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AMERICAN MATHEMATICAL SOCIETY Research in Collegiate Mathematics Education. V Annie Selden, Tennessee Technological University, Cookeville, Ed Dubinsky, Kent State University, OH, Guershon Hare I, University of California San Diego, La jolla, and Fernando Hitt, C/NVESTAV, Mexico, Editors This volume presents state-of-the-art research on understanding, teaching, and learning mathematics at the post-secondary level. The articles are peer-reviewed for two major features: (I) advancing our understanding of collegiate mathematics education, and (2) readability by a wide audience of practicing mathematicians interested in issues affecting their students. This is not a collection of scholarly arcana, but a compilation of useful and informative research regarding how students think about and learn mathematics. This series is published in cooperation with the Mathematical Association of America. CBMS Issues in Mathematics Education, Volume 12; 2003; 206 pages; Softcover; ISBN 0-8218-3302-2; List $49;AII individuals $39; Order code CBMATH/12N044 MATHEMATICS EDUCATION Also of interest .. RESEARCH: AGul<lelbrthe Mathematics Education Research: Hothomatldan- A Guide for the Research Mathematician --lllll'tj.M...,.a.,-- Curtis McKnight, Andy Magid, and -- Teri J. Murphy, University of Oklahoma, Norman, and Michelynn McKnight, Norman, OK 2000; I 06 pages; Softcover; ISBN 0-8218-20 16-8; List $20;AII AMS members $16; Order code MERN044 Teaching Mathematics in Colleges and Universities: Case Studies for Today's Classroom Graduate Student Edition Faculty Edition Solomon Friedberg, Boston College, Chestnut Hill, MA This series is published in cooperation with the Mathematical Association of America. CBMS Issues in Mathematics Education, Graduate Student Edition: Volume I 0; 200 I; 67 pages; Softcover; ISBN 0-8218-2823-1 ; list $16;AII individuals $13; Order code CBMATH/1 ON044 CBMS Issues in Mathematics Education, Faculty Edition: Volume I 0; 200 I; 158 pages; Softcover; ISBN 0-8218-2875-4; list $29; All individuals $23; Order code CBMATH/1 O.FN044 The Mathematical Education ofTeache rs This series is published in cooperation with the Mathematical Association of America. CBMS Issues in Mathematics Education, Volume II; 2001; 145 pages; Softcover; ISBN 0-8218-2899-1 ; List $24;AII individuals $19; Order code CBMATH/1 I N044 For many more publications of interest, visit the AMS Bookstore www.amsbookstore.org I-800-321-4AMS (4267), in the U.S. and Canada, or 1-40 1-455-4000; fax: 1-40 1-455-4046; email: [email protected]. American Mathematical Society, 20 I Charles Street, Providence, Rl 02904-2294, USA ~104 International Mathematics· Research Notices Editors Website: http://imrn.hindawi.com Morris Weisfeld IMRN provides very fast publication of research articles of high current interest in all Managing Editor areas of mathematics. All articles are fully refereed and are judged by their contribution to advancing the state of the science of mathematics. Issues are published as frequently as Dan Abramovich necessary. IMRN is expected to publish 80± issues in volume 2004. The articles ofiMRN are Enrico Arbarello reviewed/indexed in COMPUMATH Citation Index, Current Contents, lSI Alerting Services, Joseph Bernstein Mathematical Reviews, Science Citation Index, SciSearch, and Zentralblatt fUr Mathematik. Enrico Bombieri There are no page charges. Submissions are made by email to [email protected]. Richard E. Borcherds New print subscribers shall receive a free copy of all back volumes, i.e., volumes 1991- 2003. Alexei Borodin New and current online subscribers shall receive "perpetual" online access to volumes Jean Bourgain 1991- 2004. Contact [email protected] for more details. Marc Burger ARTICLES Tobias Golding FORTHCOMING Corrado DeConcini • A Cuspidality Criterion for the Functorial Product on GL(2) x GL(3) PercyDeift with a Cohomological Application, Dinakar Ramakrishnan and Song Wang Robbert Dijkgraaf • A New Proof of Steinberg's Fixed-Point Theorem, G. I. Lehrer S. K. Donaldson • A Stacky Semistable Reduction Theorem, Martin Olsson Yakov Eliashberg • Associated Primes of Local Cohomology Modules and of Frobenius Powers, Edward Frenkel Anurag K . Singh and Irena Swanson Emmanuel Hebey • Bounded Geodesics in Moduli Space, Dmitry Kleinbock and Barak Weiss Dennis Hejhal • Gap Probability in the Spectrum of Random Matrices and Asymptotics of Polynomials Helmut Hofer Orthogonal on an Arc of the Unit Circle, I. V. Krasovsky Gerhard Huisken • l -Functions of Exponential Sums over One-Dimensional Affi.noids: Newton over Yasutaka Ihara Hodge, Hui June Zhu Michio Jimbo • Minimality and Nondegeneracy of Degree-One Ginzburg-Landau Vortex as a Hardy's Kurt Johansson Type Inequality, Manuel del Pi no, Patricio Felmer, and Michal Kowalczyk Masaki