Notices of the American Mathematical Society ISSN 0002-9920 springer.com New and Noteworthy of the American Mathematical Society Piecewise-smooth Dynamical Lie Sphere Geometry An Introduction to Bayesian Volume 54, Number 9 2ND October 2007 Systems With Applications to EDITION Scientifi c Computing Theory and Applications Submanifolds Ten Lectures on Subjective Computing M. di Bernardo , University of Bristol, UK; University T. E. Cecil , College of the E. Somersalo , Helsinki University of Technology, of Naples Federico II, Italy; C. Budd , University of Holy Cross, Worcester, MA, USA Helsinki, Finland; D. Calvetti , Case Western Reserve Bath, UK; A. Champneys , University of Bristol, UK; This book provides a modern treatment of Lie’s University, Cleveland, OH, USA P. Kowalczyk , University of Bristol, UK; University of geometry of spheres, its applications and the study This book has been written for undergraduate and Exeter, UK of Euclidean space. It begins with Lie’s construction graduate students in various areas of mathematics This book presents a coherent framework for of the space of spheres, including the fundamental and its applications. It is for students who are understanding the dynamics of piecewise-smooth notions of oriented contact, parabolic pencils of willing to get acquainted with Bayesian approach to and hybrid systems. An informal introduction spheres and Lie sphere transformation. The link with computational science but not necessarily to go expounds the ubiquity of such models via Euclidean submanifold theory is established via the through the full immersion into the statistical numerous. The results are presented in an informal Legendre map. This provides a powerful framework analysis. It has also been written for researchers style, and illustrated with many examples. The book for the study of submanifolds, especially those working in areas where mathematical and statistical The Character is aimed at a wide audience of applied mathemati- characterized by restrictions on their curvature modeling are of central importance, such as biology cians, engineers and scientists at the beginning spheres. and engineering. Table for E postgraduate level. Almost no mathematical This new edition contains revised sections on taut 8 background is assumed other than basic calculus submanifolds, compact proper Dupin submanifolds, 2007. Approx. 215 p. (Surveys and Tutorials in the and algebra. reducible Dupin submanifolds, Lie frames and frame Applied Mathematical Sciences, Volume 2) page 1122 reductions. Completely new material on isopara- Softcover 2007. Approx. 510 p. 234 illus. (Applied Mathemat- metric hyperspaces in spheres, Dupin hyperspaces ISBN 978-0-387-73393-7 $39.95 ical Sciences, Volume 163) Hardcover with three and four principle curvatures is also ISBN 978-1-84628-039-9 $99.00 included. An Introduction to Manifolds Paul Halmos: L. W. Tu , Tufts University, Medford, MA, USA The Riemann Hypothesis 2nd ed. 2008. Approx. 305 p. 14 illus. (Universitext) In His Own Words Softcover This book introduces the fundamental theory of A Resource for the Affi cionado and Virtuoso ISBN 978-0-387-74655-5 approx. $49.95 manifolds in a readable but rigorous manner. In Part page 1136 Alike I the theory of diff erential forms on Rn is presented P. Borwein , S. Choi , B. Rooney , Simon Fraser Semiparallel as a natural bridge between calculus and the theory University, Burnaby, BC, Canada; A. Weirathmueller , Submanifolds in of manifolds. Once this intuitive foundation is laid, University of Western Ontario, London, ON, Canada manifolds are defi ned in Part II, and several San Diego Meeting Space Forms examples considered. In Parts III and IV tangent This book presents the Riemann Hypothesis, spaces are introduced, along with Lie groups and connected problems, and a taste of the body of Ü. Lumiste , University of page 1225 Lie algebras. Throughout, the author emphasizes theory developed towards its solution. It is targeted Tartu, Estonia the connection between tangent spaces and the at the educated non-expert. Almost all the material This book off ers a familiar methods of linear approximation from is accessible to any senior mathematics student, comprehensive survey to calculus. With this background in place, calculus on and much is accessible to anyone with some date of the theory of manifolds is studied, and important topological university mathematics. The appendices include a semiparallel submani- invariants, such as the de Rham cohomology, are selection of original papers that encompass the folds. Introduced