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Notices of the American Mathematical Society June/July 2006 of the American Mathematical Society ... (I) , Ate._~ f.!.o~~Gffi·u.­ .4-e.e..~ ~~~- •i :/?I:(; $~/9/3, Honoring J ~ rt)d ~cLra-4/,:e~ o-n. /'~7 ~ ~<A at a Gift from fL ~ /i: $~ "'7/<J/3. .} -<.<>-a.-<> ~e.Lz?-1~ CL n.y.L;; ro'T>< 0 -<>-<~:4z_ I Kumbakonam li .d. ~ ~~d a. v#a.d--??">ovt<.·c.-6 ~~/f. t:JU- Lo,.,do-,......) ~a page 640 ~!! ?7?.-L ..(; ~7 Ca.-uM /3~~-d~ .Y~~:Li: ~·e.-l a:.--nd '?1.-d- p ~ .di.,r--·c/~ C(c£~r~~u . J~~~aq_ f< -e-.-.ol ~ ~ ~/IX~ ~ /~~ 4)r!'a.. /:~~c~ •.7~ The Millennium Grand Challenge .(/.) a..Lu.O<"'? ...0..0~ e--ne_.o.AA/T..C<.r~- /;;; '7?'E.G .£.rA-CLL~ ~ ·d ~ in Mathematics C>n.A..U-a.A-d ~~. 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The Bookstore is your source for Database • Surveys & Outreach detailed information on AMS publications and provides the opporttmity to keep informed about feature sales. www.ams.org/bookstore MEET your colleagues at upcoming AMS meetings and conferences, and also find out about other upcoming mathematical conferences around the world www.ams.org/meetings FIND help and resources for high school, undergraduate, and graduate students and their advisors www.ams.org/outreach USE an array of tools for researchers and mathematical authors throughout the website www.ams.org LEARN about the latest mathematical news and perspectives by reading the Math in the Media, Feature Tony Phillips' Ta~e on columns, and Mathematical Moments Math in the Medsa I ...... y ~ of·-:.::-.. * .. ~ --~--- Hot~••''~ · ' www.ams.org/public-awareness VISIT THE AMS BOOTHS AT ICM (Booth Numbers 8, 9, and 18) Open Access Mathematics Journals from Hindawi ~ Immediate, universal, and unrestricted access maximizes the impact of published research ~ Authors retain copyright under the terms of the Creative Commons Attribution License ~ Streamlined submission and peer review process at http://www.h i ndawi.com/mts/ ~ 11 diverse Open Access Mathematics journals /O)JlffffceneJnt ltJlstJ/ IE<qruuatt tJl[)J Jilt§ <avntcd/ NcomtHJnt<e(aur I\\;Jfcecclhkaunul <C§ Discrete Dynamics in Nature and Society i9~\\e" . ~~ ru n < ~ .l 'c ~~-' lN"•"' • ' ~• ~rl~0/'Ni;::un,; taat\\em~t\tS an" oet\s\on .st\entes Mathematical Problems in Engineering Theory, Methods, and Applications NEW [c) FORTHCOMING from Birkhiiuser An Invitation to Quantum Cohomology Dirac Operators in Representation Theory Kontsevich's Formula for Rational Plane Curves JING-SONG HUANG , Hong Kong University of Science and JOACHIM KOCK, UniversitatAutiinoma de Barcelona, Barcelona, Spain; Technology, Hong Kong, China; PAVLE PANDZIC, University of ISRAEL VAINSENCHER, Universidade Federal de Minas Gerais, Pampulha- Bela Horizonte, Brazil Zagreb, Croatia This book is an elementary introduction to stable maps and quantum cohomology, starting with an introduction to This monograph presents a comprehensive treatment stable pointed curves, and culminating with a proof of the associativity of the quantum product. The viewpoint is of important new ideas on Dirac operators and Dirac mostly that of enumerative geometry, and the red thread of the exposition is the problem of counting rational cohomology. Dirac operators are widely used in physics, plane curves. Emphasis is given throughout the exposition to examples, heuristic discussions, and simple appli­ differential geometry, and group-theoretic settings cations of the basic tools to best convey the intuition behind the subject. The book demystifies these new quan­ (particularly, the geometric construction of discrete tum techniques by showing how they fit into classical algebraic geometry. series representations). The related concept of Dirac The book is ideal for se lf-study, as a text for a mini-course in quantum cohomology, or as a special topics text in a cohomology, which is defined using Dirac operators, is a sta~dard course in intersection theory. The book will prove equally useful to graduate students in the classroom far-reaching generalization that connects index theory setting as to researchers in geometry and physics who wish to learn about the subject. in differential geometry to representation theory. Using Dirac operators as a unifying theme, the authors dem­ 2006/APPROX. 