DEVANEY, K. josic, andY. SHAPIRO, Singular perturbations of quadratic maps, to appear in Intl. ]. Bifur. Chaos. [5] R. L. DEYANEY and M. KRYCH, Dynamics of Exp(z), Ergordic Theory Dynam. Systems 4 (1984), 35-52. [6] B. KARPINSKA, Hausdorff dimension of the hairs without endpoints for Ae 2 , C. R. Acad. Sci. Paris Ser. I Math.

328 (1999), 1039- 1044. [7]]. MAYER, An explosion point for the set of endpoints of the Julia set of Aexp(z), Ergodic Theory Dynam. Systems 10 (1990), 177-184. [8] C. McMuLLEN, Area and Hausdorff dimension of Julia sets of entire functions, Trans. Amer. Math. Soc. 300 (1987), 329-342. [9]]. MILNOR, Dynamics in One Complex Variable, Vieweg, 1999. [10]]. MILNOR and TAN LEI, A "Sierpinski Carpet" as Julia set. Appendix F in Geometry and dynamics of quadratic rational maps, Experiment. Math. 2 (1993), 37-83. [11] G. T. WHYBURN, Topological characterization of the Sierpinski curve, Fund. Math. 45 (1958), 320-324.

P~t~r Winkl~r ISBN: 1-56881-201-9; January 2004 . Paperback; 176 pp.; $15.00 (tent.)

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Puzzle solution available at A K Peters booth #302 at the Joint Mathematics Meetings, January 7-10,2004 in Phoenix, AZ. A K Peters, Ltd. 63 South Ave., Natick, MA 01 760-4626 Tel: (508) 655-9933 Fax: (508) 655-5847 www.akpeters.com 1 [email protected]

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Donald C. Spencer (1912-2001) joseph]. Kahn, Phillip A. Griffiths, Hubert Goldschmidt, Enrico Bombieri, Bohous C enkl, Paul Garabedian,

Louis Nirenberg

joseph]. Kahn Donald C. Spencer died on December 23, 2001. He was born on April2 5, 1912, in Boulder, Colorado. He was an undergraduate at the University of Colorado (B.A. in 1934) and at the Massachusetts Institute of Technology (B.S. in Aeronautical Engineering in 1936) and a graduate student in mathematics at Cambridge University(Ph.D. in 1939, Sc.D. in 1963). His doctoral thesis, "On a Hardy-Littlewood problem of diophantine approximation and its generalizations", was written under the direction of ]. E. Littlewood and initiated Spencer's remarkable mathematical career. Spencer taught at M.I.T. (1939-42), at Stanford (1942-50 and 1963-68), and at Princeton (1950-63 and 1968-78). He was the Eugene Higgins Professor at Princeton (1971-72) and the Henry Burchard Fine Professor at Princeton (1972-78). He received the degree Sc.D. honoris causa from Purdue University (1971) and was the joint recipient with A. C. Schaeffer of the B6cher Memorial Prize (1948). He was a member of the U.S. National Academy of Sciences (from 1961), a fellow of the American Academy of Arts and Sciences (from 196 7), and a recipient of the National Medal of Science (1989). He was the author of numerous important research papers and four influential books (see [1], [2], [3], [4], [5]).

Spencer's mathematical work is truly impressive and spans many fields in which he made fundamental contributions. Before coming to Princeton, he worked in number theory on lattice points and joseph ]. Kohn is professor of mathematics at Princeton University. His email address is kohn@pri nee ton. edu. jANUARY

2004

on sequences of integers; in applied mathematics on fluid mechanics; and in the theory of one complex variable on univalent functions, on conformal mappings, and on Riemann surfaces. At Princeton, Spencer's research turned to several complex variables and complex manifolds. He collaborated with Kunihiko Kodaira, who is also widely Donald C. Spencer recognized as one of the great mathematical pioneers of the twentieth century. Together, Spencer and Kodaira developed the modern theory of deformations of complex manifolds into a major tool, the basis for a large body of subsequent research. This work has had and continues to have tremendous influence in large segments of mathematics, including the theory of several complex variables, differential geometry, algebraic geometry, and mathematical physics. In fact, Spencer's work with Kodaira was one of the most remarkable mathematical collaborations of the twentieth century; its only parallel is the famous Hardy-Littlewood work. To give a feeling for the excitement generated by these efforts, I quote from the introduction to Kodaira's book (Complex Manifolds and Deformations of Complex Structures,

Springer-Verlag, 1981): In order to clarify this mystery, Spencer

and I developed the theory of deformations of compact complex manifolds.

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Just as Spencer had an unfailing instinct for how to approach mathematical research, so he also had an unfailing instinct for how to inspire both students and fellow mathematicians. Recently Victor Guillemin, professor of mathematics at M.I.T., wrote the following tribute: When I first met Don Spencer, I was a twenty-two-year-old graduate student, and Spencer was in his mid-forties and at the height of his fame. Kodaira-Spencer was the most exciting development of that era in differential geometry, the early sixties equivalent of Seiberg-Witten, and I and a lot of my fellow graduate students were caught up in this excitement and working on Spencer sequences, Spencer cohomology, the Spencer theory of deformations, etc. This was the state of affairs when I first met Don in the fall of 1960; and therefore, not surprisingly, the thing I most remember about him was his incredible kindness and empathy for young people. I have had several older colleagues who have been able, as one says, to "bridge the generation gap", but there is no one I've ever known who had this quality to the extent that Spencer did. Some of us took advantage of it and must at times have bored him silly with the catalogue of our accomplishments and aspirations. But he was unfailing nonjudgmental and sympathetic. More than that, one could feel that his interest in these aspirations was the genuine commodity, and not just feigned to make us feel good. One's ego at 22 is a fragile vessel, and Don instinctively knew this. For that (as for much else) I remember Don as the kindest, nicest person I've ever known.

After retirement in Durango, CO.

The process of the development was the most interesting experience in my whole mathematical life. It was similar to an experimental science developed by the interaction between experiments (examination of examples) and theory. In this book I have tried to reproduce this interesting experience; however I could not fully convey it. Such an experience may be a passing phenomenon which cannot be reproduced. Furthermore, in 1987 Kodaira wrote in his letter to the President's Committee on the National Medal of Science: Spencer's contributions to mathematics go far beyond his published papers. He exerted tremendous influence on his collaborators and students. His enthusiasm knew no limit and was contagious. In Princeton he was always surrounded by a group of mathematicians who shared his enthusiasm and collaborated in the research of complex analysis (I was one of them). In the 1950s the theory of complex manifolds was developed extensively in Princeton. The driving force behind this development was in fact Spencer's enthusiasm. At the same time, Spencer introduced the use of potential theory in the study of complex manifolds with boundaries, and in particular formulated the "d-bar-Neumann problem", which has led to very important developments in both several complex variables and partial differential equations. In the last decade of his career, Spencer worked on overdetermined systems of partial differential equations and on pseudogroups. In all his work Spencer shows remarkable originality and insight. His influence on his students, his collaborators, and his many friends also has had a lasting impact on twentieth-century mathematics. 18

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In 1978 Spencer retired from Princeton and moved to Durango, Colorado. There he became very active in the conservation and ecology movements and also an avid hiker. He soon made many friends and became well known in the area. The city of Durango designated April 25 as "Don Spencer Day". After his retirement, Don Spencer kept in touch with his many friends and colleagues, always inspiring, supportive, and full of enthusiasm. Don was my thesis adviser, mentor, colleague, and friend. I consider myself fortunate to have been so close to such a remarkable human being. Here I will give a brief account of his mathematical contributions to the theory of partial differential equations (P.D.E.). Don's contributions to P.D.E. can be divided into three groups: (1) equations arising from fluid mechanics, (2) equations arising from complex

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analysis, and (3) the theory of linear overdetermined systems. His work in (1) is discussed below by Paul Garabedian. The work in (2) is divided into two parts: equations arising from one complex variable and those from several complex variables. Here I will concentrate on the work connected with several complex variables. The contributions in (3) are discussed by Hubert Goldschmidt. The development of the theory of P.D.E. is closely linked with advances in complex analysis; in fact, Riemann's approach to the study of conformal mapping via the Dirichlet principle led to the systematic development of the theory of elliptic P.D.E. and associated variational problems. The application of these methods to the theory of several complex variables was initiated by Hodge in his theory of harmonic integrals on compact manifolds. It is this work that led H. Weyl to prove the fundamental hypoellipticity theorem, known as Weyl's lemma, which in turn led to the development of the general theory of elliptic P.D.E. The theory of harmonic integrals on compact manifolds is a crucial ingredient in the KodairaSpencer theory of deformations of complex structures. An example of this is the fundamental existence theorem proved by Kodaira, Nirenberg, and Spencer (see [6]), which is described below by P. A. Griffiths. Spencer's most spectacular contribution to the theory of P.D.E., one which has been a major influence in mathematical research, is setting down the program to generalize harmonic integrals to noncompact manifolds. Spencer called this program the a-Neumann problem. Spencer's contributions were not simply confined to his papers: they were also made through his teaching, lectures, and principally his unique remarkable ability to communicate his ideas and his enthusiasm to so many students and colleagues. His first papers in the direction of the a -Neumann problem were [7] with G. F. D. Duff and [8] with P. R. Garabedian. The a-Neumann problem for (p, q)-forms on a manifold 0 can be formulated as follows. Let L~'q(O) denote the space of square-integrable (p, q)forms on 0, let a: L~'q(O) - L~,q+ 1 (0) denote the L2 closure of a, and let a* : L~'q(O)- L~,q - 1 (0) denote the L 2 adjoint of a. The a -Neumann problem is: given a E L~,q (0), does there exist a cp E Li_'q (0) th 0 such that

for all (0, 1)-forms cp whose coefficients are in -* Coo(O) and which are in the domain of o . Here II · II~ denotes the Sobolev !-norm. Morrey's proof of this estimate works for any complex manifold with smooth strongly pseudoconvex boundary. Using the"! estimate", I proved (see [12]) that the solution of the a-Neumann problem exists for manifolds with strongly pseudoconvex smooth boundaries and that, locally near the boundary, the solution cp gains one derivative on a (in the interior it automatically gains two derivatives). Hormander, in [13], proved existence using a different approach. He used Morrey's techniques to obtain L 2 estimates of cp with weights that are singular at the boundary. In this way he was able to prove existence in L2 without assuming smoothness of the boundary or strong pseudoconvexity; all that is needed is weak pseudoconvexity. Because of interior ellipticity, Hormander's solution gains

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two derivatives locally in the interior, but there is no control near the boundary. The a-Neumann problem and the mathematics that grew out of it have had an enormous impact on the theory of several complex variables, on the theory of P.D.E., on analysis, and recently on algebraic geometry. In particular, Hormander's solution has engendered "the L 2 methods", which have been a very powerful tool. Hormander has recently written a paper (see [14]), dedicated to the memory of D. C. Spencer, which exposes this approach and its consequences. The approach, based on regularity near the boundary, has led to numerous developments. Some of these are the study of subelliptic estimates; the calculus of pseudodifferential operators; the study of the operators and Db on CR manifolds and on the Heisenberg group; and analysis on weakly pseudoconvex manifolds: global regularity and irregularity, regularity of biholomorphic and proper mappings, multiplier ideals, etc. Multiplier ideals, which arose from the study of estimates for the -Neumann problem, are currently used effectively in Kahler geometry, algebraic geometry, and the study of degenerate elliptic P.D.E. Don played an essential role in all this during the 1950s and 1960s. Apart from his own contributions, he communicated his ideas and enthusiasm to most mathematicians who worked on these questions, students and colleagues alike. These included: A. Andreotti, M. Ash, P. E. Conner, H. Grauert, L. Hormander, S. H. C. Hsiao, N. Kerzman, J. J. Kohn, M. Kuranishi, C. B. Morrey, L. Nirenberg, H. Rossi, and W. J. Sweeney. All of us found Don ready at any time to listen to us, encourage us, challenge us, and make us appreciate the importance of the enterprise. In the 1970s, 1980s, and 1990s the number of people working on these questions increased dramatically, and I am sure that Don had a direct influence on many of these also.

ab

a

References [1) D. C. SPENCER, Selecta, three volumes, World Scientific,

1985. [2) A. C. SCHAEFFER and D. C. SPENCER, Coefficient Regions

for Schlicht Functions, Amer. Math. Soc. Colloq. Publ., vol. 35, 1950. [3) M. SCHIFFER and D. C. SPENCER, Functionals of Finite Riemann Surfaces, Princeton Univ. Press, 1954. [4) H. K. NICKERSON, N. E. STEENROD, and D. C. SPENCER, Advanced Calculus, Van Nostrand, 1959. [5) A. KUMPERA and D. C. SPENCER, Lie Equations. Volume I: General Theory, Ann. of Math. Stud., No. 73, Princeton Univ. Press, 1972. (6) K. KODAIRA, l. NIRENBERG, and D. C. SPENCER, On the existence of deformations of complex analytic structures, Ann. of Math. 68 (1958), 450-459. [7) G. F. D. DuFF and D. C. SPENCER, Harmonic tensors on manifolds with boundary, Proc. Nat. Acad. Sci. U.S.A. 37 (1951), 614-619 .

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[8] P. R. GARABEDIAN and D. C. SPENCER, A complex tensor

calculus for Kahler manifolds, Acta Math. 89 (1953), 279-331. [9) D. C. SPENCER, Les operateurs de Green et Neumann sur les varietes ouvertes riemanniennes et hermitiennes, lectures given at the College de France, 195 5 (copy in the library of the Institut Henri Poincare). [10)].]. KoHN and D. C. SPENCER, Complex Neumann problems, Ann. of Math. 66 (1957), 89-140. [11) C. B. MoRREY, The analytic embedding of abstract real analytic manifolds, Ann. of Math. 68 (1958), 159-201. [12) J. ]. KoHN, Harmonic integrals on strongly pseudoconvex manifolds. I, Ann. of Math. 78 (1963), 112-148; II, Ann. of Math. 79 (1964), 450-472 . [13) L. HORMANDER, L 2 estimates and existence theorems for the operator, Acta Math. 113 (1965), 89-152. [14) __ , A history of existence theorems for the CauchyRiemann complex in L 2 spaces, ]. Geom. Anal. 13 (2003), 307-335.

a

Phillip A. Griffiths Don Spencer and his friend and collaborator Kunihiko Kodaira were the principal founders of deformation theory-a central part of modern algebraic geometry and indeed of modern mathematics. The development of Kodaira-Spencer theory, as it is now called, took place during the middle and late 1950s. With the benefit of hindsight we may see it as arising from a natural confluence of Spencer's previous interests and some of the major mathematical developments at the time. On the one hand, through his work with Schaeffer [17] and Schiffer [18], [19], [20], Spencer was intimately familiar with moduli of Riemann surfaces: firstly the by-then-classical theory of Teichmiiller for compact Riemann surfaces and secondly the more general case where the Riemann surface may have a boundary (to which Spencer and his collaborators made significant contributions). Central to the former theory are the quadratic differentials on the Riemann surface. As will be seen below, the search for their higher-dimensional analogues was a significant issue. On the other hand, three aspects of the general mathematical environment of the time were particularly relevant. Namely, this was a period of intense activity in the areas of (i) harmonic integrals, (ii) sheaf theory, and (iii) several complex variables. The first was in the tradition of Riemann, Hodge, and Weyl, among others, and was a subject to which each of Kodaira and Spencer individually made significant contributions (cf. [1], [2], [3]). Much of this work was concerned with what is now the "standard" linear elliptic theory on compact Phillip A. Griffiths is director of the Institute for Advanced Studies, Princeton. His email address is pg@i as. edu.

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manifolds, including those with boundary, and especially the Kahler case. The second was a very general theory, which for present purposes may be thought of as providing a systematic framework for analyzing the obstruction to globally piecing together solutions to a problem that has local solutions. This framework introduces the higher cohomology groups Hq(X, J) of a sheaf J on a space X. For X an n-dimensional compact complex manifold and J the sheaf associated to a holomorphic vector bundle, the duality theorem of Kodaira and Serre is

also be reflected in the two equivalent approaches to Kodaira-Spencer's deformation theory. Before turning to that theory, I would call attention to the important series of papers [7], [8], [6], [9] byKodaira and Spencer and the papers [21], [22] by Spencer which systematically applied sheaf cohomological methods to issues related to divisors and arising from classical algebraic geometry. Essentially, they introduced the exponential sheaf sequence 0 - 7l. - Ox ~ x),

where ex is the sheaf of holomorphic vector fields on X. This observation was to provide a key hint about how to measure variation of complex structure in higher dimensions. From several complex variables, important were results such as the direct-image theorem of Grauert and, especially, the Cauchy-Riemann operator a. A complex manifold may be given either by a coordinate covering {Ua, Za} with complex analytic glueing data (3)

H 1((9*) x

classes } :: Hg 1 (X) { fundamental of divisors where Hg 1 (X)

=

H 1•1 (X, (() n H 2 (X, 71.)

is the Hodge group of integral (1, 1) classes. I remember Don relating to me how he and Kodaira excitedly presented their proof to Lefschetz, who grumpily remarked that, first, he couldn't understand the fancy sheaf theory and, second, in any case he had proved the theorem. (The latter needs a caveat in that Lefschetz's argument for the semisimplicity of monodromy acting in the homology of a Lefschetz pencil was incomplete-only with Hodge's work was the result established. To this day all proofs of the (1, 1) theorem require Hodge theory.) Deformation theory had been on Spencer's mind for some time prior to his work with Kodaira (cf. [18], [17], [20]). As he explained it to me, the issue was that they did not know what should play the role in higher dimension of quadratic differentials in the Teichmilller theory on Riemann surfaces. The breakthrough came with (2). With that major "hint" everything began to fall into place, leading to the papers [11], [5], [10], [12] (and relatedly [13], [14], [23]), which brought deformation theory into the core of complex algebraic geometry. Before describing their theory, I want to say that deformation theory seems to some extent to have "been in the air". In particular, the important work by Frolicher-Nijenhuis independently established the rigidity theorem stated below, and their papers on the calculus of vector-valued differential forms influenced the work of Kodaira-Spencer as well as that of many others working in related areas.

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Turning to the Kodaira-Spencer deformation theory, intuitively a deformation of a compact complex manifold X is given by a family {XdtEB of compact complex manifolds containing X = X to as a member. In case X is a smooth complex projective algebraic variety given by homogeneous polynomial equations

{

(i)

(ii)

Zcx = fcxfl(Z(l, t) fcxfl({{ly(Zy, t), t) = {cxy(Zy, t).

scribed by the glueing data (7)(i), the vector fields

one may imagine deforming X by varying the polynomials to PA(x 0 , ... , XN, t), with PA(x 0, ... , xN, 0) = PA(x 0 , ... , XN), and setting Xt = {PA(Xo, ... , XN, t) = 0},

provided that Xt remains of constant dimension for It I < E (in which case it will be smooth). More formally, a deformation of X is given by X I

(?)

If we think of the complex manifold as being de-

X= {PA(Xo, ... , XN) = 0},

(5)

Thus around a point of X to the deformation is trivial; i.e., is biholomorphic to a product. We may then expect that the global nontriviality is measured cohomologically. In overlaps we will have (cf. (3))

(8)

ecxfl(t) =:

ar~flx),

The second implies that the Dolbeault cohomology class {(el, ed} E H~' 2 (6x) defined by the bracket [e 1 , e1 ] should be zero. Collectively the equations (11) are equivalent to

then we cannot find e z satisfying the second equation in (11), and so forth. The main result in [5] is (15) If H 2 (8x) = 0, then there exists a family (5) such that the Kodaira-Spencer mapping Pro: Tr0 B- H 1 (E>x) is an isomorphism.

are(t) = 0

so that {e(t)} E H~; 1

(ex,).

The relation between the two approaches is expressed by the result

Another stability result from Kodaira and Spencer's last paper [1 2] on deformations of complex structure is

(12) Under the Dolbeault isomorphism H 1 (E>x, ) ~

H~; 1 (E>x,)

one has

(16) If X is a Kahler manifold, then the Xr are

Pr(o/at) = {e(t)}.

also Kahler fort close to t0 .

This shows quite clearly how the Kodaira-Spencer classes give the variation of complex structure. The second method is more amenable to using the methods of linear elliptic partial differential equations for deformation theory. For example, using the continuity of the eigenvalues in the discrete spectrum of an elliptic operator, Kodaira and Spencer showed (13) (Upper semi-continuity): For t close to t0 , dimHq(Xr, Jr) :::; dimHq(Xr0 , Jr0 ) . If Hq- l(Xr, Jr0 ) = Hq+l(Xr, Jr0 ) = 0, then equality holds. As a corollary of this together with (9), they deduced the following result, which was proved independently by Frolicher and Nijenhuis. (14) IfH 1 (X,E>x) trivial. jANUARY

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=

These methods were extended by Kuranishi to prove the existence of a local universal family (5) where B is an analytic subvariety in an open neighborhood of the origin in H 1 (6x) with dimE ~ dimH 1 (E>x)- dimH 2 (E>x).

0, thenthefamily(5)islocally

As shown later by Hironaka, this result is false globally: the limit of Kahler manifolds may not be Kahler. Before turning to some other asp ects of Kodaira-Spencer deformation theory and the work it stimulated, I would like to mention one particular aspect of the one-variable work of Schiffer and Spencer that has had significant impact in current algebraic geometry. Namely, the projectivized tangent space IP'H 1 (E>x) to the local deformation of a smooth algebraic curve is, in a natural way, the image space for the bicanonical mapping (17)

which one may think of as using a basis for the quadratic differentials as homogeneous coordinates. Mathematically, if for a point p E X we let E>x(P) denote the sheaf of vector fields with a first order pole at p, then there is an exact sheaf sequence

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(18)

0 ~ 8x ~ 8x(P) ~ 8x(P)IP ~ 0.

In terms of a local coordinate z centered at p, sections of 8x(p) are

e = (~ + bo + b,z + ... ) a;az and 8x(P) I P ~ ([ is a skyscraper sheaf supported at p, and the right-hand mapping in (18) is

e

1-+

a.

The bicanonical mapping (17) then sends p to the line in H 1 (8x) spanned by (19)

(j

(~z ~), oz a =F O,

where 8 is the coboundary map 8x(P)IP

_!____.

H 1 (8x )

in the exact cohomology sequence of (18). By definition, qJzK(P) is the Schiffer variation associated top. From (19) we see that (/JzK(P) = 0

in IP'H 1 (8x(p)).

As explained to me by Don, this has the following intuitive geometric meaning: To first order, the deformation with tangent cp 2K(p) arises by leaving unchanged the complex structure on X\ {p} and changing it at p by a 8-function. This can all be made mathematically precise, and Schiffer variations have had a variety of important applications in contemporary algebraic geometry, including results on the global moduli of Riemann surfaces and on the higher Chow groups of algebraic cycles by Collino and others. In addition to variation of complex structures, Kodaira and Spencer also considered deformations of holomorphic principal bundles [11] (and their associated vector bundles) and the relative case of deformations of a compact complex codimensionone submanifold within a fixed ambient complex manifold [15], [10] (the higher codimension case being done by Kodaira). In all these cases there is a Kodaira-Spencer map encoding the first-order variation, and results (including an existence theorem) analogous to those given above were established. In [11] a rich set of examples illustrating the general theory is worked out in detail. Soon after the publication of the fundamental papers [11] there was a flood of results applying the general theory. Among these were the rigidity of simply connected homogeneous Kahler manifolds (Bott) and the rigidity of hyperbolic symmetric compact complex manifolds having no unit disc factor in their universal coverings (Calabi-Vesentini). In the case of a compact Kahler manifold, a variation of complex structure leads to a variation of 24

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Hodge structure, which has had rich applications in algebraic geometry. Moreover, the KodairaSpencer framework quickly spawned a number of deformation theories of other structures, including discrete subgroups of semisimple Lie groups (Calabi, Weil, and Matsushima, among others), and deformation theory of algebras (Gerstenhaber). Over the years these theories have been refined, expanded, extended, and applied. (I shall not attempt any summary.) In the setting of general algebraic geometry, the Kodaira-Spencer theory became quickly absorbed, adapted, and greatly extended by Grothendieck and his school. Together with the complementary study of global moduli, most especially of marked algebraic curves initiated by David Mumford, one sees that some nearly fifty years after its inception, deformation theory, both local and global, is absolutely central in modern algebraic geometry and its interfaces with other areas, including string theory (quantum cohomology) and mirror symmetry (Calabi-Yau manifolds). References [1] G. F. D. DuFF and D. C. SPENCER, Harmonic tensors on manifolds with boundary, Proc. Nat. Acad. Sci. U.S.A. 37 (1951), 614-619 . [2] _ _ , Harmonic tensors on Riemannian manifolds with boundary, Ann. of Math. 56 (1952), 128-156. [3] P.R. GARABEDIAN and D. C. SPENCER, Complex boundary value problems, Trans. Amer. Math. Soc. 73 (1952), 223-242. [4] V. K. A.M. GuGENHEIM and D. C. SPENCER, Chain homotopy and the de Rham theory, Proc. Amer. Math. Soc. 7 (1956), 144-152. [5] K. KODAIRA, L. NIRENBERG, and D. C. SPENCER, On the existence of deformations of complex analytic structures, Ann. of Math. 68 (1958), 450-459. [6] K. KODAIRA and D. C. SPENCER, On the arithmetic genera of algebraic varieties, Proc. Nat. Acad. Sci. U.S.A. 39 (195 3), 641-649. [7] _ _ , Groups of complex line bundles over compact Kahler varieties, Proc. Nat. Acad. Sci. U.S.A. 39 (1953), 868-872. [8] _ _ , Divisor class groups on algebraic varieties, Proc. Nat. Acad. Sci. U.S.A. 39 (1953), 872-877. [9] __ , On a theorem of Lefschetz and the lemma of Enriques-Severi-Zariski, Proc. Nat. Acad. Sci. U.S.A. 39 (1953), 1273-1278. [10] _ _ , A theorem of completeness for complex analytic fibre spaces, Acta Math. 100 (1958), 281-294. [11] _ _ , On deformations of complex analytic structures. I, II, Ann. of Math. 67 (1958), 328-466. [12] _ _ , On deformations of complex analytic structures. III, Ann. of Math. 71 (1960), 43-76. [13] _ _ , On the variation of almost-complex structure, Algebraic Geometry and Topology. A Symposium in Honor of S. Lefschetz, Princeton Univ. Press, 1957, pp. 139-150. [14] _ _ , Existence of complex structure on a differentiable family of deformations of compact complex manifolds, Ann. of Math. 70 (1959), 145-166 .

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[15] _ _ ,A theorem of completeness of characteristic systems of complete continuous systems, Amer. ]. Math. 81 (1959), 477-500. [16] ]. ]. KOHN and D. C. SPENCER, Complex Neumann problems, Ann. of Math. 66 (1957), 89-140. [17] A. C. SCHAEFFER and D. C. SPENCER, A variational method for simply connected domains, Construction and Applications of Conformal Maps. Proceedings of a Symposium, National Bureau of Standards, Appl. Math. Ser., No. 18, U.S. Government Printing Office, 1952, pp. 189-191. [18] M. SCHIFFER and D. C. SPENCER, A variational calculus for Riemann surfaces, A nn. Acad. Sci. Fenn. Ser. A. I. Math.-Phys. 1951, no. 93. [19] _ _ ,On the conformal mapping of one Riemann surface into another, Ann. Acad. Sci. Fenn. Ser. A. I. Math.-Phys. 1951, no. 94. [20] _ _ , Some remarks on variational methods applicable to multiply connected domains, Construction and Applications of Conformal Maps. Proceedings of a Symposium, National Bureau of Standards, Appl. Math. Ser., No. 18, U.S. Government Printing Office, 1952, pp. 193-1 98. [21] D. C. SPENCER, Cohomology and the Riemann-Roch theorem, Proc. Nat. Acad. Sci. U.S.A. 39 (1953), 660- 669. [2 2] __ , A generalization of a theorem of Hodge, Proc. Nat. Acad. Sci. U.S.A. 38 (1952), 533- 534. [2 3] _ _ , A spectral resolution of complex structure, International Symposium on Algebraic Topo logy, Universidad Nacional Aut6noma d e Mexico and UNESCO, Mexico City, 1958, pp. 68-76.

Hubert Goldschmidt I first met Don Spencer when I was a sophomore at Princeton University during the winter of 1960-6 1. I first encountered his vision of mathematics through his Advanced Calculus book [6) written with H. Nickerson and N. Steenrod, which had such an influence on a whole generation of undergraduates at Princeton, and then through an informal seminar held in his office. Don was to be my thesis advisor for my senior thesis. His enthusiasm and romantic view of mathematics, his passion for the subject permeated his teachings: research in mathematics was something to be enjoyed. His boundless energy was legendary. He also taught us to persevere in one's vision, not to b e led astray and not to deviate from one's path. I was fortunate to have been associated with Don as his student, colleague, and collaborator; to have b een led by him to the forefront of an exciting new field at its very outset; and to have witnessed all its beautiful developments over the years. In 1960 Kodaira and Spencer began extending their theory of deformation of complex structures to other classes of geometric structures. First, in [3) ~odaira considered structures corresponding to Elie Cartan's primitive pseudogroups of biholomorphic transformations. Then Kodaira and Hubert Goldschmidt is a visiting professor at Columbia University. His email address is hg@mat:h. columbia. edu.

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Eugenio Calabi, Halsey Royden, Don Spencer, and Phillip Griffiths hiking near Palo Alto, CA, in the 1960s.

Spencer [4) studied deformations of a class of G-structures which gen eralize foliations on a manifold. In his seminal paper [7), Spencer undertook a program to extend these results to structures corresponding to the pseudogroups of Lie and Elie Cartan. He had a complete vision about how to approach the theory of overdetermined systems of partial differential equations through a whole series of new tools and to use them to study the theory of deformations of pseudogroup structures. Most of it is described in [7); it would take many years to fully understand, to develop and refine everything which he formulated there, and to carry out his program. Spencer's ideas exerted a profound influence on most mathematicians who worked in this field, in particular, on M. Kuranishi, R. Batt, S. Sternberg, D. Quillen, V. Guillemin, B. Malgrange, A. Kumpera, Ng6 Van Que, and me. The pseudogroups of Lie and Cartan arise as transformation groups of geometric structures and are defined by systems of partial differential equations. Spencer's program consisted in first studying the geometric structures in terms of the ,associated systems of partial differential equations. Subsequently, it would lead to a deformation theory of structures on manifolds defined by pseudogroups which would incorporate all the fundamental mechanisms of the theory of deformation of complex structures. In particular, an exten sion 9f the Newlander-Nirenberg theorem to elliptic pseudogroups would b e required to obtain coordinates for the deformed structures and to prove the existence of local deformations. The first step was carried out by studying the system of linear partial differential equations associated to a pseudogroup in terms of Ehresmann's theory of jets and con structing a resolution of the sheaf of vector fields which are the infinitesimal transformations of the pseudogroup. This resolution was introduced in order to interpret

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Ph.D. Students of Donald C. Spencer

Arthur Grad (1948) Louis N. Howard (1953) Pierre E. Conner (1955) Robert Hermann (1956) · Joseph J. Kohn (1956) Bruce L. Reinhart (1956) Patrick X. Gallagher (1959) Alan L.. Mayer (1961) RichardT. Bumby (1962) Phillip A. Griffiths (1962) Michael E. Ash (1963) Joseph E. D'Atri (1964) W. Stephen Piper (1966) William]. Sweeney (1966) Roger A. Horn (1967) Frank W. Owens (1967) Barry MacKichan (1968) Laird E. Taylor (1968) Sherman H. C. Hsiao (1972) Robert J. V. Jackson (1972) Robert E. Knapp (1972) Charles Rockland (1972) Constantin N. Kockinos (1973) Marshall W. Buck (1974) Suresh H. Moolgavkar (1975) John E. Lindley (1977) Jack F. Conn (1978)

infinitesimal deformations as elements of a cohomology group. Here, Spencer introduced fundamental tools for the theory of overdetermined systems of partial differential equations, which marks the beginning of a new era in their study. His approach-now called Spencer theory-was more in the spirit of Lie, with a full use of modern concepts; the equations are studied directly, in contrast to the existing Cartan-Kahler theory, where they are recast within the framework of exterior differential systems. It was soon realized that this work was not limited to equations arising from pseudogroups, and a systematic study of the formal theory of overdetermined systems incorporating these methods was undertaken. In fact, the methods introduced in [7] turned out to provide most of the crucial elements for the study of overdetermined systems both from the formal point of view and within the context of realanalytic systems, and we now evoke several of their aspects: 1. To a system of linear equations or to a linear differential operator, Spencer associated complexes of differential operators, the so-called naive and sophisticated Spencer sequences. Intrinsic constructions of these sequences were later given by Bott, Quillen, and Goldschmidt. The cohomology of these complexes, which is now called the Spencer cohomology of the operator (or of the equations), is a crucial ingredient in the study of overdetermined systems; in fact, it was later shown to be equal to the cohomology arising from the compatibility conditions for the given differential operator. Quillen also provided the proof of Spencer's assertion made in [7]: if the system is elliptic, the associated sophisticated Spencer sequence is an elliptic complex. This result is in fact critical for the deformation theory of structures defined by elliptic pseudogroups. 2. Essential information about a system of differential equations is contained in its 8-cohomology (now also called Spencer cohomology) groups. In fact, they are the cohomology groups of the so-called 8-complex, which first appeared as a subcomplex

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of the Spencer sequence. Spencer asserted that this cohomology is finite-dimensional and foresaw the implications of the vanishing of certain groups. Mumford pointed out to Spencer in 1961 that the dual of the 8-complexis a Koszul complex; this remark gave a direct proof of Spencer's assertion. This led Guillemin and Sternberg to conjecture that Cartan's notion of involutiveness, as reformulated by Matsushima, is equivalent to the vanishing of the 8-cohomology. This equivalence was proved by Serre using commutative algebra and would provide the link between Spencer's theory and Cartan's methods. It is a remarkable fact that Cartan's notion of involutiveness can be recast in terms of this cohomology. Techniques from homological algebra and commutative algebra could now provide tools for the study of overdetermined systems and for new proofs of the celebrated CartanKuranishi prolongation theorem. 3. In view of proving the existence of solutions of real-analytic systems, Spencer formulated the so-called 8-estimate in terms of the 8-complex. For a real-analytic system satisfying appropriate conditions, it would give the convergence of power series solutions and thus the existence of local solutions. The 8-estimate was subsequently proved by Ehrenpreis, Guillemin, and Sternberg, and later by Sweeney. Malgrange realized that this estimate is essentially equivalent to the "privileged neighborhood theorem" of Grauert and used this theorem together with the method of majorants to prove a direct existence theorem for analytic systems (see [5]). These methods would give rise to the basic existence theorems for overdetermined systems of partial differential equations which guarantee the existence of sufficiently many formal solutions for an arbitrary system, linear or nonlinear. In the case of real-analytic systems, the results mentioned in (3) would then provide us with the existence of local solutions. In [8] Spencer formulated a generalization of the a-Neumann problem for overdetermined elliptic systems on small convex domains in the hope of proving the exactness of the sophisticated Spencer sequence associated to such equations. That this exactness holds in general for such systems is now called the Spencer conjecture. The SpencerNeumann problem was solved, and the exactness of the Spencer sequence was proved in several special cases by Spencer's students MacKichan, Sweeney, and Rockland (see [1], Chapter X). By adapting Henri Cartan's argument for the exactness of the Dolbeault sequence, in [7] Spencer also proved the exactness (in the C"' -sense) of the Spencer sequence under the assumption that the elliptic operator has real-analytic coefficients. This last result implies that the Spencer sequence of an elliptic pseudogroup, whose equations have real-analytic coefficients, is exact and gives rise

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to an interpretation of the infinitesimal deformations as elements of a cohomology group, just as in the case of complex structures. Another aspect of the methods of [7] for studying deformation theory is the recasting of the notion of an almoststructure (corresponding to the pseudogroup) as a section of one of the vector bundles appearing in a nonlinear sequence corresponding to the naive or to the sophisticated Spencer sequence. The integrability condition for the almost-structure is then formulated in terms of this sequence. The second fundamental theorem for a pseudogroup asserts the existence of coordinates for an almoststructure satisfying this requisite integrability condition. For elliptic pseudogroups whose equations have real-analytic coefficients, the second fundamental theorem was proved by Malgrange in [5]. The proof of this generalization of the NewlanderNirenberg theorem was inspired by the one which Spencer gave for the exactness (in the c oo -sense) of the sophisticated linear Spencer sequence and requires all of the mechanism developed by Spencer. This completed Spencer's program for studying deformations of structures initiated in [7] and showed that indeed Spencer had introduced all the essential components for the study of the deformation theory of pseudogroup structures. In [5] Malgrange introduced the formalism of differential calculus a la Grothendieck into the study of pseudogroups and reworked the Spencer mechanism for studying deformations of structure. Also, he clarified the correspondence between the linear Lie equations and their finite forms. Many of Spencer's ideas concerning pseudogroups now appeared in a rigorous form. Malgrange's work was utilized by Goldschmidt and Spencer in their paper [2] to study the second fundamental theorem for an arbitrary pseudogroup. They introduced the nonlinear Spencer cohomology of a transitive pseudogroup, whose vanishing implies the validity of the second fundamental theorem for the pseudogroup. By means of a spectral sequence argument involving the nonlinear sequences, they showed that this nonlinear Spencer cohomology depends only on the Lie algebras of all formal infinitesimal transformations of the pseudogroup. Many of the main ingredients of their solution of the "integrability problem" for flat pseudogroups appear here. In fact, their results concerning Spencer cohomology allowed them to use Guillemin's Jordan-Holder decompositions and Galois theory type methods to provide a proof of the second fundamental theorem for all transitive pseudogroups on Euclidean space containing the translations, the so-called flat pseudogroups. jANUARY

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Spencer and DeRham, India, 1964. References [1] R. BRYANT, S. S. CHERN, R. GARDNER, H. GOLDSCHMIDT, and P. GRIFFITHS, Exterior Differential Systems, Math. Sci. Res. lnst. Publ., vol. 18, Springer-Verlag, 1991. [2] H. GOLDSCHMIDT and D. C. SPENCER, On the non-linear cohomology of Lie equations. I, II, Acta Math. 136 (1976), 103-170, 171-239. [3] K. KoDAJRA, On deformations of some complex pseudogroup structures, Ann. of Math. 71 (1960), 224-302. [4] K. KoDAIRA and D. C. SPENCER, Multifoliate structures, Ann. of Math. 74 (1961), 52-100. [5] B. MALGRANGE, Equations de Lie. I, II, ]. Differential Geom. 6 (1972), 505-522; 7 (1972), 117-141. [6] H. K. NICKERSON, D. C. SPENCER, and N. E. STEENROD, Advanced Calculus, Van Nostrand, Princeton, NJ, 1959. [7] D. C. SPENCER, Deformation of structures on manifolds defined by transitive, continuous pseudogroups. I, II, Ann. of Math. 76 (1962), 306-398, 399-445. [8] __ , Deformation of structures on manifolds defined by transitive, continuous pseudogroups. III, Ann. of Math. 81 (1965), 389- 450. [9] _ _ , Overdetermined systems of linear differential equations, Bull. Amer. Math. Soc. 75 (1969), 179-239.

