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A Special Issue on Formal Proof Notices of the American Mathematical Society ISSN 0002-9920 ABCD springer.com New and Noteworthy from Springer Least-Squares Collected More Math Into LaTeX Finite Element Methods Papers of G. Grätzer, University of Manitoba, of the American Mathematical Society P. B. Bochev, Sandia National Bertram Winnipeg, MB, Canada December 2008 Volume 55, Number 11 Laboratories, Albuquerque, NM, USA; Kostant In this fourth edition, the reader is M. D. Gunzburger, Florida State provided with important updates on University, Tallahassee, FL, USA Volume I articles and books. An important new 1955-1966 This book provides researchers and topic is discussed: transparencies practitioners with a concise guide to the B. Kostant, (computer projections). A new online theory and practice of least-square Massachusetts visual tutorial is also available. Please finite element methods, their strengths Institute of Technology, Cambridge, visit springer.com/978-0-387-32289-6 Formal Proof and weaknesses, established successes, MA, USA for more information, or take a tour of and open problems. Editors: A. Joseph, Weizmann Institute, this unique tutorial. page 1370 Israel; S. Kumar, UNC Chapel Hill, NC, 2007. XXXIV, 619 p. 44 illus. Softcover 2009. Approx. 285 p. (Applied Mathe- USA; M. Vergne, École Polytechnique, ISBN 978-0-387-32289-6 $49.95 matical Sciences, Volume 166) Hardcover Palaiseau Cedex, France Formal Proof—The ISBN 978-0-387-30888-3 approx. $69.95 For more than five decades Bertram Generalized Four-Color Theorem Elementary Number Kostant has been one of the major Measure architects of modern Lie theory. page 1382 Theory: Primes, Virtually all of his papers are pioneering Theory Congruences, and Secrets with deep consequences, many giving Z. Wang, rise to new fields of activities. His University of A Computational Approach interests span a tremendous range of Nebraska at Formal Proof— W. Stein, University of Washington, Lie theory, from differential geometry to Omaha, NE, USA; Theory and Practice Seattle, WA, USA representation theory, abstract algebra, G. J. Klir, This is a textbook about classical and mathematical physics. It is striking Binghamton page 1395 elementary number theory and elliptic to note that Lie theory (and symmetry University, Binghamton, NY, USA curves. The first part discusses in general) now occupies an ever larger This comprehensive text examines the elementary topics such as primes, role in mathematics than it did in the relatively new mathematical area of Formal Proof— factorization, continued fractions, and fifties. This is the first volume (1955- generalized measure theory. It begins Getting Started quadratic forms, in the context of 1966) of a five-volume set of Bertram with preliminaries and new concepts, Kostant‘s collected papers. A distin- cryptography, computation, and deep followed by a detailed treatment of page 1408 open research problems. The second guishing feature of this first volume is important new results regarding various part is about elliptic curves, their Kostant‘s commentaries and summaries types of nonadditive measures and the applications to algorithmic problems, of his papers in his own words. associated integration theory. All of the Volume 55, Number 11, Pages 1361–1504, December 2008 and their connections with problems in topics are motivated by numerous 2009. Approx. 610 p. 3 illus. Hardcover number theory such as Fermat’s Last examples, culminating in a final chapter ISBN 978-0-387-09582-0 $149.00 Theorem, the Congruent Number on applications of generalized measure Problem, and the Conjecture of Birch theory. A sound background in and Swinnerton-Dyer. The Map of My Life mathematical analysis is required. G. Shimura, Princeton University, 2009. Approx. 415 p. 25 illus. (IFSR, 2009. Approx. 175 p. 45 illus. (Under- Princeton, NJ, USA graduate Texts in Mathematics) Hardcover International Series on Systems Science and Engineering, Volume 25) Hardcover ISBN 978-0-387-85524-0 $49.95 2008. VI, 212 p. 5 illus. Hardcover ISBN 978-0-387-76851-9 $79.95 ISBN 978-0-387-79714-4 $34.95 Be Sure To Take Advantage of the 2008 Yellow Sale. Find Out More at springer.com. 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 Customer Service 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. 