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Notices of the American Mathematical Society (ISSN 0002· 9920) Is Published Monthly Except Bimonthly in June/ July by Voting Information for 2006 AMS Election of the American Mathematical Society August2006 Volume 53, Number 7 The Differential Geometry and Physical Basis for the Applications of Feynman Diagrams page 744 A Fellows Program for the AMS page 754 Salt Lake City Meeting page 834 Cincinnati Meeting page 836 Storrs Meeting page 838 A Henan horseshoe (page 768) Masters of Mathematics A Historic Evolution of Ideas Euler through Time ANew look at Old Themes V. S. Varadarajan, University of California, Los Angeles, CA This book synthesizes hundreds of years of thought on Eulerian theories to place the work of the world's most prolific mathematician into the context of today's thinking. The primary focus is on Euler's work on infinite series and products and its influence on modern thought. The author examines Euler products and ties his work to the climactic developments reached by number theorists and the Langlands program. 2006; 302 pages; Hardcover; ISBN-I 0: 0-8218-3580-7; ISBN-13: 978-0-8218-3580-7; List US$59;AII AMS members US$47; Order code EULER Bourbaki ASecret Society of Mathematicians Maurice Mashaal, Pour la Science, Paris, France This book lifi:s the veil from a secret society in which spirited debate, good humor, and a unified purpose helped generate the most influential mathematical treatise of the 20th century. It chronicles how the Bourbaki group saw its mission grow into creation of a universal collection of mathematical tools, shaping thought on mathematics from 1950 to the 1970s. Remarkable photographs and rich anecdotes enliven the text. 2006; approximately 168 pages; Softcover; ISBN-I 0: 0-8218-3967-5; ISBN-13: 978-0-8218-3967-6; List US$29;AII AMS members US$23; Order code BOURBAKI US$23; Order code BOURBAKI Euclid's Phaenomena The Coxeter Legacy ATranslation and Study of a Reflections and Projections Hellenistic Treatise in Spherical Chandler Davis and Erich W. Ellers, Astronomy University of Toronto, ON, Canada, J. L. Berggren, Simon Fraser Editors University, Burnaby, BC, Canada, Comp rehensive collection of articles that and R. S. D. Thomas, University of captures the essence of Coxeter's legacy Manitoba, Winnipeg, Manitoba, Canada combination of storytelling and up-to-date information reflects the breadth of Coxetcr's contributions both within and outside math­ Thi s translati on of Euclid's Phaenomena, includes ex tensive ematics. The book includes a rich variety of beautiful illustrations. commentary that enhan ces the context and value of this impor­ ta nt histori c work. Readers get a fa scinating look at how Euclid A w ·publication of the AM.S and The Fields Institute fOr Research in Mathematical Sciences advanced knowledge in astronomy without the tools of trigonom­ (Toronto, Ontario, Canada). etry and spherical geometry. 2006; 320 pages; Hardcover; ISBN-I 0: 0-8218-3722-2; ISBN-13: 978-0-8218-3722-1 ; List US$69; All AMS members US$ 55; Order code COXETER (:0publishcd \\ ~ t h the London Mathematical Society beginning wi th Volume 4. Members of the LMS may order directly from the AMS at the AMS member price. T he LMS is registered \vith tbc Chari ry Comm.issioncrs. History of Mathematics. Volume 29; 2006; 132 pages; Softcover; ISBN-I 0: 0-8218-4072-X; ISBN - 13: 978-0-8218-4072-6; List US$29;AII AMS members US$23; Order code HMATH/29 For many more publications of interest, visit the AMS Bookstore ®AMS www.ams.org/bookstore AMERICAN M/.THBMAl'ICAL SOCIETY l-800-321-4AMS (4267), in the U.S. and Canada, or 1-401-455-4000 (worldwide); fax: 1-40 1-455-4046; email: [email protected]. American Mathematical Society, 20 I Charles Street, Providence, Rl 02904-2294 USA 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 indawi .com/mts/ ~ 11 diverse Open Access Mathematics journals JO)JlffffcenemltJI,alll /Ecq[IUlrolttJico)JDl§ iaUDlcdl Ncomllllllnlceraur , l\\.1fcecchraunulcc§ Discrete Dynamics in jl;;\\ed . Nature and society ~ n e ~ r • j 1 "J J c ,~~ <.