Enrico Bombieri The earliest mathematical works of Don Spencer, reflecting the influence of his advisor ]. E. Littlewood and Littlewood's collaborator, G. H. Hardy, were in analytic number theory. A particularly important problem on which Spencer worked was to show that a progression-free sequence of positive integers cannot have positive density. The paper [1], written jointly with Raphael Salem, disproved in a clever fashion a then widely held conjecture. The particular problem has been of lasting interest, with major progress by Szemeredi and quite recently by Gowers, who was awarded a Fields Medal in part for his work on it. In addition to this Enrico Bombieri is professor of mathematics at the Institute for Advanced Study, Princeton. His email address is eb@math. i as. edu .

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and the related paper [2], Spencer's main other works in analytic number theory were in Diophantine approximations, again reflecting the interest of the English school at that time. References [1) R. SALEM and D. C. SPENCER, The influence of gaps on

density of integers, Duke Math.]. 9 (1942), 855-872. [2) __ , On sets of integers which contain no three terms in arithmetical progression, Proc. Nat. Acad. Sci. U.S.A. 28 (1942), 561-563.

Bohous Cenkl We always called him Don. He disliked formalities and despised political intrigue. As practically the only visitor permitted from Czechoslovakia to Stanford in the 1960s, I had the good fortune to first meet him there. That was the time that the Stanford Linear Accelerator (SLAC) was being built. Don's primary research focus was the study of overdetermined linear systems, but his passion for theoretical physics was one of many side interests that he shared with Kodaira. Expanding on Don and Kodaira's seminal work on deformations of complex structures, Hermann was running a seminar on deformations in the physics department. During that year, Don and I spent endless hours discussing all types of problems beyond just mathematics and physics. Don was always pushing me to learn things that I felt were well beyond my capabilities. There was a constant stream of visitors in Don's office-Borel, Hormander, Hermann, Kohn, Nirenberg, Sternberg, and many others. Spencer in California, Don made everyone of us feel spearound 1965. cial. He never singled anyone out, but rather devoted his endless energy to those with no Ivy League education and to future Nobel Prize winners alike. He never succumbed to any attempt by some to use his name for self-promotion. After a heavy dose of mathematics, Don always planned various outdoor activities for us, like a hike above Palo Alto on the ranch of his friend Jim Rapley, a retired commander in the U.S. Navy. I have fond memories of numerous trips on horseback to theSierraswithDonandhisfarnily.Igreatlyrespected him and his life philosophy. I am personally grateful for the opportunity to have hadDon as a teacher and a very close friend to me and my family.

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Paul Garabedian Don Spencer started his career at the Massachusetts Institute of Technology doing research in the theory of functions of one complex variable. During World War II he came under the influence of Courant at New York University and started to apply variational methods to the coefficient problem for univalent functions. Max Schiffer had already initiated similar studies in Palestine that were to change the whole climate in this field. After the war they combined forces both at Stanford and at Princeton and made significant contributions to our knowledge about Riemann surfaces. Don recruited Arthur Grad to write a Ph.D. thesis at Stanford on univalent functions, and Grad went on to guide early efforts in support of applied mathematics at the Office of Naval Research and at the National Science Foundation. Al Schaeffer joined Don in a study of the differential equations for extremal functions in conformal mapping that contributed significantly to steady progress on the Bieberbach conjecture that ended with the complete solution of the problem. 1 Their work was recognized by an award of the B6cher Prize from the AMS. I was fortunate to be collaborating with Don during the period when he turned his attention from one variable to focus on major questions about complex manifolds. His generous and vigorous encouragement of his graduate students and younger colleagues led him to exert a strong influence on the direction of mathematical research in this country during the second half of the last century.

Louis Nirenberg I think I first met Don Spencer when I was a graduate student or young instructor. He came to visit Courant occasionally and would sometimes be invited to Courant's home in New Rochelle during a weekend, as I was. Later we joked about having to help take care of Courant's garden. We became friends, and it was always a great pleasure to meet with Don in Stanford, Princeton, or wherever. His love and enthusiasm for mathematics were contagious. I heard him speak many times, and though I usually had trouble following, I came away with a positive glow-I liked the melody. Dan's early work was on analytic functions of one variable, but later he expanded to complex

Bohous Cenkl is professor of mathematics at Northeastern University. His email address is

Paul Garabedian is professor of mathematics at the Courant Institute of New York University. His email address is garabedi an@ci ms. nyu. edu. 1 By Louis de Branges in 1985. Louis Nirenberg is professor emeritus at the Courant Institute of New York University. His email address is

[email protected].

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manifolds. He wrote a series of famous papers with Kodaira on deformation of complex structure. I visited the Institute for Advanced Study during the spring of 1958 and had the good fortune to write a joint paper with them. When Don tried to describe the problem to me, he kept putting it in extremely general terms. Finally I asked if he could write down a simple case. He had trouble doing this, but then Kodaira stepped to the blackboard and without saying a word, wrote down a few simple equations. Later, after the work was done, I heard Don speak on it at his and Kodaira's "Nothing Seminar". I had trouble following the talk, for Don liked to use very abstract and most general concepts. About the "Nothing Seminar": it was a seminar they ran which was completely informal, no planned program. People would talk about what they were working on, thinking about, or were stuck on. It was usually held around lunchtime and was indeed very informal. I remember once a participant had brought in his lunch, hard-boiled eggs, whose shells he scattered on the floor while Don lectured. Don didn't raise an eyebrow. In 1963 we participated in a joint Soviet-American conference on partial differential equations in Novosibirsk. There were about two dozen American and one hundred twenty-five Soviet mathematicians. Toward the end of the conference the Soviet guides and translators, mainly women, voted Don the most handsome participant. Incidentally on his way to the Soviet Union, Don stopped in Cambridge, England; he had received his Ph.D. there some decades earlier. On his arrival he went to a bank to change money. The clerk looked at him and said, "Nice to see you again, Dr. Spencer." On that visit to England he bought an umbrella, one of those long, rolled, elegant umbrellas we know from movies. Throughout the Novosibirsk conference I kept admiring it. At the end he simply presented it to me. I treasured it for years. Don had a wonderful, open personality. He was the same natural person with everyone. He was extremely generous in giving of himself, offering warmth, friendship, and attention to everyone, concerned about their problems. I consider him the most considerate person I have ever met- a great gentleman. Once, at a dinner party, people were talking about Don, praising him, etc. At the end, my wife said, "Everyone loves Don, but I like him anyway." I found it difficult to keep up with his later work. After he moved to Durango, Colorado, we didn't meet very often, but as always, each meeting was a great pleasure. Once my wife and I visited him in Durango. He took us on a tour- to various bars and taverns. He was warmly welcomed in every one. jANUARY

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Available Exclusively from the AMS ••• New Titles from the European Mathematical Society The AMS is proud to announce our newest alliance: European Mathematical Society titles are now available only from the AMS throughout North, Central, and South America. Here is a sample of forthcoming titles; many more will soon be available.

Logarithmic Combinatorial Structures: a Probabilistic Approach Richard Arratia, A. D. Barbour, and Simon Tavare, EMS Monographs in Mathematics; ISBN 3-03719-000-0; December 2003. 352 pages. Hardcover

A Course In Error-Correcting Codes Jem Justesen and Tom Heholdt EMS Textbooks in Mathematics; ISBN 3·03719-001-9; January 2004; 192 pages; Hardcover

Lectures on Partial Hyperbolicity and Stable Ergodicity Yakov Pesin Zurich Lectures in Advanced Mathematics; ISBN 3-03719·003-5; January 2004; 144 pages; Softcover

Lectures on Real Semisimple Ue Algebras and Their Representations Arkady Onishchik ESI Lectures In Mathematics and Physics; ISBN 3-03719-002-7; December 2003; 100 pages; Softcover

Uhlenbeck Compactness Katrin Wehrheim EMS Series of Lectures in Mathematics; ISBN 3-03719-004-3; January 2004; 250 pages; Softcover

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29

These are some of the many noteworthy titles published by the AMS in 2003. In this selection, you will find new ideas, innovative approaches, award-winning authors, and state-of-the-art topic coverage. Together, these carefully produced and eloquently composed volumes reflect the AMS Publishing Program. Arithmetic for Teachers

A History of Analysis

With Applications and Topics from Geometry Gary R. Jensen

Hans Niels Jahnke, Editor

2003; 383 pages; Hardcover; ISBN 0-82 18-3418-5; List $59; All AMS members $47; Order code FOAN041

A Companion to

Analysis

Copublished with the London Mathematical Society. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners.

History of Mathematics, Volume 24; 2003; 422 pages; Hardcover; ISBN 08218-2623-9; List $89; All AMS members $71; Order code HMATH/24N041

Knots and Links Dale Rolfsen

A Second First and First Second Course in Analysis T.W.Korner

AMS Chelsea Publishing; 2003; 439 pages; Hardcover; ISBN 0-8218-3436-3; List $55; All AMS members $50; Order code CHEL/346.HN041

Graduate Studies in Mathematics, Volume 62; 2004; 590 pages; Hardcover; ISBN 0-8218-3447-9; List $79; All AMS members $63; Order code GSM/62N041

Lectures on Generating Functions

Concise Numerical Mathematics Robert Plato Graduate Studies in Mathematics, Volume 57; 2003; 453 pages;453 pages Hardcover: ISBN 0-8218-2953-X; List $85; All AMS members $68; Order code GSM/57N041 Softcover: ISBN 0-8218-3414-2; L ist $55; All AMS members $44; Order code GSM/57.SN041

Grothendieck-Serre Correspondence

S.K.Lando Student Mathematical Library, Volume 23; 2003; 148 pages; Softcover; ISBN 0-8218-3481-9; List $29; All AMS members $23; Order code STML/23N041

Lectures on Harmonic Analysis Thomas H. Wolff (edited by Izabella Laba and Carol Shubin) University Lecture Series, Volume 29; 2003; 137 pages; Softcover; ISBN 08218-3449-5; List $31; AIIAMS members $25; Order code ULECT/29N041

A Mathematician's Survival Guide

Selected Topics in Integral Geometry

Graduate School and Early Career Development Steven G. Krantz

I. M. Gelfand, S. G. Gindikin, and M. I. Graev

2003; 222 pages; Softcover; ISBN 082 18-3455-X; List $28; All AMS members $22; Order code GSCMN041

Mirror Symmetry Kentaro Hori, Sheldon Katz, Albrecht Klemm, Rahul Pandharipande, Richard Thomas, Cumrun Vafa, Ravi Vakil, and Eric Zaslow Tit1es in this series are published by the AMS for the Clay Mathematics Institute (Cambridge, MA).

~

Clay Mathematics (~ Monographs, ~--Volume I; 2003; 929 _ _____- _ _...J pages; Hardcover; ISBN 0-8218-2955-6; List $124; All AMS members $99; Order code CMIM/IN041

ff£

Recurrence Sequences

2003; 600 pages; Hardcover; ISBN 08218-3424-X; List $69; All AMS members $55; Order code CGSN041

Selected Works of Phillip A. Griffiths with Commentary Enrico Arbarello, Robert L. Bryant, C. Herbert Clemens, Maurizio Cornalba, Mark L. Green, Joe Harris, David R. Morrison, and Wilfried Schmid, Editors This book is jointly published by the AMS and the International Press.

Collected Works, Volume 18; 2003; Hardcover;

Part I Analytic Geometry: 654 pages; ISBN 0-82 182086-9; List $99; All AMS members $79; Order code CWORKS/18.1N04l;

Graham Everest, Alf van der Poorten, Igor Shparlinski, and Thomas Ward

Part 2 Algebraic Geometry: 782 pages;

Mathematical Surveys and Monographs, Volume 104; 2003; 318 pages; Hardcover; ISBN 0-82 18-3387-1; List $79; All AMS members $63; Order code SURV/104N041

Part 3 Variations ofHodge Structures: 564 pages; ISBN 0-8218-2088-5; List $99; All AMS members $79; Order code CWORKS/18.3N04l;

Bilingual Edition This book is jointly published by the AMS and the Societe Mathematique de France. SMF members are entitled to AMS member discounts.

Translations of Mathematical Monographs, Volume 220; 2003; I 70 pages; Hardcover; ISBN 0-8218-2932-7; List $59; All AMS members $47; Order code MMON0/220N041

ISBN 0-8218-2087-7; List $99; All AMS members $79; Order code CWORKS/18.2N04l ;

Part 4 Differential Systems: 598 pages; SBN 0-8218-2089-3; List $99; All AMS members $79; Order code CWORKS/18.4N041;

Set. 2598 pages; ISBN 0-8218-1066-9; List $299; All AMS members $239; Order code CWORKS/l8N041

For many more RUbliGations of. interest, visit the AMS Bookstore

www.amsboo kstore.or 1-800-321-4AMS (4267), in the U. S. and Canada, or 1-40 1-455-4000; fax:1-40 1-455-4046; email: [email protected]. American Mathematical Society, 201 Charles Street, Providence, Rl 02904-2294, USA

1111111

lAMS BOOKSTOREI 1/(}4

A Tribute to Boris Weisfeiler In 1985 the mathematician Boris Weisfeiler disappeared while hiking alone in a remote area of Chile. At the time, he was a professor of mathematics at Pennsylvania State University and was widely recognized for his work in algebraic groups. What happened to him remains a mystery, and to this day it is not known whether he is still alive. Born in the Soviet Union, Weisfeiler received his Ph.D. in 1970 from the Leningrad branch of the Steklov Institute, where his adviser was E. B. Vinberg. Weisfeiler emigrated to the United States in 1975 and worked with Armand Borel at the Institute for Advanced Study. The next year he joined the faculty at Pennsylvania State University. In 1981 he became· an American citizen. Weisfeiler's disappearance has been the subject of several newspaper articles (see, for example, "Chilean Mystery: Clues to Vanished American", by Larry Rohter, New York Times, May 19, 2002; and "Tracing a Mystery of the Missing in Chile", by Pascale Bonnefoy, Washington Post, January 18, 2003). Further information about media coverage, as well as the present status of the investigation into his disappearance, may be found at http: I /wei sfei 1 er. com/boris. On the occasion of the publication in Chile of a book about Weisfeiler's disappearance, the Notices decided to present a brief tribute to his life and work What follows is a short summary of his mathematical work and a review of the book This is not an obituary, as hope remains that Weisfeiler is still alive. Nevertheless, it seems appropriate to commemorate this lost member of the mathematical community, whose absence is keenly felt. -Allyn jackson

The Mathematics of Boris Weisfeiler Alexander Lubotzky Boris Weisfeiler's mathematical activity extended over more than twenty years of research in the USSR and the USA, during which time he published three dozen research papers. All this ended abruptly in early 1985 with his disappearanceright after he had published his most influential papers. Weisfeiler's area was algebraic groups in all their aspects and directions, During his years of activity the theory of algebraic groups over algebraically closed fields had already been well understood, and Weisfeiler was part of the trend of studying the more difficult questions concerning the case when the field is not algebraically closed and the groups do not split or-even worse-are nonisotropic. His Alexander Lubotzky is the Maurice and Clara Wei/ Professor of Mathematics at the Hebrew University, jerusalem, Israel. His email address is a l exl ub@math. huj i . ac. i l.

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specialty was the positive characteristic case. In these cases the connection between the algebraic group and its Lie algebra is more subtle, and a great deal of effort was needed to study questions whose solutions in characteristic zero were pretty standard. A popular subject of that period was the study of "abstract homomorphisms" between algebraic groups; i.e., assume k and k' are fields and G and G' are algebraic groups defined over k and k', respectively, and let c:p: G(k)- G'(k') be a homomorphism of groups. The standard "wishful" result in this theory is the claim that, under suitable conditions, such a homomorphism is algebraic; i.e. there is a monomorphism of fields k - k' and after identifying k as a subfield of k', the homomorphism c:p is a homomorphism in the category of algebraic groups, i.e., given by polynomial maps. Various methods have developed to tackle such problems. Usually, one associates some geometry with the algebraic groups in the spirit of Klein's Erlangen program, as projective geometry is associated with GLn(k), and hence the map c:p induces a map between the associated geometries, which turns out to be a useful way to study the original c:p. The works of Borel, Tits, O'Meara, and others settled most questions for isotropic groups , but the

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proof. He was probably the first to see how CFSG could be used for infinite linear groups. (By now, there are proofs which do not require the CFSG; see [LS] and the references therein.) In [W2], Weisfeiler made another remarkable use of the CFSG for linear groups. He announced a sharp bound on the index of the abelian normal subgroup of finite linear subgroups of GLn. The existence of such a bound was proved by Jordan, with extensions and better bounds proven by many including Brauer and Feit. Weisfeiler's result is still, twenty years later, the best known result. Unfortunately, a detailed proof has never appeared. Boris Weisfeiler's mathematical work was suddenly and tragically cut-but his name is still remembered by all those who knew him or who work in related areas.

Boris Weisfeiler

nonisotropic cases were always of special difficulty. This was a direction in which Weisfeiler made some important contributions, but unfortunately they are too technical to be elaborated upon here. Weisfeiler is mainly remembered and quoted for the two contributions he made in the last year (1984) just before his disappearance. The first one is truly spectacular, although it took some time to realize that: In [W1] (following a partial result in [MVW]) Weisfeiler proved a strong approximation theorem for general linear groups. To get a feeling of what it says, let us take a very special case: Let SLn(Z ) be the group of n x n integral matrices of determinant one, and let r s SLn(Z ) be a Zariskidense subgroup. Then, Weisfeiler's theorem says (in fact, this case is already covered by [MVW]) that fis almost dense in SLn(Z ) in the congruence topology of SLn(Z ); i.e., its closure there is of finite index. The congruence topology of SLn(Z ) is the one for which the groups

References [LS] AlExANDER LUBOTZKY and DAN SEGAL, Subgroup Growth, Progress in Mathematics, 212, Birkhauser Verlag, Basel, 2003. [MVW] C. R. MATIHEWS, L. N. VASERSTEIN, and B. WEISFEILER, Congruence properties of Zariski-dense subgroups, I, Proc. London Math. Soc. (3) 48 (1984), no. 3, 514-532. [W1] BORIS WEISFEILER, Strong approximation for Zariskidense subgroups of semisimple algebraic groups, Ann. of Math. (2) 120 (1984), no. 2, 271-315. [W2] _ _ ,Post-classification version of Jordan's theorem on finite linear groups, Proc. Nat. Acad. Sci. USA 81 (1984), no. 16, Phys. Sci., 5278-5279.

8 Ultimo Secreta de Colonia DignidadA Book Review

{f(m) = Ker(SLn(Z ) - SLn(Z/ m Z )Im E Z }

serve as a system of neighborhoods of the identity. On the surface, this is a technical theorem comparing two topologies of SLn(Z ), but, in fact, this result has many extremely useful consequences. Being Zariski dense is a very weak condition, but having the quality of being congruence dense gives a lot of corollaries on the finite quotients of r. It says, for example, that for almost every prime number p, the finite simple group PSLn(P) is a quotient of r. For a general, finitely generated linear group r, it implies, for example, that either fis almost solvable or it has a finite index subgroup with infinitely many different finite simple quotients. It is not surprising that Weisfeiler's strong approximation theorem has since played an important role in the study of infinite linear groups,

in asymptotic group theory in general and subgroup growth in particular. (The reader is referred to [LS] and especially to Window 9, "Strong Approximation for Linear Groups", which describes some of the applications). Interestingly enough Weisfeiler used the (at that time brand new) classification of finite simple groups (CFSG) for his 32

NOTICES OF THE

Reviewed by Neal Koblitz El Ultimo Secreto de Colonia Dignidad (The Last Secret of Colonia Dignidad) Carlos Basso Santiago, Chile Mare Nostrum Publishers, 2002

Boris Weisfeiler disappeared on January 5, 1985, while hiking in a remote, mountainous area of south-central Chile near the border with Argentina. His body has never been found, and his disap-

pearance remains a mystery. The book El Ultimo Secreta de Colonia Dignidad, (The Last Secret of Colonia Dignidad) is a detailed account of the case Neal Koblitz is professor of mathematics at the University of Washington. His email address is kob 1 i tz@math. washington. edu.

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by Chilean journalist Carlos Basso. Basso bases his investigation on recently declassified U.S. Embassy cables and memos, as well as earlier published sources. Three theories have emerged about what happened: (1) Weisfeiler drowned accidentally while trying to cross a river. This was the official version promulgated by the Chilean authorities at the time. (2) He was shot by local police or a military patrol, who thought that he was a subversive infiltrator from Argentina and who covered up the incident when they realized their mistake. (3) A military patrol arrested him and handed him over to nearby Colonia Dignidad, an enclave of ultrarightist German immigrants founded and at the time still led by ex-Nazi Paul Schafer. Thinking that Weisfeiler was a "Jewish spy" working for Nazi-hunters, they imprisoned and eventually killed him. Sifting through the conflicting reports of witnesses and informants, Basso argues persuasively that the third theory is most likely correct. Ever since the U.S.-backed coup d'etat on September 11, 19 73, which ousted the democratically elected President Salvador Allende, the military dictatorship had a close relationship with Colonia Dignidad and used the colony as a place for the detention and torture of dissidents and political opponents. Even after Chile's transition to a democratic government in 1990, the colony continued to be protected by its allies in the military and intelligence services. In 1996 the government unsuccessfully tried to search the colony and to arrest Paul Schafer on child-rape charges. To this day none of the leaders of the cult have been prosecuted for their crimes. Basso's book is not without flaws. He has a ten dency toward sensationalism. For example, he asks why the U.S. Embassy delayed for over a year before starting to press the Chileans for a full investigation ofWeisfeiler's disappearance. He correctly observes that the Reagan administration had a friendly relationship with the Pinochet regime, which in turn had close ties to Colonia Dignidad. This- along with the usual bureaucratic inertiawould have been enough to explain the U.S. government's procrastination. However, Basso goes much further in his speculations. He recounts the now well-known story of how in the early years of the Cold War the U.S. relied on ex-Nazis to set up spy networks in Eastern Europe and help with other anti-Soviet operations. He also recalls President

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Reagan's controversial visit in 1985 to Bitburg, Germany, where the President laid a wreath at a cemetery where SS soldiers were buried. Basso suggests that as late as 1985 factions of the U.S. government had secret ties with and sympathy for German Nazis and that this explains the reluctance to investigate the role of Colonia Dignidad in Weisfeiler's disappearance. His argument here is unconvincing and far-fetched. Despite the weaknesses in the book, Basso has performed a valuable service. One can hope that the publication of his book in Chile will increase pressure on the government there to pursue the Weisfeiler case, determine who was responsible for his disappearance, and bring them to justice.

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International Publications AMERICAN PUBLISHER ONE

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Book Review

The Mathematics of Juggling Reviewed by Allen Knutson

The Mathematics of Juggling Burkard Polster Springer-Verlag, New York, 2003 226 pages, $39.95 ISBN 0-387-95513-5

Around 1985 three groups of jugglers (in Santa Cruz, California; in Pasadena, California; and in Cambridge, England) independently created the same notational system for juggling patterns. These numerical descriptions have been well publicized in the juggling world under the name "siteswaps" (and, even so, continue to be rediscovered by newcomers). As we will see shortly upon presentation of the basic definitions, a rather simple list of restrictions leads easily to a unique notational system. More surprising is the near-simultaneity of the discovery! The best explanation of this seems to be the huge increase in the number of jugglers worldwide in the 1980s, in no small part due to the publication of juggling for the Complete Klutz [CR) in 1978. While siteswaps have played a minor role in a number of books on ball juggling (written, naturally, for jugglers), The Mathematics of juggling is the first to put them in the forefront. Before getting to the book per se, I will explain what siteswaps are. Siteswaps What are the assumptions on a notational system that led all these people to the same solution? Some of them are restrictions on how the juggler behaves (rather strong restrictions, which we will weaken later): •The juggler throws only one ball at a time, never holding more than one in each hand. • The throws alternate hands, right left right left. Allen Knutson is professor of mathematics at the University of California, Berkeley. His email address is

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• (to avoid considering boundary conditions) The juggler has been juggling since the infinite past and will continue into the infinite future. • The throws come one per second, with right throws at even times and left throws at odd times (this can be ensured by reparametrizing the time coordinate). More notable, though, is the assumption about what one actually wants to record: • The only information kept about the ball thrown at time n E Z is when it is next thrown, at time f(n).

In particular, this assumption loses any extra detail about the throw like "under the leg", "with a triple spin" (if the objects juggled are pins rather than balls), "while telling joke #1729", etc. But it suggests a very nice mathematical theory of certain functions f : Z - Z: 1. The function f should be one-to-one, since we do not want two balls landing at the same time. 2. The function f should be onto, so that we always have a ball available to be thrown. 3. The function g(n) := f(n) - n might be required to be periodic with period p, since we are most interested in patterns that repeat. This g is really the most natural way to encode f, as its values do not change if we shift the origin in our time coordinate. 4. Since a ball thrown at time n is next thrown at time f(n), we should have f(n) > n. So each g(n) > 0. (In fact one usually wants to weaken this to g(n) ;:::: 0, but we will not get into that.) This last assumption is the most annoying one for mathematicians, as it forbids the possibility that our family {f : g is periodic with period p} might form a group-but of course it is firmly insisted upon by jugglers! For a taste of the theorems to come, the reader is invited to prove the following: if the function g is indeed periodic, then its average is the number of orbits of the permutation f. This is useful to the juggler, who interprets this average as the number of balls in the pattern.

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A "siteswap" then refers to one period of such a g. Tog we can associate a permutation living in the symmetric group Sym(Z/ p 'Z ) where p counts the number of "sites" that are then "swapped" by the balls' landing in a different order than they were thrown. Our main examples are the two best known juggling patterns: the three-ball cascade in which all balls are thrown to the same height and all cross, and the three-ball shower, or "circle juggling", in which the right hand (for most people) throws high and across and the left hand only shuttles the balls underneath, not really making a throw. The cascade is encoded by f(n) = n + 3, since while one ball is in the air the other two balls each get thrown once. The associated siteswap is just "3", or 33, or perhaps 333 , really meaning ... , 3, 3, .... (In practice one hardly ever deals with values of g above 9-these throws are very high and so extremely difficult for a juggler to control- so it is safe to dispense with the commas in between the values of g. One can also use letters to encode throws up to 3 5, making words like TEAKETTLE and even THEOREM into legal, if humanly impossible, juggling patterns. This amusing idea seems to be first due to Michael Kleber in the 1980s, but of course has been independently discovered since.) The shower is more annoying to encode as a function f-it is f(n) = n + 5 for n even, f(n) = n + 1 for n odd- and sounds better as a siteswap 51 (or 15, or 5151, etc.). While this fits with the averaging rule above, the 5 may seem unintuitively high; to see that it is right, note that after the right hand makes such a high throw, the other two balls must each make it through both hands, accounting for four throws in between. So the ball thrown as a 5 is then fifth in line to be thrown again, as it should be. How much more is there to a siteswap than the associated permutation? If we forget the g > 0 restriction and just look at the group {f: z ~ z I f(n + p) = f(n) + p, Vn}, it turns out to be the affine Weyl group Sp ~ zPof GL(p), denoted Ap- 1· Therefore, given a formula to count juggling patterns, one can exploit it to compute the Poincare series of Ap- 1 [ER). As we are now getting into serious mathematics, let us turn to the book under review. The Contents of The Mathematics of juggling Having given a great many lectures on the mathematics of juggling, to mathematicians and to jugglers, I was curious at whom this book would be aimed. I think it is fair to say that it is aimed squarely at the mathematician, with juggling patterns (and change ringing for carillons!) to serve primarily as a source of combinatorial problems. Some evidence of this bias will be given below. 36

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Of course, the author can and must make the choice of which audience to address. Because this is the first book dedicated to this topic, it is especially incumbent upon him to get the history right, since any errors are likely to be rt:peated in subsequent books. I am afraid that in this measure the book is lacking. A few examples: one of the founding fathers of siteswaps, Paul Klimek of Santa Cruz, has his name spelled "Klimak" throughout. The truly fundamental "juggling state graphs", which let one regard a juggler as a sort of finite-state automaton, are nowhere attributed to their creator, Jack Boyce. Also, much of the terminology has been changed, rather willfully, the most galling change being "siteswap" to "juggling sequence". It is hard enough communicating with people in other disciplines (e.g. physics) who have developed a theory in parallel with mathematicians and thus have different names for the same object. In this happy instance, notational confusion could have been avoided, as the jugglers have been using a largely consistent terminology for nearly twenty years. Much more mysterious than the historical and notational lapses, though, is the lack of actual siteswaps! Occasionally one will find an exhaustive list of the siteswaps fitting a given description, such as the table on page 56 of "maximal prime juggling sequences" of a given length and number of balls. The siteswaps showing up in these extremalcombinatorics tables are essentially unjugglable. (For example, most have a very high throw followed by a very low one, making it impossible for the juggler to see both balls.) As near as I could determine, the book includes only about a dozen siteswaps of any interest to jugglers, and even for those one must wait until Chapter 5. Let's take a closer look at the contents. Chapter 2, "Simple Juggling", introduces the definitions touched on above and juggling state graphs. Chapters 3 and 4 loosen the unnecessarily strict conditions we put on juggling patterns: Chapter 3, "Multiplex Juggling", studies patterns in which f is neither one-to-one nor singly valued, but instead for each n the number of balls coming in equals the number of balls going out. Chapter 4, "Multihand Juggling", allows for a setH of hands to throw at the same time, basically replacing f : Z ~ Z with f : H x Z ~ H x Z . This allows for a new concept of "duality" (which I learned about from this book), in which the roles of the hands and the balls are exchanged: according to the balls' point of view, they are sitting still, and the hands are being "thrown" back and forth! There are many mathematical results contained in these chapters, some with rather involved proofs; I would say that together these are the greatest strengths of the book. For example, in the first chapter a full five pages is spent on a rigorous VOLUME

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proof of the following result: given a sequence of natural numbers whose average is an integer, there is some permutation of it that is a siteswap. While the proof is elementary, I suspect that extremely few jugglers without mathematical training will have the fortitude to make their way through five pages of it. I would also claim that this particular theorem is of no intrinsic interest to jugglers (being one myself); this is not a value judgment, but simply indicative of the emphases of the book. Incidentally, some of the theorems are due to the late Claude Shannon, who was also the first to build a juggling robot. Chapter 5, "Practical Juggling", is perhaps rather jokingly named, given that it spends as much time discussing juggling in zero gravity as it does threeball siteswaps. Some of the physics is also discussed. For example, if each of a club juggler's hands are full for exactly the same fraction of the time as they are empty and the club juggler uses no wrist flick in order to spin the clubs, then (as first explained by the Caltech founders of siteswap, Bengt Magnusson and Bruce Tiemann, whose analysis is reproduced here) one should expect the clubs in flight to be parallel to one another. For competent jugglers, this lining up is readily observed in photographs, prompting the question (not answered here or, to my knowledge, anywhere else): What goodness function is the juggler maximizing by having each hand full exactly half the time? In my experience, mathematicians are generally very curious to see how their esoteric theories are actually of direct interest to nonmathematicians (witness, for example, the huge crowd that shows up to any "String theory for mathematicians" lecture). So it is extremely disappointing that the "What's all this good for?" section is only two pages with just one, throwaway, example. (Readers seeking more meat might consult [K].) Many siteswaps are given odd attributions, though admittedly to determine the provenance of juggling patterns is notoriously difficult. One that struck me was "Allen Knutson's baby-juggling pattern 52512 ",which presumably was attributed to me because I pointed out on the USENET news group rec. juggling [R]] that this is the pattern always used to juggle babies, as one of the three objects is never thrown high. As one can find movies of jugglers from the 1930s using this pattern to "juggle" a monkey and two balls, I hereby renounce any claim on this siteswap. At this point comes one of the longest chapters, Chapter 6, "Jingling, or Ringing the Changes", which delves into the combinatorics and group theory associated to change ringing (which in practice apparently involves traveling to a British cathedral; the author estimates that of the approximately 6,000 churches with rings of bells, only about 100 are outside Britain). In this subject the mathematjANUARY

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ical constraints partly arise from the physical setup of the bells, but mostly from the Decisions of the Central Council of Church Bell Ringers [CC]. They are very stringent, leading to a highly constrained mathematical theory, of which much is presented in this chapter. Half a page is spent on a rather tenuous connection to siteswaps (basically, both are related to permutations). I found it rather maddening that in this chapter there are far more ringing sequences with names attached than there are named juggling patterns in the entire rest of the book. And then ten pages are spent on 3-D stereograms of the Hamiltonian circuits associated to ringing sequences. What is this book's title anyway? Supplementary Material The author states his aims in the introduction as Serious Mathematics, Serious Juggling, Mathematics Education, Turn jugglers into Mathematicians, Turn Mathematicians into Jugglers, and Bell Ringing. I would say he certainly succeeds in the first and the last and am distinctly more reserved about the other aims. For both the jugglers wanting to leverage their knowledge into an appreciation of the mathematics and the mathematicians (young and old) looking to juggling for inspiration, the book could and should have gone much further into the exploration of interesting examples. There is no shortage of such examples on the World Wide Web; I direct the reader to the Juggling Information Service (the "JIS") at http: I jwww. juggling .org and in particular to http://www. juggling.org/help/siteswap. Many examples are built directly into juggling animators (also available at the JIS), some of which can also display the associated interesting mathematical objects, such as the state diagram. My personal favorite is of course [MA] [GNU]S (written by Matt Levine, Greg Warrington, and me), whereas the author recommends Jack Boyce's excellent JuggleAnim; they are both written in Java and can be run from any graphical web browser. As the author himself points out, animators provide motivation and intuition; they will make it easier for the mathematical reader to tackle the heavy combinatorial analysis required for the book's harder theorems. In case there is any confusion: this is not the book to buy in order to first learn to juggle. Indeed, no

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KING FAHD UNIVERSITY OF PETROLEUM & MINERALS

book can compare to attending a juggling club, where one is guaranteed to find friendly people eager to get one started in juggling. Most colleges and universities have such clubs; there is a list on the JIS with times of (usually weekly) meetings at http://www.juggling.org/help/meetings. Mathematics is a moving target, and there are already results too recent to appear in the book. In [W] is calculated the expectation of finding a juggler in any given state of a state graph, via Stirling numbers. Presumably this tells us something about the affine Weyl group!

DHAHRAN, SAUDI ARABIA College of Sciences - Department of Mathematical Sciences

Senior Tutor for Mathematics Learning Center The Mathematics Learning Center (MLC) invites applications for faculty positions of a Senior Tutor. The primary work is to assist the MLC Director in providing a wide range of support and enough learning resources

References [CC] Decisions of the Central Council of Church Bell Ringers, Morphet, 1989. [CR] J. CASSIDY and B. C. RIMBEAux, juggling for the Complete Klutz, Klutz Inc. [ER] R. EHRENBORG and M. READDY, Juggling and applications to q-analogues, Proceedings of the 6th Conference on Formal Power Series and Algebraic Combinatorics (New Brunswick, NJ, 1994), DiscreteMath.l57 (1996), nos. 1-3, 107-125. [K] A. KNUTSON, The site swap FAQ, http: I lwww. juggling.orglhelplsiteswaplfaq.html. [RJ] The USENET newsgroup rec. juggling, available through e.g. http: I I groups. goog l e. com. [W] G. WARRINGTON, Juggling probabilities, http: I I front.math.ucdavis.edu/math.PR/0302257.

to help students, especially at the orientation level, meet their mathematical challenges through self learning and good study habit that will help them overcome their mathematical difficulties. He will be expected to conduct Remedial Classes and Problem Solving for small group and on an individual basis.

A Ph.D. in Mathematics or Mathematics Education is required. Candidates will be assessed on excellence in teaching, previous work in a similar Center, and fluency in English. renewable contract. Competitive salaries based on qualifications and

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experience. Free furnished air-conditioned on-campus housing unit with free essential utilities and maintenance. The appointment includes the following benefits according to the University's policy: air ticket to Dammam on appointment; annual repatriation air tickets for up to four persons; assistance with local tuition fees for school-age dependent children; local transportation allowance; two months' paid summer leave; end-ofservice gratuity. KFUPM campus has a range of facilities including a medical and dental clinic, an extensive library, computing, research and teaching laboratory facilities and a recreation center. To apply: Mail, fax or e-mail cover letter and

detailed CV/Resume (including a list of research and teaching activities) and e-mail address of three professional references to: Dean, Faculty & Personnel Affairs, KFUPM Box 5005, Dhahran 31261, Saudi Arabia DEPT.No.: MATH/MLC-2370 Fax: 966-3-860-2429 E-Mail: [email protected] or [email protected] Please quote the above DEPT. REF No. in all correspondence. For additional information, please visit our website : http://www.kfupm.edu.sa/fpa/

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Book Review

Beyond the Limit The Dream of Sofya Kovalevskaya Reviewed by Ann Hibner Koblitz

Beyond the limit: The Dream of Sofya Kovalevskaya ]oanSpicci Forge Books, 2002 $26.95, 490 pp. ISBN 0-765-30233-0

Twenty-five years ago when I began research on my doctoral dissertation on the Russian mathematician, writer, and social activist Sofia Kovalevskaia (1850-1891), I was surprised to learn that m ost mathematicians I encountered had some smattering of information (often false) about her. The more diffident and cautious among them would recount their "knowledge" in the form of questions, such as "Is it true that she slept with her advisor and that he did all of h er best work?" or "Did she really abandon math for literature?" But I also met a few mathematicians whose thoughtlessness or arrogance led them to state confidently that all of Kovalevskaia's papers were erroneous or that she was awarded the Prix Bordin of the French Academy of Sciences out of gallantry. One Swedish mathematician (who will remain nameless) condescendingly chided me for b eing interested in Kovalevskaia as a mathematician at all, saying that although she might have been something of an amateur mathematician, the Cauchy-Kovalevskaia Theorem (one of her b est-known results) was her Ann Hibner Koblitz is professor of women's studies at Ariz ona State University. Her email address is

koblitz@asu. edu. jANUARY

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husband's, not hers.1 And several people took great glee in recounting to me the aphorism often attributed to Hermann Weyl that there have b een only two women in the history of mathematics, and one of them wasn't a mathematician [Kovalevskaia], while the other wasn't a woman [Emmy Noether]. :il:. w...... -rs-r,. :Jt'.,.~,.r."'. . The plethora of misinformation about Kovalevskaia made me realize that I had a larger task on my hands than I had initially supposed. Naturally, I needed to comb the archives and libraries of Russia, Sweden, and elsewhere to put together the pieces of her life and set her within the intellectual and cultural milieu of her time. But equally importantly, I wanted to trace the various legends and insinuations to their sources and uncover the roots of commonly held misperceptions. This historiographical study proved most charitable interpretation of this bit of nonsense might be that since the theorem is often called Cauchy-Kovalevskii in Western European languages ("ii" is a masculine ending for names in Russian, while "aia" is feminine), he thought that the reference must be to a man. Also, Kovalevskaia's husband, Vladimir Kovalevskii, was indeed a scientist in his own right, but he was a paleontologist, not a mathematician.

