ISSN 0002-9920 Notices of the American Mathematical Society ABCD springer.com Highlights in Springer’s eBook Collection of the American Mathematical Society September 2009 Volume 56, Number 8 Bôcher, Osgood, ND and the Ascendance NEW NEW 2 EDITION EDITION of American Mathematics forms bridges between From the reviews of the first edition The theory of elliptic curves is Mathematics at knowledge, tradition, and contemporary 7 Chorin and Hald provide excellent distinguished by the diversity of the Harvard life. The continuous development and explanations with considerable insight methods used in its study. This book growth of its many branches permeates and deep mathematical understanding. treats the arithmetic theory of elliptic page 916 all aspects of applied science and 7 SIAM Review curves in its modern formulation, technology, and so has a vital impact on through the use of basic algebraic our society. The book will focus on these 2nd ed. 2009. X, 162 p. 7 illus. number theory and algebraic geometry. aspects and will benefit from the (Surveys and Tutorials in the Applied contribution of world-famous scientists. Mathematical Sciences) Softcover 2nd ed. 2009. XVIII, 514 p. 14 illus. Invariant Theory ISBN 978-1-4419-1001-1 (Graduate Texts in Mathematics, 2009. XI, 263 p. (Modeling, Simulation & 7 Approx. $39.95 Volume 106) Hardcover of Tensor Product Applications, Volume 3) Hardcover ISBN 978-0-387-09493-9 7 $59.95 Decompositions of ISBN 978-88-470-1121-2 7 $59.95 U(N) and Generalized Casimir Operators For access check with your librarian page 931 Stochastic Partial Linear Optimization Mathematica in Action Riverside Meeting Differential Equations The Simplex Workbook The Power of Visualization A Modeling, White Noise Approach G. Hurlbert S. Wagon page 1051 H. Holden , B. Oksendal , J. Uboe , This undergraduate textbook is written This is not only an introduction to T. Zhang for a junior/senior level course on linear Mathematica 6.0, but also a tour of modern mathematics. Wagon explores In this new edition the authors build on optimization. Unlike other texts, the treatment follows the “modified Moore some of the most important areas of the theory of SPDEs driven by space-time Volume 56, Number 8, Pages 905–1064, September 2009 modern mathematics with new Brownian motion, or space-time Lévy method” approach in which examples chapters on optimization and linear and process noise. The stochastic pressure and proof opportunities are worked into integer programming. Connections are equation for fluid flow in porous media is the text in order to encourage students also made to computer science with treated, as are applications to finance. to develop some of the content through their own experiments and arguments new material on graphs and networks. 2009. XX, 305 p. 17 illus. (Universitext) while they are reading the text. 3rd ed. 2010. XVI, 658 p. 531 illus., Softcover Teacher’s version available. 16 in color. With CD-ROM. Softcover ISBN 978-0-387-89487-4 ISBN 978-0-387-75366-9 7 Approx. $69.95 2009. Approx. 430 p. 21 illus. (Undergrad- uate Texts in Mathematics) Hardcover 7 Approx. $69.95 ISBN 978-0-387-79147-0 7 Approx. $59.95 Easy Ways to Order for the Americas 7 Write: Springer Order Department, PO Box 2485, Secaucus, NJ 07096-2485, USA 7 Call: (toll free) 1-800-SPRINGER 7 Fax: 1-201-348-4505 7 Email: [email protected] or for outside the Americas 7 Write: Springer Customer Service Center GmbH, Haberstrasse 7, 69126 Heidelberg, Germany 7 Call: +49 (0) 6221-345-4301 7 Fax : +49 (0) 6221-345-4229 7 Email: [email protected] 7 Prices are subject to change without notice. All prices are net prices. Representations of U(n) (see page 915) 014311x Trim: 8.25" x 10.75" 160 pages on 40 lb Velocity • Spine: 3/16" • Print Cover on 9pt Carolina ,!4%8 ,!4%8 ,!4%8 New and Forthcoming Titles Classical and Modern Applied Algebra Introduction to Applied Numerical Analysis Codes, Ciphers and Mathematical Logic Combinatorics Theory, Methods and Discrete Algorithms, Fifth Edition Second Edition Practice Second Edition A Modern Interest Rate Mathematics in Games, Essentials of Topology Introduction to Modeling Sports, and Gambling with Applications Linear Algebra Theory and Practice The Games People Play New and Forthcoming Cohomological and The World as a Propagation of Waves Geometric Approaches to Mathematical Game and the Equations of Rationality Problems John von Neumann and Hydrodynamics New Perspectives Twentieth Century Science Jacques Hadamard Giorgio Israel, Università di Roma ‘La Fedor Bogomolov; Yuri Tschinkel, New The conception of waves as discontinuities Sapienza’, Rome, Italy; Ana Millán Gasca, York University, NY, USA (Eds.) in some level of derivative of a wave function Università Roma Tre, Rome, Italy that propagate along the bicharacteristics of This comprehensive book is a digest of the wave equation spawned many of the im- research