in 1985, semiparallel submani- computed. most important milestones in the evolution of folds have emerged as an important area of Assuming only a year of real analysis and a semester research within diff erential geometry and topology. theory connected to the Riemann Hypothesis. The Volume 54, Number 9, Pages 1113–1272, October 2007 of abstract algebra at the undergraduate level, and appendices also include some authoritative Lumiste begins with the necessary background on: with all necessary point-set topology summarized expository papers. These are the “expert witnesses” symmetric and semisymmetric Riemannian in an appendix, this book introduces manifolds at a whose insight into this fi eld is both invaluable and manifolds, smooth manifolds in space forms, and level suitable for advanced undergraduates and irreplaceable. parallel submanifolds. Semiparallel submanifolds beginning graduate students. are introduced in Chapter 4, where characteriza- 2007. Approx. 590 p. 25 illus. (CMS Books in tions of their class and several subclasses are given. 2007. Approx. 390 p. 104 illus. (Universitext) Mathematics) Hardcover In later chapters Lumiste introduces the concept of Softcover ISBN 978-0-387-72125-5 approx. $79.95 main symmetric orbit and presents all known ISBN 978-0-387-48098-5 approx. $49.95 results concerning umbilic-like main symmetric orbits. Semiparallel Submanifolds in Space Forms will appeal to both researchers and graduate students. 2008. Approx. 325 p. Hardcover ISBN 978-0-387-49911-6 approx. $79.95 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. 013279x San Diego Mission (see page 1177) Trim: 8.25" x 10.75" 160 pages on 40 lb Cougar Opaque • Spine: 1/4" • Print Cover on 9pt Carolina ,!4%8 ,!4%8 ,!4%8 Pro New & Forthcoming from Birkhäuser D-Modules, Perverse Sheaves, and Representation Theory Additional forthcoming titles in the CORNERSTONES series: RYOSHI HOTTA, Wako, Japan; KIYOSHI TAKEUCHI, Tsukuba University, Japan; TOSHIYUKI TANISAKI, Osaka City University, Japan Distributions Translated by KIYOSHI TAKEUCHI, Tsukuba University, Japan Theory and Applications The key to D-modules, Perverse Sheaves, and Representation Theory is the authors’ essential algebraic-analytic approach JOHANNES J. DUISTERMAAT; JOHAN A.C. KOLK, to the theory, which connects D-Modules to representation theory and other areas of mathematics. Signifi cant concepts both Universiteit Utrecht, The Netherlands and topics that have emerged over the last few decades are presented, including a treatment of the theory of holonomic This text is a concise, application-oriented D-modules, perverse sheaves, the all-important Riemann-Hilbert correspondence, Hodge modules, and the solution to introduction to the theory of distributions. It presents Kazhdan-Lusztig polynomials using D-module theory. To further aid the reader, and to make the work as self-contained distributions as a natural method of analysis from both as possible, appendices are provided as background for the theory of derived categories and algebraic varieties. a mathematical and physical point of view. Methods are developed to justify many formal calculations that 2007/XII, 404 PP., 66 ILLUS./HARDCOVER/ISBN 9780817643638/$89.95/PROGRESS IN MATHEMATICS, VOL. 236 do not make sense in the classical framework. The discussion emphasizes applications to the general Dynamical Systems Integrable Systems in study of linear partial differential equations. The subject in this textbook is motivated by many with Applications using Celestial Mechanics examples, exercises, hints and solutions that guide Mathematica® DIARMUID Ó’MATHÚNA, Dublin Institute for Advanced the student along a path requiring only a minimal Studies, Dublin, Ireland STEPHEN LYNCH, Manchester Metropolitan University, UK mathematical background. This work focuses on the two integrable systems of On the author’s Maple edition: 2008/APPROX. 350 PP., 25 ILLUS./HARDCOVER relevance to celestial mechanics, both of which date ISBN 9780817646721/$59.95 TENT. “The book will be useful for all kinds of dynamical back to the 18th century. Under discussion are the CORNERSTONES systems courses…. [It] shows the power of using a Kepler (two-body) problem and the Euler (two-fi xed computer algebra program to study dynamical systems, center) problem, the latter being the more complex and, by giving so many worked examples, provides and more instructive, as it exhibits a richer and more Geometric Integration Theory ample opportunity for experiments. … [It] is well varied solution structure. The present work shows that