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almost as engrossing as did my research on the circumstances of Kovalevskaia's life and work and involved questions of changing political and cultural atmosphere as well as the idiosyncrasies of individual historians, mathematicians, and other commentators. For those who know little about Kovalevskaia, let me digress for a moment to give a short summary of her life. Sofia Kovalevskaia (nee KorvinKrukovskaia) was born into a noble household in Russia in 1850. Like many young gentlewomen of her generation, she was caught up in the social and political movements of Russia in the 1860s, among which was nihilism. Adherents of this philosophy denied the value of everything in traditional tsarist society, had great faith in the power of education, believed that a transformative social revolution was imminent, and maintained that the best way to help the revolution along was through the study of the natural sciences and medicine. Kovalevskaia embraced nihilism and decided to pursue an advanced degree in mathematics. She married nihilist book publisher and sometime paleontologist Vladimir Kovalevskii in order to further her efforts to get a university-level education. Their stormy, unconventional marriage resulted in a daughter, born in 1878, and ended with Vladimir's suicide in 1883. Kovalevskaia studied in Heidelberg and Berlin with Karl Weierstrass, Leo Konigsberger, Paul DuBois-Reymond, and others and with their help in 1874 persuaded Gottingen University to recognize her three research works as sufficient for a degree. She was the first woman in the world to get a doctoral degree in mathematics in the modern sense of the term, and she was among the first women to earn advanced degrees in any subject. Because of the prejudices of the time, she had difficulty establishing herself in a professional position, and it was not until late 1883 that her colleague Gosta Mittag-Leffler was able to arrange a post for her at the newly established university in Stockholm. Kovalevskaia became an Extraordinary Professor (in modern American parlance, assistant professor) at Stockholm University in 1884 and joined the editorial board of the new journal Acta Mathematica at the same time. In the last three years of her life, Kovalevskaia received the Prix Bordin of the French Academy of Sciences for her work on the revolution of a solid body around a fixed point, a full professorship in Stockholm, and corresponding membership in the Russian Imperial Academy of Sciences (the rules had to be changed to permit her membership). At the same time she also distinguished herself as a writer; she published a much-acclaimed memoir of her childhood, several essays on political and social topics, and (in conjunction with MittagLeffler's sister, Anne Charlotte Leffler) two plays. 40

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Kovalevskaia's life was eventful. Besides her pioneering efforts to open up higher educational opportunities for women in Russia and continental Europe and her literary endeavors, she participated in the Paris Commune, aided Polish and Russian revolutionaries whenever possible, and was on cordial terms with many of the most prominent mathematical and cultural figures of her day. She numbered among her colleagues and friends the eminent mathematicians Charles Hermite, Henri Poincare, Hermann Schwarz, Carl Runge, Pafnutii Chebyshev, and Emile Picard. She was acquainted with such scientific and literary luminaries as Charles Darwin, George Eliot, Dmitri Mendeleev, Ilia Mechnikov, Ivan Sechenov, Herbert Spencer, Ivan Turgenev, Fedor Dostoevskii, Henrik Ibsen, and August Strindberg, and her salons in St. Petersburg, Moscow, and Stockholm were attended by these and other leading intellectual figures. In fact, what emerged most prominently from my research in Russian and Swedish archives and libraries was the extent to which Sofia Kovalevskaia was not, as implied in the Weyl remark cited above or in Bell's Men of Mathematics, 2 some sort of barely tolerated amateur or outsider. On the contrary, she was a participating member of the European mathematical elite: she was consulted on hiring decisions, was asked for letters of recommendation, organized conferences, and so on. Kovalevskaia actively contributed to the "mathematical culture" of late nineteenth-century Europe, and during her lifetime she was accorded the respect she deserved. It was not until her contemporaries retired or died that the legends and distortions began to surface in the European mathematical community. In the 1980s several serious works on Kovalevskaia and her mathematics appeared in English. My doctoral dissertation was published in 1983 and was soon followed by a comprehensive book on Kovalevskaia's mathematics by Roger Cooke, the English translation of a careful biography by the Soviet academician Pelageia Polubarinova-Kochina, and a volume of Contemporary Mathematics devoted to Kovalevskaia's life and mathematicallegacy. 3 Since the 1980s there have certainly been enough reliable accounts of 2 Eric Temple Bell,

Men of Mathematics (New York: Simon

and Schuster, 1937), 423-429. 3 Ann Hibner Koblitz, A Convergence of lives. Sofia Kovalevskaia: Scientist, Writer, Revolutionary (Boston and

Basel: Birkhauser, 1983; revised 2nd ed. New Brunswick, N]: Rutgers University Press, 1993); Roger Cooke, The Mathematics of Sonya Kovalevskaya (New York: SpringerVerlag, 1984); Pelageya Kochina, Love and Mathematics: Sofya Kovalevskaya (Moscow: Mir, 1985); Linda Keen, ed., The Legacy of Sonya Kovalevskaya, Contemp. Math. (Providence: American Mathematical Society, 1987).

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Kovalevskaia's life and research that one could expect the disparagement and innuendo to cease. Unfortunately, it seems as if some mathematicians are more comfortable with the old rumors and tales about their predecessors than they are with the reasoned results of careful scholarship. Eric Temple Bell's Men of Mathematics, for example, still appears to be popular despite the fact that it is riddled with errors and his section on Kovalevskaia is inaccurate and coyly sexualized. 4 And Felix Klein's idiosyncratic two-volume history of nineteenth-century mathematics (which casts doubt on Kovalevskaia's originality) is still commonly regarded by mathematicians as authoritative, even though, as Jeremy Gray noted, historians have learned "to handle [it] with care." 5 Even at the present time one occasionally comes across sexist treatment of Kovalevskaia. A few years ago the Russian edition of Playboy pasted her face onto the body of a nude masturbating woman. And just last year in Mathematical Apocrypha Steven Krantz perpetuated the canard that Kovalevskaia and her colleague Mittag-Leffler had been sexually intimate. Krantz also saw fit to illustrate his little anecdote with a photograph of "the lovely Sonja Kowalewska dressed up as a kitty kat." 6 Given the persistence of sexist silliness about Kovalevskaia, I must admit that it was with mixed emotions that I agreed to look at proof pages of Joan Spicci' s Beyond the Limit: The Dream of Sofya Kovalevskaya. Fortunately, I needn't have worried; the book is a respectful as well as entertaining treatment of its subject. Beyond the Limit is a bit difficult to categorize. Spicci uses real names and historical personages and is in most cases accurate in matters of fact. She has consulted some of the best sources on Kovalevskaia in both Russian and English and has read Kovalevskaia's collected correspondence in Russian. She has been interested in Kovalevskaia for many years, has mathematical training, and has produced translations of several of Kovalevskaia's literary works. But Spicci writes in a flowing, omnipresent narrative style, putting words in the mouths and thoughts in the minds of 4Eric Temple Bell, Men of Mathematics (New York: Simon and Schuster, 193 7). For a careful analysis of Bell's errors with regard to another mathematician, see Tony Rothman, "Genius and Biographers: The Fictionalization of Evariste Galois", A mer. Math. Monthly 89 (1982), 82-106. 5Felix Klein, Vorlesungen tiber die Entwicklung der Mathematik im 19. Jahrhundert (Berlin: Springer, 1926); jeremy Gray, "Who Would Have Won the Fields Medals a Hundred Years Ago?", Math. Intelligencer 7 (1985), 19. 6 Steven G. Krantz, Mathematical Apocrypha: Stories and

Anecdotes of Mathematicians and the Mathematical (Washington, DC: The Mathematical Association ofAmerica, 2002), 126-127.

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her characters in a manner one usually associates with the genre of romantic fiction. The book therefore has the feel of a novel, though the author refers to her study as a "historical work" (p. 7). Spicci limits herself to a relatively short but exciting period in Kovalevskaia's life. The book begins in the winter of 1865 with a description of the adolescent Sofia's infatuation with her older sister Aniuta's beau, the famous author Fedor Dostoevskii. It ends with Vladimir and Sofia happily going home together to Russia in 1874 upon the successful completion of their doctoral studies. The long narrative (close to 500 pages) stresses Kovalevskaia's determined efforts to attain a university education and doctorate in mathematics, her nihilist political beliefs and those of her sister and friends, and the on-again, off-again relationship between Sofia and Vladimir. The Kovalevskii marriage initially had been what the Russian radicals of the day called "fictitious". That is, it was arranged for the purpose of transferring Sofia from her father's control to that of her husband so that she could go abroad to study, at which point he was theoretically supposed to leave the scene. At first, Sofia appears to have had no notion that Vladimir desired to share her life. 7 Though a competent scientist, committed radical, and normally sweet-tempered person, Vladimir was a bit unstable. He could on occasion alienate his family, colleagues, and political associates with bouts of inexplicable rage or highhandedness (a facet of his personality Spicci tends to downplay). For her part, Kovalevskaia could be capricious in her dealings with Vladimir and sometimes took him for granted. The confused nature of the pair's relations during their university years in Western Europe is a major focus of Spicci's interest. I enjoyed the book very much; it is charmingly written and engrossing. Despite its length it reads quickly, and I found myself sorry when the narrative came to an end. Spicci's characterizations for the most part seem plausible. She has nicely captured the personalities as well as the psychological and political dilemmas of several of the major figures in her heroine's life, and she has a fine talent for painting Kovalevskaia against a broad backdrop of European society and culture. While I might have doubts about a few of her interpretations of her characters' motivations and beliefs, and I am almost certain that she misdates the change in the Kovalevskii marriage from fictitious to real, on the whole I thought her account was artistically satisfying as well as 7I discuss this further in A Convergence of Lives, "Career and Home Life in the 1880s: A Mathematician's Choices"; Uneasy Careers and Intimate Lives: Women in Science, Pnina Abir-Am and Dorinda Outram, eds. (New Brunswick: Rutgers University Press, 1987), 172-190.

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accurate. Several times I found myself initially resisting Spicci's take on some event, only to decide that her version was in fact believable and that the scene might have unfolded along the lines she suggested. Who will be interested in reading this book? Any mathematician or scientist with a desire to immerse herself/himself in the vanished world of nineteenth-century European intellectual and cultural life will find Beyond the Limit absorbing. The book also might be attractive to young women (possibly at the advanced high school level but more probably college age) who like to read biographies of successful women of the past. This is the kind of biography that I read avidly when I was a teenager, and although prior knowledge of Kovalevskaia's history might be helpful, it is certainly not essential for the enjoyment of this charining story.

New & Forthcoming !."'em Oxford APPLIED LONGITUDINAL DATA ANALYSIS Modeling Change and Event Occurrence Judith D. Singer and John B. Willett, Harvard University, Graduate School of Education Applied Longitudinal Data Analysis is a much-needed professional book for empirical researchers and graduate students in the behavioral, social, and biomedical sciences. It offers the first accessible in-depth presentation of two of today's most popular statistical methods: multilevel models for individual change and hazard/survival models for event occurrence {in both discrete- and continuous-time). Visit http://www.ats.ucla.edu/stat/examples/alda.htm 2003 0-19-515296-4

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NUMERICAL METHODS FOR IMAGE REGISTRATION Jan Modersitzki, University of Lubeck This well-illustrated and comprehensive text provides an introduction to the theoretical, practical, and numerical aspects of image registration, with special emphasis on medical imaging. It discusses the basic mathematical principles, including aspects from approximation theory, image processing, numerics, partial differential equations, and statistics, with a strong focus on numerical methods. (Numerical Mathematics and Scientific Computation)

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INTRODUCTION TO APPLIED STATISTICS A Modelling Approach Second Edition J. K. Lindsey, University of Liege and Lim burgs University This text is aimed at students in medicine, biology and the social sciences as well as those planning to specialize in applied statistics. It covers the basics of the design and analysis of surveys and experiments and provides an understanding of the basic principles of modeling and inference. February 2004 0-19-852894-9 0-19-852895-7

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Engle and Granger Receive Nobel Prize in Economic Sciences

On October 8, 2003, the Royal Swedish Academy of Sciences announced that the Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel, 2003, would be shared by ROBERT F. ENGLE "for methods of analyzing economic time series with time-varying volatility (ARCH)" and CLIVE W. J. GRANGER "for methods of analyzing economic time series with common trends (cointegration)." The two will share the prize amount of 10 million Swedish kroner (about US$1.3 million). Researchers use data in the form of time series, i.e., chronological sequences of observations, when estimating relationships and testing hypotheses from economic theory. Such time series show the development of GDP [gross domestic product], prices, interest rates, stock prices, etc. During the 1980s, the 2003 laureates devised new statistical methods for dealing with two key properties of many economic time series: time-varying volatility and nonstationarity. On financial markets, random fluctuations over time-volatility-are particularly significant because the value of shares, options, and other financial instruments depends on their risk. Fluctuations can vary considerably over time; turbulent periods with large fluctuations are followed by calmer periods with small fluctuations. Despite such time-varying volatility, in want of a better alternative, researchers used to work with statistical methods that presuppose constant volatility. Robert Engle's discovery was therefore a major breakthrough. He found that the concept of autoregressive conditional heteroskedasticity (ARCH) accurately captures the properties of many time series and developed methods for statistical modeling of time-varying volatility. His ARCH models have become indispensable tools, not only for jANUARY

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researchers, but also for analysts on financial markets, who use them in asset pricing and in evaluating portfolio risk. Most macroeconomic time series follow a stochastic trend, so that a temporary disturbance in, say, GDP, has a long-lasting effect. These time series are called nonstationary; they differ from stationary series, which do not grow over time but fluctuate around a given value. Clive Granger demonstrated that the statistical methods used for stationary time series could yield wholly misleading results when applied to the analysis of nonstationary data. His significant discovery was that specific combinations of nonstationary time series may exhibit stationarity, thereby allowing for correct statistical inference. Granger called this phenomenon cointegration. He developed methods that have become invaluable in systems where short-run dynamics are affected by large random disturbances and long-run dynamics are restricted by economic equilibrium relationships. Examples include the relations between wealth and consumption, exchange rates and price levels, and short- and long-term interest rates. Robert F. Engle was born in 1942 in Syracuse, New York. He received his Ph.D. from Cornell University in 1969 and is currently the Michael Armellino Professor of Management of Financial Services at New York University. Clive W. J. Granger was born in 19 34 in Swansea, Wales. He received his Ph.D. from the University of Nottingham in 1959 and is an emeritus professor of economics at the University of California, San Diego. -From news announcements of the Royal Swedish Academy of Sciences

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Demaine Receives MacArthur Fellowship

In September 2003 the John D. and Catherine T. MacArthur Foundation named twenty-four new MacArthur Fellows for 2003. Each will receive $500,000 in "no strings attached" support over the next five years. Among the fellows is ERIK DEMAINE, an assistant professor of computer science at the Massachusetts Institute of Technology. Erik Demaine is a young computer scientist who has already established a reputation for tackling and solving difficult problems. Although he actively pursues projects related to many areas of computer science, such as parallel processing architectures and algorithm complexity, Demaine is noted for his research in computational geometry. Recently, he collaborated on a proof of a longstanding conjecture known as the "carpenter's rule", which asserts that all closed polygons with non-crossing connections can be made convex (i.e., straightened out, roughly) without breaking or changing the relative length of the connections. This work reflects his broader interest in problems related to folding and bending. Such problems hold implications for both abstract mathematics and practical issues such as manufacturing methods. Demaine moves readily between the theoretical and the playful, with a keen eye to revealing the former in the latter. For example, he recently demonstrated that a popular computer game, Tetris, represents an example of a computational geometry problem that falls into the "NP-complete" category, implying explosive growth in difficulty with no shortcuts available. Demaine has also invented problems and solutions related to other areas of recreational mathematics (e.g., origami, combinatorial games). Through his eclectic choices for research topics and his prodigious and prolific 44

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output, Demaine has demonstrated an appetite for challenges that cross disciplinary boundaries and a capacity to synthesize ideas from disparate approaches. Erik Deniaine received a B.Sc. (1995) from Dalhousie University and an M.Math. (1996) and Ph.D. (2001) from the University of Waterloo. In 2001 he became an assistant professor in the Department of Electrical Engineering and Computer Science and in the Laboratory for Computer Science at MIT. Demaine has presented more than fifty papers at national and international conferences, published dozens of articles in professional publications, written chapters for five books, and coedited two books. He is currently coauthoring a book, Folding and Unfolding in Computational Geometry.

The MacArthur Fellows Program is designed to emphasize the importance of the creative individual in society. Fellows are selected for the originality and creativity of their work and the potential to do more in the future. Candidates are nominated, evaluated, and selected through a rigorous and confidential process. No one may apply for the awards, nor are any interviews conducted with nominees. The MacArthur Fellows Program places no restrictions on how recipients may use the $500,000, and no reports are required. The year 2003 is one of particular significance for the John D. and Catherine T. MacArthur Foundation, marking its twenty-fifth year of grant making. As one of the largest private philanthropic foundations in the United States, MacArthur has awarded more than $3 billion in grants since it began operations in 1978, and today has assets of approximately $4 billion.

AMS

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Mathematics People Undenstrauss and Soundararajan Awarded 2003

contributions to the modular representation theory of Heeke algebras and quantum algebras. The Autumn Prize is awarded to an individual who has made outstanding contributions to mathematics within the previous five years. KENGO HIRACHI of the University of Tokyo and SHIGENORI MATSUMOTO of Nihon University were awarded the Geometry Prizes. Hirachi was recognized for his contributions to parabolic invariant theory of the Bergman kernel of strongly pseudoconvex domains. Matsumoto was honored for his research at the intersection of dynamical systems and the theory of foliations on low-dimensional manifolds. MASAKI IZUMI of Kyoto University, MASATOSHI FUKUSHIMA of Kansai University, and KIMIO MIYAJIMA of Kagoshima University were awarded the Analysis Prizes. Izumi received the award for work on subalgebras and group actions for operator algebras. Fukushima was honored for study of Dirichlet forms and Markov processes, and Miyajima was recognized for research on the deformation theory of strongly pseudoconvex CR structures and isolated singularities. The Takebe Prize for outstanding research was established to encourage young mathematicians in their research. The Takebe Senior Prize is awarded to recipients chosen from nominations by members of the Mathematical Society of Japan. The Takebe Junior Prize is awarded to selfnominated applicants. The Takebe Prizes for 2003 were awarded as follows. The Takebe Senior Prizes were awarded to OsAMu FUJINO of Nagoya University for research on the logarithmic abundance theorem and its applications; to AKIKo SHIMA of Tokai University for the study of 2-knots using projection diagrams and quandle cohomologies; and to MINORU ITOH of Kyoto University for the study of Capelli identities. The Takebe Junior Prizes were awarded to SoNG liANG of Nagoya University for research on the precise estimates of the large deviation principle; to REIKA FUKUIZUMI of Tohoku University for research in stability and instability of standing waves for nonlinear dispersive equations; to REI INOUE of Tokyo University for research on discrete integrable systems by algebraic analytical methods; to ToMOMI KAwAMURA of Aoyama Gakuin University for research. on unknotting numbers based on four-dimensional geometry and links of divides; and to KENICHI BANNAI of Nagoya University for work on p-adic polylogarithms.

Salem Prize The Salem Prizes for the year 2003 have been awarded to ELON LINDENSTRAuss of the Clay Mathematics Institute and the Courant Institute of Mathematical Sciences and to KANNAN SoUNDARARAJAN of the University of Michigan. Lindenstrauss was honored for his contributions to ergodic theory, particularly the proof of the quantum unique ergodicity conjecture for arithmetic hyperbolic surfaces. Soundararajan was recognized for contributions to the area of Dirichlet L-functions and related character sums. Previous recipients of the Salem Prize include: N. Varopoulos (1968), R. Hunt (1969), Y. Meyer (1970), C. Fefferman (1971), T. Korner (1972), E. M. Nikishin (1973), H. Montgomery (1974), W. Beckner (1975), M. R. Herman (1976), S. B. Bochkarev (1977), B. E. Dahlberg (1978), G. Pisier (1979), S. Pichorides (1980), P. Jones (1981), A B. Aleksandrov (1982), ]. Bourgain (1983), C. Kenig (1984), T. Wolff (1985), N. G. Makarov (1986), G. David (1987), ]. L. Journe (1987), A L. Volberg (1988), ].-C. Yoccoz (1988), S. V. Konyagin (1990), C. McMullen (1991), M. Shishikura (1992), S. Treil (1993), K. As tala (1994), H. Eliasson (1995), M. Lacey (1996), C. Thiele (1996), T. Wooley (1998), F. Nazarov (1999), T. Tao (2000), 0. Schramm (2001), S. Smirnov (2001), and X. Tolsa (2002). The prize, established in memory of Raphael Salem, is awarded yearly to young researchers for outstanding contributions in the field of analysis. The 2003 prize committee consisted of ]. Bourgain, C. Fefferman, P. Jones, N. Nikolski, P. Sarnak, and ].-C. Yoccoz.

-jean Bourgain, Institute for Advanced Study

Prizes of the Mathematical

Sodety of Japan The Mathematical Society of Japan (MSJ) has awarded a number of prizes for 2003. SusuMU ARIKI of the Research Institute for Mathematical Sciences, Kyoto, received the Autumn Prize for his jANUARY 2004

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-From an MS] announcement OF

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Mathematics People

Kuo Wins Information-Based Complexity Young Researcher Award FRANCES Kuo of the University of New South Wales, Sydney, Australia, has been awarded the first Information-Based Complexity Young Researcher Award. The award recognizes significant contributions to information-based complexity by a researcher who has not reached his or her thirty-fifth birthday by September 30 of the year the award is given. The prize consists of $1,000 and a plaque. The award committee comprised Stefan Heinrich, University of Kaiserslautern; Joseph F. Traub, Columbia University; Greg Wasilkowski, University of Kentucky; Arthur G. Werschulz, Fordham University; and Henryk Wozniakowski, Columbia University and University of Warsaw. -joseph F. Traub, Columbia University

NSF CAREER Awards for 2002 and2003 The Division of Mathematical Sciences (DMS) of the National Science Foundation (NSF) has honored twenty mathematicians in fiscal year 2002 and nineteen in fiscal year 2003 with Faculty Early Career Development (CAREER) awards. The NSF established the awards to support promising scientists, mathematicians, and engineers who are committed to the integration of research and education. The grants run from four to five years and range from $200,000 to $500,000 each. For 2002 the CAREER grant awardees and the titles of their grant projects are: Scorr AHLGREN, University of Illinois at Urbana-Champaign: Number Theory Research and Outreach; LuCA CAPOGNA, University of Arkansas: Integration of Research and Education in the Study of Analysis and Partial Differential Equations in Carnot-Caratheodory Spaces; RoBERT GHRIST, Georgia Institute of Technology: Topological Methods in Applied Mathematics; T!LMANN GNEITING, University of Washington: Self-Similarity: Roadblock or Breakthrough?; BRENDAN HASSETT, Rice University: Algebraic Geometry of Moduli Spaces; }AN HESTHAVEN, Brown University: Towards Robust and Efficient High-Order Adaptive Computational Methods for Conservation Laws in Complex Geometries-Analysis, Implementation, and Applications; ZHEZHEN }IN, Columbia University: Semiparametric Regression Models for Censored Data; ALEXANDER KisELEV, University of Chicago: Solutions, Spectrum, and Dynamics of Schrodinger Operators; Do RON LEVY, Stanford University: Partial Differential EquationBased Image Processing with Applications to Radiation Oncology; YI LIN, University of Wisconsin: Research and Education of Flexible Methods for Statistical Modeling and Prediction; YuRI Lvov, Rensselaer Polytechnic Institute: Development and Applications of Weak Turbulence Theory;

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IGOR MINEYEV, University of South Alabama: Homology and Geometry of Groups; BROOKE SHIPLEY, Purdue University: Realizing Derived Equivalences; GREGORY SMITH, College of William and Mary: The Dynamics of IP3-Sensitive Calcium Release Sites; FRANK SorriLE, University of Massachusetts at Amherst: Computation, Combinatorics, and Reality in Algebraic Geometry with Applications; SHANKAR VENKATARAMANI, University of Chicago: Singularities and Microstructure-Multiple Scale Analysis for Nonlinear Partial Differential Equations, Geometric Problems, and the Physical Sciences; ]AN VERSCHELDE, University of illinois: NLApack: Software for Numerical Algebraic Geometry; ANTHONY YEZZI, Georgia Institute of Technology: Unifying Segmentation and Other Image Processing Problems via Variational Partial Differential Equations; and YIJUN Zuo, Arizona State University: Statistical Depth Functions and Their Applications. For 2003 the CAREER grant awardees and the titles of their grant projects are: GUILLAUME BAL, Columbia University: Time Reversal and Inverse Problems in Wave and Particle Propagation; DoNATELLA DANIELL!, Purdue University: Analytic and Geometric Aspects of Partial Differential Equations; }OHN ETNYRE, University of Pennsylvania: Knot Theory and Dynamics in Contact Geometry; MoHAMMAD GHOMI, Georgia Institute of Technology: Classical Problems in Differential Geometry, Topology, and Convexity; Ko HoNDA, University of Southern California: Contact Structures and Low Dimensional Topology; DMITRY KLEINBOCK, Brandeis University: Dynamical Systems on Homogeneous Spaces and Applications to Number Theory; SERGEY LOTOTSKY, University of Southern California: Stochastic Partial Differential Equations and Applications; RANJAN MAITRA, University of Maryland, Baltimore County: Methodology for Statistical Computing in Massive Datasets: Parallel Approaches to Cluster and MCMC Estimation; MADHU NAYAKKANKUPPAM, University of Maryland, Baltimore County: Large-Scale Semidefinite Programming; RAMAN! PILLA, Case Western Reserve University: New Directions in Mixture Models and Their Applications; CHIARA SABATII, University of California at Los Angeles: Statistical and Computational Tools for the Analysis of High Dimensional Genetic Data; SYLVIA SERFATY, New York University: Statics and Dynamics of Singularities in Some Models from Material Science; KoNSTANTINA TRIVISA, University of Maryland at College Park: Systems of Conservation Laws and Related Models in Applied Sciences-Math Awareness and Outreach; RAvi VAKIL, Stanford University: Intersection Theory on Moduli Spaces; ERic VANDEN EIJNDEN, New York University: Transition Pathways in Complex Systems: Theory and Numerical Methods; VAN Vu, University of California at San Diego: Sharp Concentration and Probabilistic Methods; THOMAS WITELSKI, Duke University: Mathematical Modeling of Microfluidic Dynamics and Transport; and CHONGCHUN ZENG, University of Virginia: Perturbation Problems in PDE Dynamics.

NOTICES OF THE AMS

-From an NSF announcement

VOLUME 51, NUMBER 1

Mathematics People

Trjitz:insky Memorial Awards Presented The AMS has made awards to eight undergraduate students through the Waldemar J. Trjitzinsky Memorial Fund. The fund is made possible by a bequest from the estate of Waldemar]., Barbara G., and Juliette Trjitzinsky. The will of Barbara Trjitzinsky stipulates that the income from the bequest should be used to establish a fund in honor of the memory of her husband to assist needy students in mathematics. For the 2003 awards the AMS chose seven geographically distributed schools to receive one-time awards of $4,000 each. The mathematics departments at those schools then chose students to receive the funds to assist them in pursuit of careers in mathematics. The schools are selected in a random drawing from the pool of AMS institutional members. Waldemar J. Trjitzinsky was born in Russia in 1901 and received his doctorate from the University of California Berkeley in 1926. He taught at a number of institutions before taking a position at the University of Illinois, Urbana-Champaign, where he remained for the rest of his professional life. He showed particular concern for students of mathematics and in some cases made personal efforts to ensure that financial considerations would not hinder their studies. Trjitzinsky was the author of about sixty mathematics papers, primarily on quasi-analytic functions and partial differential equations. A member of the AMS for forty-six years, he died in 1973. Following are the names of the selected schools for 2003, the names of the students receiving Trjitzinsky awards, and brief biographical sketches of the students. Bryn Mawr College: THIDA S. AYE. Aye was born in Yangon, Myanmar, and graduated.from high school at the age of fourteen. She was awarded a scholarship to study at the Cambridge Center for Sixth Form Studies in Cambridge, England, and completed a general certificate of education in both ordinary and advanced levels. At Bryn Mawr she majors in mathematics and physics and minors in economics. She has participated in undergraduate research programs at Bryn Mawr, studying computer modeling and nonlinear dynamics, and at Princeton University, studying Monte Carlo simulations of critical parameters of polymers. She is currently doing research on the wavelet analysis of financial derivatives. She plans to attend graduate school to study applied mathematics. Minnesota State University at Mankato: ANDREW RicHARD TACKMANN. Tackmann majors in mathematics and minors in statistics and economics and is a member of the Honors Program. He works as a resident advisor on campus and was inducted into the National Residence Hall Honorary. He is also a volunteer tutor for the School Age Literacy Program. He enjoys intramural sports and plans to pursue a career in actuarial science. University of Maryland at Baltimore County: MARIA CHRISTIN LLEWELLYN. Llewellyn grew up in West Virginia before moving to Maryland. After high school she received an appointment to the United States Naval Academy, but jANUARY

2004

after a brief attendance there decided to pursue her interest in the intelligence field outside of the military. She majors in mathematics and computer science, works full time, and maintains a high A average. She enjoys swimming, running, and traveling, and plans to attend graduate school to study pure mathematics. Colorado College: RAHBAR VIRK. Virk was born and raised in India. He came to the United States in 2001 to study physics but decided to pursue mathematics after becoming interested in number theory. His interests include philosophy, physics, computer science, playing 8-ball pool, reading, and chess. He plans to attend graduate school in mathematics. California State University, Hayward: SARAH DEIWERT and ANGELA MARTINHO. Deiwert has maintained a ·3.96 average while raising two sons and working part time as an artist. She is "outstanding-intelligent, hard working, and motivated," said Russell Merris of the Department of Mathematics. She enjoys reading, writing, and collecting teddy bears. She hopes to work in the scientific community and plans to teach algebra to other adults. Martinho is a firstgeneration college student who plans to teach high school and eventually obtain a master's degree in mathematics. She is an accomplished swimmer and received an AllAmerican Honorable Mention in two swimming events this year. After undergoing two shoulder surgeries, she improved her swimming performance and was named the most inspirational swimmer on her team. Lehigh University: TiMOTHY P. LEWIS. Lewis is a mathematics major and plans to pursue a second degree in computer science or electrical engineering. As a student at Owen J. Roberts High School in Pottstown, Pennsylvania, he was selected for the Lehigh Valley American Regions Math League team and attended the Hampshire College Summer Studies in Mathematics program in Amherst, Massachusetts. In his freshman year at Lehigh he maintained a 4.0 average in mathematics and a 3.9 overall average. He was the high scorer for the university on the Putnam examination. He plays rugby and is a competitive weightlifter and "diehard Eagles fan." State University of New York at Potsdam: BISHAL THAPA. Thapa was born and raised in Nepal, where he placed in the top ten in a nationwide examination. He came to New York to study computer science, then fell in love with mathematics. As a freshman he won awards as the top student in two calculus classes. He is now·taking graduate mathematics classes as a junior. He tutors many students who appreciate his ability to explain clearly and his enthusiasm for mathematics. For further information about the Trjitzinsky Memorial Fund, contact the AMS Development Office, 201 Charles Street, Providence, RI, 02904-2294; email: development@ ams.org; telephone: 401-455-4111.

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-Elaine Kehoe

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Mathematics Opportunities

Deadlines and Target Dates at theDMS The Division of Mathematical Sciences (DMS) of the National Science Foundation (NSF) has a number of programs in support of mathematical sciences research and education. Listed below are some of the programs and their deadlines or target dates for the year 2004. Some dates are tentative; please refer to the program announcement or contact the program director for more information. First week of January 2004 (target date): Mathematical Biology part of Applied Mathematics (includes all proposals for Research in Undergraduate Institutions [RUI]) January 15, 2004 (target date): Mid-Career Methodological Opportunities Late January 2004 (deadline; see solicitation): Major Research Instrumentation (MRI) Program; Scientific Computing Research Environments for the Mathematical Sciences (SCREMS) February 1, 2004 (target date): Research Planning Grants and Career Advancement Awards for Minority Scientists and Engineers Early April 2004 (target date; see solicitation): CBMS Regional Research Conferences in the Mathematical Sciences June 30, 2004 (deadline): Joint DMS/NIGMS Initiative to Support Research Grants in the Area of Mathematical Biology July 2004 (deadline; see solicitation): Faculty Early Career Development (CAREER) Program August 15, 2004 (target date): Mid-Career Methodological Opportunities August 20, 2004 (deadline): Letters of intent for Focused Research Groups (FRG) in the Mathematical Sciences September 15, 2004 (deadline): Research Experiences for Undergraduates (REU) sites September 16, 2004 (deadline): Enhancing the Mathematical Sciences Workforce in the 21st Century (includes Vertical Integration of Research and Education in the Mathematical Sciences [VIGRE]) September 17, 2004 (deadline): Proposals for Focused Research Groups (FRG) in the Mathematical Sciences 48

October 15, 2004 (deadline): Mathematical Sciences Postdoctoral Research Fellowships November 13, 2004 (deadline): University-Industry Cooperative Research Programs in the Mathematical Sciences November 22, 2004 (deadline): Interdisciplinary Grants in the Mathematical Sciences (IGMS) Proposals for conferences, workshops, and special years that are submitted to the Statistics and Probability program or to the Topology and Foundations program can be sent at any time. However, proposals for these activities that are submitted to all other DMS programs (Analysis, Algebra and Number Theory, Applied Mathematics, Computational Mathematics, and Geometric Analysis) must be submitted according to the target dates for those programs. Proposals for supplements for Research Experiences for Undergraduates may be submitted at any time. For further information consult the DMS website at http://www.nsf.gov/mps/divisions/dms/news/ c_deadl i nes. htm. The mailing address is Division of Mathematical Sciences, National Science Foundation, Room 1025,4201 Wilson Boulevard, Arlington, VA 22230. The telephone number is 703-292-5111. -From a DMS announcement

ONR Young Investigator Program The Office of Naval Research (ONR) sponsors a Young Investigator Program to support academic scientists and engineers who have recently received Ph.D. or equivalent degrees and who show exceptional promise for doing creative research. Awards of up to $100,000 per year for three years are made, and additional funds may be provided based on need. The program is open to United States citizens, nationals (native residents of a U.S. possession), and permanent residents who hold tenure-track or permanent faculty positions at U.S. universities and who received their graduate degrees on or after November 1,1998.

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Proposals in mathematical, computer, and information sciences should be sent to: Office of Naval Research (FY04 YIP under BAA 04-002), Attn: Director, Mathematical, Computer, and Information Sciences Division, ONR Code 311, Room 607,800 North Quincy Street, Arlington, VA 222175660. Proposals must be received by 4:00p.m. Eastern Standard Time on January 8, 2004: For further information and instructions for proposal preparation, see the ONR website, http: I /www. on r. navy. mi 1 /sci_ tech/ i ndust ria1 lyi p. htm, or call 703-696-4314.

-From an ONR announcement

Collaborations in Mathematical Geosdences The National Science Foundation supports a program called Collaborations in Mathematical Geosciences (CMG). The purposes of the CMG activity are: (A) to enable collaborative research at the intersection of mathematical sciences and geosciences, and (B) to encourage crossdisciplinary education through summer graduate training activities. Research topics under (A) should fall within one of three broad themes: (1) mathematical and statistical modeling oflarge, complex geosystems; (2) representing uncertainty in geosystems; or (3) analyzing large geoscience data sets. · Research projects supported under this activity should be essentially collaborative in nature. Research groups should include at least one mathematical scientist and at least one geoscientist. Projects under category (A) should be of three to four years in duration. It is not the intent of this activity to provide general support for infrastructure. Projects under category (B) are not restricted to topics (1)- (3). The award duration for category (B) will be two years. The CMG program announcement is available on the Web at http: I lwww. ns f. gov l pubsyslodsl getpub. cfm?nsf04508. The proposal deadline is January 14, 2004.

- From an NSF announcement

News from AIM The American Institute ofMathematics (AIM) announces that applications are being accepted to fund ten graduate students enrolled at U.S. institutions to attend a 10-day course, "Recent Perspectives inRandomMatrixTheory and Number Theory", to be held March 29 to AprilS, 2004, at the Isaac Newton Institute in Cambridge, England. Information about the school can b e obtained at http: I l www. · newton.cam.ac.uklprogramm esi RMAi rmaw02.html. An online application form may b e filled out at http:ll www.aimath.orglnewtonsc hoolapplication. html. jANUARY

2004

The deadline for applications is January 10, 2004. The funding is being provided by a grant from the National Science Foundation (NSF).

- AIM announcement

News from the MBI The Mathematical Biosciences Institute (MBI) at The Ohio State University announces its 2003-2004 scientific program. Winter Quarter 2004: Mathematical Modeling and Signal Transduction. January 5-9, 2004: Tutorial on "Signal Transduction"; January 26-30,2004: Workshop 3-"Signal Transduction I: The Many Roles of Calcium" (Organizers: James Sneyd and Mike Sanderson); February 16-19, 2004: Tutorial on "Signal Transduction"; March 8-12, 2004: Workshop 4-"Signal Transduction II: Muscles and Motility" (Organizers: James Sneyd and Ed Pate). Spring Quarter 2004: Immune Models and Host-Pathogen Dynamics. May 6-7, 2004: Tutorial on Immunology and Intracellular Processes (speakers include Denise Kirschner and Tom Kepler); May 10-14, 2004: Workshop 5-"Immunology Models: Cell Signaling and Immune Dynamics" (Organizers: Denise Kirschner, Jennifer Linderman, and Sergei Pilyugin); June 17-18, 2004: Tutorial on "Pathogens and Host-Pathogen Interaction" (speakers include Denise Kirschner and others); June 21- 25 , 2004: Workshop 6"Modeling Host-Pathogen Interactions" (Organizers: Denise Kirschner and Tom Kepler). Summer Program, July 19-August 6, 2004. This educational program consists of a one-week tutorial and a two-week team project. The participants are graduate students. College instructors and qualified undergraduates will also be considered. The tutorial and projects will focus on cell processes, with emphasis on signal transduction within a cell and among cells. 2004-2005 Scientific Program: Genomics, Proteomics, Bioinformatics. The year will begin with one-week tutorials on rnicroarrays and a one-week tutorial on statistical methods in genomics. The following workshops are planned. Autumn quarter 2004: "Analysis of Gene Expression Data: Principles and Applications" and "Regulatory Networks". Winter quarter 2005 : "Computational Proteomics and Mass Spectrometry" and "Emerging Genomic Technologies and Data Integration Problems". Spring quarter 2005 : "Biomarkers in HIV and Cancer Research" and "Evolutional Genornics". For more information visit the MBI web site at: http: I I mbi . osu . e du. Applications for postdoctoral fellowships, workshop participation, and long-term visits are available on the Web.

- MBI announcement

News from the SAMSI The Statistical and Applied Mathematical Sciences Institute (SAMSI) of the National Science Foundation (NSF) aims to forge a synthesis of the statistical sciences and the applied mathematical sciences and disciplinary science.

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(;j) At the Joint Meetings

Curren t Events in Mathem atics An AMS Special Session Organized by AMS President

David Eisenbud The Interior-Point Revolution in Optimization: History, Recent Developments and Lasting Consequences Margaret H. Wright conveys the excitement that remains after almost 20 years of intense, at times frenzied, research on evolution of interior-point methods from the controversies of 1984 to the present.

What Is Motivic Integration? Thomas C. Hales describes the motivic integral to the nonspecialist together with a few of the numerous applications it has found in logic and geometry.

It Is Easy to Determine Whether or Not a Given Integer Is Prime Andrew Granville explains the polynomial time primality test of Agrawal, Kayal and Saxena, with complete proofs, and puts the result and ideas into appropriate historical context.

Perelman's Recent Work on the Classification of 3·Manifolds John W. Morgan presents statements of the Poincare Conjecture and Thurston's Geometrization Conjecture, to show the relationship between them, and outlines some of the main ideas in G. Perelman's approach to proving these conjectures.