013971x Four-color hypermaps (see page 1427) Trim: 8.25" x 10.75" 144 pages on 40 lb Cougar Opaque • Spine: 5/16" • Print Cover on 9pt Carolina LATEX LATEX LATEX Volume 2008 Open Access Journals Abstract andApplied Analysis in Mathematics Your research wants to be free! Hindawi Publishing Corporation http://www.hindawi.com Advances in Difference Equations Advances in Mathematical Physics Submit your manuscripts at Hindawi Publishing Corporation http://www.hindawi.com Volume 2008 Hindawi Publishing Corporation Volume 2008 http://www.hindawi.com http://www.hindawi.com 7 Volume 2008 6 Advances in Discrete Dynamics in 9 5 Operations Nature and Society 1 8 Boundary An International Multidisciplinary Research and Review Journal Research Value 7 Problems 6 Differential Equations 7 and Nonlinear Advances in Mechanics Numerical Analysis Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation3 Volume 2008 Hindawi Publishing Corporation http://www.hindawi.com Volume 2008 Hindawi Publishing Corporation http://www.hindawi.com 2 http://www.hindawi.com Volume 2008 http://www.hindawi.com http://www.hindawi.com Volume 2008 Fixed Point Theory International Journal of and Applications Journal of Applied Mathematics Mathematics and Mathematical Sciences International Journal of International Journal of Differential Combinatorics Equations Hindawi Publishing Corporation http://www.hindawi.com Volume 2008 Hindawi Publishing Corporation Volume 2008 Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com http://www.hindawi.com Volume 2008 http://www.hindawi.com Volume 2008 http://www.hindawi.com Volume 2008 Journal of Journal of Journal of Mathematical Applied JAMSA Inequalities Probability and Applications Problems in Mathematics and Journal of Applied Mathematics Engineering and Stochastic Analysis and Statistics Theory, Methods, and Applications Decision Sciences Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com Volume 2008 Hindawi Publishing Corporation http://www.hindawi.com Volume 2008 http://www.hindawi.com Volume 2008 http://www.hindawi.com Volume 2008 http://www.hindawi.com Volume 2008 New and Forthcoming from Birkhäuser Nonlinear Partial Fourier–Mukai and Nahm Stable Homotopy Around the Diff erential Equations Transforms in Geometry and Arf-Kervaire Invariant Asymptotic Behavior of Solutions and Mathematical Physics VICTOR P. SNAITH, University of Sheffi eld, UK Self-Similar Solutions CLAUDIO BARTOCCI, Università degli Studi di Genova, This monograph describes important techniques MI-HO GIGA; YOSHIKAZU GIGA, both Giga Laboratory, Italy; UGO BRUZZO, SISSA, Trieste, Italy; DANIEL of stable homotopy theory, both classical and new, HERNANDEZ RUIPEREZ, Universidad de Salamanca, Spain University of Tokyo, Japan; JÜRGEN SAAL, University of applying them to the long-standing unsolved problem Konstanz, Germany This book examines the differential-geometric of the existence of framed manifolds with odd This work will serve as an excellent fi rst course constructions of (Nahm) as well as the algebro- Arf-Kervaire invariant. Opening with an account of the in modern analysis. Key topics in nonlinear PDEs geometric approach to (Fourier–Mukai functors) necessary algebraic topology background, the book as well as several fundamental tools and methods transforms in geometry and math physics. Also proceeds in a quasi-historical manner drawing from are presented; few prerequisites are required of included is a considerable amount of material the author’s contributions over several decades. A new the reader. Challenging exercises, examples, and scattered in the literature and not systematically technique entitled “upper triangular technology” is illustrations help explain the rigorous analytic basis organized in any existing textbook or monograph. introduced, which enables the author to relate Adams for the Navier–Stokes equations, mean curvature fl ow operations to Steenrod operations and thereby to equations, and other important equations describing 2009/APPROX. 300 PP./HARDCOVER recover most of the important classical Arf-Kervaire real phenomena. The main focus of the text is on ISBN 9780817632465/$74.95 TENT. invariant results. The fi nal chapter briefl y relates the PROGRESS IN MATHEMATICS showing how self-similar solutions are useful in book to the contemporary motivic stable homotopy studying the behavior of solutions of nonlinear PDEs, theory of Morel-Voevodsky. especially those of parabolic type. Number Theory 2009/APPROX. 250 PP./HARDCOVER 2009/APPROX. 350 PP., 20 ILLUS./HARDCOVER Structures, Examples, and Problems ISBN 9783764399030/$79.95 TENT. ISBN 9780817641733/$99.00 TENT. TITU ANDREESCU, The University of Texas at Dallas, PROGRESS IN MATHEMATICS Richardson, TX, USA; DORIN ANDRICA, ‘Babes-Bolyai’
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