184 PP./HARDCOVER onstrate how some of the most important results in ISBN 0-8176-4456-3/$49.95 representation theory fit together when viewed from PROGRESS IN MATHEMATICS, VOLUME 249 this perspective. An exce ll ent contribution to the mathematical literature of representation theory, this se lf-contained exposition AGeometric Approach to A Beginner's Guide to offers a systematic examination and panoramic view of Differential Forms Graph Theory the subject. The material will be of interest to research­ DAVID BACHMAN, Pitzer College, Claremont, CA Second Edition ers and graduate students in representation theory, differential geometry, and physics. This text presents differential forms from a geometric W.D. WALLIS, Southern Illinois University, Carbondale, IL perspective accessible at the sophomore undergradu­ "Altogether the book gives a comprehensive introduction 2006/X, 198 PP./HARDCOVER ISBN 0-8176-3218-2/$59.95 ate level. The book begins with basic concepts such as to graphs, their theory and their application ... The use MATHEMATICS: THEORY & APP LICATIONS partial differentiation and multiple integration and of the text is optimized when the exercises are solved" gently develops the entire machinery of differential - SIMULATION NEWS EUROPE (REVIEW OF THE forms. The author approaches the subject with the idea FIRST EDITION) that complex concepts can be built up by analogy from Topics in the Theory of This concisely written textbook is intended for an simpler cases, which, being inherently geometric, often introductory course in graph theory for undergraduate Algebraic Function Fields can be best understood visuall y. mathematics majors or advanced undergraduate and GABRIEL DANIEL VILLA SALVADOR, CINVESTAV del lPN, Each new concept is presented with a natural picture graduate students from the many fields that benefit Mexico City, Mexico that students can easily grasp. Algebraic properties then from graph-theoretic applications. This Second Edition The subject of algebraic function fields of one va riable follow. The text is designed to support three distinct includes new chapters on labeling and communications is used in several areas of mathematics: complex course tracks: third semester (multivariable) calculus, networks and small worlds, as well as expanded begin­ analysis, algebraic geometry, and number theory. This sophomore-level vector calculus, and an advanced ner's material in the early chapters, including more ex­ text applies an arithmetic-algebraic viewpoint to the undergraduate or beginning graduate topics course for amples, exercises, hints and solutions to key problems. study of function fields as part of the algebraic theory of physics or mathematics majors. numbers. The author does not ignore the geometric and 2006/APPROX. 300 PP., 120 ILLUS./SOFTCOVER 2006/APPROX. 160 PP., 33 ILLU S./HARDCOV ER ISBN 0-8176-4484-9/$3 9.95 (TENT.) analytic aspects of function fields, but focuses on an in­ ISBN 0-8176-4499-7/$39.95 (TENT.) depth examination from a number-theoretic perspec­ tive. The exposition explains both the similarities and fundamental differences between function fields and The Legacy of Mario Pieri in Geometry and Arithmetic number fields , including many examples to motivate ELENA A. MARCHISOTTO, California State University, Northridge, CA; understanding and further study. The book can serve as JAMES T. SMITH, San Francisco State University, San Francisco, CA a text for a graduate course in number theory or an This book is the first of two volumes that together will provide a broad picture of Mario Pieri's work. ln this vol­ advanced graduate topics course. ume, English translations are given for two of Pieri's most important results: his postulates for arithm etic, which 2006/APPROX. 685 PP., 20 ILLUS./HARDCOVER Peano judged superior to his own, and his foundation of elementary geometry on the basis of point and sphere, ISBN 0-8176-4480-6/$69.95 (TENT.) which Alfred Tarski used as a basis for his own system. Additionally, his papers are examined in relation to the MATHEMATICS: THEORY & APPLICATIONS research of others, notably Peano and Tarski.
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