Its 2004 program is on the topic Multiscale Model Development and Control Design. The major workshops already scheduled are: january 17-21,2004: Tutorials and Opening Workshop February 15-17, 2004: Workshop on Multiscale Phenomena in Soft Matter Nanomaterials April15-17, 2004: Workshop on Fluctuations and Continuum Equations in Granular Flow Additional miniworkshops, to be scheduled, will address specific issues associated with multiscale modeling, homogenization, large-scale simulation, reduced-order systemmodels, and robust control design and implementation. In 2005 SAMSI will offer programs on Computational Biology of Infectious Diseases (September 2004-May 2005), on Social Sciences (September 2004-May 2005), and on Data Assimilation (January 2005-June 2005). SAMSI is accepting proposals for future research programs. Contact Jim Berger, email: berger@samsi. info; Tom Banks, email: htbanks@eos. ncsu. edu; Alan Karr, email: [email protected]; or Steve Marron, email: marron@ email . unc. edu. For more information see the SAMSI website, http: I /www. samsi . info.

- From a SAMSI announcement

Departmen ts Coorclinate Job Offer Deadlines A group of mathematical sciences departments has adopted an agreement to coordinate deadlines for acceptance of postdoctoral job offers. The purpose is to ensure that applicants do not have to make decisions about job offers before the results of the National Science Foundation (NSF) postdoctoral fellowship competition are announced. The agreement applies only to offers of postdoctoral positions and not tenure-track positions, and only to applicants who are less than two years past the Ph.D. The departments have agreed not to require these applicants to decide about a job offer before Monday, February 9, 2004. The NSF has agreed to notify postdoctoral fellowship recipients no later than Friday, january 31, 2004. The list of participating departments, together with additional information, may be found on the Web at http://www.am s.org/employm ent/postdocoffers. html.

-Allyn jackson

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Experimental "Current Events" Session at Joint Meetings

Fan and Caldwell Scholarships Awarded

At the Joint Mathematics Meetings in Phoenix in January 2004, AMS president David Eisenbud is organizing an experimental special session on "Current Events". The session will feature four expository lectures on topics at the frontier of mathematical research. The format for the t alks follows the model of the famous Bourbaki Seminars, in that mathematicians with especially strong expository skills speak on work not their own, and a written version of the talk is prepared beforehand and distributed at the session. But there are some novel features too. Each talk in the session will begin with a general, nontechnical presentation of the topic, lasting about twenty minutes. There will be a short break, and then the talk will continue with a more detailed presentation of how the topic is used in a particular setting. For the session in Phoenix, the speakers and their lecture titles are: Margaret H. Wright, Courant Institute of Mathematical Sciences: "The interior-point revolution in optimization: History, recent developments, and lasting consequences" Thomas C. Hales, University of Pittsburgh: "What is motivic integration?" Andrew Granville, Universite de Montreal: "It is easy to determine whether or not a given integer is prime" John W. Morgan, Columbia University: "Perelman's recent work on the classification of 3-manifolds" The session will take place on Friday, January 9, 2004, starting at 1:00 p .m . For further details, consult the Web page for the Phoenix Joint Meetings, http: I / www. ams . org/amsmtgs/2 078_int ro.ht ml.

The AMS awarded ten scholarships to students attending programs for mathematically talented high school students held in summer 2003. Nine Ky and Yu-FenFan Scholarships and one Roderick P. C. Caldwell Scholarship were awarded. The scholarships are intended to cover the tuition for the programs. The names of the students receiving Fan Scholarships, their high schools, their hometowns, and the programs they attended (in parentheses) are: RuTH DHANARAJ, Carmel High School, Carmel, Indiana (Stanford University Mathematics Camp (SUMaC)); MOHAMED DIMBIL, Westmont High School, Campbell, California (SUMaC, Stanford University); ANAsTASSIA FEDYK, Albany High School, Albany, California (USA Mathcamp); MARIA GUIRGUIS, Brooklyn Technical High School, Brooklyn, New York (Hampshire College Summer Studies in Mathematics); OLGA MANDELSHTAM, University High School, Irvine, California (SUMaC, Stanford University); JANE (JINGWEN) OUYANG, Francis Lewis High School, Fresh Meadows, New York (Hampshire College Summer Studies in Mathematics); ELENA UDOVINA, Hathaway Brown High School, Shaker Heights, Ohio (Ross Mathematics Program, Ohio State University); VALERICA VULPE, Mircea Eliade Lyceum, Chisinau, Republic of Moldova (SUMaC, Stanford University); SHAMIKA WALKER, Judson High School, San Antonio, Texas (SWT Honors Summer Math Camp, Southwest Texas State University); and TINGTING XrE, Corona del Sol High School, Tempe, Arizona (PROMYS, Program in Mathematics for Young Scientists, Boston University). Receiving a Roderick P. C. Caldwell Scholarship was TIFFANY Ko, Terre Haute South Vigo High School, Terre Haute, Indiana (PROMYS, Program in Mathematics for Young Scientists, Boston University). The Fan Scholarships are supported by the Society's Ky and Yu-Fen Fan Endowment. This endowment was established through a gift by Ky Fan and his wife, Yu-Fen Fan. Income from the endowment supports mathematics in

- A llyn jackson jANUARY

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Inside the AMS

China and mathematically talented high school students in the U.S. The Caldwell Scholarships were endowed by a gift from Winifred A. Caldwell in memory of her husband, Roderick P. C. Caldwell. The scholarships are part of the AMS Epsilon Fund, which supports programs for mathematically talented high school students.

-Allyn jackson

AMS Partidpates in Celebration of von Neumann's Birth In October 2003 various scientific groups held celebrations

within Hungary to mark the 1 OOth anniversary of the birth of John von Neumann. Former AMS president Arthur Jaffe of Harvard University attended to represent the Society at the meetings and at the dedication of a commemorative plaque, jointly sponsored by the Hungarian and American Mathematical Societies. Jaffe also presented one of the mathematical talks at the event. The celebration of John von Neumann's birth came as the culmination of an entire year dedicated to von Neumann's genius. Three overlapping conferences took place at the Hungarian Academy of Sciences, with a common program on Wednesday morning, October 15. The subjects of the scientific meetings were: scientific computation and dynamical systems, computers and computer science, and operator theory and mathematical physics. President Ferenc Meidl of Hungary attended the entire Wednesday morning session, which was common to all three meetings. Jaffe made brief remarks, recalling that von Neumann lived half his life in the United States. Because von Neumann was the only modern scientist whose work engendered both Nobel Prizes and Fields Medals, one could make the case that his influence on science, technology, and society was greater than any other mathematician in the twentieth century. Jaffe also read excerpts from letters of greetings sent by David Eisenbud, president of the AMS, and Bruce Alberts, president of the National Academy of Sciences. He presented the originals to E. Szilveszter Vizi, president of the Hungarian Academy of Sciences. Later that day there was a dedication of a holographic portrait of John von Neumann, which stands prominently in the lobby of the Hungarian Ministry of Information Technology and Communication. The minister presented the first John von Neumann Awards to Marina von Neumann Whitman and to Charles Simonyi. Guests were given a tour of the exhibit on the history of the digital computer by the president of the computer society, Gy6z6 Kovacs. The dedication of the plaque took place at noon on Thursday, October 16. The large stone plaque was placed on the birth home of John von Neumann and was jointly sponsored by the Bolyai Mathematical Society (Hungarian Mathematical Society) and the American Mathematical Society. 52

The von Neumann home is on the corner of a busy thoroughfare and a side street (which the police closed for the halfhour ceremony). Von Neumann grew up in a wealthy family. His birth house is an impressive four-story stone building with over twenty rooms, although today it is divided into a number of apartments. Remarkably, just a short distance away another plaque on a building commemoArthur Jaffe in front of rates the fact that John von Neumann Kemeny lived there as a commemorative plaque in student and that he was Budapest. the inventor of the Basic computer language. The day was brisk but beautiful. There were three very short speeches: two in Hungarian, one in English. The event began with Kalman Kovacs, the minister for information technology and communication. Professor Imre Csiszar, president of the Bolyai Society, attended the dedication, but Professor Denes Petz, organizer of the meeting, gave the official greeting on behalf of the Bolyai Society. Jaffe spoke last on behalf of the AMS, emphasizing the importance of the public recognition of scientists and mathematicians to inspire a younger generation of students to pursue scientific careers. The entire event received extensive coverage in Budapest, both by television and by the newspapers. Although the Hungarian president spent his entire Wednesday morning participating in the celebration of von Neumann's legacy, the American ambassador was absent from the meeting altogether. He sent his cultural attache to the dedication on Thursday.

-Based on a report from Arthur Jaffe

Deaths of AMS Members R. G. BARTIE, of Ann Arbor, MI, died on September 18, 2003. From 1976 to 1978 and 1986 to 1990 he was executive editor of Mathematical Reviews . He was a member of the Society for 54 years. EcKEHART HoTZEL, retired, Fraunhofer-Gesellschaft, Germany, died on September 28, 2003.BornonMay2, 1937, he was a member of the Society for 3 3 years. GERHARD]. NEUBAUER, of the University of Konstanz, Germany, died on August 6, 2003. Born on May 21, 1930, he was a member of the Society for 40 years. DoNALD WESTERN, of lancaster, PA, died on September 17, 2003. Born on May 7, 1915, he was a member of the Society for 61 years.

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Reference and Book List

The Reference section of the Notices is intended to provide the reader with frequently sought information in an easily accessible manner. New information is printed as it becomes available and is referenced after the first printing. As soon as information is updated or otherwise changed, it will be noted in this section. Contacting the Notices The preferred method for contacting the Notices is electronic mail. The editor is the person to whom to send articles and letters for consideration. Articles include feature articles, memorial articles, communications, opinion pieces, and book reviews. The editor is also the person to whom to send news of unusual interest about other people's mathematics research. The managing editor is the person to whom to send items for "Mathematics People", "Mathematics Opportunities", "For Your Information", "Reference and Book List", and "Mathematics Calendar". Requests for permissions, as well as all other inquiries, go to the managing editor. The electronic-mail addresses are noti ces@math. ou. edu in the case of the editor and noti ces@ams. org in the case of the managing editor. The fax numbers are 405-325-7484 for the editor and 401-331-3842 for the managing editor. Postal addresses may be found in the masthead. jANUARY

2004

Upcoming Deadlines December 15, 2003: Applications for AMS Epsilon Fund grants. See http://www.ams.org/careersedu/epsi l on. html or contact Membership and Programs Department, AMS, 201 Charles Street, Providence, RI 02904; telephone: 800-321-4267, ext . 4105; email: prof-serv@ ams. org. December 17, 2003: Applications for NRC-Ford Foundation Postdoctoral Fellowships. See http: I I

www7.nationalacademies.org / fellowships/ applyonline.html. December 22, 2003: Applications for funding to attend MSRI workshop on Algorithmic, Combinatorial, and Applicable Real Algebraic Geometry. See http:/ /www.msri .org/. December 31 , 2003: Nominations for NSF Waterman Award. See http://www.fastlane . nsf.gov/ fastlane.jsp. December 31, 2003: Entries for Cryptologia paper competitions. See

Where to Find It A brief index to information that appears in this and previous issues. AMS Bylaws-November 2003, p. 1283 AMS Email Addresses-November 2003, p. 1266 AMS Ethical Guidelines- ]une/]uly 2002, p. 706 AMS Officers 2002 and 2003 (Council, Executive Committee Publications Committees, Board of Trustees)- May 2003, p. 594 ' AMS Officers and Committee Members-October 2003, p. 1115 Backlog of Mathematics Research journals-September 2003, p. 961 Conference Board of the Mathematical Sciences-September 2003, p. 945 Information for Notices Authors- ]une/]uly 2003, p. 706 Mathematics Research Institutes Contact Information-August 2003,

p. 821 National Science Board-January 2004, p. 54 New journals for 2002-]une/]uly 2003, p. 708 NRC Board on Ma~hematical Sciences and Their Applications-March 2003,

p. 383 NRC Mathematical Sciences Education Board-April 2003, p. 489 NSF Mathematical and Physical Sciences Advisory Committee-February

2003,p.261 Program Officers for Federal Funding Agencies-October 2003, p. 1107

(DoD, DoE); December 2003, p. 1429 (DMS Program Officers); December 2003, p. 1430 (NSF Education Program Officers)

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Reference and Book list http://www.dean.usma.edu/math/ pubs/cryptol ogi a/, or contact Cryptologia, Department of Mathematical Sciences, United States Military Academy, West Point, NY 10996; email: [email protected]. January 2, 2004: Applications for Fields Institute postdoctoral fellowships. See http: I /www. fields.utoronto.ca/programs/ scientific/04-05/string-theory/. January 8, 2004: Proposals for the ONR Young Investigator Program. See "Mathematics Opportunities" in this issue. January 9, 2004: Applications for National Defense Science and Engineering Graduate Fellowships. See http://www.asee.org/ndseg/ preface. cfm. january 10, 2004: Applications for AAUW Educational Foundation Fellowships and Grants. See http: I I www.aauw.org/3000/fdnfelgra/ se l ectprof. html. January 10, 2004: Grants for graduate students to attend Newton Institute course on random matrices and number theory. See "News from AIM" in "Mathematics Opportunities" in this issue. January 14, 2004: Collaborations in Mathematical Geosciences. See "Mathematics Opportunities" in this issue. January 15, 2004: Applications for AMS-AAAS Mass Media Fellowships. See http://ehrweb.aaas.org/ massmedi a. htm, or contact AAAS Mass Media Science and Engineering Fellows Program, 1200 New York Avenue, NW, Washington, DC 20005; telephone 202-326-6760; fax 202-3719849; or the AMS Washington Office, 1527 Eighteenth Street, NW, Washington, DC 20036; telephone 202588-1100; fax 202-588-1853; email: amsdc@ams. org. January 15, 2004: Nominations for Popov Prize. Contact Ronald A. DeVore, Director, Industrial Mathematics Institute, Department of Mathematics, University of South Carolina, , Columbia, SC 29208. January 26, 2004: Scientific Computing Research Environments for the Mathematical Sciences. See "Mathematics Opportunities" in this issue. 54

January 31, 2004: Applications for postdoctoral fellowships at the Institut Mittag-Leffler. See http: I I www.ml.kva.se. February 1, 2004: Applications for National Research Council Research Associateships. See http: I /www4. nationalacademies.org/pga/rap. nsf, or contact Research Associateship Programs, Keck Center of the National Academies, 500 Fifth Street, NW, GR322A, Washington, DC 20001; telephone 202-334-2760; fax 202-3342759; email: rap@nas. edu. February 1, 2004: Applications for AWM Travel Grants and AWM Mentaring Travel Grants. See http: I jwww. awm-math.org/travelgrants.html, or contact Association for Women in Mathematics, 4114 Computer and Space Sciences Building, University of Maryland, College Park, MD 207422461; telephone 301-405-7892; email: awm@math. umd. edu. February 1, 2004: Nominations for Eillopean Mathematical Society prizes. See http://www.math.kth.se/ 4ecm/nomi nation. html, or write to: 4ECM Organizing Committee, Professor Ari Laptev, Department of Mathematics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden;email:[email protected] or uunur@nur. usr. pu. ru. February 27, 2004: Nominations for Clay Mathematics Institute Liftoff Fellowships. See "Mathematics Opportunities" in this issue. March 4, 2004: Applications for EDGE Summer Program. See http: I I www.edgeforwomen.org/index.html. March 31, 2004: Nominations for 2004 Prize for Achievement in Information-Based Complexity. See "Mathematics Opportunities" in this issue. March 31, 2004: Nominations for Third World Academy of Sciences prizes. See http: I /www. i ctp. trieste.it/-twas/twas_prizes. html. May 1, 2004: Applications for National Research Council Research Associateships. See http: I /www4. nationalacademies.org/pga/rap. nsf, or contact Research Associateship Programs, Keck Center of the National Academies, 500 Fifth Street, NW, GR322A, Washington, DC 20001; NOTICES OF THE AMS

telephone 202-334-2760; fax 202-3342759; email: rap@nas. edu. May 1, 2004: Applications for AWM Travel Grants. See http: I /www. awm-math.org/travelgrants.html, or contact Association for Women in Mathematics, 4114 Computer and Space Sciences Building, University of Maryland, College Park, MD 207422461; telephone 301-405-7892; email: [email protected]. June 30, 2004: Proposals for DMS/NIGMS Program in Mathematical Biology. See http: I /www. nsf. govI pubs/2002/nsf02125/nsf02125. htm. August 1, 2004: Applications for National Research Council Research Associateships. See http: I /www4. nationalacademies.org/pga/rap. nsf, or contact Research Associateship Programs, Keck Center of the National Academies, 500 Fifth Street, NW, GR322A, Washington, DC 20001; telephone 202-334-2760; fax 202-3342759; email: [email protected].

National Science Board The National Science Board (NSB) is the policymaking body for the National Science Foundation. Listed below are the current members of the NSB. For further information, visit the website http: I jwww. nsf. gov /nsb/. Barry C. Barish

Linde Professor of Physics California Institute of Technology Steven Beering

President Emeritus Purdue University Ray Bowen

Former President Texas A&M University Delores M. Etter

Professor of Electrical Engineering United States Naval Academy Nina V Fedoroff

Willaman Professor of Life Sciences Director, Life Sciences Consortium Director, Biotechnology Institute Pennsylvania State University Pamela A. Ferguson

Professor of Mathematics Grinnell College VOLUME 51, NUMBER 1

Reference and Book List Kenneth M. Ford Director, Institute for Human and Machine Cognition University of West Florida

Maxine Savitz General Manager Honeywell and Technology Partnerships (retired)

Daniel E. Hastings Associate Director, Engineering Systems Division Massachusetts Institute of Technology

Luis Sequeira J. C. Walker Professor Emeritus Department of Bacteriology and Plant Pathology University of Wisconsin

Elizabeth Hoffman President University of Colorado System

Daniel Simberloff Nancy Gore Hunger Professor of Environmental Science Department of Ecology and Evolutionary Biology University of Tennessee

Anita K. ]ones Quarles Professor of Engineering and Applied Science Department of Computer Science University of Virginia George M. Langford Professor, Department of Biological Science Dartmouth College Jane Lubchenco Wayne and Gladys Valley Professor of Marine Biology Distinguished Professor of Zoology Oregon State University joseph A. Miller ]r. Senior Vice President and Chief Technology Officer Corning, Inc. Diana S. Natalicio (vice chair) President University of Texas at El Paso Douglas D. Randall Professor of Biochemistry Director, Interdiscplinary Program on Plant Biochemistry-Physiology University of Missouri Robert C. Richardson Vice Provost for Research Professor of Physics Cornell University Michael G. Rossmann Hanley Distinguished Professor of Biological Sciences Purdue University

jANUARY

2004

]o Anne Vasquez Past President, National Science Teachers Association Consultant, McGraw-Hill Companies Warren M. Washington (chair) Senior Scientist and Section Head National Center for Atmospheric Research john A. White ]r. Chancellor University of Arkansas Mark S. Wrighton Chancellor Washington University in St. Louis Rita R. Colwell (member ex officio) Director, National Science Foundation

Book List The Book List highlights books that have mathematical themes and are aimed at a broad audience potentially including mathematicians, students, and the general public. When a book has been reviewed in the Notices, a reference is given to the review. Generally the list will contain only books published within the last two years, though exceptions may be made in cases where current events (e.g., the death of a prominent mathematician, coverage of a certain piece of mathematics in the news) warrant drawing readers' attention to older books. Suggestions for books to include on the list may be sent to [email protected]. NOTICES OF THE

AMS

*Added to Book Ust since the list's last appearance.

1 089 and All That: A journey into Mathematics, by David Acheson. Oxford University Press, July 2002. ISBN 0-19-851623-1. Abel's Proof: An Essay on the Sources and Meaning of Mathematical Unsolvability, by Peter Pesic. MIT Press, May 2003. ISBN 0-262-16216-4. After Math, by Miriam Webster. Zinka Press, June 1997. ISBN 0-96471711-5. (Reviewed October 2003.) All the Mathematics You Missed (But Need to Know for Graduate School), by Thomas A. Garrity. Cambridge University Press, December 2001. ISBN 0-521-79707-1. The Art of the Infinite: The Pleasures of Mathematics, by Robert Kaplan and Ellen Kaplan. Oxford University Press, March 2003. ISBN 0-19514743-X. Beyond the Limit: The Dream of Sofya Kovalevskaya, by Joan Spicci. Forge, August 2002. ISBN 0-76530233-0. (Reviewed in this issue.) The Book of My Life, by Girolamo Cardano. New York Review of Books Classics Series/Granta. ISBN 1-59017016-4. Calculated Risks: How to Know When Numbers Deceive You, by Gerd Gigerenzer. Simon & Schuster, March 2003. ISBN 0-743-25423-6. California Dreaming: Reforming Mathematics Education, by Suzanne M. Wilson. Yale University Press, January 2003. ISBN 0-300-09432-9. (Reviewed November 2003.) Codebreakers: Arne Beurling and the Swedish Crypto Program during World War II, by Bengt Beckman. Translated by Kjell-Ove Widman. AMS, February 2003. ISBN 0-8218-2889-4. (Reviewed September 2003.) The Constants of Nature: From Alpha to Omega-The Numbers That Encode the Deepest Secrets of the Universe, by John D. Barrow. Jonathan Cape, September 2002. Pantheon Books, January 2003. ISBN 0-37542221-8. Correspondance GrothendieckSerre, Pierre Colmez and Jean-Pierre Serre, editors. Societe Mathematique de France, 2001. ISBN 2-85629-104-X. (Reviewed October 2003.) 55

Reference and Book List

Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists, by Joel Best. University of California Press, May 2001. ISBN 0-520-21978-3. (Reviewed February 2003.) Doing Mathematics: Convention, Subject, Calculation, Analogy, by Martin H. Krieger. World Scientific, April 2003. ISBN 9-812-38200-3. Einstein's Clocks, Poincare's Maps: Empires of Time, by Peter Galison. W. W. Norton, August 2003. ISBN 0-393-02001-0. Emergence of the Theory of Lie Groups: An Essay in the History of Mathematics, 1869-1926, by Thomas Hawkins. Springer-Verlag, 2000. ISBN 0-387-98963-3. (Reviewed June/July 2003.) *Everything and More: A Compact History of Infinity, by David Foster Wallace. W. W. Norton, October 2003. ISBN 0-393-00338-8. Four Colors Suffice: How the Map Problem Was Solved, by Robin Wilson. Princeton University Press, March 2003. ISBN 0-691-11533-8. The Fractal Murders, by Mark Cohen. Muddy Gap Press, May 2002. 0-9718986-0-X. (Reviewed October 2003.) Gamma: Exploring Euler's Constant, by Julian Havil. Princeton University Press, May 2003. ISBN 0-691-09983-9. Geometrical Landscapes: The Voyages of Discovery and the Transformation of Mathematical Practice, by Amir R. Alexander. Stanford University Press, September 2002. ISBN 0804-73260-4. Geometry: Our Cultural History, by Audun Holme. Springer, April 2002. ISBN 3-540-41949-7. The Glass Wall: Why Mathematics Can Seem Difficult, by Frank Smith. Teachers College Press, July 2002. ISBN 0-807-74241-4 (paperback), 0-807-74242-2 (cloth). Godel's Proof, by Ernest Nagel and James R. Newman. New York University Press, revised edition, February 2002. ISBN 0-8147-5816-9. The Golden Ratio: The Story of Phi, the World's Most Astonishing Number, by Mario Livio. Broadway Books, October 2002. ISBN 0-7679-0815-5. Imagining Numbers (particularly the square root of minus fifteen), by 56

Barry Mazur. Farrar, Straus and Giroux, February 2003. ISBN 0-374-17469-5. (Reviewed November 2003.) In Code: A Mathematical journey, by Sarah Flannery and David Flannery. Workman Publishing, May 2001. ISBN 0-761-12384-9. (ReviewedApril2003.) Isaac Newton, by James Gleick. Pantheon Books, May 2003. ISBN 0-37542233-1. (Reviewed December 2003.) It Must Be Beautiful: Great Equations of Modern Science, Graham Farmelo, editor. Granta Books, February 2002. ISBN 1-862-0 74 79-8. (Reviewed March 2003.) janos Bolyai, Euclid, and the Nature of Space, by Jeremy]. Gray. MIT Press, May 2003. ISBN 0-262-57174-9. Kepler's Conjecture: How Some of the Greatest Minds in History Helped Solve One of the Oldest Math Problems in the World, by George G. Szpiro. John Wiley & Sons, January 2003. ISBN 0-4 71-08601-0. Linked: The New Science of Networks, by Albert-Liszl6 Barabasi. Perseus Publishing, May 2002. ISBN 0-738-20667-9. M. C. Escher's Legacy: A Centennial Celebration, edited by Doris Schattschneider and Michele Emmer. Springer, January 2003. ISBN 3-54042458-X. (Reviewed April 2003.) Math through the Ages: A Gentle History for Teachers and Others, by William P. Berlinghoff and Fernando Q. Gouvea. Oxton House, 2002. ISBN 1881929-21-3. Mathematical Apocrypha: Stories and Anecdotes of Mathematicians and the Mathematical, by Steven G. Krantz. Mathematical Association of America, July 2002. ISBN 0-883-85539-9. Mathematical Constants, by Steven R. Finch. Cambridge University Press, August 2003. ISBN 0-52181805-2. Mathematical Reflections, by Peter Hilton, Derek Holton, and Jean Pedersen. Springer, December 1996. ISBN 0-387-94770-1. (Reviewed February 2003.) Mathematical Vistas, by Peter Hilton, Derek Holton, and Jean Pedersen. Springer-Verlag, January 2002. ISBN 0-387-95064-8. (Reviewed February 2003.) Mathematicians under the Nazis, by Sanford L. Segal. Princeton UniNOTICES OF THE

AMS

versity Press, July 2003. ISBN 0-69100451-X. Mathematics and the Roots of Postmodern Thought, by Vladimir Tasic. Oxford University Press, 2001. ISBN 0-195-13967-4. (Reviewed August 2003.) Mathematics by Experiment: Plausible Reasoning in the 21st Century, by David Bailey, Jonathan Borwein. A K Peters, September 2003. ISBN 1-56881136-5. Mathematics Elsewhere: An Exploration of Ideas across Cultures, by Marcia Ascher. Princeton University Press, September 2002. ISBN 0-69107020-2. (Reviewed May 2003.) Mathematics for the Imagination, by Peter M. Higgins. Oxford University Press, November 2002. ISBN 0-19860460-2. The Mathematics of juggling, by Burkard Polster. Springer, November 2002. ISBN 0-387-95513-5. (Reviewed in this issue.) Mathematics: A Very Short Introduction, by Timothy Gowers. Oxford University Press, October 2002. ISBN 0-192-85361-9. Memoirs of a Proof Theorist: Godel and Other Logicians, by Gaisi Takeuti. Translated by Mariko Yasugi and Nicholas Passell. World Scientific, February 2003. ISBN 981-238-279-8. The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time, by Keith ]. Devlin. Basic Books, October 2002. ISBN 0-465-01729-0. (Reviewed September 2003.) More Mathematical Astronomy Morsels, by Jean Meeus. Willmann-Bell Inc., 2002. ISBN 0-943396-743. The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics, by Marcus Du Sautoy. Harper-Collins, April 2003. ISBN 0066-21070-4. A New Kind of Science, by Stephen Wolfram. Wolfram Media, Inc., May 2002. ISBN 1-5 79-5 5008-8. (Reviewed February 2003.) The One True Platonic Heaven: A Scientific Fiction of the Limits of Knowledge, by John L. Casti. Joseph Henry Press, May 2003. ISBN 0-309-08547-0. Origami 3 , edited by Thomas Hull. A K Peters, July 2002. ISBN 1-56881181-0. VOLUME

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Reference and Book list Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem, by John Derbyshire. Joseph Henry Press, March 2003. ISBN 0-309-08549-7. Remarkable Mathematicians, by loan James. Cambridge University Press, February 2003. ISBN 0-52152094-0. The Riemann Hypothesis: The Greatest Unsolved Problem in Mathematics, by Karl Sabbagh. Farrar Straus & Giroux, April 2003. ISBN 0374-25007-3. Science in the Looking Glass, by E. Brian Davies. Oxford University Press, August 2003. ISBN 0-19852543-5. The Search for Certainty: A Philosophical Account of Foundations of Mathematics, by Marcus Giaquinto. Oxford University Press, October 2002. ISBN 0-198-75244-X. Six Degrees: The Science of a Connected Age, by Duncan J. Watts. W. W. Norton & Company, February 2003. ISBN 0-393-04142-5. Sync: The Emerging Science of Spontaneous Order, by Steven Strogatz. Hyperion, February 2003. ISBN 0-78686844-9. Travels in Four Dimensions: The Enigmas of Space and Time, by Robin Le Poidevin. Oxford University Press, February 2003. ISBN 0-19-875254-7. What Are the Odds? The Chances of Extraordinary Events in Everyday Life, by JeffersonHane Weaver. Prometheus Books, February 2002. ISBN 1-57392933-6. What the Numbers Say: A Field Guide to Mastering Our Numerical World, by Derrick Niederman and David Boyum. Broadway Books, April 2003 . ISBN 0767-90998-4. The Zen of Magic Squares, Circles, and Stars: An Exhibition of Surprising Structures across Dimensions, by Clifford A. Pickover. Princeton University Press, January 2001. ISBN 0-691-07041-5. (Reviewed March 2003.)

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8:30AM (901)

8:45AM .,. (902) 9:00AM (903) 9:1 SAM .,. (904)

9:00AM .,. (895)

9:45AM (906)

On Some Selection Problems with Applications to Lifetime Data.

10:00AM (907)

J>

144

Hands-on experiments in inferential statistics . Preliminary report. Mohammad Salmassi, Framingham State College (993-N1-491)

Using Simulations to Teach the Meaning of the P-Value. Using Visual Tools in the Teaching of Hypothesis Testing. Using Simulations, Permutations and Randomizations to Help Students Understand P-values. Preliminary report. Teaching Statistical Inference to In-service Middle School Teachers : Methodologies, Activities, and Projects. Preliminary report. Barbara A Wainwright, Salisbury University (993-N1-559)

10:30AM .,. (909)

An Interdisciplinary Approach to Teaching Statistics to Undergraduate Life Science Majors Provides Numerous Opportunities for Data Analysis Projects Involving Inference. Debora.h Lurie *, James Watrous, Saint joseph's University, and DeniseMarie Ratterman , Saint joseph's University (993-N1-266)

Estimating the Conditional Distribution Function. Rod Freed, California State University at Dominguez Hills , and Senem Alkan * , Bucconi University (993-62-1 096)

What does a P-value mean? Patricia B Humphrey, Georgia Southern University (993-N1-544)

Robin H Lock, St. Lawrence University (993-N1-502) 10 :1 SAM ... (908)

Thomas T. john * , Syracuse University, and Pinyuen Chen, Department of Mathematics, Syracuse University (993-62-1 5 SO) 9:1 SAM (896)

Question based presentation of inferential methods. Michael D Landrigan, Idaho State University (993-N1-548)

Christopher J. Lacke, Rowan University (993-N1-392)

On the Chernoff bound for efficiency of quantum hypothesis testing. Vladislav Kargu i ne, Cornerstone Research (993-62-3 73)

Order Statistics, Uniform Distributions, and Confidence Intervals.

Murray H. Siegel, Sam Houston State University (993-N1-28)

Detection of Changes in the arrival rates of a Poisson Process.

C Klaassen, University of Amsterdam, Eun-Joo Lee* and Frits H Ruymgaart, Texas Tech University (993-62-950) 8:45AM (894)

9:30AM (905)

Assessing Occupational Exposure Via the One-way Random Effects Model.

Estimating linear functionals of indirectly observed input functions. Preliminary report.

Developing an Understanding of Confidence intervals for Proportions.

Michael I Ratliff, Northern Arizona University (993-N1-560)

J>

Mario Kay Brown, SUNY Binghamton (993-62-976) 8:30AM (893)

Why Do We Check Assumptions for Inference? Allan J. Rossman * and Beth L. Chance, Cal Poly San Luis Obispo (993-N1-407) ,

Daniel J Teague, NC School of Science and Mathematics (993-N1-744)

Kalimuthu Krishnamoorthy and Huizhen Guo* , University of Lou isiana at Lafayette (993-62-383) 8:1 SAM (892)

Simulation Study of the Small Sample Properties of Maximum Likelihood Estimators in an Accelerated Failure Time Model with Censored Observations. Mahmoud A Yousef*, Central Missouri State University, and Raja Nassar, LA Tech University (993-62-1 363)

AMS Session on Statistics 8:00AM - 9:55 AM

Comparing Two Methods of Handling Tied Event Times. Preliminary report.

10:45AM .,. (91 0)

NOTICES OF THE

AMS

Hypothesis Test Selection: A Practical Method. Preliminary report. Sue B Schou, Idaho State University (993-N1-32)

VOLUME

51,

NUMBER

1

Phoenix, AZ, Friday, january 9- Program of the Sessions MAA Session on Math and the Arts, II 8:00AM- 10:55 AM Organizers : Ann Robertson, Connecticut College john M. Sullivan, University of Illinois, Urbana Reza Sarhangi, Towson University Nathaniel A. Friedman , State University of New York, Albany 8:00AM Visualizing Mathematics through Digital .,. (911) Photography. Preliminary report. Marcia Birken, Rochester institute of Technology (993-01-481) 8:20AM Vectors, Computer Art and Toy Story. .,. (912) Timothy P. Chartier, Davidson College (993-01-929) 8:40AM Computational Aesthetics: Mathematical Methods .,. (913) for Evaluating Art. Gary R. Greenfield, University of Richmond (993-01-840) 8:55AM Break 9 :20AM Recursion in Nature, Mathematics and Art. .,. (914) Preliminary report. Anne M. Burns, Long Island University, C.W. Post Campus (993-01-657) 9:40AM Dahlia Flowers in Art, Nature, and Mathematics . .,. (91 5) Preliminary report. Gwen Laura Fisher, Cal Poly State University, San Luis Obispo (993-01-274) 1 0:00AM Tilings & Quilts . .,. (916) Mary Candace Williams, Pima Community College (993-01-848) 10 :20AM .,. (917)

Myriad of Mosaics. Maria K Robinson, Seattle University (993-01-1385)

10:40AM .,. (918)

Discovery or Creation?: Mathematical Platonism and the Visual Arts. Mark D. Schlatter, Centenary College of Louisiana (993-01-368)

9 :30AM Mapping a 1-to-7 Correspondence Between Nand Q .,. (925) Using Imbedded Loops, Conditionals, and Arrays. Preliminary report. N. R. Nandakumar* , Delaware State University, and Michael J. Bosse, Morgan State University (993-P1-324)

One Time Pad Encryption. Robert P. Webber, Longwood University (993-P1-91) 1 O:OOAM A Programming Pearl. .,. (927) Arnold Lebow, Yeshiva University (993-P1-786) 10:1 SAM "Magic Numbers " Approach to Introducing Binary .,. (928) Number Representation in Introductory Computer Science Courses. Gerald W. Kruse, Juniata College (993-P1-667) 10:30AM Understanding the Magic: Teaching Cryptography .,. (929) with just the Right Amount of Mathematics. Joshua Holden, Rose-Hulman Institute of Technology (993-P1-24 7) 1 0:45AM The Perfect Shuffle: Mathematical Apologetics. .,. (930) Preliminary report. David J Hunter, Westmont College (993-P1-806)

9:45AM .,. (926)

MAA Session on Mathematics Experiences in Business, Industry, and Government 8:00AM- 10:35 AM Organizers : Philip E. Gustafson, Mesa State College Michael G. Monticino, University of North Texas 8:10AM Mathematics and Materials-Stretching Hooke 's Law . .,. (931) Stanley J Russell * , Motorola (Retired), and Frank J Attanucci, Scottsdale Community College (993-Q1-21) 8:25 AM Mathematicial Models in Transportation Planning .,. (932) and Traffic Operations. Donald A. Sokol, Lisle . Illinois (993-Q1-1 36)

Developing and Validating a Metric for the Hiring of Fee Based Practitioners for the United States Military Entrance Processing Command. Preliminary report. Randy E White * and Edgar K Rugenstein, United States Military Academy (993-Q1-241) 8:55 AM Designing a Robust Range Imaging System. (934) Nathan D Cahill * , Lawrence A Ray and Joseph F Revelli, Eastman Kodak Company (993-Q1-1 592) 9 :1OAM PSL Preservers and Barker Codes of Odd Length. .,. (935) Gregory Emmett Coxson, Lockheed Martin Naval Electronic and Surveillance (993-Q1-30) 9:25AM A Leg in Both Worlds: Consulting in Academics. .,. (936) Michael G Monticino, University of North Texas (993-Q1-1313) 9:40AM Industry Problems That Require Concepts Rather .,. (93 7) Than Technical Detail. Preliminary report. Richard J Cleary, Bentley College (993-Q1-336) 9:55AM Development of a Mathematics Course for .,. (938) Biotechnology through an Industrial Externship. Kenneth M. Levasseur, UMass Lowell (993-Q1-98) 1 0 :1OAM Mathematics in the Hedge Funds Arena. .,. (939) Ranjan Bhaduri , Northwater Capital Management Inc. (993-Q1 -1113) 10:25AM The Life and Death of a Silicon Valley Startup .,. (940) Company. Preliminary report. Mark Stamp, San Jose State University (993-Q1-1660)

8:40AM .,. (933)

MAA Session on Applications of Mathematics in Computer Science 8:00AM- 10:55 AM Organizer:

8:00AM .,. (919) 8:1 SAM .,. (920)

8:30AM .,. (921) 8:45AM .,. (922) 9 :00AM .,. (923) 9 :15AM .,. (924)

jANUARY

William A. Marion, Valparaiso University An Application of Binomial Trees for Pricing a Stock Option. Daniel Birmajer, Nazareth College (993-P1-736) Programming to Complete Magic Squares. Preliminary report. N. R. Nandakumar* , Delaware State University, and Michael j. Bosse, Morgan State University (993-P1-323) Check Digits and Error Correction. Preliminary report. Lew Ludwig, Denison University (993-P1-291)

From Cyclic Sums to Projective Planes . Roger E. Zarnowski, Angelo State University (993 -P1 -808) A Catalan Project in Discrete Mathematics . Brian Hopkins, Saint Peter's College (993-P1-869) An Analytic Approach to a Tic-Tac-Toe Program. Preliminary report. John Gately, Roosevelt University (993-P1-979)

2004

NOTICES OF THE

AMS

145

Program of the Sessions - Phoenix, AZ, Friday, january 9 (cont'd.) MAA General Contributed Paper Session, V

9:30AM .,.. (953)

8:00 AM - 10:40 AM

8:00AM .,.. (941) 8:1 SAM .,.. (942) 8:30AM .,.. (943)

8:45AM (944)

9:00AM .,.. (945)

9:1 SAM .,.. (946) 9:30AM 9:45AM (94 7)

1O:OOAM .,.. (948) 10:1 SAM .,.. (949)

10:30AM .,.. (950)

Organizers: Laura J. Wallace, California State University, San Bernardino jacqueline A. Jensen, Sam Houston State University Gary W. Towsley, SUNY at Geneseo Michael A. jones, Montclair State University Shawnee L. McMurran, California State University at San Bernardino Encouraging Artistic Expression via Mathematical Exploration in the Core Curriculum. John C Nardo, Oglethorpe University (993-Z1-445) Linking Art, Geometry, and Calculus . Ruth G. Favro* and David E. Bindschadler, Lawrence Technological University (993-Z1-1 319) The Effects of Using Notebook Computers (MS Excel) in an Undergraduate Business Calculus Course. Preliminary report. Stephanie P. Edwards* and Clarre Johnston, University of Dayton (993-Z1-3 79) Finding and Using Pre-Calculus Learning Objects. Preliminary report. Robert H Hoar and jeff S. Baggett*, University of Wisconsin - La Crosse (993-Z1-1631) Modeling in Elementary Calculus. Preliminary report. Thomas C Craven, University of Hawaii (993-Z1-474) Circular Inversion with Geometer's Sketchpad. Preliminary report. Colin L Starr, Willamette University (993-Z1-219) Break. Tracking student success in an integrated calculus/precalculus course. Laura A Taalman, James Madison University (993-Z1-45l) . An Upper-Division Geometry Course Designed around the NCTM Standards. Preliminary report. Robert Talbert, Franklin College (993-Z1-339) Making Geometry Come Alive with The Geometer's Sketchpad. Dawn R Slavens, Midwestern State University (993-Z1-595) DIP-Based Projects for Linear Algebra. Mohamed Allali , Chapman University (993-Z1-398)

1O:OOAM (954)

10 :30AM .,.. (955)

Is the English Version of the Theory of Incommensurability Commensurable with Its Chinese Translation? Yibao Xu, CUNY, Graduate Center & BMCC (993-01-694) Science in Translation: The Transmission of Probability Theory into late Imperial Chinese Mathematical Culture (7 880-1911). Andrea Eberhard-Breard, CUNY Graduate Center (New York)/ CNRS (Paris) (993-01-583) "Everybody makes errors": The intersection of De Morgan'slogicandprobability, 1837- 1847. Adrian Rice, Randolph-Macon College (993-01-205)

AMS Invited Address 9:00 AM - 9:50 AM (956)

Almost every observation, a mathematical theory of measurement. James A. Yorke, University of Maryland (993-37-05)

ASL Invited Address 9:00AM-9:50AM (957)

The proof-theoretic strength of some combinatorial principles. Steffen Lempp, University of Wisconsin

MAA Minicourse #12: Part B 9:00 AM - 11 :00 AM Incorporating discrete mathematics in the preparation of K-12 mathematics teachers Organizer: Lolina Alvarez, New Mexico State University

MAA Minicourse #1: Part B 9:00AM- 11:00 AM Designing and evaluating assessments for introductory statistics. Organizers : Beth L. Chance, California Polytech State University, San Luis Obispo Robert C. Delmas, University of Minnesota Allan J. Rossman, California Polytech State University, San Luis Obispo

PME Council

MAA Minicourse #7: Part B

8:00AM- 11:00 AM

9:00AM - 11:00 AM Origami in undergraduate mathematics courses. Organizer: Thomas C. Hull, Merrimack College

AMS-MAA Special Session on History of Mathematics, I 8:30 AM - 10:50 AM

MAA Special Presentation

Organizers: joseph W. Dauben, Lehman College (CUNY)

8:30AM .,.. (951) 9:00AM (952)

146

9:00AM- 11:00 AM

Karen V. H. Parshall, University of Virginia David E. Zitarelli, Temple University Analytic Geometry: Descartes versus Fermat. Maria Sol de Mora, ICREA, Barcelona (993-01-31 0) The Brachistochrone Problem and its Sequels. Rudiger Thiele, University of Leipzig (993-01-627)

NOTICES OF THE AMS

Mathematics for business decisions (repeated from 1:00 p.m. to 3:00p.m. and 5:00p.m. to 7:00p.m., Friday). · Organizers : Richard B. Thompson, University of Arizona Christopher Lamoureux, University of Arizona

VOLUME 51, NUMBER 1

Phoenix, AZ, Friday, january 9- Program of the Sessions MAA Poster Session on Projects Supported by the NSF

ASL Invited Address

9:00 AM - 11 :00 AM

10:00 AM - 10:50 AM

Assessment of student learning in undergraduate mathematics: Works in progress. Organizers: William E. Haver, Virginia Commonwealth University Bernard L. Madison, University of Arkansas

(958)

On theories of modules of fields with endomorph isms. Francoise M. Point, University of Mons-Hainaut

AMS Special Presentation 1 0:00 AM - 11 :00 AM

Who wants to be a mathematician?

