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New and Forthcoming Books in Mathematics New and Forthcoming Books in Mathematics Contents Mail orders All orders from individuals must be prepaid or charged on American Express, VISA Highlights..........................................p. 3 or MasterCard. Forthcoming titles can be ordered now and will be shipped when they become available. Please feel free to share this information with your colleagues. Logic and Combinatorics ...................p. 4 The order form may be photocopied. Algebra .............................................p. 5 Phone orders Number Theory..................................p. 8 To place a telephone order of $25 or more between the hours of 9:00 AM and 5:00 PM ET Monday through Friday: call 1-800-872-7423 in the U.S. and Canada. Geometry and Topology ..................p. 10 In Mexico call 55 5519 59 39. Analysis and Probability ...................p. 12 Library orders Mathematical Physics.......................p. 15 Libraries are encouraged to use their wholesalers. Mathematical Biology ......................p. 17 Text Statistics ..........................................p. 19 Please visit us at www.cambridge.org/us/textbooks to request an examination copy of a textbook. You may also speak with a college sales representative at toll free Fluid Dynamics and Solid 1 866 257 3385 or email your request to [email protected] Mechanics....................................p. 21 Book Proposals Applied Math and Computational Science........................................ p. 23 We are always pleased to hear about new book proposals. Please contact our Mathematics editor, Roger Astley, at [email protected] Computer Science ...........................p. 26 Web orders General Interest...............................p. 30 To place an order or to view a complete listing of Cambridge University Press books Journals .................................Order Form in print, please visit our web site at: www.cambridge.org/us. If you would like to be on our electronic mailing list and receive regular information about our new books, please visit: www.cambridge.org/alerts Selected backlist online sale The best of the backlist is available at a 20% discount, only at www.cambridge.org/us/promotion/math 32 Avenue of the Americas Cover: Image from Super Fractals, by Michael Fielding Barnsley New York, NY 10013-2473 Catalog cover design by Logan Johnson & Paul Hanger Mathematics challenging offer a glimpse of deep Highlights results that engage mathematicians today, while even the easiest prompt Lectures on the Ricci readers to think about mathematics. All come with solutions, many with hints, and Flow SuperFractals most with illustrations. Whether you are Peter Topping Michael Fielding Barnsley an expert or amateur mathematician, this University of Warwick Australian National University, Canberra book will delight for a lifetime. After describing the basic properties of, SuperFractals is the long-awaited 2006/374 pp./85 line diagrams and intuition behind, the Ricci flow, core successor to Fractals Everywhere,in 87228-6/Hb/$85.00 elements of the theory are discussed, which the power and beauty of Iterated 69395-0/Pb/$34.99 including consequences of various forms Function Systems (IFS) were introduced of maximum principle, issues related to CAMBRIDGE UNIVERSITY PRESS existence theory, and basic properties of and applied to producing startling and CONGRATULATES TERENCE TAO, original images that reflect complex WINNER OF A 2006 FIELDS singularities in the flow. A detailed structures found, for example, in nature. MEDAL! exposition of Perelman’s entropy This provoked the question of whether functionals is combined with a description there is a deeper connection between of Cheeger-Gromov-Hamilton topology, geometry, IFS, and codes on the Additive Combinatorics compactness of manifolds and flows to show how a ‘tangent’ flow can be one hand and biology, DNA, and protein Terence Tao development on the other. Now, 20 years University of California, Los Angeles extracted from a singular Ricci flow. later, Barnsley brings the story up to date Van H. Vu Finally, all these threads are pulled by explaining how IFS have developed in Rutgers University, New Jersey together to give a modern proof of order to address this issue. New ideas Additive combinatorics is the theory of Hamilton’s theorem that a closed three- such as fractal tops and superIFS are counting additive structures in sets. This dimensional manifold which carries a introduced, and the classical deterministic theory has seen exciting developments metric of positive Ricci curvature is a approach is combined with probabilistic and dramatic changes in direction in spherical space form. ideas to produce new mathematics and recent years, thanks to its connections Contents: 1. Introduction; 