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Notices of the American Mathematical Society ISSN 0002-9920  Springer.Com Notices of the American Mathematical Society ISSN 0002-9920 springer.com New and Noteworthy from Springer Elementary Dirichlet Series Braid Groups Advanced Linear and Modular Forms C. Kassel , V. Turaev , Université Louis Algebra 3rd Edition G. Shimura , Princeton University, New Pasteur - CNRS, Strasbourg, France S. Roman , Irvine, California of the American Mathematical Society Jersey Braids and braid groups form the central For the third edition, the The main topics of the book are the critical topic of this text. The authors begin with an author has: added a new chapter on August 2007 Volume 54, Number 7 values of Dirichlet L-functions and Hecke L- introduction to the basic theory associative algebras that includes the well functions of an imaginary quadratic fi eld, highlighting several defi nitions of braid known characterizations of the fi nite- and various problems on elliptic modular groups and showing their equivalence. The dimensional division algebras over the real forms. As to the values of Dirichlet L- relationship between braids, knots and links fi eld (a theorem of Frobenius) and over a George Mackey (1916–2006) functions, all previous papers and books is then investigated. Recent developments fi nite fi eld (Wedderburn’s theorem); reiterate a single old result with a single old in this fi eld follow, with a focus on the polished and refi ned some arguments; page 824 method. After a review of elementry Fourier linearity and orderability of braid groups. upgraded some proofs; added new analysis, the author presents completely This excellent presentation is motivated by theorems, including the spectral mapping new results with new methods, though old numerous examples and problems . theorem; corrected all known errors; Do Loops Explain Consciousness? results will also be proved. Other notable enlarged the reference section considerably. 2007. Approx. 320 p., 60 illus. (Graduate features include new results on classical Review of I Am a Strange Loop Texts in Mathematics) Hardcover Eisenstein series, a discussion of 3rd ed.2007. Approx. 520 p. 25 illus. isomorphism classes of elliptic curves with ISBN 978-0-387-33841-5 approx. $59.95 (Graduate Texts in Mathematics, Volume page 852 complex multiplication in connection with 135) Hardcover An Introduction to Echo their zeta function and periods, and a new ISBN 978-0-387-72828-5 approx. class of holomorphic diff erential operators Analysis $69.95 Chicago Meeting that send modular forms to those of a Scattering Theory and Wave diff erent weight. Propagation Number page 928 2007. Approx. 150 p. (Springer G. Roach , Strathclyde University, UK Theory Monographs in Mathematics) Hardcover This introduction reviews the principal Volume I: New Brunswick Meeting ISBN 978-0-387-72473-7 approx. $59.95 mathematical topics required for Tools and approaching wave propagation and Diophantine page 931 scattering problems, and shows how to Piecewise-smooth Dynamical Equations Systems develop the required solutions. The emphasis is on concepts and results Volume II: Albuquerque Meeting Theory and Applications rather than on the fi ne detail of proof. Each Analytic and M. di Bernardo , University of Bristol, chapter ends with a bibliography pointing Modern Tools page 933 to more detailed proofs. UK; University of Naples Federico II, H. Cohen , University of Bordeaux, France Italy; C. Budd , University of Bath, UK; 2007. Approx. 305 p. (Springer A. Champneys , University of Bristol, UK; The central theme of this book is the P. Kowalczyk , University of Bristol, UK; Monographs in Mathematics) Hardcover solution of Diophantine equations, i.e., University of Exeter, UK ISBN 978-1-84628-851-7 $119.00 equations or systems of polynomial equations which must be solved in integers, The primary purpose of this book is to Wave Propagation and rational numbers or more generally in introduce a coherent framework for algebraic numbers. This theme, in particular, understanding the dynamics of piecewise- Time Reversal in Randomly is the central motivation for the modern Volume 54, Number 7, Pages 817–952, August 2007 smooth and hybrid systems. An informal Layered Media theory of arithmetic algebraic geometry. In introduction asserts the ubiquity of such J. Fouque , North Carolina State Univer- this text, this is considered through three of models with examples drawn from sity; J. Garnier , Université de Paris VII, its most basic aspects. mechanics, electronics, control theory and Paris, France; G. Papanicolaou , Stanford physiology. The main thrust is to classify University, California; K. Solna , University of Vol. I 2007. XXII, 650 p. (Graduate Texts complex behaviour via bifurcation theory in California, Irvine in Mathematics, Volume 239) Hardcover a systematic yet applicable way. The key ISBN 978-0-387-49922-2 $59.95 concept is that of discontinuity-induced This book gives a systematic and self- bifurcation, which generalises diverse contained presentation of wave Vol. II 2007. XII, 500 p. (Graduate Texts phenomena such as grazing, border- propagation in randomly layered media in Mathematics, Volume 240) Hardcover collision, sliding, chattering and the period- using the asymptotic theory of ordinary adding route to chaos. diff erential equations with random ISBN 978-0-387-49893-5 $59.95 coeffi cients. 