MAA Project NExT Panel Discussion

Organizers: Michael A. Breen, AMS Annette W. Emerson, AMS William T. Butterworth, Barat College of DePaul University

9:00 AM - 1 0:30 AM

Writing expository mathematics. Organizers: jed Herman, University of Wisconsin at Stevens Point jennifer Hontz, Meredith College George W. Moss, University of Virginia's College at Wise Lowell W. Reineke, Indiana Panelists: University-Purdue Ezra Brown, Virginia Tech Frank A. Farris, Santa Clara University Underwood Dudley, DePauw University Keith J. Devlin, Stanford University

Math on the Web 10:00 AM - 5:30 PM

Go to the Math on the Web Pavilion for the complete schedule of presentations.

AMS Invited Address 10:05 AM- 10:55 AM

(959)

Random planar curves and conformal invariance. Gregory F. Lawler, Cornell University (993-60-11)

MAA Special Presentation

AMS-MAA Invited Address

9:00 AM - 10:20 AM

11 : 1 0 AM -

(960)

Proposal writing workshop for grant applications to the NSF division of undergraduate education. Organizers: Elizabeth J. Teles, NSF Division of Undergraduate Education , Calvin L. Williams, NSF Division of Undergraduate Education Lee L. Zia, NSF Division of Undergraduate Education

NOON

Mathematical challenges in molecular biology. Bonnie Berger, Massachusetts Institute of Technology (993-92-03)

AMS Colloquium Lectures: Lecture Ill 1:00PM-2:00PM

(961)

Conformal invariants and partial differential equations. Part Ill. Sun-Yang Alice Chang, Princeton University (993-53-10)

MAA Panel Discussion 9:00 AM - 1 0:20 AM

ASL Invited Address

Preparing mathematicians to educate teachers. Organizers : Alan C. Tucker, SUNY at Stoney Brook Bernard L. Madison, University of Arkansas at Fayetteville Panelists: Ed Dubinsky, Cincinnati, Ohio Alan C. Tucker, SUNY at Stoney Brook

1:00PM-1:50PM

(962)

Cofinal types of topological directed orders. Slawomir Solecki, University of Illinois Urbana

MAA Student Lecture 1:00PM-1:50PM

Exhibits and Book Sales

.,. (963)

Mathematical Art Exhibit

AMS-MAA Special Session on Mathematical Techniques in Musical Analysis, II

9:30 AM - 5:30 PM

Organizers: Robert Fathauer, Tessellations Company, Phoenix, Arizona Nat Friedman, ISAMA, SUNY at Albany Reza Sarhangi, Bridges Conference, Towson University

jANUARY

2004

Fractal Calculus Project. Mark M Meerschaert, University of Nevada (993-A0-532)

9:30 AM - 5:30 PM

1:00 PM - 5:50 PM

NOTICES OF THE

Organizers: Judith L. Baxter, University of Illinois at Chicago Robert W. Peck, Louisiana State University

AMS

147

Program of the Sessions - Phoenix, AZ, Friday, january 9 (cont'd.)

~

1:OOPM (964)

Filtered Point Symmetry and Dynamical Voice-Leading . Preliminary report. Jack Douthett*, TVI Community College, and Richard Plotkin, University of Chicago (993-37-632)

1:30PM ~ (965)

AMS-SIAM Special Session on Mathematical Modeling in Neuroscience, Biomedicine, Genetics, and Epidemiology, Ill 1:00 PM - 5:50 PM

Spirlz. Preliminary report. Stephen Soderberg, Library of Congress

Organizers : Steven M. Baer, Arizona State University

(993-00-1 31 0) 2:00PM (966)

Classification Schemes of Global Musical Compositions and Grothendieck Topoi.

lvo D. Dinov, University of California Los Angeles

Guerino B. Mazzola, CS Department, University of Zurich (993-1 8-85) 2:30PM (967)

A computer-aided exploration of the transformational process in Xenakis' Nomos Alpha.

3:00PM (968)

Moreno Andreatta, lrcam-Cnrs (993-20-11 08) Tone System and Mental Process. Preliminary report. Thomas Noll, Technical University of Berlin

Frank C. Hoppensteadt, Arizona State University Hal L. Smith, Arizona State University ~

Pitch-Class lsometries. Preliminary report.

~

1:30PM (980)

4:30PM ~ (971)

~

A double epidemic model for the SARS propagation.

Pitch combinatoriality in gapped spaces.

Tuen Wai Ng* , The University of Hong Kong, Gabriel Turinici, lnria Rocquencourt Domaine de Voluceau, Rocquencou, and Antoine Danchin, Genetique des Genomes Bacteriens, lnstitut Pasteur

jon Wild, Harvard University (993-00-1 397)

(993-92-542)

Robert W. Peck, Louisiana State University (993-5 5-899)

4:00PM ~ (970)

Modelling the spatia-temporal dynamics of nuclear proteins. Preliminary report. Gerda de Vries, University of Alberta (993-92-1666)

(993-51-1485) 3:30PM ~ (969)

1:OOPM (979)

Statistical Aspects of john Cage's Etudes Australes.

2:00PM (981)

Preliminary report. Murray Bremner* and Mik Bickis, University of Saskatchewan (993-62-236)

5:00PM (972)

A Mathematical Model describing the MetriCity of Musical Pieces.

5:30PM

Anja Volk, DJE Department of Industrial and Systems Engineering (993-92-1 590) Discussion.

Global Kinetic Imaging for Fluoro-Deoxy-Giucose with Positron Emission Tomography. Cristina Negoita* and Rosemary A Renaut, Arizona State University (993-92-1 067)

~

2:30PM (982)

Improving the Accuracy of Segmentation Algorithms for Magnetic Resonance Imaging. Rick Archibald*, The Center for System Science and Engineering Rese, Kewei Chen, Arizona Center for Alzheimer's Disease Research, Anne Gelb and Rosemary Renaut, Arizona State University (993-65-480)

AMS-MAA Special Session on History of Mathematics, II

3:00PM (983)

David A Peterson*, Charles W Anderson, Michael J Kirby and Michael H Thaut, Colorado State University (993-68-1 341)

1:00PM - 3:50 PM

Organizers: Joseph W. Dauben, Lehman College (CUNY) Karen V. H. Parshall, University of · Virginia David E. Zitarelli, Temple University ~

1 :OOPM (973)

~

3:30PM (984)

Conceptions of General Analysis in Nineteenth-Century Mathematics. Preliminary

4 :00PM (985)

Karen V. H. Parshall, University of Virginia

On Weierstrass' theory of analytic functions. Umberto Bottazzini, Universita di Palermo, Italy

~

4:30PM (986)

jules Tannery and the Mathematical Research Community in France , 1870-1914. Preliminary report. W Thomas Archibald, Acadia University

(993-92-887) 5:00PM (987)

"Some unsolved problems of theoretical dynamics". An unpublished paper by George Birkhoff Preliminary report. June E Barrow-Green, Open University, UK (993-01-597)

3:30PM ~ (978)

148

Two-dimensional finite element analysis to assess flow characteristics of an in vitro aneurysm model. Dawn A Lott*, Michael Siegel, Hans R Chaudhry, New Jersey Institute of Technology, and Charles J Prestigiacomo, New Jersey Medical School

(993-01-221) 3:00PM (977)

Sports-related concussion: An application of functional magnetic resonance imaging. William Eddy, Carnegie Mellon University

(993-01-615) 2:30PM ~ (976)

Dynamic Behavior of a Delay-Differential Equation Model for the Hormonal Regulation of the Menstrual Cycle. Leona Harris Clark*, US Environmental Protection Agency, Paul M Schlosser, CIIT Centers for Health Research, and James F Selgrade, North Carolina State University (993-92-974)

Creating a Mathematical Area: The Case of Arthur Cayley, j.). Sylvester, and Invariant Theory. (993-01-734)

2:00PM (975)

Modeling mixed microbial growth: Connecting theory and experiment. Preliminary report. Sergei S Pilyugin*, University of Florida, Gregory T Reeves, Princeton University, and Atul Narang, University of Florida (993-92-1162)

report. Craig G Fraser, University of Toronto (993-01-226) 1:30PM ~ (974)

Feature Selection as a Precursor to Modeling in High-Dimensional Scientific Discovery.

(993-76-624) 5:30PM (988)

Singular Vectors and Protein Motifs in Mathematical Phylogeny.

Who invented Steiner triple systems- and why?

Jeffery J. Leader* , Rose-Hulman lnst. of Tech., and Gary W. Stuart, Indiana State University

Robin J. Wilson, Open University, UK (993-01-352)

(993-92-1421)

NOTICES OF THE

AMS

VOLUME

51,

NUMBER

1

Phoenix, AZ, Friday, january 9- Program of the Sessions AMS-SIAM Special Session on Classical and Nonlinear Special Functions, II

3 :00PM (1 003)

Typicality of recurrence for (aperiodic) Lorentz gases. Preliminary report. Marco Lenci, Stevens Institute of Technology (993-37-584)

1:00 PM - 5:50 PM

Organizers: Peter A. Clarkson, University of Kent Francisco Marcellan, Universidad Carlos Ill Peter A. McCoy, U. S. Naval Academy 1:OOPM (989)

4 :00PM (1 005)

Percy A Deift, Courant Institute, NYU

Sequence of distribution functions involving Pain/eve II.

4:30PM ._ (1 006)

Jinho Baik, University of Michigan (993-60-829) 2:OOPM ._ (991)

3:00PM (993)

A topological model for a perturbed quadratic family. Preliminary report.

Dimension product structure of hyperbolic sets. Boris Hasselblatt* , Tufts University, and Jorg Schmeling, Lund Institute of Technology (993-37-626)

Rational Solutions of the Pain/eve Equations and Associated Special Polynomials.

5:00PM (1 007)

Peter A Clarkson, University of Kent (993-34-596) 2:30PM (992)

Modeling a Gas of Hard Non-Spheres. John D Cowan, Tufts University (993-37-406)

Robert L Devaney, Boston University, Monica Moreno Rocha*, Tufts University, and Stefan Siegmund, Boston University (993-3 7-1 002)

The Pain/eve property: a Riemann-Hilbert approach. (993-34-11 75)

1:30PM (990)

3 :30PM ._ (1 004)

Smoothness of Linearization Near a Hyperbolic Fixed Point. Misha Guysinsky, Pennsylvania State University, Boris Hasselblatt, Tufts University, and Victoria Rayskin*, UCLA (993-37-66)

Pain/eve Transcendents and Random matrices. Alexander R Its, Indiana University Purdue University Indianapolis (993-33-856)

5:30PM (1 008)

Justification of the Existence of a Group of Asymptotics of the General Fifth Pain/eve Transcendent.

Hyperbolicity, Homogeneity, and Labor-Managed Oligopolies. Marek R Rychlik*, University of Arizona, and Weiye Li, Los Alamos National Laboratory (993-34-1 066)

Youmin Lu*, Bloomsburg University, and Zhoude Shao, Millersville University (993-34-1 249) 3:30PM (994)

Accurate calculation of Mathieu functions with an application to acoustic radiation from elliptic cylinders. Arnie Lee Van Buren* and Jeffrey E Boisvert, Naval Undersea Warfare Center (993-33-668)

4:00PM (995)

AMS Special Session on Current Events 1:00 PM - 5:10 PM

Organizer:

Digital Library of Mathematical Functions: A Project Report. Daniel W Lozier, National Institute of Standards and Technology (993-33-1146)

4:30PM (996) 5:00PM (997)

1:OOPM (1 009)

The /nee equation. A New Asymptotic Series for the Gamma Function and Improved Stirling Formula Estimates. The Role of Orthogonal Polynomials in the Analysis of Laser Propagation. Preliminary report.

The Interior-Point Revolution in Optimization: History, Recent Developments, and Lasting Consequences. Margaret H. Wright, Computer Science Department, Courant Institute of Mathematical Sciences (993-49-1 022)

Hans W Volkmer, University of Wisconsin-Milwaukee (993-33-715) 2:00PM (1 01 0)

Xiquan Shi* and Fengshan Liu, Delaware State University (993-33-279) 5:30PM (998)

David Eisenbud, Mathematical Sciences Research Institute and University of California Berkeley

What is motivic integration? Thomas C Hales, University of Pittsburgh (993-14-1 309)

3 :00PM ._ (1 011)

Reza Malek-Madani and Peter A. McCoy*, U.S. Naval Academy (993-33-986)

It is easy to determine whether or not a given integer is prime. Andrew Granville, Universite de Montreal (993-11-695)

AMS-A WM Special Session on Coding, Geometry, and Hyperbolic Dynamics, Ill

4:00PM

Break

4 :30PM (1 012)

Perelman's recent work on the classification of 3-manifo/ds. Preliminary report. John W Morgan, Columbia University (993-5 7-161)

1:00 PM - 5:50 PM

Organizers: Svetlana R. Katok, The Pennsylvania State University Boris Hasselblatt, Tufts University

AMS Special Session on Continued Fractions, II

1:OOPM (999)

A proof of the Pugh-Shub theorem .

1 :00 PM -' 5:50 PM

1:30PM (1 000)

Stability of mixing for hyperbolic flows .

2:00PM (1 001)

Keith Burns* and Arnie Wilkinson, Northwestern University (993-37-45) Michael Field*, University of Houston, Jan Melbourne, University of Surrey, and Andrew Torok, University of Houston (993-37-411)

Organizers: James G. Mclaughlin, Trinity College Nancy J. Wyshinski, Trinity College 1 :OOPM ._ (1 013)

Absolutely Continuous Invariant Measures for Non-Uniformly Expanding Maps. Preliminary report. Huyi Hu * , Michigan State University, and Sandro Vaienti, Centre de Physique Theorique, CNRS

William B. Jones, University of Colorado, Boulder (993-30-1195) 2:00PM (1 014)

jANUARY

Equilibrium States for Maps of the Interval. Samuel Senti*, IUPUI, and Yakov Pesin, The Pennsylvania State University (993-37-436)

2004

Transcendence of continued fractions with bounded partial quotients. Preliminary report. J. Leslie Davison, Laurentian University (993-11-930)

(993-3 7-460) 2:30PM (1 002)

Analytic Theory and Application of Continued Fractions, A Survey.

NOTICES OF THE

2:30PM (1 01 5)

Truncated rational moment problems and quadratures. Preliminary report. Xin Li, University of Central Florida (993-41-1 33 5)

AMS

149

Program of the Sessions - Phoenix, AZ, Friday, january 9 (cant' d.) 3 :00PM (1 016)

Simultaneous diophantine approximation to successive powers of a real algebraic integer. Doug Hensley, Texas A&M University (993 -11-1164)

3 :30PM (1 017)

AMS Special Session on Smooth Dynamical Systems and Applications, I 1:00 PM - 5:50 PM

Continued Fractions Associated with Solution of a Wave Equation. Preliminary report.

Organizers: Qiu-dong Wang, University of Arizona Maciej P. Wojtkowski, University of Arizona

Brian A. Hagler, University of Texas of the Permian Basin (993-33-849) ~

4 :00PM (1 018)

An Euler-Minding theorem for G-continued fractions.

~

Geumlan Choi *, University of Illinois, and Douglas Bowman, Northern Illinois University (993-11-1 026) 4 :30PM (1 019)

On a class of classical polynomials, uniformly approximating the checkmark function. P D Dragnev*, D A Legg and D W Townsend, Indiana-Purdue University (993-41-1 073)

5:OOPM (1 020)

The Many Vistas of Continued Fractions.

1:OOPM (1 030)

(993-3 7-49) 1:30PM (1 031)

2:OOPM (1 032)

G Brock Williams , Texas Tech University (993-30-111)

Asymptotic behavior of continuity statistic for time series analysis. Takashi Nishikawa*, Southern Methodist University, Ying -Cheng Lai, Arizona State University, and Louis M. Pecora, Naval Research Laboratory (993-37-766)

Richard A Mollin, University of Calgary

Applications of Brooks's Continued Fraction Parameter to Riemann Surfaces and QC Maps.

The Central Limit Theorem for Non-Gibbsian measures. Nicolai T A Haydn, University of Southern California (993 -37-1425)

(993-11 -756) 5:30PM (1 021)

Transition to chaos in random dynamical systems. Ying-Cheng Lai, Arizona State University

2:30PM (1 033)

Hyperbolic reguler polynomial endomorphisms of IC 2 : topology of julia sets. Preliminary report. Malgorzata S. Stawiska, Purdue University (993-32-81 2)

Tube-log Riemann Surfaces.

AMS Special Session on Modern Function Theory, I

3 :00PM (1 034)

Ricardo Perez Marco, UCLA (993-37-1239)

1:00 PM - 5:50 PM

3 :30PM (1 03 5)

Spectrum and Geometric Realization of Pisot Tiling Spaces (preliminary report). Preliminary report.

1 :OOPM (1 022)

Organizers: Beth Schaubroeck, U. S. Air Force Academy Peter L. Duren, University of Michigan, Ann Arbor john A. Pfaltzgraff, University of North Carolina at Chapel Hill

4 :00PM (1 036)

Trajectories of quadratic differentials on algebraic Riemann surfaces and Hermite-Pade approximants.

4:30PM (1 03 7)

Alexander I. Aptekarev, Keldysh Institute of Applied Mathematics, Moscow, Russia (993-30-775) 2 :00PM (1 023)

Strong asymptotics for jacobi polynomials with varying nonstandard parameters. A.B.J. Kuijlaars, Katholieke Universiteit Leuven, and A. Martinez-Finkelshtein *, University of Almeria (993-33-832)

3:00PM (1 024)

3:30PM (1 025)

Jaroslaw M Kwapisz, Montana State University (993-37-1201)

5:30PM (1 039)

AMS Special Session on Arithmetical Algebraic Geometry, I

(993-41-1533)

1:00 PM - 5:50 PM

Random growth models and Riemann-Hilbert problems. Asymptotic analysis of Random Matrices and Riemann-Hilbert problems. Construction of weighted biharmonic Green functions. Sampling and Interpolation on Riemann Surfaces. Alexander P Schuster*, San Francisco State University, and Dror Varolin, University of Illinois

1 :OOPM (1 040)

Finite unions of interpolating sequences. Preliminary report. Daniel H Luecking, University of Arkansas

modular forms . (993-11-726)

1:30PM (1 041) 2:00PM (1 042)

Crystalline cohomology and homotopy theory. Martin Olsson, MIT (993-11-684)

Vanishing Cycles in Rigid Cohomology. Preliminary report. Richard M. Crew, University of Florida (993-14-1187)

2:30PM (1 043)

(993-30-1194)

150

Organizers : Kirti Joshi, University of Arizona Minhyong Kim, University of Arizona Adrian Vasiu, University of Arizona Slopes of the Up operator acting on overconvergent L J Kilford, California Institute of Technology

(993 -30-1 324) 5 :30PM (1 029)

Singularity confinement and algebraic integrability. Stephane Lafortune* and Alain Goriely, University of Arizona (993-39-566)

Jinho Baik, University of Michigan, Thomas Kriecherbauer, Ruhr-Universitaet, Bochum, Kenneth Mclaughlin, University of North Carolina, and Peter Miller* , University of Michigan

Rachel J Weir, University of Virginia (993-30-801) 5:00PM (1 028)

Remarkable Dynamics of an Overcompensatory Leslie Population Model. Preliminary report. Howard Weiss * and llie Ugarcovici, Penn State University (993-3 7-949)

Semiclassical Asymptotics for General Orthogonal Polynomials with Discrete Weights.

Kenneth Dean T-R Mclaughlin, University of North Carolina at Chapel Hill (993-60-1615) 4:30PM (1 02 7)

Long time asymptotics in averaging. Dmitry Dolgopyat, University of Maryland (993-37-784)

5:00PM (1 038)

Jinho Baik, University of Michigan (993-60-943) 4:00PM (1 026)

Non-contractible isolating blocks. George A Kozlowski, Krystyna M Kuperberg * , Auburn University, and Klaudiusz Wojcik, Jagiellonian University (993-58-1135)

Overconvergence and the de Rham-Witt complex. Preliminary report. James M Borger, University of Chicago (993-14-725)

NOTICES OF THE AMS

VOLUME 51, NUMBER 1

Phoenix, AZ, Friday, january 9 - Program of the Sessions 3 :00PM (1 044)

Drinfe/'d-lhara relations for p-adic multi-zeta values.

Ahmed Mohammed, Ball State University John M. Neuberger, Northern Arizona State University John W. Neuberger, Un iversity of North Texas

Sinan Unver, University of Chicago (993-14-891) 3:30PM (l 045) 4 :00PM (1046)

The de Rham-Witt complex in mixed characteristic. Lars Hesselholt, Massachusetts Institute of Technology (993-14 -1 529)

Tate classes on a product of modular surfaces.

1:00PM (l 059)

Preliminary report. Andrew H Knightly, University of Rochester

Michael A. Karls* and Ahmed Mohammed, Ball State University (993-34-568)

(993-11-1247) 4 :30PM (1047)

Pseudo-differential equations connected with p-adic forms and /gusa's local zeta functions.

1:30PM (1060)

Preliminary report. W. A. Zuniga, Barry U. (993 -14-772) 5:00PM (l 048) 5 :30PM (1 049)

A Geometric )acquet-Langlands Correspondence. David F Helm, Harvard University (993-11-1252) p-adic Lafforgue: a road map. Preliminary report. Kiran S Kedlaya, MIT (993-11-353)

2:30PM (1 062)

Francois A van Heerden, Utah State University 3:00PM (l 063)

3:30PM (1064)

Groupoids and fibered addition and product formulae for Nielsen Numbers. Preliminary report.

2:30PM (1 053) 3:00PM (1 054)

~

4 :00PM (1 065)

Area-minimizing surfaces in 3D polytopes in R 4 , and invariant minimizers in Rn. Frank Morgan, Williams College (993-49-1 54)

Homotopy Minimal Periods on Solvmanifolds.

Characterizing Fixed Point Sets in a Given Homotopy Class.

Upper estimates for solutions to superlinear nonsymmetric elliptic boundary value problems. Preliminary report. Alfonso Castro*, Harvey Mudd College, and Monica Clapp, Universidad Nacional Autonoma de Mexico (993 -35-1 3 70)

Lefschetz and Nielsen numbers in Control Theory. Edward C Keppelmann *, University of Nevada Reno, and Waclaw Marzantowicz, A. Mickiewicz U of Poznan (993-57-140)

Positive Solutions For A Class Of Elliptic Boundary Value Problems. Preliminary report. Stephen B. Robinson * and Andrew Arndt, Wake Forest University (993-35-1519)

Philip R. Heath, Memorial University of Newfoundland (993-5 5-546)

2 :00PM (l 052)

Some multiplicity results for asymptotically linear problems in rn:.N. (993-35-1268)

Organizers : Robert F. Brown, University of California Los Angeles Mark S. Burgin, University of California Los Angeles

Peter Saveliev, Marshall University (993-55-186)

The IVP for the nonlinear heat equation in weighted Sobo/ev spaces. Victor L Shapiro, Un iversity of California at Riverside (993 -35-53)

1:00 PM - 5:20 PM

1:30PM (1 051)

Harnack Type Inequalities for some Semilinear Elliptic Equations with Critical Sobolev Exponent. Lei Zhang, Texas A&M (993-35-811)

2 :00PM (1061)

AMS Special Session on Fixed Points: Theory and Application, Ill

1:00PM (1 050)

Integrability of Blow-up solutions to some non-linear differential equations. Preliminary report.

4 :30PM (1066)

Continuous Newton 's Method and a Nash -Moser Inverse Function Theorem. J W Neuberger, University of North Texas (993-35-641)

Models for josephson junctions.

Christina L Soderlund, UCLA (993-5 5-1 06)

5:OOPM (1 067)

Jacob Rubinstein, Indiana University (993-35-830)

The Lefschetz-Hopf Theorem and Axioms for the Lefschetz Number.

5:30PM (1 068)

Some recent results concerning oo -harmonic functions.

Martin Arkowitz*, Dartmouth College, and Robert F Brown, University of California, Los Angeles

Tilak Bhattacharya, Bishop's University (993-35-579)

(993-5 5-90) 3:30PM (1 055)

Transfers and Jiang's Nielsen theory for periodic points. Preliminary report.

4 :00PM (1 056)

A Type of Nonlinear Vector and Matrix Equations and Their Corresponding Sequences.

4 :30PM (1 057)

Xiquan Shi and Fengshan Liu *, Delaware State University (993-1 5-193) On the preimage J- 1 (a) of a point. Preliminary report. Peter N Wong * , Bates College, and Daciberg L Goncalves, University of Sao Paulo (993-5 5-1 558)

Daniel Henry Gottlieb, Purdue (993-55-36)

5 :00PM (l 058)

Iteratively Regularized Gauss-Newton-type Algorithm with Simultaneous Updates of Inverse Derivative.

AMS Special Session on Low-Dimensional Topology, II 1:00 PM- 5:50PM

Organizer: Tim D. Cochran , Rice University 1:00PM (1069) 1:30PM (1 070)

Alexandra Smirnova, Georgia State University (993 -65-162 5)

AMS Special Session on Nonlinear Partial Differential Equations and Variational Problems, II

2:00PM (1 071) 2 :30PM (1 072)

1:00 PM - 5:50 PM

Organizers: David A. Hartenstine, University of Utah

jANUARY

2004

NOTICES OF TilE AMS

Distance calculations in the curve complex. John Hempel, Rice University (993-57-1359)

Orderability of certain 3-manifo/d groups. Preliminary report. Sergio Fenley, Florida State University, Rachel Dedwydd Roberts* , John Shareshian, Washington University in St Louis, and Melanie Stein, Trinity College (993-57-1297)

Higher-Order Linking Forms for 3-Manifo/ds. Preliminary report. Constance Leidy, Rice University (993 -5 7-988)

Singular symplectic forms on 4-manifo/ds. Robion C. Kirby*, University of California, Berkeley, and T. David Gay, Univers ity of Quebec at Montreal (993-57-396)

151

Program of the Sessions - Phoenix, AZ, Friday, january 9 (cant' d.) 3 :00PM (l 073)

3 :30PM (l 074)

On the Homotopy Classification of 2-Complexes. Preliminary report. jens Harlander, Western Kentucky University, and jacqueline A jensen*, Sam Houston State University (993-55 -933)

Generalizations of quandle cocycle invariants and Alexander modules from quandle modules. Masahico Saito, University of South Florida (993-5 7-851)

4 :00PM (l 075)

The topology of 4-manifolds which admit a symplectic form and a circle action. Preliminary report. Scott j Baldridge , Indiana University (993-57-619)

4 :30PM (l 076)

On a characterization of nugatory crossings. Xiao-Song Lin, University of California, Riverside (993 - 57-1289)

5:00PM (1 077)

A topologicaiiHX relation in three and four dimensions. james Conant* , University of Tennessee , Knoxville, Rob Schneiderman, Courant Institute, and Peter Teichner, UC San Diego (993-57-204)

5:30PM .,. (l 078)

2:00PM (1 083)

Ziva Deutsch* , jerusalem College, Israel, and Micha A. Perles, Hebrew University (993-52-234) 2 :15PM (1 084) 2:30PM (1 085)

(993-5 5-841)

Lie groups of automorphisms of para-f-manifolds. Preliminary report. A. Rucki, Oklahoma City, OK (993-53-1407)

One-Dimensional Metric Foliations on Compact Semisimple Lie Groups. Preliminary report.

3 :00PM (l 087)

A Notion of Rectifiability for Hypersurfaces in Carnot Groups.

Marius I Munteanu, SUNY-Oneonta (993 - 53-1619)

3 : 15PM 3 :30PM (l 088)

Daniel R Cole, Dartmouth College (993-53-1652) Break

Ehresmann Connection Related to Orbit Stratification in Compact Semi Simple Lie Algebras. Preliminary report. Roxana Costinescu * , Millersville University of Pennsylvania, and Serge Preston, Portland State University (993-53-1671)

3:45PM (1 089)

Total Gauss curvature of complete minimal submanifolds. Preliminary report. Tracy Bowers, Moravian College (993-53-1685)

4:00PM (1 090)

MAA Minicourse # 13: Part 8

The minimal marked length spectrum of Riemannian two-step nilmanifolds. Ruth Gornet, University of Texas at Arlington, and Maura B Mast* , University of Massachusetts Boston

1:00 PM - 3:00 PM

(993-53-1687)

The Fibonacci and Catalan numbers. Organizer:

An Integral Formula On Seifert Bundles. A Fawaz, The University of Texas of the Permian Basin (993-53-1325)

2:45PM (l 086)

Finite Abelian Group Actions on Orientable 5 1 -Bundles Over Orientable Surfaces. Preliminary report. Caroline Maher Boulis, Florida State University

A Fine Classification of Closed Planar Sets According to Their Non-Convexity.

Ralph P. Grimaldi , Rose-Hulman Institute of Technology

4:15PM (1 091 )

Special PL manifolds as PL shape o-fibrators. Prelim inary report. Violeta Vasilevska, The University of Tennessee (993-57-1 03 7)

MAA Minicourse #2: Part 8

4 :30PM (1 092)

A Morse Theory Approach to studying Graph-Configuration Spaces. David G.C. Handron, Carnegie Mellon University

1:00 PM - 3:00 PM

(993-57-1314)

Hands-on discrete math with technology. Organizers : Douglas E. Ensley, Shippensburg University Kate McGiveny, Shippensburg University

4:45PM (1 093)

Diagrammatic Reducibility and Labeled Oriented Tree Complexes. Preliminary report. Travis R Keirn, St. Edward's University (993 -57-1612)

5 :00PM (1 094)

On m-sectorial Schrodinger operators with singular potentials on manifolds of bounded geometry. Ognjen B Milatovic, University of Toledo

MAA Minicourse #8: Part 8

(993-58-458)

1:00 PM - 3:00 PM

5 : 15PM (1 095)

Some mathematics of Leonhard Euler. Organizers: William W. Dunham, Muhlenberg College Edward C. Sandifer, Western Connecticut State University

A New Homotopy Invariant for Distinguishing [G, 2]-Complexes. Preliminary report.

Katherine S. Byler, California State University, Fresno (993-57-1 088)

AMS Session on Probability and Stochastics 1:00PM-4:10PM

AMS Session on Geometry

1:OOPM .,. (1 096)

1:00 PM - 5:25 PM 1 :OOPM .,. (1 079)

Preliminary report. John C. Wierman, Johns Hopkins University

A new solution for Hilbert's third problem. David Benko, Te x as A and M University (993-51-92)

1:15PM A Euclidean Area Theorem via Laguerre Geometry. .,. (1 080)

Robert D. Knight, University of Guam

(993-60-2 77)

1:15PM Random Harmonic series. Preliminary report . .,. (1 097)

(993-51-1241) 1:30PM (1 081)

152

David Baker, University of California, Santa Barbara (993-60-11 58)

Fuzzy Geometry of Space. Reza R Ahangar, Kansas Wesleyan University (993-51-1701)

1:45PM ... (1 082)

An improved site percolation threshold universal formula for two-dimensional matching lattices ..

1:30PM 1:45PM .,. (1 098)

Even Astral Configurations. Leah Wrenn Berman, Ursinus College (993-52-209)

NOTICES OF THE AMS

Break

Decompositions of Exponential Distributions on Semigroups. Preliminary report. Kyle Siegrist* and Boris Kunin, University of Alabama in Huntsville (993-60-1 572) VOLUME 51, NUMBER 1

Phoenix, AZ, Friday, january 9- Program of the Sessions

...

2:00PM (1 099)

Transient Solution to the Time-Dependent Multi-server Poisson Queue. Preliminary report.

2 :30PM .,. (111 3)

Margaret Isabelle Doig, University of Notre Dame

Barbara Haas Margolius, Cleveland State University (993-60-127) 2: 15PM (1100)

(993-05-11 03)

An lnvariance Principle for Semimartingale Reflecting Brownian Motions in Piecewise Smooth Domains.

2 :30PM

W Kang * and R J Williams, UCSD (993-60-11 3) Break

2:45PM (1101)

Malliavin calculus applications to hypoel/iptic heat kernel inequalities.

2:45PM .,. (1114) 3:OOPM (111 5)

(993-60-1 703)

3:15PM (11 03)

3:30PM (1104)

...

3:45PM (11 OS) 4:00PM (1106)

Ergodic Type Theorems for Actions of Semi-groups with Finite Number of Generators on von Neumann Algebras.

3:15PM .,. (1116)

Genady Ya. Grabarnik'' , IBM Thomas J. Watson Research Center, Alexander A Katz, St. John's University, and Laura Shwartz, UNISA

3 :30PM .,. (111 7)

(993-60-1112)

3:45PM 4 :00PM .,. (111 8)

Kendall distribution functions. Roger B. Nelsen * , Lewis & Clark College, Jose Juan Quesada Molina, Universidad de Granada1 Jose Antonio Rodriguez Lallena and Manuel Ubeda Flores, Universidad de Almeria (993-60-872)

On Convergence of Choquet Capacity Functionals. Preliminary report. Ding Feng * and Tonghui Wang, New Mexico State University (993-60-622) Limits of Finite State Markov Chains. Preliminary report . Michael L Green , Cal Poly Pomona (993-60-828)

Conditional integral transforms and convolution products. Preliminary report. Bong Jin Kim, Daejin University, Byoung Soo Kim, Yonsei University, and David L. Skoug'' , University of Nebraska-Lincoln (993-60-1 2 57)

Some topics on circular colorings. Preliminary report. Che Zhongyuan, Penn State Beaver (993-05-1 082) Unit bar-visibility representations of triangulated polygons. Preliminary report. Alice M Dean* , Skidmore College, Ellen Gethner, University of Colorado at Denver, and Joan P Hutchinson, Macalester College (993-05-1 077)

Tai Melcher, University of California, San Diego 3 :00PM (11 02)

Bounds on the run length of Hamiltonian cycles in grid graphs.

Flexibility of Toroidal Embeddings. Neil Robertson, Ohio State University, Xiaoya Zha* , Middle Tennessee State University, and Vue Zhao, University of Central Florida (993-05-871)

The Structure of Uniformly 2-Connected Graphs. Donald A Nelson, Middle Tennessee State University (993-05-800) Break Pebbling Diameter Three Graphs. Preliminary report. Boris Bukh, University of California, Berkeley (993-05-781)

4:15PM .,. (111 9)

4:30PM .,. (11 20) 4:45PM 5:00PM .,. (1121)

5:15PM .,. (1122)

Domination iDot Critical Graphs. Preliminary report. Tamara A Burton* and Melissa M Matthews, Rochester Institute of Technology (993-05-2 59) Ordered Colorings in Graphs. Preliminary report . Darren A Narayan * and Victor Kostyuk, Rochester Institute of Technology (993-05-25 7) Break Cages of degree k are k-edge-connected. Michael H. Moriarty, Worcester, Massachusetts, and Peter R. Christopher* , Worcester Polytechnic Institute (993-05-11 92)

The incidence coloring conjecture for graphs of maximum degree 3. Maksim I Maydanskiy, UC Berkeley (993-05-588)

5 :30PM .,. (1123)

AMS Session on Graph Theory

(993-05-1 366)

1:00 PM - 6:2 5 PM 1 :OOPM (11 07)

1:15PM .,. (11 08) 1:30PM (11 09)

1:45PM .,. (111 0) 2:00PM (1111)

Homogeneous Embeddings and Stratified Graphs. Gary Chartrand, Western Michigan University, Donald W VanderJagt, Grand Valley State University, and Ping Zhang * , Western Michigan University (993-05-589)

Graph powers and k-ordered Hamiltonicity. Preliminary report. Denis Chebikin, MIT (993-05-1606)

5:45PM .,. (1124)

6 :00PM .,. (112 5)

Independent Sets In Triangle-Free Cubic Planar Graphs. Christopher Carl Heckman'', Arizona State University, and Robin Thomas, Georgia Institute of Technology (993-05-514)

Gary Chartrand, Western Michigan University, David Erwin * , Trinity College, Donald W VanderJagt, Grand Valley State University, and Ping Zhang, Western Michigan University (993-05-1600)

Multidesigns of the multipartite graph .