2. Riemannian geometry algorithms that open a whole theory that with areas such as number theory, ergodic background; 3. The maximum principle; 4. could have applications in computer theory, and graph theory. This graduate- Comments on existence theory for parabolic PDE; graphics, bioinformatics, economics, signal level textbook will allow students and 5. Existence theory for the Ricci flow; 6. Ricci flow processing, and beyond. For the first time, researchers easy entry into this fascinating as a gradient flow; 7. Compactness of Riemannian these ideas are explained in book form field. Here, for the first time, the authors manifolds and flows; 8. Perelman’s W entropy functional; 9. Curvature pinching and preserved and illustrated with breathtaking pictures. bring together the many different tools curvature properties under Ricci flow; 10. Three- Contents: and ideas that are used in the modern manifolds with positive Ricci curvature and Part I. Geometries and Transformations: 1. Codes, theory, presenting them in an accessible, beyond. metrics and topologies; 2. Transformations of coherent, and intuitively clear manner, and London Mathematical Society Lecture points, sets, pictures and measures; 3. Semigroups providing immediate applications to Note Series on sets, measures and pictures; Part II. Iterated 2006/124 pp. Function Systems: 4. IFS acting on measures; 5. problems in additive combinatorics. The 68947-3/Pb/$45.00 More on IFS; Part III. Applications to Graphics: 6. power of these tools is well demonstrated Digital content production; 7. Image compression; in the presentation of recent advances 8. Super IFS. such as Szemerédi’s theorem on 2006/464 pp./250 color figures arithmetic progressions, the Kakeya 84493-2/Hb/$35.00 Percolation conjecture and Erdos distance problems, Bela Bollobás and the developing field of sum-product Oliver Riordan estimates. The text is supplemented by a Trinity College, Cambridge The Art of Mathematics large number of exercises and new Percolation theory was initiated some fifty Coffee Time in Memphis results. years ago as a mathematical framework Bela Bollobás Contents: for the study of random physical Trinity College, Cambridge Prologue; 1. The probabilistic method; 2. Sum set processes such as flow through a estimates; 3. Additive geometry; 4. Fourier analytic Can a Christian escape from a lion? How methods; 5. Inverse sumset theorems; 6. Graph disordered porous medium. It has proved quickly can a rumor spread? Can you fool theoretic methods; 7. The Littlewood-Offord to be a remarkably rich theory, with an airline into accepting oversize problem; 8. Incidence geometry; 9. Algebraic applications beyond natural phenomena baggage? Recreational mathematics is full methods; 10. Szemerédi’s theorem for k = 3; 11. to topics such as network modelling. The Szemerédi’s theorem for k > 3; 12. Long of frivolous questions where the arithmetic progressions in sumsets; Bibliography. aims of this book are twofold. First, to mathematician’s art can be brought to Cambridge Studies in Advanced present classical results in a way that is bear. But play often has a purpose. In Mathematics accessible to non-specialists. Second, to mathematics, it can sharpen skills, provide 2006/530 pp./635 exercises describe, for the first time in a book, amusement, or simply surprise, and books 85386-9/Hb/$85.00 recent results of Smirnov in conformal of problems have been the stock-in-trade invariance, and outline the proof that the of mathematicians for centuries. The critical probability for random Voronoi questions range in difficulty; the most percolation in the plane is 1/2. It will be essential for mathematicians, physicists, 3 www.cambridge.org/us/mathematics Mathematics electrical engineers, and computer varying levels of technicality, the real scientists working in this exciting area. interplay between these two ancient Logic and Contents: disciplines. The story involves physics, Preface; 1. Basic concepts; 2. Probabilistic tools; biology, psychoacoustics, the history of Combinatorics 3. Percolation on Z2 - the Harris-Kesten Theorem; science, and digital technology as well as, 4. Exponential decay and critical probabilities - theorems of Menshikov and Aizenman & Barsky; of course, mathematics and music. 5. Uniqueness of the infinite open cluster and Contents: critical probabilities; 6. Estimating critical Preface; Introduction; Acknowledgements; 1. How to Prove It probabilities; 7. Conformal invariance - Smirnov’s Waves and harmonics; 2. Fourier theory; 3. A A Structured Approach Theorem; 8. Continuum percolation; Bibliography; mathematician’s guide to the orchestra; 4. Index; List of notation. Consonance and dissonance; 5. Scales and 2nd Edition 2006/334 pp./112 line diagrams temperaments: the fivefold way; 6. More
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