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ISS N 0002 -9920 of the American Mathematical Society April 2003 Volume 50, Number 4 An Introduction to Analysis on Metric Spaces page 438 Artful Mathematics: The Heritage of M. C. Escher page 446 Filling in Escher's blank space (see page 457) The Open Computer Algebra System ,.;' MuPAD Pro - [DtffEq.mnb] fo:B. MuPAD Pro is a full-featured computer algebra system in an integrated and 0 30 Vtewer - [VCamKiem2.vca] < Edit View Tools Animation Window Help open environment for symbolic and numeric computing . The MuPAD language has a Pascal-like syntax and allows imperative, functional, and object­ oriented programming . Its domains and categories are like object-oriented MuP .AJ) recognized an inhomogenous linear differential equation classes that allow overriding and corresponding homogenous system is expresse~ using a new ide overloading methods and operators, The differential equation y'"'(x) - 5y"(x) + 4 y(x) = 2 cos(x) o inheritance, and generic algorithms. 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Tools for Scientific Creativity Since 1981 Toll -free: 877-724-9673 • E-mail: [email protected] OUTSTANDING NEW MATHEMATICS BOOKS !57 AFFINE HECKE ALGEBRAS AND ORTHOGONAL POLYNOMIALS An Introduction to Logic, Induction Cohomology of Numerical Analysis and Sets Vector Bundles and Syzygies Endre Siili and David Mayers Thomas Forster Jerzy Weyman Written primarily for undergraduate mathe­ Philosophical considerations are given Derails the exposition of the geometric maticians, this study of numerical analysis is careful discussion in this introduction, technique of calculating syzygies. No based on real world problems. The authors placing the notion of inductively defined prior knowledge of representation theory develop the necessary machinery including sets (recursive datatypes) at the center of the is assumed. Includes chapters on several iteration, interpolation, boundary value exposition, resulting in an original analysis applications, with numerous exercises. problems and finite elements, keeping an of well-established topics. Cambridge Tracts in Mathematics !49 eye on the analytical basis for the work. London Mathematical Society Student Texts 56 0-521-62197-6 Hb $55.00* Includes historical notes on rhe development 0-521-82621-7 Hb $65.00* of the subject. 0-521-53361-9 Pb $23.00* 0-521-81026-4 Hb $80.00* Affine Heeke Algebras and 0-521-00794-1 Pb $29.00* Orthogonal Polynomials Probability Theory I. G. Macdonald The Logic of Science Chaos A satisfactory and coherent theory of E. T.Jaynes A Mathematical Introduction orthogonal polynomials in several variables, Edited by G. 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Throughout, the emphasis and can serve as templates for solving other selection of exercises. is on concrete examples which originate in problems. classical algebraic geometry. 0-521-81658-0 Hb $95.00* 0-521-01687-8 Pb $40.00* 0-521-82404-4 Hb $90.00 London Mathematical Society Lecture Note 0-521-53094-6 Pb $35.00 Series 296 0-521-52548-9 Pb $40.00* •prices subject to change CAMBRIDGE 800-872-7423 Available in bookstores or from UNIVERSITY PRESS us.cambridge.org/mathematics NEW f6 NOTEWORTHY from Birkhiiuser Forthcoming! Forthcoming! The Evolution Problem Schubert Varieties Derivatives in General Relativity V. LAKSHMIBAI, Northeastern University, Boston, MA; and Integrals of S. KLAINERMAN, Princeton Universirty, Princeton, NJ; and C.S. SESHADRI, Chennai Mathematical Institute, F. NICOLO, University of Rome Tor Vergata, Rome, Italy Chennai, India; and P. LIITELMANN, Universite Louis Multivariable Functions Pasteur, Strasbourg, France This monograph examines A. GUZMAN, The City College of New York, CUNY, New York, NY The algebro-geometric study of Schubert varieties the global aspects of the has had a considerable impact on the theory of algebraic This work examines derivatives and integrals of functions problem of evolution groups, leading to the construction of natural bases of of several real variables. Topics include differentiability equations in general representations of the full linear group, the orthogonal and its relation to partial derivatives, directional deriva­ relativity. Central to the group, and the symplectic group. The character formu­ tives and the gradient, surfaces, inverse and implicit work is a revisit of the las that emerge connect to monomial theory and to functions, integrability and properties of integrals, and proof of the global stability recent developments in path models, Frobenius split­ the theorems of Fubini, Stokes, and Gauss. Reflecting of Minkowski space, as lings, and quantum groups. Written by three leading the order of development in calculus, the text treats presented by Christodoulou mathematicians in algebraic geometry, group theory, limits, continuity, derivatives, and integrals with general­ and Klainerman (1993). and combinatorics, this self-contained exposition on izations from and analogies to elementary results, such as This text focuses on a Schubert varieties unfolds systematically and includes the second-derivative test and the Chain Rule. Historical new self-contained proof relevant introductory material, making it ideal for a comments, discussions of strategies and alternative paths of the main part of that graduate course or for self-study. to problems, and a conversational style make the book result which concerns ideal for advanced undergraduates in pure mathematics. the full solution of the radiation problem in vacuum for 2003/APPROX. 352 PP./HARDCOVER/$49.50 (TENT.) arbitrary asymptotic flat initial data sets. 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