MAA Session on Math and the Arts, Ill

Atif Abueida '', University of Dayton, and Mike Daven, Mount Saint Mary College (993-05-1 588)

1:00 PM - 4:55 PM

New Bounds on lsoperimetric Numbers of Platonic Graphs. (993-05-1 514)

The Elimination Procedure for the Competition Number is Not Optimal. Preliminary report. Stephen G. Hartke, Rutgers University (993-05-1127)

jANUARY

On the subword complexity of finite words. Irina Gheorghiciuc, University of Pennsylvania (993-05-146)

6:15PM .,. (11 26)

y-labelings of graphs.

The linear complexity of the adjacency matrix of a graph. Preliminary report. David L. Neel, Seattle University, and Michael E. Orrison * , Harvey Mudd College (993-05-1551)

Dominic Lanphier, Kansas State University, and Jason Rosenhouse", James Madison University 2:15PM .,. (1112)

Radio-Chromatic Numbers for Powers of Paths . Preliminary report. Allen J Schwenk, Western Michigan University

2004

1:OOPM .,. (1127)

NOTICES OF THE

AMS

Organizers : Ann Robertson, Connecticut College John M. Sullivan, University of Illinois, Urbana Reza Sarhangi, Towson University Nathaniel A. Friedman, State University of New York, Albany The .Art of Star Polygons. Preliminary report. Reza Sarhangi, Towson University (993-01-1626)

153

Program of the Sessions - Phoenix, AZ, Friday, january 9 (cont'd.) 1:20PM .,. (11 28)

l :40PM .,. (1129)

2:00PM .,. (1130) 2:15PM 2:40PM .,. (1131)

3:00PM .,. (1132)

3:20PM .,. (11 33) 3:40PM .,. (1134) 3:55PM 4:20PM .,. (1135)

4 :40PM (1136)

Visualizing the tightening of knots. Preliminary report. Jason Cantarella*, University of Georgia, Michael Piatek and Eric Rawdon , Duquesne University (993-01-1419) Geometric Representations of nth Hulls of Knotted Curves. Preliminary report. John W. Foreman, University of Georgia (993-01-1422) What 's the Best Way to Make Polyhedral Models? Helmer Aslaksen , National Un iversity of Singapore (993-01-1219) Break Mathematics for poets (and drummers): The mathematics of rhythm. Rachel W Hall, Saint Joseph's University (993-01-505) A Mathematical Measure of Preference in African Rhythm. Preliminary report. Godfried T. Toussaint, School of Computer Science , McGill University (993-01-845) Triangular Music. Jonathan L Merzel* and Michael D Golden, Soka University of Ame rica (993-01-301) Teaching Basic Music Theory from a Mathematical Perspective. Timothy A Johnson, Ithaca College (993-01 -942) Break Art, Mathematics, and Visualization. Pamela Davis Kivelson, Stanford University, and Katherine Socha*, Michigan State University (993-01-397) Art and Mathematics: A Liberal Arts Mathematics course. David Hartz, College of St Benedict (993-01-1543)

MAA Session on Teaching and Learning of Undergraduate Mathematics, I 1:00PM - 3:55 PM

1 :OOPM .,. (1137)

l :30PM .,. (ll 38)

2:00PM .,. (1139)

2:30PM .,. (1140)

3:00PM .,. (1141)

154

Organ izers : Anne E. Brown, Indiana University South Bend Marilyn P. Carlson , Arizona State University Draga D. Vidakovic, Georgia State University Following the path of evolution: Student constructions of the concept of solution to a differential equation. Debasree Raychaudhuri, California State University at Los Angeles (993-Rl-1383) Lizzie and subgroups: A case study report on the role of affect. Preliminary report. Jennifer A Bergner, Salisbury University (993-R 1-365) A Theoretical Model for Describing and Assessing Students ' Understanding of the Function Concept. Brian R O'Callaghan, Southeastern Louisiana University (993-Rl -275) Undergraduates' understanding of distance and angle as they explore Euc/idean,spherical, and taxicab geometries. Preliminary report. Stephen D Blair, Portland State University (993-Rl-750) Exploring the Culture of a Non-Traditional Mathematics Classroom. Carol E. Seaman* and Jennifer Earles Szydlik, University of Wisconsin Oshkosh (993-R 1-160)

3:30PM .,. (1142)

An Examination of the Knowledge Base for Teaching and Instructional Practice of Two Undergraduate Mathematics Faulty Teaching Calculus. Kimberly B. Santucci *, Thomas C. DeFranco and jean McGivney-Burelle, University of Connecticut (993-Rl-421)

MAA Session on My Favorite Demo: Innovative Strategies for Mathematics Instructors, I 1:00 PM - 3:55 PM

l :OOPM .,. (1143) l :1 5PM .,. (1144) 1:30PM .,. (1145)

l :45PM (1146)

2:00PM .,. (1147)

2:30PM .,. (1148)

3:00PM .,. (1149) 3:15PM .,. (11 50) 3:30PM .,. (11 51) 3:45PM .,. (1152)

Organizers: David R. Hill, Temple University Lila F. Roberts, Georgia Southern Un iversity Demonstrating Linear Transformations with Morphing. John F. Putz, Alma College (993-Sl-220) Computer Visualizations for Calculus . Lew Ludwig *, Denison University, and Keith Howard, Kenyon College (993-Sl-418) Exploring Distributions and Random Samples with Sampler(TM) . Clifford H. Wagner, Pennsylvania State University at Harrisburg (993-Sl-428) Motivating the Dihedral Group Through Quilting Squares. James E Hamblin, Shippensburg University (993-Sl-531) Visualizing Mathematical Models via Spreadsheets: Part 1- Population Models. Deane E. Arganbright* , University of Tennessee at Martin, and Erich Neuwirth, University of Vienna (993-Sl-223) Visualizing Mathematical Models via Spreadsheets: Part //-Retirement Financing. Erich Neuwirth *, University of Vienna, and Deane E. Arganbright, University of Tennessee at Martin (993-Sl-225) Maple Demos for Multivariable Calculus . Karl J Havlak, Angelo State University (993-Sl-188) Cross-sections and contours using Play-Doh. Pallavi Jayawant, University of Arizona (993-Sl-500) From the Unit Circle to the Trigonometric Functions. Sarah L Mabrouk, Framingham State College (993-Sl -557) Discovering the Five Platonic Solids . Jackie A Hall, Longwood University (993-Sl-487)

MAA Session on Mathematical Models of the Environment 1:00 PM- 3:55 PM

1 :OOPM .,. (1153) l : l 5PM .,. (1154) l :30PM .,. (1155)

NOTICES OF 1HE

AMS

Organizers : Karen D. Bolinger, Clarion University William D. Stone, New Mexico Institute of Mining & Technology Ahlam E. Tannouri, Morgan State University Applied Graph Theory in the Classroom . Kimberly jordan Burch, Montclair State University (993-Tl-l 532) Mathematical Models in ''The Iowa Environment". Daniel Alexander, Drake University (993-Tl-1534) A Stochastic Model of Wind Velocities at the Kennedy Space Center. Brian E. Smith*, McGill University, and Francis J• Merceret, National Aeronautics and Space Administration (993-Tl-270)

VOLUME

51,

NUMBER

1

Phoenix, AZ, Friday, january 9- Program of the Sessions 1:45PM .,.. (11 56)

Modeling the Color Changes in Tree Foliage: A Differential Equations Group Project.

1 :OOPM (1173)

Michael R. Huber* and Brian J. Lunday, United States Military Academy (993-T1-1 79) 2:00PM .,.. (1157) 2:20PM .,.. (11 58) 2:40PM .,.. (1159) 3:00PM (11 60)

Modeling Population Genetics . William P. Fox* , Jeffrey Camper and Richard D. West, Francis Marion University (993-T1-1535)

Shea D Burns, North Carolina A&T State University 1:OOPM (1174)

Remote Sensing Techniques.

1 :OOPM (11 75)

Elyn Rykken, Muhlenberg College (993-T1-227)

Modeling the Spread of a Carrier Dependent Infectious Disease: Effect of Migration from Environmentally Degraded Habitat.

3:40PM .,.. (1162)

Population Growth Mathematical Models. S. Narasimha Murthy, Addis Ababa University (993-T1-2 3)

1 :OOPM (11 76)

1 :OOPM (11 77)

1:00 PM - 3:00 PM Organizer: 1 :OOPM (1163)

Jon W. Scott, Montgomery College

Development of Interactive Material for the Constructivist Teaching of Mathematical Proof to Future Teachers. Doug Ensley and Winston Crawley* , Shippensburg University

1 :OOPM (1164)

1:OOPM (11 7 8)

1 :OOPM (1165)

1:OOPM (11 66)

1:OOPM (11 81)

Collaborative Research: A Problem Based Calculus Sequence.

1 :OOPM (1 1 83)

1 :OOPM (1184)

1 :OOPM (11 72)

Mathematics On Demand. linda Braddy*, Anne E Fine and Mickle Duggan, East Central University

1 :OOPM (11 86)

A Problem and Reasoning Based Curriculum for Preservice Elementary Educators: Understanding Mathematics Deeply for Teaching. Using Both the ALEKS Learning and Assessment Computer Program and Conceptual Activities in a College Developmental Mathematics Course. Collaborative Research: Adaptation and Implementation of Activity and Web-Based Materials into Post-Calculus Introductory Probability and Statistics Courses. Tracy Goodson-Espy, University of Alabama in Huntsville

1 :OOPM (1187)

Collaborative Research: Adaptation and Implementation of Activity and Web-Based Materials into Post-Calculus Introductory Probability and Statistics Courses. M. leigh Lunsford, University of Alabama in Huntsville

1:OOPM (11 88)

Quantitative Methods for Public Policy.

Collaborative Research: Adaptation and Implementation of Activity and Web-Based Materials into Post-Calculus Introductory Probability and Statistics Courses. Ginger Holmes Rowell, Middle Tennessee State University

David Bressoud, Macalester College

jANUARY 2004

Enhancing the Mathematical Understanding of Students in Chemistry.

Judith Flowers, University of Michigan-Dearborn 1 :OOPM (11 85)

Teaching Introductory Combinatorics by Guided Group Discovery. Kenneth Bogart, Dartmouth College

1:OOPM (1171)

Discovery-based Science and Mathematics in an Environmental Context.

Shahriar Shahriari * and Erica Flapan, Pomona College

Seeing the Connections: Promoting Profound Understanding of Secondary Mathematics. Steve Benson*, Education Development Center, Karen Graham, University of New Hampshire, Neil Portnoy, Stony Brook University, and AI Cuoco, Education Development Center

1:OOPM (11 70)

Motivating Geometry through Computation and Visualization.

Richard Goldthwait, Youngstown State University

The PascGalois Project: Visualizing Abstract Algebra. Michael Bardzell * and Kathleen Shannon, Salisbury University

1:OOPM (11 69)

Interactive Modular Mathematics Education. William Feldman* and Wayne Mackey, University of Arkansas

Stephanie Fitchett*, Florida Atlantic University, and Blake Mellor, Loyola Marymount University

Shing So, Central Missouri State University 1 :OOPM (11 68)

Bridging the Vector Calculus Gap: Episode II. Tevian Dray* and Corinne A Manogue, Oregon State University

David Finn, Rose-Hulman Institute of Technology 1:OOPM (1 1 82)

Collaborative Research: A Problem Based Calculus Sequence. Ted Mahavier* and Dale Daniel, Lamar University

1 :OOPM (1167)

1:OOPM (11 80)

Collaborative Research: A Problem Based Calculus Sequence. Charles Allen '' and Carol Browning, Drury University

Community College Mathematics Integration Project. Stephen Drake* , Northwestern Michigan College, and Carolyn Drake, Dennos Museum Center

Demos with Positive Impact. David R Hill * , Temple University, and lila F Roberts, Georgia College and State University

Promoting Active Learning and Collaboration in Calculus with the Investigative Classroom. Meighan I Dillon, Southern Polytechnic State University

1:OOPM (11 79)

MAA Poster Session on Projects Supported by the NSF Division of Undergraduate Education.

Improving Mathematical Skill and Attitudes of Under-prepared College Freshmen. Rosalie Dance* and Ludence A Romney, University of the Virgin Islands

Polynomial Models for Real World Applications . Michael J. Bosse* , Morgan State University, and N. R. Nandakumar, Delaware State University (993-T1-317)

Lexington Collaborative for Reform and Improvement of Middle Mathematics. lillie Crowley* , Lexington Community College, and Carl lee, University of Kentucky

Prawal Sinha, Indian Institute of Technology Kanpur (993-T1-84) 3:20PM .,.. (1161)

Teacher Preparation, Mathematics and Technology: A National Dialogue. Ruth Collins, Delaware Technical and Community College

An Air Pollution Transport Model . James A. Walsh, Oberlin College (993-T1-62)

Incorporating Technology and Multidisciplinary Applications in a Team-Taught Lecture-Laboratory Calculus Course.

NOTICES OF THE

AMS

155

Program of the Sessions - Phoenix, AZ, Friday, january 9 (cont'd.) 1 :OOPM (1189)

Establishing the National Curve Bank.

1:OOPM (1 209)

Shirley B Gray*, Stewart Venit and Randolf Cooper, California State University Los Angles

Applying Advanced Distributed Teaching and Learning to Pre-Calculus Mathematics. Hal Schlais, University of Wisconsin System, Robert Hoar*, University of Wisconsin-LaCrosse, and Paul Sundheim, University of Wisconsin Colleges

WeBWorK in the Mathematics Curriculum.

1 :OOPM (11 90)

Jeffrey J Holt, University of Virginia

1 :OOPM (1 1 91)

Training Environmental Statisticians - Tomorrow 's Problem Solvers.

1:OOPM (1 21 0)

Kyle Siegrist, University of Alabama in Huntsville

William F Hunt*, Kimberly Weems and William Swallow, North Carolina State University

1 :OOPM (1 211)

Improving Calculus: Developing Concepts Through Good Questions.

1 :OOPM (1 21 2)

Stem and Tendril: Vertically Integrated Statistics Laboratories.

1 :OOPM (11 92)

Maria Terrell, Cornell University

Enhancing Student Preparation for Calculus via a Web-Based Homework System. Michael D Hvidsten * and Charles Pastor, Gustavus Adolphus ·college

1 :OOPM (11 93)

john Verzani *, Andrew Poje and Deborah S. Franzblau, The College of Staten Island

Exploring Geometry: Integrated Textbook and Software for College Geometry.

1:OOPM Project WELCOME. (1213) James E White *, The Mathwright Library, Dan Kalman, American University, and William Hawkins, University of the District of Columbia

Michael D Hvidsten, Gustavus Adolphus College 1 :OOPM (1194) 1:OOPM (11 95)

A Sophomore-Level Transition Course. Michael A Jones* and Arup Mukherjee, Montclair State University

1:OOPM (1214)

Development of an Undergraduate Diffraction Course. David Kammler, Southern Illinois University, Carbondale

1:OOPM (1196)

1:OOPM (1215)

Phaser: A Universal Simulator for Dynamical Systems Built on java Technology. Huseyin Kocak* and 'Brian Coomes, University of Miami

Core Mathematics.

1:OOPM (1197)

Gary Krahn * and Don Small, U.S. Military Academy

1:OOPM (11 98)

Teaching Discrete Mathematics via Primary Historical Sources.

1 :OOPM (1200) 1 :OOPM (1201) 1 :OOPM (1202)

1:OOPM (1 204)

1 :OOPM (1205) 1 :OOPM (1206) 1 :OOPM (1207) 1:OOPM (1208)

156

Nancy Zumoff*, Kennesaw State University, Christopher Schaufele, retired, Paul Latiolais, Portland State University, and Philippe laval, Kennesaw State University

Pathways through Algebra. Wade Ellis*, West Valley College, and Terrie Teegarden, San Diego Mesa College

Web-Based Math Homework. John W jones, Arizona State University

1 :OOPM (1 21 7)

Adapting Innovative Projects for Student Improvement. Mary Kay Abbey* and jon Scott, Montgomery College

Improving Preservice Mathematics Teachers' Understanding of Fundamental Concepts in the Secondary Mathematics Curriculum. John Lorch*, Elizabeth Bremigan and Ralph Bremigan, Ball State University

MAA Special Presentation

Reform College Algebra in a Tribal College Setting.

1:00 PM - 3:00 PM

Russell Lundgren, Chief Dull Knife College

Mathematics for business decisions (repeated from 5:00p.m. to 1:00 p.m., Friday).

Mathematics for Future Secondary Teachers. James J Madden, Lou isiana State Univers ity & Agricultural and Mechanical College

Organizers : Richard B. Thompson, University of Arizona Christopher Lamoureux, University of Arizona

Knot Theory for Preservice and Practicing Secondary Mathematics Teachers. Neil Portnoy, Stony Brook University, and Thomas Mattman* , California State University, Chico

1:OOPM (1 203)

A Versatile, Technology-Intensive EarthMath.

1 :OOPM (1216)

jerry Lodder, New Mexico State University 1:OOPM (11 99)

The Probability/Statistics Object Library.

Implementation of WeBWorK Delivering Internet-Based Homework In College Algebra Classes. Coreen Mett* and Neil Sigmon, Radford University

MAA Panel Discussion

Broadening the Scope of Statistical Education through Technology.

1:00 PM - 2:20 PM

Deborah Nolan* and Terence Speed, University of California Berkeley

Voices of the partner disciplines: Building on the MAA curriculum foundations project.

A Course in Scientific Simulation .

Organizers: Tevian Dray, Oregon State University Deborah Hughes Hallett, University of Arizona Matthias Kawski, Arizona State University William G. McCallum, University of Arizona Corinne A. Manogue, Oregon State Panelists: University Ron Roedel, Arizona State University Michael Zeilik, University of New Mexico

Mike O'leary, Towson University

WeBWorK - a Web-Based Homework System. Arnold K Pizer*, Michael E Gage and Vicki Roth, University of Rochester

A Computer Activity Approach to College Geometry. Barbara E Reynolds *, Cardinal Stritch University, and William E Fenton, Bellarmine University

Biomathematics in the Undergraduate Curriculum. Raina Robeva*, Robin Davies, james Kirkwood, Sweet Briar College, Michael Johnson, Boris Kovatchev and Marty Straume, University of Virginia

NOTICES OF THE

AMS

VOLUME

51,

NUMBER

1

Phoenix, AZ, Friday, january 9- Program of the Sessions NAM Granville-Brown-Haynes Session of Presentations by Recent Doctoral Recipients in the Mathematical Sciences

MAA Panel Discussion 1:00 PM - 2:20 PM

Session for chairs: The chair's role in teaching teachers. Organizers: Catherine M. Murphy, Purdue University Calumet Daniel P. Maki, Indiana University Panelists : Jim Lewis, University of Nebraska-Lincoln Alan C. Tucker, SUNY at Stony Brook

2:15PM-4:00PM

RMMC Board of Directors 2:15PM-4:10PM

MAA Presentations by Teaching Award Recipients 2:30 PM - 4:00 PM

ASL Invited Address

(1 228)

2:00 PM - 2:50 PM

(1229)

(1 21 8)

Vaught's Conjecture.

MAA Invited Paper Session on Assessment of Student Learning in Undergraduate Mathematics

MAA Session on Philosophy of Mathematics 2:00 PM - 6:30 PM

2:30PM - 6:25 PM

Organizers: Roger A. Simons, Rhode Island College Satish C. Bhatnagar, University of Nevada, Las Vegas

Philosophy of Mathematics: What, Who, Where, How and Why. Charles R. Hampton, The College of Wooster (993-U1-528)

2:25PM .,.. (1220)

On The Nature of Mathematical Thought and Inquiry: A Prelusive Suggestion. Padraig M Mcloughlin, Morehouse College (993-U1-13 31)

2:50PM The Interpretation of Probability is Perhaps an .,.. (1 22 1) ///-Posed Question. Paolo Rocchi, IBM (993-U1-185) 3:1OPM Minireception sponsored by the SIGMAA on the Philosphy of Mathematics. 3:40PM When is a proof a proof? (1222) joseph Auslander, University of Maryland College Park (993-U 1-1266) 4:05 PM The Poetic View of Mathematics. .,.. (1223) Jerry P. King, Lehigh University (993-U1 -1080) 4: 30PM "You cannot solder an Abyss with Air"- the Role of .,.. (1 224) Metaphor in Mathematics. Preliminary report. Lawrence D'Antonio, Ramapo College of New Jersey (993-U1-376) 4:50PM Minireception sponsored by th e SIGMAA on the Philosphy of Mathematics. 5:20PM The NonEuclidean Revolution Makes Relativism .,.. (1225) Available to the Rest of the World. Preliminary report. Michael J. Bosse, Morgan State University (993-U1 -294) 5:45PM The tension and the balance between mathematical .,.. (1226) concepts and student constructions of it. Debasree Raychaudhuri, California State University at Los Angeles (993-U1-1 564) 6 :1OPM On Code/'s Proof and the Relation Between .,.. (1 227) Mathematics and the Physical World. Preliminary report. G. Arthur Mihram*, Princeton, N.j., and Danielle Mihram, University of Southern California (993-U 1-408)

jANUARY

2004

Clueless.

Olympia Nicodemi, SUNY at Geneseo (1230) A S.N.A.P. Math Fair. Andrew C.-F. Liu, University of Alberta

R.W. Knight, Oxford , UK

2:00PM .,.. (1219)

Functions for the world. Thomas A. Garrity, Williams College

Organizers: Bernard L. Madison, University of Arkansas at Fayetteville William E. Haver, Virginia Commonwealth University 2:30PM Assessment of a New American Program in the .,.. (12 31) Middle East. Thomas W Rishel, Weill Cornell Medical College (993-Z3-46) 2:50PM An assessment of the contribution of two general .,.. (1232) education mathematics courses in the quantitative

reasoning skills of students. Aimee J Ellington , Virgini a Commonwealth University (993 -Z3-63) 3:1OPM Core Assessment- Past, Present, Future. Preliminary .,.. (1233) report. Melissa A Hardeman* and Tracy A Watson, University of Arkansas at Little Rock (993-Z3 -26 7) 3:30PM Involving the Entire Department in Assessment. (1234) Preliminary report. Dick Jardine, Keene State College (993-Z3-605) 3:50PM Assessing the Mathematics Major with a Bottom-Up .,.. (1235) Approach. Preliminary report. Sarah V. Cook, Was hburn University (993-Z3-520) 4 :1OPM Assessment-To Make It Work, Keep It Simple. .,.. (1236) Thomas C. McMillan* and Jim Fulmer, University of Arkansas at Little Rock (993-Z3-246) 4 :30PM An online mathematics assessment, placement and .,.. (1237) exit testing project. Preliminary report. Jerry A Johnson*, lnmaculada Aban and Jeff Mortensen, University of Nevada, Reno (993-Z3 -89) 4 :50PM Undergraduate Program Assessment at a Research .,.. (1238) I University. Preliminary report. Katherine J. Mawhinney*, Appalachian State University, and JeffreyS. Scroggs, Nort h Carolina State University (993-Z3-51 9) 5:1OPM Lessons Learned: Assessment Results at a Two-Year .,.. (1 239) College. Preliminary report. Larry A Burgess* and Richard P Vaughn, Paradise Valley Community College (993-Z3 -30 3) 5:3 0PM Assessing the Mathematics Major: A Triangulated (1240) Approach. Preliminary report. Katherine Safford Ramus * and Brian P. Hopkins, Saint Pet er' s College (993-Z3-638)

N OTICES OF THE

AMS

157

Program of the Sessions - Phoenix, AZ, Friday, january 9 (cont'd.) 5:50PM ..,. (1 241)

Developing an Appropriate and Effective Culminating Experience for Your Mathematics Majors. Preliminary report.

MAA Minicourse #3: Part 8 3:15PM- 5:15PM

M Paul Latiolais*, Joyce O'Halloran and Karen Marrongelle, Portland State University (993-Z3-877) 6:10PM (1 242)

Computation and discovery in the number theory classroom.

Using Portfolios for Departmental Assessment.

Organizer:

Scott A Smith* and Laurie B Hopkins, Columbia College (993-Z3-922)

Clifford A. Reiter, Lafayette College

MAA Minicourse #9: Part 8 MAA Invited Paper Session on the Use of Hand-Held Technology in College and University Developmental Algebra Classrooms

3:15PM- 5:15PM

PMET: Preparing mathematicians to educate teachers, grades 7-12.

2:30 PM - 5:30 PM

Organizers: Holly Hirst, Appalachian State University Jack Y. Narayan, SUNY College at Oswego

Organizers : Wade Ellis, Jr., West Valley College Edward D. Laughbaum, The Ohio State University 2 :30PM ..,. (1243)

Using Technology to Connect Developmental Mathematics to College Algebra.

ASL Invited Address

Selina Vasquez, Southwest Texas State University 3:30 PM - 4:20 PM

(993-Z4-99) 3:00PM ..,. (1244)

Using Hand Held Technology to Address Math Anxiety in the Developmental Mathematics Classroom.

(1 249)

Byunghan Kim, Massachusetts Institute of Technology

Peg Greene, Florida Community College .at Jacksonville (993-Z4-73) 3:30PM ... (1245)

Intermediate Algebra for the Visual Learner: Using a Graphing Calculator to "See" Characteristics of Quadratic Functions. Katherine R Struve, Columbus State Community College (993-Z4-476)

4 :00PM (1 246)

4 :30PM ..,. (124 7)

Using Handheld Software Applications (Apps) to Visualize Geometric Behaviors of Functions and their Relation to Real-World Data.

London Mathematical Society 3:30 PM - 5:00 PM

This session includes a Society meeting and an Invited Address by Gerard van der Geer.

Margo L. Mankus, Texas Instruments (993-Z4-325)

MAA Committee on Undergraduate Student Activities and Chapters Undergraduate Poster Session

Impact of hand-held technology on student learning and curriculum dynamics .

4:00 PM - 6:30 PM

Mercedes A McGowen, William Rainey Harper College (993-Z4-803) 5:00PM (1248)

Developmental Algebra with Function as an Underlying Theme. Edward D Laughbaum, The Ohio State University (993-Z4-48)

AMS Committee on Science Policy-AMS Committee on the Profession Panel Discussion

Organizer:

4:10PM-7:00PM

Organizers : Michael E. Gage, University of Rochester Arnold K. Pizer, University of Rochester Vicki Roth, University of Rochester Jeffrey J. Holt, University of Virginia John W. Jones, Arizona State University

A walk through the math pipeline from end to end. Moderator: Jane Hawkins, University of North Carolina at Chapel Hill Panelists: James Sethian, University of California Berkeley Olga R. Beaver, Williams College Jessica S. Sidman, Mount Holyoke College james Bonn, CNA Corporation Timothy W. Lant, Arizona State University Angela Herro, Arizona State University

MAA Minicourse # 14: Part 8

Mario U. Martelli, Claremont McKenna College

MAA Invited Paper Session on WeB WorK, a Web-Based Homework System, II

2:30 PM - 4:00 PM

4:1OPM ..,. (1250) 4:40PM (1251)

WeBWorK Effectiveness in Rutgers Calculus . Charles A Weibel '' and Lew Hirsch, Rutgers University (993-Z2-1 243)

Using WeBWorK at the Secondary School Level. Mark W Schmitt, Detroit Country Day School (993-Z2-l381)

5:1OPM ..,. (1252) 5:40PM ... (1253)

3:15PM-5:15PM

Responding to Webwork. Jeff Achter, Colorado State University (993-Z2-897)

WeB WorK Developments at Union College: New Problems, Answer Checkers and Graders for Multivariable Calculus. Davide P Cervone, Union College (993-Z2-121 0)

Introduction to mathematical card tricks. Organizers : Colm K. Mulcahy, Spelman College Jeffrey A. Ehme, Spelman College

158

The type-definable group configuration under the generalized type-amalgamation.

NOTICES OF THE

6:1OPM (1 2 54)

AMS

Running a Large WeBWorK Operation (Part I). William K Ziemer, California State University Long Beach (993-Z2-1 011)

VOLUME

51,

NUMBER

1

Phoenix, AZ, Saturday, january 10- Program of the Sessions

~

6:40PM (12 55)

Running a Large WeBWorK Operation (Part 2). Preliminary report. john W jones*, Arizona State University, and Jeffrey J Holt, University of Virginia (993-Z2-994)

MAA Panel Discussion 5:45 PM - 7:00 PM

Environmental mathematics. Organizer: Patricia Clark Kenschaft, Montclair State University Mohammed Moazzam, Salisbury State Panelists: University Barry Schiller, Rhode Island College William Stone, New Mexico Institute of Mining and Technology

AMS-MAA Government Speaker 4:20PM-5:10PM (1256)

Title to be announced. Michael S. Turner, National Science Foundation (993-00-1 741)

ASL Session for Contributed Papers, I

Mathematical Reviews Reception

4:30PM-5:15PM

6:00 PM - 7:00 PM

4:30PM (1257) 4:55PM (1258)

A substructure of the lattice of Pi~ classes. Rebecca Weber, University of Notre Dame Dynamical topological logic of Cantor space. Grigori Mints* and Ting Zhang, Stanford University

SIGMAA on the History of Mathematics Annual Meeting and Inaugural Annual Address 6:00 PM - 8:3Q PM

S/GMAA on Research on Undergraduate Mathematics Education

Organizer:

Amy Sheii-Gellasch, SIAM-Germany

MAA Authors' Reception 4:30 PM - 6:30 PM

Business meeting and invited address by Chris Rasmussen. Organizer: Anne E. Brown, Indiana University South Bend

6:00 PM - 7:30 PM

MAA Musical Presentation 7:00 PM - 8:30 PM

The mathematics of acoustic paradoxes. Presenter: Erich Neuwirth, University of Vienna

MAA Special Presentation 5:00 PM - 7:00 PM

Mathematics for business decisions. Organizers : Richard B. Thompson, University of Arizona Christopher Lamoureux, University of Arizona

MAA Project NExT Reception 8:30 PM - 1 0:30 PM

Saturday, January 10

MAA Business, Industry and Government Welcoming Reception

}oint Meetings Registration

5:00 PM - 6:00 PM

7:30 AM - 2:00 PM

AMS Session on Combinatorics, II

University of Michigan Reception

7:45 AM - 10:40 AM

5:00 PM - 7:00 PM

University of Illinois at Urbana-Champaign Department of Mathematics Reception 5:1 5 PM - 7:1 5 PM

~

7:45AM (1259)

~

8:00AM (1260)

~

8:1 SAM (1261)

~

8:30AM (1262)

~

8:45AM (1263)

~

9 :00AM (1264)

Probabilistic Analysis of the Random Dynamic Assignment Problem. Michael Z Spivey, Samford University (993-05-208) Guessing Secrets. Preliminary report. Eden Hochbaum*, Brown University, and Boris Bukh, University of California, Berkeley (993-05-1120)

NAM Reception, Banquet, and Cox-Talbot Address 5:30 PM - 9:00 PM

New Mexico State University Mathematics Association Reception 5:30 PM - 7:00 PM

University of Wisconsin-Madison Department of Mathematics Reception 5:30 PM - 7:00 PM

jANUARY

2004

NOTICES OF THE

AMS

A Multiplicity Problem Related to Schur Numbers. Daniel Schaal*, South Dakota State University, and Hunter Snevily, University of Idaho (993-05-1654) A Multiplicity Problem for a Linear Inequality. Wojciech Kosek*, Colorado College, Daniel Schaal, South Dakota State University, and Dusty Sabo, Southern Oregon University (993-05-1664) How many Squares are there, Mr. Franklin?: Constructing and Enumerating Franklin Squares. Maya Mohsin Ahmed, UC Davis (993-05-835) Three-Color Rado Numbers for an Inequality. Brenda J Johnson* and Daniel Schaal, South Dakota State University (993-05-944)

159

Program of the Sessions - Phoenix, AZ, Saturday, january 10 (cont'd.)

~

9:1 SAM (1265)

9:30AM 9:45AM ~ (1266)

Totally Magic Labelings of Graphs.

8:30AM (1277)

Bill Calhoun * , Kevin Ferland, Lisa Lister and John Pol hill, Bloomsburg University (993-05-1 349) Break

Roger M Nisbet*, UCSB, and Edward McCauley, University of Calgary (993-92-1 093)

On the Number of Binary Necklaces of Length n where O's and 7's are Interchangeable . Preliminary

9:00AM (1278)

report. William L Crowley, United States Military Academy, West Point (993-05-1672) 1 0:00AM (1267)

9 :30AM (1279)

~

(993-92-1 027)

Regular Difference Triangle Sets and Monotonic Directed Designs.

1 O:OOAM (1280)

Wensong Chu*, Charles J Colbourn, Arizona State University, and Solomon W Golomb, University of Southern California (993-05-1 094)

AMS Special Session on Nonassociative Algebra, I

Lih-lng Wu Roeger, Texas Tech University

~

1 0:30AM (1281)

9:00AM (1272)

9:30AM (1273) 1 0:00AM (1274)

Organizers: Murray R. Bremner, University of Saskatchewan Irvin R. Hentzel, Iowa State University Luiz A. Peresi, University of Sao Paulo Iterated loop algebras. Preliminary report. Bruce N. Allison, University of Alberta

(993-92-762)

AMS Special Session on Multiscale and Oscillatory Phenomena: Modeling, Numerical Techniques, and Applications, II 8:00 AM - 10:50 AM

Gradings on Simple Nonassociative Algebras.

Organizers: Richard Tsai, Princeton University Luminita A. Vese, University of California Los Angeles

Yuri Bahturin, Memorial University of Newfoundland (993-17-901)

Cohomology of Frobenius kernels.

8:00AM (1282)

Christopher P Bendel*, University of Wisconsin-Stout, Daniel K Nakano, University of Georgia, and Cornelius Pillen, University of South Alabama (993-20-977) Intermediate Wakimoto modules for Affine s[ (n + 1). Ben L Cox* , College of Charleston, and Vyacheslav Futorny, University of Sydney (993-1 7-11 33)

Stanley J Osher, Level Set Systems, Inc 9:00AM (1 283) 9:30AM (1284)

Preliminary report. John R. Faulkner, University of Virginia

1 O:OOAM (1285)

AMS Special Session on Competitive and Adaptative Dynamics in Ecology, II

1 0:30AM (1286)

Organizers: Carlos Castillo-Chavez, Los Alamos National Laboratory Yang Kuang, Arizona State University Bai-Lian Li, University of California Riverside Horst R. Thieme, Arizona State University

Analysis of a discontinous Galerkin and eddy viscosity method for Navier-Stokes.

AMS Special Session on Modern Function Theory, II 8:00AM- 10:50 AM

Organizers: Beth Schaubroeck, U. S. Air Force Academy Peter L. Duren, University of Michigan, Ann Arbor John A. Pfaltzgraff, University of North Carolina at Chapel Hill

Periodic coexistence of four species on three essential resources. Bingtuan Li*, University of Louisville, and Hal L Smith, Arizona State University (993-92-1 085)

160

Curvelets and Linear Hyperbolic Equations. Emmanuel J Candes and Laurent Demanet* , California Institute of Technology (993-35-1714)

S Kaya* and Beatrice Riviere, University of Pittsburgh (993-76-745)

8:00AM- 10:50 AM

8:00AM (1276)

ENO Wavelet-ELLAM Schemes for Linear Transport Equations with Piecewise Smooth Data. Preliminary report. Jiangguo Liu*, Bojan Popov, Texas A&M University, Hong Wang, University of South Carolina, and Richard E. Ewing, Texas A&M University (993-65-96)

An estimate of the number of parameters defining the varieties of n-dimesional alternative and jordan algebras. lryna Kashuba, University of Sao Paulo

Coupled Continuum and Atomistic Modeling of Solids. Xiantao Li, Princeton University (993-74-153)

Hopf duals, algebraic groups, and jordan pairs.

(993-17-1101)

Computing Multivalued Solutions to Hyperbolic Equations and Applications to Geometric Optics and Schrodinger Equations. (993-65-758)

(993-1 7-269) 1 0 :30AM (1275)

Investigating the Mechanisms of Androgen-Independent Relapse Associated with Human Prostate Cancer. Trachette Jackson, University of Michigan

(993-1 7-1188) 8:30AM (1271)

Discrete May-Leonard Competition Model-the Ricker Type. Preliminary report. (993-39-524)

8:00 AM - 1 0:50 AM

8:00AM (1270)

Interpretation of the May-Leonard Model of Three Species Competition as a Food Web in a Chemostat. Gail S.K. Wolkowicz, McMaster University

(993-05-249) 1 0:30AM (1269)

Competition and biological stoichiometry: linking rRNA:protein ratio in cells to species competition in food webs via N:P ratios. lrakli Loladze*, Simon A. Levin, Princeton University, Yang Kuang, James J. Elser, Arizona State University, Bo Deng, University of Nebraska, Lincoln, and William F. Fagan, University of Maryland, College Park (993-92-1 083)

Coloring metric spaces.

Jeong-Hyun Kang* and Zoltan Furedi , University of Illinois at Urbana-Champaign (993-05-1678) 1 0:1 SAM Hadamard's 0-7 determinant problem. Preliminary ~ (1268) report. Radoslav M. Dimitric, Texas A&M University

Effects of stoichiometry on growth and reproduction of individual organisms and on population dynamics. Preliminary report.

NOTICES OF THE

AMS

VOLUME

51,

NUMBER

1

Phoenix, AZ, Saturday, january 10- Program of the Sessions 8:00AM (1287)

8:30AM (1288)

9 :00AM (1 289)

9:30AM ,.. (1 290)

1O:OOAM (1291)

Holomorphic mappings of circular domains onto convex domains inn dimensional space. Preliminary

8:30AM (1 297)

report. Ted J Suffridge, University of Kentucky (993-32-630)

New symplectic 4-manifo/ds with b+=1. Preliminary report. Scott J Baldridge, Indiana University (993-53-620)

9 :00AM (1298)

On the geometric structures necessary for Nahm transform. Preliminary report.

Construction of convex mappings of p-bal/s in

c2 .