papers by leading specialists in “In view of the numerous major biographies of portant advances to both the purely math- the fi eld and gives indications for future von Neumann that have appeared, … and the ematical theory of hyperbolic equations, as research in rationality problems. Topics innumerable lesser treatments, what special well as the more physical and engineering- discussed include the rationality of quo- insight have Israel and Gasca brought to our oriented treatments of the subject of wave tient spaces, cohomological invariants of understanding of their subject? Everything motion. In mathematics, one can follow the quasi-simple groups of Lie type, rationality mentioned in this review can be found in their implications of this work into the subse- of the moduli space of curves, and rational book’s intense and detailed descriptions of the quent lectures that Hadamard gave on the points on algebraic varieties. cultural and scientifi c background of the times, Cauchy problem for linear partial differen- Contributors: F. Bogomolov; T. Petrov; and of the genesis of ideas that accompany tial equations. But one should regard this Y. Tschinkel; Ch. Böhning; G. Catanese; and extend beyond von Neumann’s work, masterful treatise not only as a precursor to I. Cheltsov; J. Park; N. Hoffmann; S. J. Hu; as well as in the explications of his work the later lectures on the Cauchy problem, M. C. Kang; L. Katzarkov; Y. Prokhorov; in terms that should be comprehensible but as a complementary work in which he A. Pukhlikov to the laity. Israel and Gasca’s book is an impressive accomplishment and a valuable establishes the roots of the mathematical theory in continuum mechanics. 2010. APPROX. 300 P. 10 ILLUS. contribution to and resource for burgeoning HARDCOVER von Neumanniana.” —SIAM News 2009. APPROX. 300 P. HARDCOVER ISBN 978-0-8176-4933-3 CA. $89.95 ISBN 978-3-7643-9968-9 $109.00 2009. XII, 207 P. HARDCOVER PROGRESS IN MATHEMATICS PROGRESS IN MATHEMATICAL PHYSICS ISBN 978-3-7643-9895-8 $129.00 SCIENCE NETWORKS. HISTORICAL STUDIES, Topics in Operator VOL. 38 Dynamical Systems with Semigroups Applications using MAPLE Shmuel Kantorovitz, Bar Ilan University, Partial Differential Stephen Lynch, Manchester Metropolitan Ramat Gan, Israel Equations University, UK This monograph is concerned with the Second Edition 2010. 2ND ED. APPROX. 500 P. 350 ILLUS. interplay between the theory of operator Emmanuele DiBenedetto, Vanderbilt SOFTCOVER semigroups and spectral theory. The ba- University, Nashville, TN, USA ISBN 978-0-8176-4389-8 CA. $59.95 sics on operator semigroups are concisely covered in this self-contained text. Part “The author’s intent is to present an Now in softcover I deals with the Hille–Yosida and Lumer– elementary introduction to pdes... In Phillips characterizations of semigroup contrast to other elementary textbooks on Iterated Maps on the generators, the Trotter–Kato approximation pdes...much more material is presented theorem, Kato’s unifi ed treatment of the on the three basic equations: Laplace’s Interval as Dynamical exponential formula and the Trotter prod- equation, the heat and wave equations... Systems uct formula, the Hille–Phillips perturbation The presentation is clear and well Pierre Collet, École Polytechnique, theorem, and Stone’s representation of organized...The text is complemented by Palaiseau, France; Jean-Pierre Eckmann, unitary semigroups. Part II explores gener- numerous exercises and hints to proofs.” Université de Genève, Switzerland alizations of spectral theory’s connection to —Mathematical Reviews (on the fi rst edition) operator semigroups. 2009. 2ND ED. XX, 390 P. 18 ILLUS. 2009. REPRINT OF THE 5TH PRINTING OF 2010. APPROX. 305 P. HARDCOVER HARDCOVER THE HARDCOVER EDITION ISBN 978-0-8176-4931-9 CA. $89.95 ISBN 978-0-8176-4551-9 CA. $59.95 XII, 248 P. 67 ILLUS. SOFTCOVER PROGRESS IN MATHEMATICS CORNERSTONES ISBN 978-0-8176-4926-5 CA. $49.95 MODERN BIRKHÄUSER CLASSICS #!,, s&!8 s% -!),ORDERS BIRKHAUSERCOMsWWWBIRKHAUSERCOM Please mention promotion #14329x 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 Birkhäuser Verlag AG by E-mail: [email protected] 14329x Notices of the American Mathematical Society September 2009 Communications 942 WHAT IS…the Complex Dual to the Real Sphere? Simon Gindikin 948 Proving Yourself: How 916 to Develop an Interview Lecture John Swallow 952 Donaldson and Taubes Features Receive 2009 Shaw Prize 954 What Is New in 916 Bôcher, Osgood, and the Ascendance III. Formatting References of American Mathematics at Harvard G. Grätzer Steve Batterson 958 Ask Professor Nescio By the start of the second decade of the twentieth 962 NSF Fiscal Year 2010 Budget century, the mathematics department at Harvard Request University was arguably the strongest in the United States. Yet this rise to mathematical prominence of Commentary America’s oldest university was remarkably recent and rapid.