2007. Approx. 504 p. 234 illus. (Applied 2007. X, 440 p. (Stochastic Modelling and Mathematical Sciences, Volume 163) Applied Probability, Volume 56) Hardcover Hardcover ISBN 978-0-387-30890-6 $79.95 ISBN 978-1-84628-039-9 $99.00 Easy Ways to Order for the Americas Write: Springer Order Department, PO Box 2485, Secaucus, NJ 07096-2485, USA Call: (toll free) 1-800-SPRINGER Fax: +1(201)348-4505 Email: [email protected] or for outside the Americas Write: Springer Distribution Center GmbH, Haberstrasse 7, 69126 Heidelberg, Germany Call: +49 (0) 6221-345-4301 Fax : +49 (0) 6221-345-4229 Email: [email protected] Prices are subject to change without notice. All prices are net prices. 013170x Lipman Bers in Prague, 1934 (see page 925) Trim: 8.25" x 10.75" 136 pages on 40 lb Cougar Opaque • Spine: 3/16" • Print Cover on 9pt Carolina LATEX LATEX LATEX Pro AMERICAN MATHEMATICAL SOCIETY Mathematical Surveys and Monographs Series This series of high-level monographs is designed to meet the need for detailed expositions in current research fields. Each volume in the Mathematical Surveys and Monographs series gives a survey of the subject along with a brief introduction to recent developments and unsolved problems. New from this series... Harmonic Analysis on Commutative Spaces Joseph A. Wolf, University of California, Berkeley, CA Mathematical Surveys Volume 142; 2007; approximately 392 pages; Hardcover; ISBN: 978-0-8218-4289-8; and Monographs Volume 142 List US$99; AMS members US$79; Order code SURV/142 Harmonic Analysis on Commutative Algebraic Geometric Codes: Basic Notions Spaces Michael Tsfasman, Serge Vla˘dut¸, and Dmitry Nogin Joseph A.Wolf Volume 139; 2007; 338 pages; Hardcover; ISBN: 978-0-8218-4306-2; List US$89; AMS members US$71; Order code SURV/139 American Mathematical Society Mathematical Systolic Geometry and Topology Surveys and Monographs Volume 139 Algebraic Mikhail G. Katz, Bar Ilan University, Ramat Gan, Israel Geometric Volume 137; 2007; 222 pages; Hardcover; ISBN: 978-0-8218-4177-8; List US$69; Codes: AMS members US$55; Order code SURV/137 Basic Notions The Ricci Flow: Techniques and Applications MichaelTsfasman Part I: Geometric Aspects SergeVla˘dut¸ Dmitry Nogin Bennett Chow, Sun-Chin Chu, David Glickenstein, Christine Guenther, James Isenberg, Tom Ivey, Dan American Mathematical Society Knopf, Peng Lu, Feng Luo, and Lei Ni Volume 135; 2007; 536 pages; Hardcover; ISBN: 978-0-8218-3946-1; List US$109; AMS members US$87; Order code SURV/13 View the entire Mathematical Surveys and Monographs series by visiting www.ams.org/bookstore/survseries. 1-800-321-4AMS (4267), in the U. S. and Canada, or 1-401-455-4000 (worldwide); fax:1-401-455-4046; email: [email protected]. American Mathematical Society, 201 Charles Street, Providence, RI 02904-2294 USA New & Forthcoming from Birkhäuser Advanced Algebra A History of Abstract Algebra Conformal Groups in ANTHONY W. KNAPP, State University of New York, Stony ISRAEL KLEINER, York University, Toronto, ON, Canada Geometry and Spin Structures Brook, USA Prior to the nineteenth century, algebra meant the PIERRE ANGLÈS, Université Paul Sabatier, Toulouse, France Basic Algebra and Advanced Algebra systematically study of the solution of polynomial equations. By the This book provides a self-contained overview of the develop concepts and tools in algebra that are vital to twentieth century it came to encompass the study of role of conformal groups in geometry and every mathematician, whether pure or applied, abstract, axiomatic systems such as groups, rings, and mathematical physics. It features a careful aspiring or established. fi elds. This presentation provides an account of the development of the material, from the basics of intellectual lineage behind many of the basic concepts, Advanced Algebra includes chapters on modern Clifford algebras to more advanced topics; each results, and theories of abstract algebra. The algebra which treat various topics in commutative and chapter covers a specifi c aspect of conformal groups development of abstract algebra was propelled by the noncommutative algebra and provide introductions to and conformal spin geometry. All major concepts are need for new tools to address certain classical the theory
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