Kashiwara Kiran S. Kedlaya Carlos Kenig Sergiu Klainerman Toshiyuki Kobayashi Maxim Kontsevich Igor Krichever Shigeo Kusuoka Gilles Lebeau Joachim Lohkamp Nikolai Makarov Yu. l. Manin Barry Mazur Haynes Miller Shinichi Mochizuki Fabien Morel Michael Rapoport N. Yu. Reshetikhin Igor Rodnianski Peter Sarnak Freydoon Shahidi Stanislav Smirnov Michael Struwe G. Tian John Toth Takeshi Tsuji David Vogan Dan Voiculescu Hindawi Publishing Corporation , 410 Park Avenue, 15th Floor, #287 pmb, New York, Andrei Zelevinsky HINDAWI NY 10022, USA; Fax 1-866-446-3294 (USA, toll-free) Maciej Zworski NEW f6 FORTHCOMING from Birkhiiuser Mathematical Theory Regularity Theory for Linear Algebra Second Edition of Diffraction Mean Curvature Flow J. H. KWAKand S. HONG, both, Pohang University of A. SOMMERFELD (Author) K. ECKER, Freie Universitiit, Berlin, Germany Science and Technology, Pohang, Republic of Korea R. J. NAGEM, Boston University, Boston, MA; M. ZAMPOLLI, NATO SACLANT Undersea Research Centre, La Spezia, Italy; and This work focuses on the motion of surfaces whose ':41ogical development of the subject .. all the G. SANDRl,Boston University, Boston, MA (Translators) normal velocity at every point is given by the mean curvature at that point; this geometric heat flow process important theorems and results are discussed in A. Sommerfeld's Mathematische Theorie der Diffraction terms of simple worked examples. The student's is called mean curvature flow. Mean curvature flow and marks a milestone in optical theory, full of insights that related flows are important tools in mathematics and understanding is tested by problems at the end of are still relevant today. In a stunning tour de force, each subsection, and every chapter ends with mathematical physics. This work presents techniques in Sommerfeld derives the first mathematically rigorous the study of singularities of mean curvature flow and is exercises. " -CURRENT SCIENCE solution of an optical diffraction problem. This com­ (REVIEW OF THE FIRST EDITION) largely based on the work of K. Brakke, although more plete translation, reflecting substantial scholarship, is recent developments are presented as well: for exam­ Acornerstone of undergraduate mathematics, the first publication in English of Sommerfeld's original ple, relations to regularity theory for minimal surfaces, science, and eHgineering, the fundamentals of work. The extensive notes by the translators are rich in as in Allard's and de Giorgi's work. linear algebra are given a clear and rigorous historical background and provide many technical presentation in this text. With emphasis on both details for the reader. 2004/144 PP., 16 ILLUS./HARDCOVER/$ 129.00 ISBN 0-8176-3243-3 theory and computation, the authors cover linear 2004/190 PP., 381LLUS./HARDCOVER/$54.95 PROGRESS IN NONLINEAR DIFFERENTIAL EQUATIONS AND THEIR equations, matrices, determinants, and vector ISBN 0-8176-3604-8 APPLICATIONS, VOL 57 spaces, and continue on to complex vector spaces, PROGRESS IN MATHEMATICAL PHYSICS, VOL 35 inner products, quadratic forms, and Jordan canonical form. Approximation Theory Semiconcave Functions, From Taylor Polynomials to Wavelets KEY TOPICS AND FEATURES: Thorough treatment of the basics, with a particular focus on linear Hamilton-Jacobi 0. CHRISTENSEN and K. L. CHRISTENSEN, both, recurrence, difference, and differential equations Equations, and Technical University of Denmark, Lyngby, Denmark • Avariety of applications of linear algebra to This concisely written book gives an elementary intro­ diverse fields, such as economics, physics, and Optimal Control duction to a classical area of mathematics-approxima­ computer science • Rich selection of examples P. CANNARSA and C. SINESTRARI, both, Universitii di Roma tion theory-in a way that naturally leads to the modern and explanations, with a wide range of exercises at 'Tor Vergata', Roma, Italy field of wavelets. The exposition demonstrates the the end of every section. This text is a exposition of the theory of semiconcave dynamic nature of mathematics and how classical This second edition includes substantial revisions, functions, and of the role they play in optimal control disciplines influence many areas of modern mathemat­ new material on minimal polynomials and diagonal­ and Hamilton-Jacobi equations. The first part of the ics and applications. The emphasis is on ideas rather ization, and several illuminating figures and book covers general theory, encompassing all key than technical details and proofs. diagrams. Valuable for theoretical and applied results and illustrating them with significant examples. KEY TOPICS AND FEATURES: Description of wavelets in courses, this work is also ideal for self-study. The latter part is devoted to applications concerning
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