Preliminary report. Jerry R. Muir, Jr.* , Rose-Hulman Institute of Technology, and Ted J. Suffridge, University of Kentucky (993-32-955)

Regularity properties of Loewner chains in several variables. Jan Graham *, University of Toronto, Gabriela Kohr and Mirela Kohr, Babes-Bolyai University (993-32 -893) On Hyerbolical/y Convex Functions. Preliminary report. Roger W Barnard'' , Texas Tech University, GLenny Ornas, McNeese State University, Kent Pearce and G Brock Williams, Texas Tech University (993-30-656)

Maximizing A Class of Functiona/s over Hyperbolically Convex Functions. Gerard L Ornas* , Roger W Barnard and Kent Pearce, Texas Tech University (993-30-142)

1 0 :30AM (1292)

Marcos Jardim , University of Massachusetts at Amherst (993-53-228) 9:30AM Ca/abi-Yau Connections with Torsion on Toric (1299) Bundles. Yat Sun Poon * , UC Riverside, Gueo Grantcharov, Florida International University, and Dimitar Grantcharov, University of Alberta (993-53-1152) 1 0 :00AM Geometric Quantization of the Geodesic Flow of the (1 300) Compact Rank-One Symmetric Spaces. Preliminary report. Dimitar V Grantcharov, University of Alberta (993-51-1 068) 1 0:30AM Geometric Inequalities for Submanifo/ds in (1301) Sasakian Manifolds. Preliminary report . lon Mihai, Bucharest University (993-53-119)

AMS Special Session on Arithmetical Algebraic Geometry, II 8:00 AM - 10:50 AM

Convexity properties of the hyperbolic density.

Organizers : Kirti Joshi, University of Arizona Minhyong Kim , University of Arizona Adrian Vasiu, University of Arizona

Preliminary report. William Ma* , Pennsylvania College of Technology, and David Minda, University of Cincinnati (993-30-138)

8:00AM (1 302)

AMS Special Session on Smooth Dynamical Systems and Applications, II

8:30AM (1303)

8:00 AM - 10:40 AM

9 :00AM (1304)

Organizers: Qiu-dong Wang, University of Arizona Maciej P. Wojtkowski, University of Arizona 8:00AM (1 293)

Generic hydrodynamic instability via contact homology.

Diophantine approximation and self-conformal measures. Preliminary report. Mariusz Urbanski, University of North Texas (993-37-231)

1 0 :00AM (1295)

9 :30AM (1305)

Gaussian Hypergeometric Functions, and Traces of Heeke Operators.

On the p-order of the Shafarevich-Tate groups of elliptic curves via Kolyvagin 's method. Byungchul Cha, Johns Hopkins University (993-11-1286)

1 O:OOAM (1 306)

The number of extensions of a number field with fixed degree and bounded discriminant. Jordan S Ellenberg '', Princeton University, and Akshay Venkatesh, Massachusetts Institute of Technology (993-11-903)

Actions of lattices on /ow-dimensional manifolds. John Franks'' , Northwestern University, and Michael Handel, Lehman College CUNY (993-37-1177)

The Motivic DCA. Roy Joshua, Institute for Advanced Study/Ohio State University (993-14-873)

Sharon M Frechette*, College of the Holy Cross, Ken Ono, University of Wisconsin, Madison, and Matthew Papanikolas, Texas A&M University (993-11-141)

Robert Ghrist* , University of Illinois, Urbana-Champaign, and John Etnyre, University of Pennsylvania (993-3 7-1 528) 9:00AM (1294)

p-adic Periods of Modular Elliptic Curves. Shuzo Takahashi, University of Arizona (993-11-1 091)

1 0:30AM (1307)

The rank of the Morde/1-Weil groups of elliptic curves over large fields . Bo-Hae lm, Indiana University, Bloomington (993-11-814)

AMS Special Session on Geometric Structures on Manifolds, I

AMS Special Session on Value Distribution Theory in Classical and p-Adic Function Theory, I

8:00 AM - 10:50 AM

8:00 AM - 10:50 AM

Organizers: Tedi C. Draghici, Florida International University Gueo V. Grantcharov, Florida International University Philipe Rukimbura, Florida International University 8 :00AM (1296)

jANUARY

Time/ike minimal surfaces via loop groups.

Organizers: Alain Escassut, Universite Blaise Pascal llpo Laine, University of joensuu Chung-Chun Yang, Hong Kong University of Science and Technology 8:00AM (1308)

Magdalena D Toda* , Texas Tech University, and Junichi lnoguchi, Utsunomyia University, Japan (993-53-155)

2004

NOTICES OF THE

Interplay of coefficient behavior and solution behavior for complex differential equations in the unit disk, Preliminary report. Preliminary report . Linda R. Sons, Northern Illinois University (993-30-1369)

AMS

161

Program of the Sessions - Phoenix, AZ, Saturday, january 10 (cant'd.) 8:30AM (1 309)

9 :00AM (1 31 0)

Linear differential equations and logarithmic derivative estimates.

AMS Special Session on Low-Dimensional Topology, Ill

Igor Chyzhykov, Lviv National University, Gary G Gundersen*, University of New Orleans, and Janne Heittokangas, University of Joensuu (993-30-995)

8:00 AM - 10:50 AM

Organizer: 8 :00AM (1320) 8 :30AM (1321) 9:00AM (1322) 9:30AM (1323)

Growth estimates for analytic solutions of complex linear differential equations. Preliminary report. janne Heittokangas, University of Illinois at Urbana-Champaign, Risto Korhonen*, Loughborough University, and Jouni Rattya, University of joensuu (993-34-776)

9:30AM .- (1 311)

On solutions of linear differential equations with bounded Nevanlinna characteristic. Preliminary report. Janne Heittokangas*, University of Illinois at Urbana-Champaign, Risto Korhonen, Loughborough University, and Jouni Rattya, University of joensuu (993-30-590)

1 O:OOAM (1312)

1 0:30AM (1 31 3)

Random iteration of analytic maps. Tuen Wai Ng*, The University of Hong Kong, Alan F. Beardon, T. K. Carne, University of Cambridge, and David Minda, University of Cincinnati (993 -30-970)

Ultrametric Gelfand Transforms. Nicolas Mainetti, LLAIC - Universite d' Auvergne (993-13-1233)

1 0:00AM (1 324)

1 0:30AM (1325)

Patricia E Bauman*, Hala Jadallah and Daniel Phillips, Purdue University (993-35-1549) 8:30AM .. (1 31 5)

On Generalized and Viscosity Solutions of Nonlinear Elliptic Equations. David Hartenstine* and Klaus Schmitt, University of Utah (993-35-839)

9:00AM (1 31 6)

9:30AM (1 31 7)

Domain geometry and the Pohozaev Identity. JeffS McGough*, Gregg T Stubbendieck, South Dakota School of Mines and Technology, and Jeff Mortensen, University of Nevada Reno (993-35-634)

Solvability of parabolic variational inequalities in Banach spaces. Matthew Rudd, University of Texas at Austin

1O:OOAM

(1 31 8)

invariant of a hyperbolic 3-manifold. Spin Bordism Invariants of the Mapping Class Group.

8:00AM-9:55AM

8:1 SAM (1327)

If People Were Papers and Papers Were People. Preliminary report. Jerrold W. Grossman, Oakland University (993-01-639)

Undecidable Lattices of Finite Dimensional Steinitz Exchange Systems. Preliminary report. Lisa R Galminas*, Northwestern State University of LA, and John W Rosenthal, Ithaca College (993-03-1644)

8:30AM (1328)

Embedding modular lattices as principal filters in the lattice of Computably Enumerable Vector Spaces. Preliminary report. Rumen D Dimitrov, Western Illinois University (993-03-1674)

8:45AM .- (1 329) 9:00AM .- (1330)

Geometric Reasoning. Tevian Dray* and Corinne A. Manogue, Oregon State University (993-97-1 594)

The number sense of preservice elementary school teachers. Preliminary report. Yea-ling Tsao, Overseas Chinese Institute of Technology (993-97-280)

9:1 SAM .. (1 331)

Getting Students to Discuss Linear Algebra via Email. Matt lnsall, University of Missouri- Rolla (993-97-576)

9:30AM .. (1 332)

Mathematical Connections: For Example, "How To Teach Radicals In Less Than 5 Minutes" (Grades 6-7 6). Preliminary report. Juli D'Ann Ratheal, West Texas A & M University (993-97-1147)

9:45AM .. (1 333)

Teacher Reflection and Collaboration in the Form of Lesson Study: The Effects on Student Achievement in Mathematics. Diane Barrett* and Laurie Riggs, Cal Poly, Pomona

Young measure minimizers in nonlinear membrane theory.

(993-97-1 585)

Existence and Asymptotic Boundary Behavior of Blow-up Solutions to Weighted Quasilinear Equations. Preliminary report.

MAA Session on Teaching and Learning of Undergraduate Mathematics, II 8:00AM- 10:55 AM

Organizers : Anne E. Brown, Indiana University South Bend

Ahmed Mohammed, Ball State University (993-35-1211)

162

The Doubled-Delta Move on Ordered Links. Preliminary report . Carol Gwosdz Gee, Rice University (993-57-1180) The H 3 (PSL(2, C), Z) class and Chern-Simons

(993-35-1150)

Marian Bocea, Carnegie Mellon University (993-49-120) 10:30AM (1 31 9)

Concordance of boundary links. Jerome P Levine, Brandeis University (993-57-975)

AMS Session on History, Foundation and Mathematics Education

8:00AM - 10:50 AM

A Variational Approach to Solving the Time-Dependent Ginzburg-Landau Equations in Three Space Dimensions. Preliminary report.

New obstructions to doubly slicing knots. Taehee Kim, Rice University (993-57-1184)

Aaron Heap, Rice University (993-55-707)

AMS Special Session on Nonlinear Partial Differential Equations and Variational Problems, Ill

8:00AM (1 314)

Tim D Cochran, Rice University (993-57-1168)

Walter D Neumann, Barnard College, Columbia University (993-57-911)

8:00AM .. (1 326)

Organizers: David A. Hartenstine, University of Utah Ahmed Mohammed, Ball State University john M. Neuberger, Northern Arizona State University John W. Neuberger, University of North Texas

Tim D. Cochran, Rice University

Filtrations of Classical Knots.

NOTICES OF THE

AMS

VOLUME

51,

NUMBER

1

Phoenix, AZ, Saturday, january 10- Program of the Sessions Marilyn P. Carlson , Arizona State University Draga D. Vidakovic, Georgia State University 8:00AM ,... (1334)

8:20AM ,... (1335)

Mathematics Anxiety and Learned Helplessness. Preliminary report. Joseph Franke Kolacinski, University of Miami (993-R 1-498)

Strange Attractors and Chaos as a Theoretical Framework for Understanding the Dynamics of Student Attitudes toward Mathematics. Zaur Berkaliev, California State University (993-R1-347)

8:40AM ,... (1 336)

Improving student performance and sense-making in Liberal Arts Mathematics. Shandy Hauk'', Robert A. Powers, April D. Judd and Jenq-Jong Tsay, U. of Northern Colorado (993-R1-1399)

9:00AM ,... (1 3 3 7)

Using Web Based Technology to enhance College Algebra. Gary Hagerty, Black Hills State University (993-R 1-264)

9:20AM ,... (1338) 9:40AM (1339)

Wh en We Need The Sage On The Stage. Patricia L Hale, Cal Poly Pomona (993-R 1-195)

Student use of software to verify geometrical statements. Preliminary report. Jeff Connor'', Barbara Grover and Laura Moss, Ohio University (993-R 1-1 31 7)

1O:OOAM A Transformation of Pre-service Mathematics Teachers' Definitions of Mathematics.

,... (1340)

Carmen Marie Latterell, University of Minnesota Duluth (993-R 1-19) 10:20AM ,... (1 341)

Characteristics of Prospective Teachers' Posed Problems.

9:00AM ,... (1 34 7)

Bert Wachsmuth, Seton Hall University (993-S1-437) 9 :15AM Pulling Ropes and Plumbing Lines: Introducing ,... (1 348) Geometry with a Neolithic Tool Kit. Stephen J Luecking, DePaul University (993-S1-282) 9:30AM The Curved Cube. Preliminary report. ,... (1349) Roland Minton* , Roanoke College, and Gregory Minton, Salem High School (993-S1-302) 9:45AM Taylor Series: The Movie. ,... (1 3 50) Rachel W Hall, Saint Joseph's University (993-S 1-507) 1 0:00AM Using technology to illustrate level curves. ,... (1351) Jeffry L. Hirst* and Holly P. Hirst, Appalachian State University (993-S 1-42 7) 1 0:1 SAM Visual aids for volumes of revolution and 3D (1 3 52) functions in Calculus. Preliminary report. Tamara B Veenstra, University of Redlands (993 -S1 -363) 1 0:30AM Voronoi Diagrams and the Geometric Notion of ,... (1353) Proximity. Bruno Guerrieri, Florida A&M University (993-S1-345) 1 0:45AM Discovering Derivative Rules. (1354) Sharon Sue Emerson-Stonnell, Longwood University (993-S 1-545)

MAA Session on Focus on Integrating Graphic Handhe/ds into Collegiate Mathematics 8:00AM- 10:55 AM Organizers: Charles E. Hofmann, LaSalle University Joseph R. Fiedler, California State Univers ity, Bakersfield

Todd A. Grundmeier, California Polytechnic State University, San Luis (993-R1 -283) 1 0:40AM ,... (1 342)

Undergraduate Mathematical Knowledge for High School Teaching. Preliminary report. Bradford R Findell* and R Judith Reed , University of Georgia (993 -R1-1416)

8:00AM ,... (1355)

8:00AM - 10:55 AM Organizers : David R. Hill, Temple University Lila F. Roberts, Georgia Southern University 8:00AM ,... (1 34 3)

8:30AM ,... (1 345)

Our Favorite Level Curves and Linear Regression Demos. Agnes M. Rash* , Saint joseph' s University, and jean Marie McDill, California Polytechnic State U. (993 -S1 -401)

8:4 5AM ,... (1 346)

Using a POP quiz to Introduce Statistics to the Weary. Preliminary report.

8:45AM ,... (1358) 9:00AM ,... (1359)

2004

Integrating algebra-capable calculators into a number theory with cryptography course. David B Gove, California State University, Bakersfield (993 -V1 -765) Palm Pilot Mathematics & Programming. Preliminary report. Olga Yiparaki, IBM (993 -V1 -405)

Using a Tl-83 to Motivate Theorems and Reinforce Concepts in Precalculus Classes. james A. Nickerson, Gallaudet University (993 -V1 -3 78)

9: 1 SAM (1360)

Im pact of Graphing Calculator Use on Precalculus Students' Understanding of Polynomial, Rational, and Exponential Functions: Results and Re flections. Becky Krakowski, University of Dayton (993 -V1-41 9)

9:30AM ,... (1 36 1)

Discovering Derivatives of Familiar Functions Using a Graphing Calculator. Murray H. Siegel, Sam Houston State University (993 -V1 -29)

9:4 5AM ,... (1 362)

Jane M Wilburne, Shippensburg Univers ity (993-S1 -390)

jANUARY

New Ways of Assessment in CAS-oriented mathematical Education- New Experiences, First results. Otto Wurnig, Institute of Mathematics (993-V1 -36 2)

8:3 0AM ,... (1 357)

The Utility of Catenaries to Electric Utilities.

Sharon M. Barrs, James P. Braselton, Lorraine M. Braselton, Georgia Southern University, and Lila F. Roberts* , Georgia College & State University (993 -S1 -377) 8:15AM Seeing is believing: Visuals on Demand. Preliminary ,... (1 344) report. Jennifer A Bergner* , Salisbury University, and Donald Spickler, Salisbury Universtiy (993-S 1-388)

About the experiences how to integrate computers or CAS-calculators in Mathematical Education in Austria. Otto Wurnig, Institute of Mathematics (993-V1-364)

8:15AM ,... (1356)

MAA Session on My Favorite Demo: Innovative Strategies for Mathematics Instructors, II

Tablet PC and Mathematics: A Match Made in Heaven.

NOTICES OF THE

Enhancing University Students' Mathematical Understanding Through the Use of Handheld Data Collection Devices. Preliminary report. jorgen J Berglund , CSU, Chico (993-V1 -328)

AMS

163

Program of the Sessions - Phoenix, AZ, Saturday, january 10 (cant'd.) 1O:OOAM ,.. (1 363) 10:15AM ,.. (1364)

Modeling Heat Flow in a Thermos. Michael A. Karls * and James E. Scherschel, Ball State University (993-Vl-289)

Meaningful Contexts and Calculator Exploration Increase Students' Mathematical Understanding. James Sandefur, Georgetown University (993-Vl-537)

10:30AM ,.. (1 365)

8:00AM ,.. (1376)

Using Handheld Technology In The Classroom: Lessons From Novices. 8:30AM ,.. (1378)

Constructing Geometric Understandings for Prospective Elementary Teachers through Dynamic Visualization on the Tl 83+. Barbara Johnson Pence, San Jose State Univ (993-Vl-1 030)

8:45AM (1379)

8:20AM ,.. (1 368) 8:40AM ,.. (1 369)

The Pythagorean Theorem of Baseball. Michael A jones and linda A Tappin *, Montclair State University (993-Wl-796)

Run Production in Baseball: a Markov Chain Model. Thomas W. Polaski, Winthrop University (993-W1-332)

Whether You Win or Lose, It 's How the Overtime is Played: A Markov Chain Analysis of the National Football League's Overtime Rules. Michael A Jones, Montclair State University (993-Wl-372)

9:00AM ,.. (1 3 70)

Moral Hazard on the Mound: the Economics of Plunking. Doug Drinen, University of the South (993-Wl-947)

9:20AM ,.. (13 71)

9:40AM ,.. (1 3 72) 1O:OOAM ,.. (1373)

May the Best Team Win: The Mathematics of Scoring a Cross-Country Running Race.

9:1 SAM (1381)

Paul Kochanowski * and Morteza Shafii-Mousavi, Indiana University South Bend (993-Zl-202) Safety Deposit: what it really costs us. Preliminary report. Youngna Choi *, Montclair State University, and Yeomin Yoon, Seton Hall University (993-Z1-41 5)

9:30AM Temperature Models for Two Room Systems. ,.. (1 382) J K Denny* and C A Yackel, Mercer University (993-Z1-239) 9:45AM Will the Real Most Valuable Player Please Stand Up? ,.. (1 383) Preliminary report. Joseph Evan* and Daniel J. Ghezzi, King's College (993-Z1-1143) 1O:OOAM Teaching Combinatorics Using Guided Discovery. (1 384) Mark A Miller, Marietta College (993-Z1-984) 10:1 SAM Computer Science Majors Coding Graph Algorithms ,.. (1385) and Simulating Automata. Edward Aboufadel, Grand Valley State University (993-Z1-1 94) 10:30AM On general convergence and polynomiography in ,.. (1 386) computing roots of unity. Vi Jin* , Rutgers University, and Bahman Kalantari, Rutgers University (993-Z1-11 56)

Stephen Szydlik, University of Wisconsin Oshkosh (993-Wl-201)

A WM Workshop

The Tournament-Ranking Family of Four.

8:20 AM - 5:00 PM

Charles Redmond, Mercyhurst College (993-Wl-838)

This session consists of several parts listed separately throughout this program. All meeting participants are invited to attend all presentations.

Sabermetrics: Giving College Credit for Studying Baseball. Michael R Huber* and Gabriel Costa, United States Military Academy (993-Wl-190)

10:20AM ,.. (1374) 10:40AM ,.. (1 3 75)

Catenary or Parabola? Curtis J. Feist, Southern Oregon University (993-Zl-1 346)

A Demonstration of Teaching and Applying Baye's Formula.

8:00AM- 10:55 AM

8:00AM ,.. (1367)

Leg-slope generation of Pythagorean triples. Preliminary report. Daniel Drucker*, Wayne State University, and Fat C Lam, Gallaudet University (993-Zl-1 013) Partitions and Groups. Preliminary report. Michael J. Grady, Southern Utah University (993-Zl-97)

9:00AM ,.. (1 380)

MAA Session on Mathematics and Sports, I

Organizers : Sean L. Forman, Saint Joseph's University Douglas Drinen, University of the South

Counting Handshakes to Sums of Powers of Integers. Thomas J Pfaff, Ithaca College (993-Zl-237)

8:1 SAM ,.. (1377)

Gregory N Hartman*, University of Arizona, and Russel 0 Carlson, University of Arizona (993-Vl-486) 10:45AM (1 366)

Shawnee L. McMurran, California State University at San Bernardino

Organizers: Catherine A. Roberts, The College of the Holy Cross Jodie D. Novak, University of Northern Colorado

The New Football Coach's Dilemma: Overtime. Vince Schielack, Texas A&M University (993-Wl-504)

"Real" Data Comparisons, Game Theory, and Operations Research in the Game of Baseball. Robert V Stack and Monty G Fickel *, Chadron State College (993-Wl-111 7)

AMS-MAA Special Session on History of Mathematics, Ill 8:30 AM - 10:50 AM

MAA General Contributed Paper Session, VI

Organizers: joseph W. Dauben, Lehman College . (CUNY)

8:00 AM - 10:40 AM Organizers : Laura J. Wallace, California State University, San Bernardino Jacqueline A. Jensen, Sam Houston State University Gary W. Towsley, SUNY at Geneseo Michael A. Jones, Montclair State University

164

David E. Zitarelli, Temple University 8:30AM (1387)

Thomas Harriot's Treatise on Figurate Numbers and Finite Differences. Preliminary report. Janet L. Beery, University of Redlands (993-01-1 078)

9:00AM ,.. (1 388)

NOTICES OF 1HE

AMS

Humanizing mathematical biographies. Preliminary report. John W Dawson, Penn State York (993-01-217) VOLUME

51,

NUMBER

1

Phoenix, AZ, Saturday, january 10- Program of the Sessions

~

9:30AM (1 389)

Mathematician as Artist: Marston Morse

David M. Strong, Pepperdine University

(7 892-1977). Preliminary report.

Joanne E. Snow* and Colleen M. Hoover, Saint Mary's College (993-01-288) 1 0:00AM .,.: (1390)

Learning some of the basics of historical research through the movies. Preliminary report. Alejandro R Garciadiego, UNAM , Mexico (993-01-647)

1 0:30AM ~ (1391)

MAA Panel Discussion 9:00 AM - 10:20 AM

Mathematicians and mathematics teacher educators working together to improve K-12 mathematics education.

Mathematics and Opera: The mathematical work of the opera singer jerome Hines. Preliminary report. T. Christine Stevens, Saint Louis University (993-01-675)

Organizer: Panelists :

A WM Workshop: Presentations by Recent Women Ph.D.s and Graduate Students, I 8:30 AM - 10:20 AM 8:30AM (1 392) 9:00AM (1393) 9:30AM (1394)

1O:OOAM (1395)

Finite-to-One Mappings on f3N - N. Katherine J. Mawhinney, Appalachian State University Real and Topological Stable Rank.

MAA Panel Discussion

Marian K. Hukle, University of Kansas

Measurably dominating randomness: some measurable similarities between set theory and recursion theory regarding dominating functions .

9:00 AM - 10:20 AM

Natasha Dobrinen * and Stephen G. Simpson, The Pennsylvania State University

Doctorates in mathematics education: Where do they go? What do they do? How can mathematics departments contribute?

Inequalities for geometric lattice invariants.

Organizer:

Kathryn Nyman, Texas A&M University

Panelists :

AMS Committee on Education Panel Discussion 8:30 AM - 10:00 AM

The evaluation of state mathematics standards: How can mathematicians contribute? Moderator: Roger E. Howe, Yale University Panelists: Johnny W. Lott, NCTM and University of Montana Laura McGiffert, Achieve, Inc. R. James Milgram, Stanford University

9:00 AM - 10:20 AM

Nonpermanent instructors: implications and issues. Organizers : Teri J. Murphy, University of Oklahoma Natasha M. Speer, Michigan State University

9:00AM - 9:50 AM

When topology meets chemistry. Erica L. Flapan, Pomona College (993-A0-1 5)

NAM Panel Discussion 9:00 AM - 10:00 AM

ASL Invited Address 9:00AM-9:50AM (1397)

Robert E. Reys, University of Missouri-Columbia Douglas B. Aichele, Oklahoma State University Rick Billstein, University of Montana Ira J. Papick, University of Missouri

AMS-MAA Committee on Teaching Assistants and Part-Time Instructors Panel Discussion

MAA Invited Address

(1396)

jodie D. Novak, University of Northern Colorado jack Price, National Council of Teachers of Mathematics judith E. jacobs, NCTM and AMTE Randall J, Swift, Calfornia State Polytech University Pomona Jodie D. Novak, University of Northern Colorado

Exhibits and Book Sales

Computable classification.

9:00 AM -

Julia Knight, University of Notre Dame

NOON

MAA Minicourse # 15: Part 8

Mathematical Art Exhibit

9:00 AM - 1 1:00 AM

9:00 AM -

Fair enough? Mathematics of equity.

NOON

Organizers : Robert Fathauer, Tessellations Company, Phoenix, Arizona Nat Friedman, ISAMA, SUNY at Albany Reza Sarhangi, Bridges Conference, Towson University

Organizers: John C. Maceli, Ithaca College Stanley E. Seltzer, Ithaca College

MAA Minicourse #4: Part 8 9:00 AM - 11 :00 AM

Employment Center

java applets in teaching mathematics. Organizers : Joe Yanik, Emporia State University

jANUARY

2004

9:00 AM -

NOTICES OF THE

AMS

NOON

165

Program of the Sessions

Phoenix, AZ, Saturday, january 10 (cant' d.)

Math on the Web

MAA Business Meeting

9:30 AM - 11 :00 AM

11 : 10 AM - 11 :40 AM

Go to the Math on the Web Pavilion for the complete schedule of presentations.

AMS Business Meeting 11:45 AM- 12:15 PM

ASL Invited Address NAM Claytor-Woodard Lecture

10:00 AM- 10:50 AM (1 398)

1:00PM-1:50PM

Supercompactness measures. Steve jackson, University of North Texas

ASL Invited Address

NAM Business Meeting

1:00PM-1:50PM (141 2)

10:00 AM- 10:50 AM

Torsion-free groups in some a-minimal structures. Kobi Peterzil, Haifa, Israel

MAA Retiring Presidential Address

AMS-MAA Special Session on Mathematical Techniques in Musical Analysis, Ill

10:05 AM- 10:50 AM (1 399)

1:00 PM - 5:50 PM

Fallacies in elementary statistics. Ann E. Watkins, California State University, Northridge (993·A0·1 3)

Organizers : Judith l. Baxter, University of Illinois at Chicago Robert W. Peck, Louisiana State University

A WM Workshop: Poster Session by Women Graduate Students

1:00PM (1413)

10:30 AM- 11:00 AM 10 :30AM (1400)

David L. Clampitt, Yale University (993-11-11 78) 1:30PM (i 414)

On the Complexity of the Endomorphism Problem for Free Groups. Laura Ciobanu, Rutgers University

10:30AM (1401) 10:30AM (1402) 10:30AM (1403)

2:00PM (141 5)

Lie 2·algebras. Alissa S. Crans, University of California, Riverside

Characterizing Multivariab/e Low-Pass Filters. Eva Curry, Rutgers University

Singularities in Conformal Geometry: from POE to Topology.

~

Convergence of a Spacetime Discontinuous Galerkin Method to a weak solution of Temple Systems.

~

Radial parts of invariant differential operators on Grassmann manifolds.

3:00PM (1417)

~

3:30PM (1418)

r-matrices on Lie Supera/gebras. Gizem Karaali, University of California, Berkeley

Density of Closed Geodesics in Compact Nilmanifolds Defined by Compact Semisimple g -modules. .

~

Alternating Quadrisecants of Knots.

10 :30AM (1409)

Application of the Generalized Singular Value Decomposition to Face Recognition.

Elizabeth Denne, University of Illinois at Urbana-Champaign

~

Generalized Foulkes' Conjecture and Tableaux Construction. Rebecca Vessenes, California Institute of Technology

10:30AM (1411)

5:00PM (1421)

5:30PM

A Topological Model of Motivic Analysis of Music: Theory and Implementation. A geometric model of continuous musical spaces. Clifton D Callender, Florida State University (993-51-1212)

Knots, Braids and Chord Diagrams, As New Musical Structures. Coincident histories or historical coincidence? Concurrent developments in nineteenth-century group theory and music theory. Nora A Engebretsen, Bowling Green State University (993-01-1646) Discussion.

AMS-MAA Special Session on History of Mathematics, IV 1:00 PM - 3:50 PM

A Blowing Up Algorithm for Calculating Rings of Integers.

Organizers : Joseph W. Dauben, Lehman College (CUNY) David E. Zitarelli, Temple University

Sarah Hutcheson Jahn, University of Illinois at Chicago

166

Aspects of Saturation and Ordering in Twelve-Tone Music. Preliminary report.

Franck j . Jedrzejewski , Atomic Energy Commission (CEA-INSTN) (993-54-31 5)

Peg Howland, University of Minnesota, Department of Computer Science and Engineering 1 0:30AM (1410)

4 :00PM (1419) 4 :30PM (1420)

Rachelle DeCoste, University of North Carolma, Chapel Hill 10 :30AM (1408)

The Role of Mathematics in the Construction of Musical Scales. Preliminary report.

Chantal Buteau, Swiss Federal Institute of Technology Zurich (993-54-1237)

Olga Kurgalina, Tufts University 10 :30AM (1406) 10:30AM (1407)

Winding modes around the circle of fifths. Vittorio Cafagna* and Domenico Vicinanza, DMI University of Salerno (993-05-935)

Ciro G Scotto'' and Robert D Morris, Eastman School of Music (993-20-1663)

Katarina Jegdic, University of Illinois at Urbana-Champaign 10 :30AM (1405)

2:30PM (1416)

Well-formed Scales and the Stern Brocot Tree. Norman A Carey, Eastman School of Music (993-11-1 046)

Richard J Krantz, Metropolitan State College of Denver (993-00-737)

Maria del Mar Gonzalez, Princeton University 10:30AM (1404)

Cardinality Equals Variety for Chords, with a Note on the Twin Primes Conjecture.

NOTICES OF THE

AMS

VOLUME

51,

NUMBER

1

Phoenix, AZ, Saturday, january 70- Program of the Sessions 1 :OOPM .- (1422)

Contributions of Ferdinand Hassler to Early American Science. Preliminary report.

AMS Special Session on Competitive and Adaptative Dynamics in Ecology, Ill

V. Frederick Rickey, West Point (993-01-1 007) 1:30PM .- (1423)

Edward V. Huntington and the Apportionment Debate of 1920-1940. Preliminary report.

1:00 PM- 5:50 PM

Thomas L. Bartlow, Villanova University (993-01-329)

Organizers: Carlos Castilla-Chavez, Los Alamos National Laboratory

The Texas-Polish Connection in Topology: Competition and Cooperation.

Yang Kuang, Arizona State University

Albert C. Lewis, Indiana Univ. - Purdue Univ. Indianapolis (993-01-356)

Bai-Lian Li, University of California Riverside

2:30PM .- (1425)

From Vienna to New York: Abraham Wald's Converging Communities.

Horst R. Thieme, Arizona State University

3:OOPM .- (1426)

A (very) brief history of the problem of resolution of singularities of algebraic surfaces. Preliminary

2:00PM .- (1424)

Patti W. Hunter, Westmont College (993-01-713) 1 :OOPM (1438)

Sergei V. Petrovskii*, Shirshov Institute of Oceanology, Bai-Lian Li, Department of Botany and Plant Sciences, and Horst Malchow, Institute of Environmental Systems Research (993-92-969)

report. Chris Christensen, Northern Kentucky University (993-01-1 02) 3:30PM .- (1427)

Algebraic topology chez Bourbaki. Preliminary report. John McCleary, Vassar College (993-01-664)

1:30PM .- (1439)

1:00PM- 5:50PM

1:OOPM (1428) 1:30PM (1429)

2 :00PM .- (1440)

Relatively free coa/gebras. Mikhail V. Kochetov, Carleton University (993-1 7-1 390)

Matrices over octonions and orbits of exceptional groups.

2:30PM (1441)

2 :30PM (1431)

Representations of rank 3 algebras. Georgia Ben kart, University of Wisconsin, and Alicia Labra*, Universidad de Chile (993-1 7-45 5)

One-sided Modules and unital bimodules over jordan supera/gebras. Consuela Martinez, Universidad de Oviedo, Spain (993-1 7-802)

3:00PM (1432) 3:30PM (1433)

3:00PM (1442)

4:00PM (1444)

4:30PM (1435) 5:00PM (1436) 5:30PM (143 7)

jANUARY

4 :30PM (1445)

Octonions and Exceptional Superalgebras.

The Dynamics of Two Viral Infections in a Single Host Population with Applications to Hantavirus.

Competition of pathogen strains against the background of host immune response. A. Pugliese, University of Trento (993-92-1 246)

Imbedding of Lie Triple Systems into Lie Algebras. Preliminary report. Oleg Smirnov, College of Charleston (993-17-1375)

5:OOPM (1446)

John H Conway, Princeton University, and Derek A Smith*, Lafayette College (993-1 7-1614)

Dynamics of the Nonautonomous Beddington -DeAngelis Predator-Prey System. Meng Fan*, Northeast Normal University, and Yang Kuang, Arizona State University (993-34-1 090)

Octonion Multiplication Theorems. 5:30PM (1447)

An Age-structured Epidemic Model in a Patchy Environment. Preliminary report. Wendi Wang, Southwest Normal University, and Xiaoqiang Zhao*, Memorial University of Newfoundland (993-34-761)

Structurable tori. Yoji Yoshii, University of Saskatchewan (993-1 7-961)

2004

Climate and competition: the effect of moving range boundaries on habitat invasibility.

Linda J. S. Allen*, Texas Tech University, Michel Langlais, University de Bordeaux, and Carleton J. Phillips, Texas Tech University (993-92-555)

Reciprocity between some bi-linear and tri-lininear algebras. Michel L. Racine, University of Ottawa (993-17-1323)

On the impossibility of coexistence of infinitely many strategies.

A. B. Potapov* and M.A. Lewis, University of Alberta (993-92-698)

S. Okubo, University of Rochester (993-17-628) 4:00PM (1434)

Coexistence in a metapopulation model with explicit local competition dynamics. Preliminary report.

Mats Gyllenberg, University of Turku (993-92-727) 3:30PM (1443)

Identities in jordan Algebras. Kevin M McCrimmon, University of Virginia (993-17-525)

Localized interactions and biological diversity. Preliminary report. Frederick RAdler*, University of Utah, and Helene C Muller-Landau, NCEAS (993-92-822)

Zhilan Feng* , Rob Swihart, Purdue University, Yingfei Yi, Georgia Institute of Technology, and Huaiping Zhu, York University (993-34-610)

Sergei Krutelevich, University of Ottawa (993-1 7-966) 2 :00PM (1430)

Modeling agricultural ecosystem dynamics under Bt resistant pest invasion. Alexander B Medvinsky*, Institute for Theoretical & Experimental Biophysics, Russian Academy of Sciences, Andrew Y Morozov, Department of Botany & Plant Sciences, University of California, Vassili V Velkov, Institute of Biochemistry & Physiology of Microorganisms, Russian Academy of Sciences, Bai-Lian Li, Department of Botany & Plant Sciences, University of California, Mikhail S Sokolov, Research Center for Toxicology and Hygienic Regulation of Biopreparations, and Horst Malchow, Institute of Environmental Systems Research, University of Osnabrueck (993-92-907)

AMS Special Session on Nonassociative Algebra, II

Organizers: Murray R. Bremner, University of Saskatchewan Irvin R. Hentzel, Iowa State University Luiz A. Peresi, University of Sao Paulo

Exactly Solvable Models of Nonlinear Population Dynamics Related to Biological Invasions .

NOTICES OF THE

AMS

167

Program of the Sessions - Phoenix, AZ, Saturday, january 10 (cant' d.) AMS Special Session on Multiscale and Oscillatory Phenomena: Modeling, Numerical Techniques, and Applications, /II

2:30PM (1458)

Albert Baernstein II * , Washington University, Daniel Girela and jose Angel pelaez, Universidad de Malaga (993-30-1332)

1:00 PM - 5:50 PM 3:00PM (1459)

Organizers: Richard Tsai , Princeton University Luminita A. Vese, University of California Los Angeles 1:OOPM (1448)

2:00PM (1449)

3:30PM (1460)

Eitan Tadmor'' , University of Maryland, Suzanne Nezzar and Luminita Vese, University of California Los Angeles (993 -41-719)

4:00PM (1461)

Functional minimization models for image decomposition and texture modeling. Preliminary 4 :30PM (1 462)

Wavelet based schemes for image decomposition by variational functiona/s .

Univalent harmonic mappings and extrema/length. Preliminary report. Allen Weitsman, Purdue University (993-30-957)

Harmonic Maps onto Star Shaped Domains. Preliminary report. Jane McDougall * , Colorado College, Peter Duren, University of Michigan, and Beth Schaubroeck, U. S. Air Force Academy (993-30-165 7)

Symmetries of extremal functions for inequalities in univalent function theory. Eric D Schippers , University of Michigan, Ann Arbor (993-30-1 04)

Ingrid Daubechies, Princeton University, and Gerd Teschke'' , University of Bremen (993 -49-1 524) 3 :00PM (1451)

Landau's Theorem for Planar Harmonic Mappings. Michael Dorff'' , Brigham Young University, and Maria Nowak, Maria Curie-Sklodowska University (993-30-705)

A multiscale image representation using hierarchical (BV, L 2 ) decompositions.

report. Luminita A. Vese, UCLA (993-49-888) 2:30PM (1450)

Hardy spaces, spaces of Dirichlet type, and univalent functions.

5:00PM (1463)

Image Decomposition Via the Combination of Sparse Representations and a Variational Approach. Preliminary report.

Geometric and subordination properties of solutions of a differential equation: A preliminary report. Preliminary report. Stacey A Mueller, University of Kentucky

(993-30-523) 5:30PM Duals and Envelopes of Some Hardy-Lorentz spaces. (1464) Marc R Lengfield, Florida State University (993-46-770)

j.-L. Starck, CEA-Saclay, DAPNIA/SEDI-SAP, Service d'Astrophysiq, M. Elad * , Computer Science Department, Technion Israel lnsti, and D. Donoho, Department of Statistics, Stanford University (993-49-1231) 3:30PM (1452)

Solving a variational image restoration model which involves L co constraints. Preliminary report. Stephane Lintne r , Caltech, and Francois Malgouyres'', Universite Paris 13 (993-49-774)

4:00PM (1453)

Restoration of wavelet coefficients by minimizing a specially designed objective function. Preliminary

AMS Special Session on Smooth Dynamical Systems and Applications, /II 1:00 PM - 4:50 PM

Organ izers: Qiu-dong Wang, University of Arizona Maciej P. Wojtkowski, University of Arizona

report . Sylvain Durand and Mila Nikolova*, CMLA (CNRS-UMR 8536) (993-49-91 0) 4:30PM (1454)

Adaptive multivariate approximation: Comparing Wavelets and piecewise polynomials.

~

Jorge L. Rebaza, Southwest Missouri State Universisty (993-65-823)

Shai Dekel * , ReaiTimelmage, and Dany Leviatan, Tel -Aviv University (993-41 -731) 5:00PM (1455) 5:30PM

1:OOPM Application of Smooth Schur Factorizations in the (1465) . Continuation of Separatrices. Preliminary report.

Efficient algorithms for multisca/e data processing.

1:30PM (1466)

The Brin quadrilateral argument for skew products over basic sets. Preliminary report.

2:00PM (1467)

Keith Burns'', Northwestern University, and Matthew Nicol, University of Surrey (993-3 7-1 339) Strange Adding Machines. Prel iminary report. Louis Block, james Keesling, University of Florida, and Michal Misiurewicz* , Indiana UniversityPurdue University Indianapolis (993-3 7-687)

Anna C Gilbert, AT&T Labs-Research (993-68-158) Discussion.