~ t~at\\e"'~t\tS a"d oet\slo" st\e"tes Mathematical Problems in Engineering Theory, Methods, and ApplicationS NEW f6 FORTHCOMING from Birkhauser Vortices in the Magnetic Complex Variables History of Banach Spaces Ginzburg-landau Model with Applications and Linear Operators S. PONNUSAMY, Indian Institute of Technology, Madras, ALBRECHT PIETSCH, University of lena, Germany ETIENNE SANDIER, Universite Paris-12 Val-de-Marne, Chennai, India; HERB SILVERMAN, College of Charleston, Creteil, France; SYLVIA SERFATY, CMIA, Ecole Normale Banach spaces figure prominently in the study of func­ Superieure de Cachon, France sc tional analysis, having applications to integral and Complex numbers can be viewed in several ways: as an book presents the mathematical study of vortices differential equations, approximation theory, harmonic Thi ~ element in a field, as a point in the plane, and as a two­ of the two-dimensional Ginzburg-Landau model, an analysis, convex geometry, numerical mathematics, dimensional vector. Examined properly, each perspec­ im(1ortant phenomenological model used to describe analytic complexity, and probability theory. This work is tive provides crucial insight into the interrelations bet­ sup1erconductivity. The vortices, identified as quantized devoted to a comprehensive treatment of the history of ween the complex number system and its parent, the ani6unts of vorticity of the superconducting current Banach spaces and (abstract bounded) linear oper­ real number system. The authors explore these relation­ localized near points, are the objects of many obser­ ators. While other comprehensive texts on Banach ships by adopting both generalization and specialization vational and experimental studies, both past and pre­ spaces focus on developments before 1950, this one is methods to move from real variables to complex variab­ se~t. The Ginzburg-Landau functionals considered mainly devoted to the second half of the 20th century. les, and vice versa, while simultaneously examining their include both the model cases with and without a Banach space theory is presented as a part of a broad analytic and geometric characteristics. magnetic field. mathematics context, using tools from such areas as set The engaging exposition is replete with discussions, The work acts a guide to the various branches of Ginz­ theory, topology, algebra, combinatorics, probability remarks, questions, and exercises, motivating not only burg-Landau studies, provides context for the study of theory, and logic. Equal emphasis is given to both spaces understanding on the part of the reader, but also de­ vortices, discusses current research and results, and and operators. veloping the tools needed to think critically about mathe­ presents a list of open problems in the field. It will 2006/APPROX., 880 PP., 821LLUS./HARDCOVER berlefit mathematicians, physicists, and graduate stu­ matical problems. The material includes numerous examples and applications relevant to engineering stu­ ISBN 0-8176-4367-2/$109.00 (TENT.) dents having either an introductory or an advanced dents, along with some techniques to evaluate various knowledge of the subject. types of integrals. 20d6/APPROX. 290 PP., 151LLUS./HARDCOVER Mathematical Analysis 2006/X, 510 PP., 1091LLUS./HARDCOVER ISBN 0-8176-4316-8/$69.95 (TENT.) Linear and Metric Structures ISBN 0-8176-4457-1/$59.95 PROGRESS IN NONLINEAR DIFFERENTIAL EQUATIONS and Continuity ANP THEIR APPLICATIONS MARIANO GIAQUINTA, Scuola Normale Superiore, Pi sa, AGeometric Approach Italy; GIUSEPPE MODICA, Universitii degli Studi di Firenze, Italy Number Theory to Differential Forms DAVID BACHMAN, Pitzer College, Claremont, CA This self-contained work on linear and metric struc­ An Introduction via the Distribution tures focuses on studying continuity and its applications of Primes This text presents differential forms from a geometric to finite- and infinite-dimensional spaces. The book, BENJAMIN FINE, Fairfield University, Fairfield, CT; perspective accessible at the sophomore undergradu­ replete with examples, observations, exercises, and GERHARD ROSENBERGER, Universitiit Dortmund, ate level. The book begins with basic concepts such as illustrations, may be used in a classroom setting, for Germany partial differentiation and multiple integration and self-study by advanced undergraduate and graduate gently develops the entire machinery of differential students, and as a valuable reference for researchers This book provides an introduction and overview of forms. The author approaches the subject with the idea in mathematics, physics, and engineering. number theory based on the distribution and properties that complex concepts can be built up by analogy from of primes. This unique approach provides both a firm simpler cases, which, being inherently geometric, often 2006/XVIII, 470 PP., 1281LLUS. background in the standard material as well as an over­ HARDCOVER/ISBN 0-8176-4374-5/$149.00 can be best understood visually. Each new concept is view of the whole discipline. 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