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. 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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. 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