AMS Special Session on Modern Function Theory, /II

2:30PM (1468)

1:00PM- 5:50PM

1:OOPM

Alexei V. Penskoi, Centre de Recherches Mathematiques, Universite de (993-3 7-771)

Organizers : Beth Schaubroeck, U. S. Air Force Academy Peter L. Duren , University of Michigan, Ann Arbor John A. Pfaltzgraff, University of North Carolina at Chapel Hill

~

Schwarz-Christoffel maps to surfaces in space.

~

3:00PM (1 469)

Ruben Flores Espinoza, Universidad de Sonora

R Collins and Ken Stephenson, University of Tennessee (993-30-1174)

Convergence of the Zipper Algorithm for Conformal Mapping. Preliminary report. Donald E. Marshall *, University of Washington, and Steffen Rohde, University of Washington

3:30PM (1470)

4 :00PM (1471) 4 :30PM (1472)

From local to global ergodicity: An algebraic approach. Nandor Simanyi, The University of Alabama at Birmingham (993-37-485) Billiards with slow mixing rates. Preliminary report. Nikolai I Chernov, University of Alabama at Birmingham (993-37-535)

Strange Attractors in Periodically-kicked Limit cycles and Hopf Bifurcations. Qiudong Wang, University of Ar izona (993-37-960)

(993-30-1515)

168

The zero curvature equation and the reducibility problem for fiberwise linear dynamical systems. (993-34-11 71)

(1456) Tobin A Driscoll*, University of Delaware, Charles 2:00PM (1457)

Double bracket equations, Volterra system and topology of the manifold of zero-diagonal jacobi matrices with fixed spectrum.

NOTICES OF THE

AMS

VOLUME 51, NUMBER 1

Phoenix, AZ, Saturday, january 70- Program of the Sessions AMS Special Session on Geometric Structures on Manifolds, II

3:00PM (1485)

Explicit local fundamental classes and Riemann-Roch via formal power series. Preliminary report. Henri A Gillet, University of Illinois at Chicago

1:00 PM - 5:50 PM

(993-14-1391)

Organizers: Tedi C. Draghici, Florida International University Gueo V. Grantcharov, Florida International University

3:30PM (1486)

Fabrice Orgogozo, Princeton University (993-14-1261)

Philipe Rukimbura, Florida International University 1:OOPM (1473)

4:00PM (1487)

2:00PM (1475)

Mahler measure and Coxeter links. Eriko Hironaka, Florida State University (993-11-509)

The Yamabe problem for almost Hermitian manifolds.

4 :30PM (1488)

Heberto del Rio*, CIMAT, and Santiago R. Simanca, IMS Stony Brook (993-58-1357) 1:30PM (14 74)

Bloch's conductor formula and Milnor numbers of isolated singularities.

Hilbert's Tenth Problem for function fields of surfaces over C. Kirsten Eisentraeger, Institute for Advanced Study (993-11-1 069)

Isotropic Kahler Hyperbolic Twistor Spaces. Preliminary report. D. E. Blair*, Michigan State University, J. T. Davidov and 0. K. Muskarov, Bulgarian Academy of Sciences (993-53-167) Contact manifolds and Dirac structures. Preliminary report. Aissa Wade, Penn State University, University Park

5:00PM (1489)

Real aspects of the Kontsevich 's moduli space of stable maps of genus zero curves. Seongchun Kwon, MSRI (993-14-51)

5:30PM (1490)

Shimura's conjecture over function fields . W. Dale Brownawell, Penn State University, and Matthew A. Papanikolas*, Texas A&M University (993-11-1016)

(993-53-592) 2:30PM (1476)

Examples of non d w -exact locally conformal symplectic forms. Augustin Banyaga, The Pennsylvania State University, University Park PA 16802 (993-53-242)

3 :00PM (1477) 3 :30PM (1478)

The Einstein equations and G-structures.

AMS Special Session on Value Distribution Theory in Classical and p-Adic Function Theory, II 1:00 PM - 5:50 PM

Richard Cleyton, UC Riverside (993 -5 3-1 639) Organizers: Alain Escassut, Universite Blaise Pascal llpo Laine, University of joensuu Chung-Chun Yang, Hong Kong University of Science and Technology

Einstein Metrics on Spheres. Charles P Boyer'' , Krzysztof Galicki, University of New Mexico, and Janos Kollar, Princeton University (993-5 3-1 044)

4:00PM (1479) 4:30PM (1480)

Low-Dimensional Homogeneous Einstein Manifolds. Christoph Boehm, Universitaet Kiel, and Megan M Kerr* , Wellesley College (993-53-1254)

1:30PM (1492)

(993-53-968)

(993 -11-1 086) 2 :00PM (1493)

Vestsilav D Apostolov, Universite du Quebec Montreal (993-5 3-1 3 77)

Logarithmic forms and rigid analytic Picard theorems. William Cherry'', University of North Texas, and Min Ru, University of Houston (993-32-573)

(993-53-678)

Kahler reduction of metrics with holonomy G 2 .

Non-archimedean analogues of the Ahlfors Islands Theorem: holomorphic and meromorphic cases. Robert L. Benedetto, Amherst College

On the classification of weakly Bochner flat Kahler metrics on compact six-manifolds. Preliminary report. Christina Wiis Tonnesen-Friedman, Union College

5 :30PM (1482)

The Functional Equation P(j) = Q(g) in a p-adic field. Alain P. Escassut* , Universite Blaise Pascal, France , and Chung C Yang, University of Science and Technology of Hong Kong (993-11-1236)

Classification of conformally-Einstein Kahler metrics. Gideon Maschler'' , University of Toronto, and Andrzej Derdzinski, Ohio State University

5:OOPM (1481)

1:OOPM (1 491)

a

2 :30PM (1494)

Entire solutions of certain partial differential equations. Bao Qin Li, Florida International University (993-32-807)

AMS Special Session on Arithmetical Algebraic Geometry, Ill

3 :00PM (1495)

Hardy spaces on Hopf manifolds. Preliminary report. John Ryan '', University of Arkansas, and R. S. Krausshar, Ghent University, belgium (993-58-1124)

1:00 PM - 5:50 PM

Organizers : Kirti Joshi , University of Arizona Minhyong Kim, University of Arizona Adrian Vasiu, University of Arizona 1 :OOPM (1483) 2:00PM (1484)

New perspectives in Arakelov geometry. Caterina Consani *, University of Toronto, and Matilde Marcolli, MPI-Bonn (Germany) (993-14-992)

Around Morde/1-Lang and Manin-Mumford.

3:30PM (1496)

Kwang C Shin, University of Missouri-Columbia (993-34-908) 4:00PM (1497)

cos rrp type theorems for meromorphic functions . John Rossi *, Virginia Tech, and PC Fenton, University of Otago (993-30-547)

4:30PM (1498)

A note on frequency of the zeros of solutions to linear differential equations with polynomial coefficients. Preliminary report.

Preliminary report. A Pillay, University of Illinois at Urbana-Champaign

Enid M Stein bart, Georgia Institute of Technology (993-34-1294)

(993-11-85 7)

jANUARY

2004

On Spectral Theory for Non-Self-Adjoint Periodic Schrddinger Operators.

NOTICES OF THE

AMS

169

Program of the Sessions - Phoenix, AZ, Saturday, January 10 (cont'd.) 5:OOPM (1 499)

On the location of the zeros of Bessel functions and complex oscillation theory.

1:30PM (1 51 2)

Yik Man Chiang, Hong Kong University of Science & Technology (993-30-1039) ~

5:30PM (1 500)

Jozef H. Przytycki*, George Washington University, Marta M. Asaeda, University of Iowa, and Adam S. Sikora, 5.U.N .Y. Buffalo and lAS (993-57-895)

Growth of Pain/eve transcendents. Aimo Hinkkanen, University of Illinois at Urbana-Champaign, and llpo Laine*, University of Joensuu, Finland (993-30-1228)

Benjamin Himpel, Indiana University, Bloomington (993-58-1199) 2:30PM (1514)

1:00 PM - 5:50 PM 3:00PM (1515)

Organizers: David A. Hartenstine, University of Utah Ahmed Mohammed, Ball State University John M. Neuberger, Northern Arizona State University John W. Neuberger, University of North Texas

3:30PM (1516)

4 :00PM (1 51 7)

Necksizes of singular Yamabe metrics on punctured spheres. Preliminary report.

2:30PM (1504)

3:00PM (1505)

~

3:30PM (1506)

4 :00PM (1507)

4:30PM (1 508)

5:00PM (1 51 9)

On indefinite Schrodinger equations.

The Links-Gould invariant from the Kontsevich integral. Energy minimization problems and other relations arising from electrodynamics on subdomains of s 3 . Preliminary report. R jason Parsley, University of Pennsylvania (993-54-148)

Hossein T Tehrani *, David Costa, UNLV, and Miguel Ramos, University of Lisbon (993-35-1197)

Diffusion in Poro-Plastic Media. R. E. Showalter*, Oregon State University, and U. Stefanelli, lstituto di Matematica Applicata e Tecnologie lnformatiche- CNR (993-35-673) Bubble clusters. Preliminary report. Pablo Padilla* , University of Mexico, and H Clara Garza, IlMAS (993-35-683)

MAA Minicourse # 11: Part 8 1:00 PM - 3:00 PM

Developing your department's assessment plan.

Spreading of electrically charged microdrop/ets.

Organizers : William G. Marion, Valparaiso University Bonnie Gold, Monmouth University

Santiago I Betelu *, University of North Texas, and Marco Fontelos, Universidad Rey Juan Carlos (993-76-230)

A Variable Metric Descent Method for Curve and Surface Fairing. Robert J Renka, University of North Texas (993-65-661)

MAA Minicourse #16: Part 8

The Wey/ Problem With Nonnegative Gaussian Curvature.

1:00

PM -

3:00

PM

Getting students involved in undergraduate research.

A variational method for the inverse groundwater problem.

Organizers: Aparna W. Higgins, University of Dayton Joseph A. Gallian, University of Minnesota, Duluth

lan W. Knowles* and Aimin Van, University of Alabama at Birmingham (993-35 -1342) 5:30PM (1 51 0)

A classification of isometry groups of a Seifert fibered space N which is double covered by a lens space L. Preliminary report.

Nathan C Geer, University of Oregon (993-54-953)

Sobo/ev gradients: application to phase separation and shape memory materials.

Marcus A. Khuri , Stanford University (993-53-1523) 5:00PM (1 509)

Type one invariants for knotted graphs, and criteria for graph planarity. Preliminary report.

Ryo Ohashi, Saint Louis University (993-57-467) 4 :30PM (1 51 8)

Sultan Sial, London, Ontario (993-82-633) 2:00PM (1503)

Perturbative and Integral Structures of TQFT's. Preliminary report. Thomas Kerler, The Ohio State University (993-57-11 00) Knot Concordance. Preliminary report. Swatee Naik, University of Nevada, Reno and Indiana University (993-5 7-642)

Ted Stanford, New Mexico State University (993-57-1242)

Rob Kusner, U. Mass . Amherst, and jesse Ratzkin *, U. Utah (993-53-1155) 1:30PM (1 502)

A splitting formula for spectral flow on closed 3 -manifolds.

2:00PM (1 51 3)

AMS Special Session on Nonlinear Partial Differential Equations and Variational Problems, IV

1:OOPM (1501)

Khovanov homology of links in !-bundles over surfaces. Preliminary report.

Existence result for periodic solutions of a class of Hamiltonian systems with super quadratic potential. Leonard Karshima Shilgba, Yokohama National University, Japan (993-37-348)

MAA Minicourse #5: Part 8

AMS Special Session on Low-Dimensional Topology, IV

1:00 PM - 3:00 PM

1:00 PM - 5:20 PM 1:OOPM (1 511)

170

Visual linear algebra. Organizers: Eugene A. Herman, Grinnell College Michael D. Pepe, Seattle Central Community College Eric P. Schulz, Walla Walla Community College

Organizer: Tim D. Cochran, Rice University Knots and generalized Arf invariants. Preliminary report. Kent E Orr*, Indiana University, Bloomington, and Tim D Cochran , Rice University (993-57-1675)

NOTICES OF THE

AMS

VOLUME

51,

NUMBER

1

Phoenix, AZ, Saturday, january 70- Program of the Sessions AMS Session on Combinatorics, Ill ~

1 :40PM (1 532)

1:00 PM - 3:40 PM ~

~

1:OOPM (1520)

1:15PM (1521)

~

1:30PM (1522)

~

1:45PM (1 523) 2:00PM (1 524)

~

2:15PM (1525)

~

2:30PM 2:45PM (1 526)

~

3:00PM (1527)

~

3:15PM (1528)

~

3:30PM (1529)

Optimal Pebbling (Part 1). Preliminary report. Tracii Friedman* , Mesa State College, and Cynthia j. Wyels, California Lutheran University (993-05-1547) Optimal Pebbling (Part II). Preliminary report. Cynthia J Wyels * , California Lutheran University, and Tracii Friedman, Mesa State College (993-05-1552)

Frank Wattenberg, United States Military Academy (993-C1-192) ~

~

~

Delivering Internet-Based Homework in Mathematics Classes at Radford University with WeBWorK. Preliminary report.

3:00PM

Wisconsin's Networking Project for Improvement of Mathematics Education.

Zs. Szaniszlo* , Valparaiso University, and Zs. Tuza, Computer and Automation Institute, Hungarian Academy of Sciences (993-05-431)

.,. (l 5 36)

Ramsey Numbers of Stars Versus Wheels of Similar Sizes.

MAA Session on Mathematics and Sports, II

Aleksandra Korolova, MIT (993-05-1230) Break

Linda G. Thompson, Carroll College (993-Cl-265)

1:00 PM - 3:1 5 PM Organizers: Sean L. Forman, Saint joseph's University Douglas Drinen , University of the South

Coupon Collecting with Quotas. Russell J. May, Morehead State University (993-05-1183)

Topics in fractional domination of graphs. Robert R Rubalcaba* , Auburn University, Matthew P Walsh , Indiana-Purdue University, and Peter D Johnson, Auburn University (993-05-1616)

The Failure of Greedy-Type Algorithms. Preliminary report. Gareth L Bendall * , University of Kentucky, and Francois Margot, Carnegie Mellon University (993-05-5 30) The Renyi-Uiam pathological liar game. Preliminary report. Robert B. Ellis* , Texas A&M University, Vadim Ponomarenko, Trinity University, and Catherine H. Van, Texas A&M University (993-05-1 345)

~

A Comprehensive Graphing System on the Web: Bringing Graphs to Life.

1:OOPM (1537)

~

1:20PM (1 538)

~

1:40PM (1 539)

~

2:00PM (1 540)

~

2:20PM (1 541)

~

2:40PM (1 542)

~

3:00PM (1543)

HORSEing Around with Mathematics. Paul R Coe* , Dominican University, and William T Butterworth, Barat College of DePaul University (993-Wl-1 503)

Using Sport to Teach Mathematics and Statistics. Preliminary report. Reza Noubary, Bloomsburg University (993-Wl-1 562)

Modeling Spectator Movement In the Stadium. Preliminary report. Michael j. Bosse* , Morgan State University, and N. R. Nandakumar, Delaware State University (993-Wl-316)

The Use of Sports Data in an Introductory, Applied Statistics Course. John D. McKenzie, Jr., Babson College (993-W1-489) Productivity in the Came of Baseball. Preliminary report. C T Zahn, San Diego, California (993-Wl-709)

Monte Carlo Simulation of Baseball Seasons and NCAA Basketball Tourneys. Preliminary report. Sean L Forman, Saint Joseph's University (993-Wl-846)

MAA Session on Technology in Mathematics Teacher Preparation Courses, II 1:00PM-5:15PM Organizers: Mary Ann Connors, Westfield State College Christine Browning, Michigan University, Kalamazoo

Using Blackboard to Motivate Students to Look for Mathematics. Preliminary report.

2004

Factors Affecting Win-Loss Probability Of Baseball Games And The Accuracy Of Setting Odds. Philip B Riley, James Madison University (993-Wl-1253)

Erica L Johnson, St. John Fisher College (993-Cl-1 208)

jANUARY

Project REALMS-Rich lmmersive and Interdisciplinary 3-D Settings to Crab and Hold Our Students. Preliminary report.

Neil P Sigmon * and Coreen Mett, Radford University (993-Z1-198)

Degree conditions for cross-intersecting set systems.

Barry Cherkas, Hunter College & Ph.D. Program in Urban Education (993-C1-360) 1:20PM (1531)

2:40PM (1535)

Melanie Wood, University of Cambridge (993-05-578)

Organizers : Marcelle Bessman, jacksonville University Marcia P. Birken, Rochester Institute of Technology Mary L. Platt, Salem State College Brian E. Smith, McGill University

~

He/i-Math: A Web-based Student Engagement with Mathematical Sciences and a Helicopter.

Thomas Lainis *, Frank Wattenberg, Eileen Kowalski and William jones, US Military Academy (993-Cl-444)

1:00PM-3:15PM

~

2:20PM (1 534)

Graph Pegging and the Pegging Number.

MAA Session on Uses of the WWW that Enrich and Promote Learning, II

1 :OOPM (1530)

2:00PM (1 533)

john A. Picciuto* and Mike Phillips, United States Military Academy (993-C1-1 78)

Geir T Helleloid*, Stanford University, Philip Matchett, Cambridge University, David Moulton, Princeton, New Jersey, and Madeeha Khalid , University of Warrick (993-05-561)

Graph Pegging: Powers and Products.

Using Web-based materials featuring rich immersive settings, customizable actors and both java- and Shock Wave-based Lite App/ets in Mathematics and Science.

NOTICES OF THE

AMS

171

Program of the Sessions - Phoenix, AZ, Saturday, january 10 (cant' d.)

~

1:OOPM (1 544)

Effective Introduction to the Use of Geometer's Sketchpad For Pre-service Elementary Teachers.

~

Preliminary report. Kimberly McGinley Vincent, Washington State University (993-X1-492) 1:20PM ~ (1 545)

1:15PM (1558)

(993-Y1-564) 1:30PM (1559)

A Sketchpad Project for Future Elementary School Teachers.

(993 -Y1-1 539)

(993 -X1-434) 1 :40PM (1 546)

~

2 :00PM (1547)

Explorations with Geometer's Sketchpad. Preliminary report. Pallavi Jayawant, University of Arizona (993-X1-503)

Discovering geometry in collaborative groups using Geometer's Sketchpad. Preliminary report.

~

1:45PM (1 560)

~

2:00PM (1561)

~

2:15PM (1 562)

~

2 :30PM (1 563)

(993-X1-245)

Technology in the Geometry Course for Prospective Elementary Teachers.

~

2:40PM (1 549)

Integrated math and technology courses for prospective and practicing teachers. (993-X1-254)

~

(993-X1-319) ~

3 :20PM (1 5 51)

2 :45PM (1564)

Teacher Preparation in the Use of Computer Algebra Systems. Preliminary report. Michael J. Bosse*, Morgan State University, and N. R. Nandakumar, Delaware State University

~

(993-X1-587) ~

4:00PM (1553)

4 :20PM (1 5 54) 4:40PM (1 55 5)

3:15PM (1566)

~

5:00PM (1556)

~

3:30PM (1 567)

Constructing Puzzles To Promote Mathematical Thinking. Preliminary report. M. Munakata, Montclair State University

3:45PM (1 568)

~

Are we getting what we pay for? Preliminary report. Queen Wiggs, The North Carolina School of Science and Mathematics (993-X1-599)

4:00PM ~ (l 569)

Math Anxiety as a Resource: Strategies for the First Days of Class. Debra K Borkovitz, Wheelock College (993-Y1-380)

Virtual Manipulatives in the Mathematics for Elementary School Teachers Course. ~

4:15PM (15 70)

Preparing Teachers to Use Technology and Effective Pedagogy in a Mathematics Content Course.

Math is a journey, not a destination. L. Christine Kinsey, Canisius College, and Teresa E. Moore* , Ithaca College (993-Y1-384)

Invert the Stereotypical Classroom and Multiply the Interest in Math. Teresa D. Magnus, Rivier College, Nashua NH (993-Y1-446)

~

4:30PM (1571)

Teaching the "Neglected Constituency": A Mathematics Course for Preservice Elementary School Teachers (with Lessons for Other Courses). David G. Poole, Trent University (993-Y1-552)

4:45PM (1 572)

1:00PM- 5:25 PM

Opening Students' Hearts and Minds to Mathematics. Preliminary report. Fang Chen, Oxford College of Emory University

Organizers : Caren L. Diefenderfer, Hollins University Janet L. Anderson, Hope College Elizabeth G. Yanik, Emporia State University

"If at First You Don't Succeed ... ": Building Mathematical Confidence with Problem-Solving Portfolios.

(993-Y1-1679) 5 :OOPM ~ (1 573)

Problem-based Inquiry Seminar Courses. Preliminary report. John Koker, University of Wisconsin Oshkosh (993-Y1-184)

5 : 15PM ~ (15 74)

Penelope H Dunham, Muhlenberg College

Using group work and journals to enhance students' perceptions of their abilities to do mathematics in a "Math for Liberal Arts" course. Therese L Bennett, Southern Connecticut State University (993-Y1-426)

(993-Y1-529)

172

Improving Student's Attitudes Using Motivational Theory as a Basis for Classroom Management and Assessment.

(993-Y1-341)

MAA Session on Strategies that Work to Positively Change Student Attitudes Toward Mathematics, II

1:OOPM ~ (1557)

Persist in

(993-Y1-327)

(993-X1-371)

Rajee Amarasinghe, California State University, Fresno (993-X1-330)

to

Theresa A Laurent, St Louis College of Pharmacy

A Monte Carlo Simulation : Geometric Probability and the Law of Large Numbers.

A. Susan Gay, University of Kansas (993-X1-488)

Encouraging Young Women Mathematics. (993-Y1-50)

Rose Elaine Carbone, Clarion University

~

3:00PM (1565)

Comparing Experimental and Theoretical Probabilities: The Coin Flip Game. Preliminary report. Trisha A. Bergthold, San Jose State University

Math and Basketball: A Skill-Building Paradigm. Keri A. Kornelson, Texas A&M University

Carol G. Williams, Abilene Christian University

Using Problem Solving to Develop a Game Winning Strategy. Dennis M Kern, Texas A&M University-Texarkana

3:40PM (1552)

Changing Students' Perception of Mathematics through An Integrated, Collaborative, Field-Based Approach To Teaching and Learning Mathematics.

(993-Y1-9-36)

(993-X1-342) ~

Changing the Focus from the Teacher to the Learner. Preliminary report.

Preliminary report. Ham ide Dogan-Dunlap, University of Texas at El Paso (993-Y1-1636)

Patricia Baggett* , New Mexico State University, and Andrzej Ehrenfeucht, University of Colorado 3:00PM (1550)

Negative Attitudes Towards Mathematics-How to Break the Vicious Cycle . Preliminary report.

Janet Andersen, Hope College (993-Y1-1 380)

Barbara J Pence, San Jose State University (993-X1-1 029)

Encouraging Students to Read Mathematics. Mary D Shepherd, Northwest Missouri State University (993·Y1-1 582)

Margaret L Gruenwald , University of Southern Indiana (993-Y1-61 7)

Vesna Kilibarda, Indiana University Northwest 2:20PM (1548)

Games and Hands-On Activities to Enhance Learning of Mathematics for Non-science Majors. Annela R Kelly, University of Louisiana at Monroe

Timothy D Comar, Benedictine University

~

Creating Mathematics Ambassadors. Preliminary report. Dora Cardenas Ahmadi, Morehead State University

NOTICES OF THE

AMS

VOLUME

51,

NUMBER

1

Phoenix, AZ, Saturday, january 70- Program of the Sessions MAA General Contributed Paper Session, VII

1:OOPM .,. (1 587)

1:00 PM - 4:20 PM

Organizers: Laura J. Wallace, California State University, San Bernardino Jacqueline A. jensen, Sam Houston State University Gary W. Towsley, SUNY at Geneseo Michael A. Jones, Montclair State University Shawnee L. McMurran, California State University at San Bernardino 1 :OOPM .,. (15 75)

Calculator Detective: Preservice elementary teachers compare calculators and discover that machines do not replace thinking. Preliminary

report. Susan L Addington, California State University San Bernardino (993-Zl-51 5) 1: 15PM Diffy. Preliminary report . .,. (1576) Tracy Dawn Hamilton, California State University Sacramento (993-Zl-472) 1:30PM .,. (1577)

Text Supplements that Help Instructors Teach: Experience and Vision. Larry Copes* , ISEM, St. Paul, MN, and Joan Lewis , Key Curriculum Press (993-Zl-1224)

1:45PM .,. (1578)

2:00PM .,. (1579)

Instructional Supplements for College Algebra and Below.

The Topology of DNA-Protein Interactions .

Dorothy Buck, Brown University (993-Z5-1 043) 1:30PM Knotted Polygons in IR. 3 . Preliminary report . .,. (1 588) Jorge Alberto Calvo , North Dakota State University (993-Z5-1255) 2 :00PM .,. (1589)

Minimum Lengths for Flat Knotted Bands of a Given Width . Preliminary report. Louis H. Kauffman, University of Illinois at Chicago (993-Z5-1487)

2:30PM .,. (1 590) 3 :00PM (1 591)

Knots in Dynamical Systems. Steve Kennedy, Carleton College (993-Z5-1603)

Detecting Topological and Geometric Information from a Discrete Set of Points in Euclidean Space . David Letscher, Saint Louis University (993-Z5-1 584)

3:30PM .,. (1 592)

Braids and the Yang-Baxter Equation: An Application of Knot Theory to Physics. Alissa S. Crans, University of California, Riverside (993-Z5-1649)

MAA CUPM Subcommittee on Curriculum Renewal Across the First Two Years Panel Discussion 1:00 PM - 2:20 PM

What are colleges doing with students with AP placement?

Beth A. Osikiewicz, Kent State University Tuscarawas (993-Zl-11 76)

Organizer:

Experience Teaching Elementary Algebra with DevMap.

Panelists:

M. Anne Dow, Maharishi University of Management (993-Zl-1610) 2 :15PM .,. (1 580) 2 :25PM 2 :45PM .,. (1 581)

Reforming College Algebra. Elizabeth J. Kreston, University of the Incarnate Word (993-Zl-461) Break Student Preparedness for Calculus. Preliminary report. R. N. Mohapatra, University of Central Florida (993-Zl-1 700)

3 :00PM .,. (1582)

MAA Special Presentation 1:00 PM - 2:20 PM

An Activities Based Topics Course in Mathematics for Liberal Arts Majors. Preliminary report.

Oral presentations: Let's talk about it! Organizers: Tom J. Linton, Central College Suzanne Doree, Augsburg College Nancy L. Hagelgans, Ursinus College Richard J. Jardine, Keene State University

Jay A Malmstrom, Oklahoma City Community College (993-Zl-1 3 55) 3 : 15PM Definitions: Now and Then . Preliminary report . .,. (1 583) Greisy W Winicki - Landman, California State Polytechnic University, Pomona (993-Zl-868) 3:30PM .,. (1 584)

3:45PM .,. (1 585)

An analysis of undergraduate mathematics textbooks and courses for prospective elementary teachers. Preliminary report. Raven M. Wallace *, Michigan State University, Helen Siedel and Andreas Stylianides, University of Michigan (993-Zl-359)

MAA-Young Mathematicians Network Panel Discussion

Integrated Mathematics- A Function Approach (!MFA).

1:00 PM - 2:20 PM

What can you do with a degree in mathematics?

James L. Smith, McCurdy School (993-Z1-892) 4:00PM .,. (1 586)

Organizers : John A. Vano, University of Wisconsin Madison Kim Roth, Wheeling Jesuit University · Panelists: Andrew Sterrett, Jr., Denison University Patrick D. McCray, Pfizer and Illinois Institute of Technology David E. Hammett, Oakwood School, Burbank, California Robert L. Wilson, University of Wisconsin, Madison

Problem-Driven Courses in the Middle School and Secondary Mathematics Preservice Curricula. Kathleen D. Lopez* and Victor P. Schneider, University of Louisiana at Lafayette (993-Zl-688)

MAA Invited Paper Session on Applications of Topology to Biology, Chemistry, and Physics 1:00 PM - 3:50 PM

Organizers : Erica L. Flapan, Pomona College Dorothy Buck, Brown University

JANUARY

Martin E. Flashman, Humboldt State University Shahriar Shahriari, Pomona College Morton Brown, University of Michigan Wade Ellis, Jr., West Valley College Susan Kornstein, The College Board

2004

NOTICES OF THE

AMS

173

Program of the Sessions - Phoenix, AZ, Saturday, january 10 (cont'd.) A WM Workshop Panel Discussion

MAA CUPM Subcommittee on Curriculum Renewal Across the First Two Years

1:00 PM- 2:25 PM

2:45 PM - 4:05 PM

Shaping a career in mathematics. Moderator: Jodie D. Novak, University of Northern Colorado Panelists: Tracy Fischer, Motorola Joan P. Hutchinson, Macalester College Barbara L. Keyfitz, University of Houston Rachel A. Kuske, University of British Columbia Janet M. McShane, Northern Arizona University Anne V. Shepler, University of North Texas

How to implement curriculum change. Organizer: Donald B. Small, U.S. Military Academy Moderator: Gary W. Krahn, U.S. Military Academy Panelists: Mike Moody, Olin University Stephen B. Maurer, Swarthmore College Jeff Floyd, Texas A & M University

MAA Minicourse #6: Part B 3:15PM-5:15PM

Using interactive labs to explore abstract algebra topics. Organizers: Allen C. Hibbard, Central College Kenneth M. Levasseur, University of Massachusetts at Lowell

ASL Invited Address 2:00 PM - 2:50 PM (1 593)

Canonical Structure in the Universe of Set Theory.

ASL Invited Address

Matthew Foreman, University of California, Irvine (993-03-1270)

3:30 PM - 4:20 PM (1598)

A WM Workshop: Presentations by Recent Women Ph.D.s and Graduate Students, II

Quantum algorithms and group representation theory. Leonard Schulman, California Institute of Technology

2:30 PM - 4:40 PM 2 :30PM (1594)

Comparison of Histograms for Use in Cloud Modeling. Lisa Bloomer, Middle Tennessee State University

3:00PM (1 595)

4 :30PM

3:30 PM - 4:2 5 PM

Combinatorial Results Motivated by Computational Biology. Christine E. Heitsch, University of Wisconsin, Madison

3:30PM (1 596) 4 :00PM (1 597)

MAA Session on Applications of Mathematics in Computer Science, II

lmplicitization via Syzygies.

Organizer: 3:30PM .,.. (1 599)

Haohao Wang, Southeast Missouri State University 3:45PM (1600)

A combinatorial approach to finding root multiplicities in some indefinite type Kac-Moody algebras. Vicky Williams, Appalachian State University Closing remarks.

4 :00PM .,.. (1601)

4:15PM (1602)

2:30 PM - 3:30 PM

Panelists:

MAA Special Presentation

Examples of the Application of Statistics and Probability to Computer Science. Preliminary report. Numeric Methods, Modeling and Computer Science Majors.

3:30 PM - 4:25 PM Organizers : Charles E. Hofmann, LaSalle University Joseph R. Fiedler, California State University, Bakersfield

2:45 PM - 4:45 PM

They know, we know, that they don't know: Integrating Technology into Teaching and Assessment. Preliminary report. Alex J Heidenberg* , John Wasko and Elizabeth Schott, United States Military Academy (993-V1-1330)

Informal session on actuarial education.

174

Ronald Mullin and Ayan Mahalanobis* , Florida Atlantic University (993-P1-825)

MAA Session on Focus on Integrating Graphic Handhelds into Collegiate Mathematics, II

3:30PM .,.. (1603)

Organizers : Krzysztof Ostaszewski, Illinois State University Curtis Huntongton, University of Michigan

An alternative representation of finite fields .

Paul J Kapitza, Illinois Wesleyan University (993 -P1-1 001)

Revisiting crossroads: Continuing the dialogue on two-year college mathematics. Susan S. Wood, J. Sargeant Reynolds Community College Judy E. Ackerman , Montgomery College Susan S. Wood, J. Sargeant Reynolds Community College

Applications of Algebras in Computer Science. John W. Davenport, East Central University (993-P1 -706)

Juana Sanchez* and Yan He , UCLA Dept of Statistics (993-P1-852)

MAA Panel Discussion

Organizer:

William A. Marion, Valparaiso University

3:45PM .,.. (1604)

NOTICES OF THE

AMS

Exploring Families of Functions. Charles E Hofmann, LaSalle University (993-V1-496)

VOLUME

51,

NUMBER

1

Phoenix, AZ, Saturday, january 70- Program of the Sessions

~

4:00PM (1605) 4 :1 SPM (1606)

Teaching Composition of Functions.

AMS Banquet

Roseanne S Hofmann, Montgomery County Community College (993-V1-497)

7:30 PM - 10:00 PM

Integrating algebra-capable calculators into "Geometric Linear Algebra," a course for High School Teachers. joseph R Fiedler, CSU Bakersfield (993-V1-404)

Michel L. Lapidus AMS Associate Secretary Riverside, California

james j. Tattersall MAA Associate Secretary Providence, Rhode Island

MAA Special Presentation 3:45PM-4:45PM

Math Horizons, a magazine for students. Organizers : Arthur T. Benjamin, Harvey Mudd College Jennifer j. Quinn, Occidental College

MAA CUPM Subcommittee on Curriculum Renewal Across the First Two Years Panel Discussion 4:1 5 PM- 5:35 PM

How to assess problem solving. Organizer: Donald B. Small, U.S. Military Academy Moderator: Kathleen G. Snook, Consortium for Mathematics and Its Applications jack Bookman, Duke University Panelists: Alex J. Heidenberg, U.S. Military Academy William j. Haver, Virginia Commonwealth University Bonnie Gold, Monmouth University

ASL Session for Contributed Papers, II 4:30PM-6:05PM 4:30PM (1607) 4 :55PM (1608)

Comparing classes of Finite Structures. Sara Miller*, Wesley Calvert, D. Cummins and j.F. Knight, University of Notre Dame

The isomorphism problem for classes of computable structures. Wesley Calvert, University of Notre Dame

5:20PM (1 609)

!:!.~-categorical structures 6.~ + 1 -categorical.

need not be relatively

John Chisholm, Western Illinois University 5:45PM Minima of initial segments of sequences of reals. (161 0) Jeffry l. Hirst, Appalachian State University

ASL Session for Contributed Papers, Ill 4:30 PM - 6:05 PM 4:30PM (1611)

Ergodic theorems in subsystems of second order arithmetic. Ksenija Simic, Carnegie Mellon University

4:55PM (1 61 2)

The probabilistic method and Ramsey theory in bounded arithmetic. Kerry Ojakian, Carnegie Mellon University Phone: none

5:20PM (1613) 5:45PM (1614)

Compatibility in logical varieties. Mark Burgin, UCLA

On automorphism groups of countable arithmetically saturated models of Peano arithmetic. Ermek S. Nurkhaidarov, University of Connecticut

AMS Banquet Reception 6:30 PM - 7:30 PM

jANUARY

2004

NOTICES OF THE

AMS

175

Meetings and Conferences of the AMS Associate Secretaries ofthe AMS Western Section: MichelL. Lapidus, Department of Mathematics, University of California, Sproul Hall, Riverside, CA 92521-0135; e-mail: l api dus@math. ucr. edu; telephone: 909787-3113. Central Section: Susan J. Friedlander, Department of Mathematics, University of Illinois at Chicago, 851 S. Morgan (MI C 249), Chicago, IL 60607-7045; e-mail: susan@math. nwu. edu; telephone: 312-996-3041. The Meetings and Conferences section of the Notices gives information on all AMS meetings and conferences approved by press time for this issue. Please refer to the page numbers cited in the table of contents on this page for more detailed information on each event. Invited Speakers and Special Sessions are listed as soon as they are approved by the cognizant program committee; the codes listed are needed for electronic abstract submission. For some meetings the list may be incomplete. Information in this issue may be dated. Up-to-date meeting and conference information can be found at www. am5. orglmeeti ng5l.

Eastern Section: Lesley M. Sibner, Department of Mathematics, Polytechnic University, Brooklyn, NY 11201-2990; e-mail: lsi bner@duke. poly. edu; telephone: 718-260-3505. Southeastern Section: John L. Bryant, Department of Mathematics, Florida State University, Tallahassee, FL 32306-4510; e-mail: bryant@math. fsu. edu; telephone: 850-644-5805.

2006 January 12-15 2007 January 4-7 2008 January 6-9 2009 January 7-10

Meetings: 2003 December 17-20 2004 January 7-10 March 12-13 March 26-27 April3-4 Aprill7-18 May 13-15 October 16-17 October 16-17 October 23-24 November 6-7 2005 January 5-8 March 18-19 April 2-3 April8-10 April16-17 June 16-19 October 15-16 October 21-22

Bangalore, India

p.85

Phoenix, Arizona Annual Meeting Tallahassee, Florida Athens, Ohio Los Angeles, California Lawrenceville, New Jersey Houston, Texas Nashville, Tennessee Albuquerque, New Mexico Evanston, Illinois Pittsburgh, Pennsylvania

p.86

Atlanta, Georgia Annual Meeting Bowling Green, Kentucky Newark, Delaware Lubbock, Texas Santa Barbara, California Mainz, Germany Johnson City, Tennessee Lincoln, Nebraska

p.87 p. 89 p.91 p.92 p.93 p. 94 p . 94 p.94 p.95

p.95 p.95 p.96 p.96 p.96 p.96 p.96 p.97

San Antonio, Texas Annual Meeting

p.97

New Orleans, Louisiana Annual Meeting

p.97

San Diego, California Annual Meeting

p.97

Washington, DC Annual Meeting

p.97

Important Information regarding AMS Meetings Potential organizers, speakers, and hosts should refer to page 84 in the January 2004 issue of the Notices for general information regarding participation in AMS meetings and conferences. Abstracts Several options are available for speakers submitting abstracts, including an easy-to-use interactive Web form. No knowledge of L:tf£X is necessary to submit an electronic form, although those who use L:tf£X may submit abstracts with such coding, and all math displays and sirnilarily coded material (such as accent marks in text) must be typeset in L:tf£X. To see descriptions of the forms available, visit http: I I www. am5. org/ab5tract5/i n5tructi on5. html, or send mail to ab5-5ubmit@am5 .org, typing help as the subject line; descriptions and instructions on how to get the template of your choice will be e-mailed to you. Completed email abstracts should be sent to abs-submi t@ am5 . o rg , typing s ubmi 55 ion as the subject line. Questions about abstracts may be sent to abs- i nfo@ams. o rg . Paper abstract forms may be sent to Meetings & Conferences Department, AMS, P.O. Box 6887, Providence, RI 02940. There is a $20 processing fee for each paper abstract. There is no charge for electronic abstracts. Note that all abstract deadlines are strictly enforced. Close attention should be paid to specified deadlines in this issue. Unfortunately, late abstracts cannot be accommodated.

Conferences: (See http://www.ams.org/meetings/ for the most up-to-date information on these conferences.) February 12-16: AAAS Annual Meeting, Seattle, WA. June 5-July 24, 2004: Joint Summer Research Conferences in the Mathematical Sciences, Snowbird, Utah. (See November 2003 Notices, page 1363.)

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NOTICES OF THE

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