ISSISSSSNN0 0002000022-99-992020 Notices of the American Mathematical Society 35 Monticello Place, Pawtucket, RI 02861 USA Society Distribution Center American Mathematical AMERICAN MATHEMATICAL SOCIETY For the Avid Reader of the American Mathematical Society Computational Mathematics Everywhere Markov Chains and Topology Martin Aigner and Ehrhard Mixing Times June/July 2011 Volume 58, Number 6 An Introduction Behrends, Freie Universität Berlin, David A. Levin, University of Oregon, Germany, Editors Herbert Edelsbrunner, Duke Eugene, OR, Yuval Peres, Microsoft University, Durham, NC, and Translated by Philip G. Spain Research, Redmond, WA, and University of California, Berkeley, CA, Geomagic, Research Triangle Park, Everyday examples of how NC, and John L. Harer, Duke and Elizabeth L. Wilmer, Oberlin Phase Plots of Complex mathematics permeates the real College, OH University, Durham, NC world, in far-ranging areas from Functions: A Journey in An introduction to the often compact discs to climate change An introduction to the modern difficult concepts of algebraic 2010; 330 pages; Softcover; ISBN: 978-0- approach to the theory of Markov Illustration topology in a way motivated by 8218-4349-9; List US$49; AMS members chains, emphasizing probabilistic page 768 applications US$39.20; Order code MBK/72 methods 2009; 371 pages; Hardcover; ISBN: 978-0- 2010; 241 pages; Hardcover; ISBN: 978-0- 8218-4739-8; List US$65; AMS members 8218-4925-5; List US$59; AMS members A Mathematical Medley US$52; Order code MBK/58 Mathematicians of US$47.20; Order code MBK/69 Fifty Easy Pieces on Mathematics Gaussian Elimination The Knot Book George G. 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Petkovic´, University of Mickiewicz University, Poznan´, between various parts of Nis, Serbia Poland, Editors Ithaca Meeting mathematics, designed to help the A publication of Gdan ´sk University Press. Distributed Recreational mathematics used as undergraduate see an integrated Volume 58, Number 6, Pages 761–888, June/July 2011 page 871 a framework for communicating body of knowledge non-exclusively worldwide by the American Mathematical Society. brilliant ideas in mathematical 2010; 243 pages; Softcover; ISBN: 978-0- thought 8218-4979-8; List US$55; AMS members 2010; 186 pages; Hardcover; ISBN: 978- 83-7326-798-5; List US$55; AMS members Winston-Salem Meeting 2009; 325 pages; Softcover; ISBN: 978-0- US$44; Order code MBK/75 US$44; Order code BANACH 8218-4814-2; List US$36; AMS members page 874 US$28.80; Order code MBK/63 Port Elizabeth Meeting page 879 TEXTBOOKS About the Cover: Forty-six years FROM THE AMS of topology from the differentiable viewpoint (see page 819) Trim: 8.25" x 10.75" 128 pages on 40 lb Velocity • Spine: 1/8" • Print Cover on 9pt Carolina noti-jun-jul-2011-cover.indd 1 5/25/11 9:22 AM TEX LATEX XXTE E QUANTITATIVE FINANCE RENAISSANCE TECHNOLOGIES, a quantitatively based financial management firm, has openings for research and programming positions at its Long Island, NY research center. 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So, for those of you who thought that other system was the right answer for math, we respectfully say, “Sorry, that’s not correct.” 800.955.8275 webassign.net/math Notices of the American Mathematical Society June/July 2011 Communications 794 Remembering Johannes J. 794 Duistermaat (1942–2010) Victor Guillemin, Álvaro ~ 815 Pelayo, San Vu Ngoc,. Alan Weinstein, Coordinating Editors 812 WHAT IS…a Resplendent Structure? Roman Kossak 820 Doceamus: The Common 768 Core State Standards— Education Reform and Us Solomon Garfunkel Features 823 The State of High School The June/July issue features three quite distinct aspects of Textbooks modern mathematics. John Milnor (recent Abel laureate and a Guershon Harel and father of differential topology) recounts the modern history of W. Stephen Wilson the subject of differential topology. Elias Wegert and Gunter 828 What Is New in ? Semmler present some new graphical representations of com- plex functions. And Joseph Grcar recounts the complex (and IV. WYSIWYG G. Grätzer little-known) history of the technique of Gaussian elimination. Among the Communications articles is a remembrance of the 831 Milnor Receives 2011 Abel remarkable mathematician Johannes Duistermaat. Prize —Steven G. Krantz, Editor 833 Valiant Receives 2010 Turing Award Commentary 768 Phase Plots of Complex Functions: A Journey in Illustration 765 Opinion: Math Sciences 2025 Elias Wegert and Gunter Semmler Tom Everhart, Mark Green, Scott Weidman 782 Mathematicians of Gaussian 766 Letters to the Editor Elimination 810 I Want to Be a Joseph F. Grcar Mathematician: A Conversation with Paul 804 Differential Topology Forty-six Years Halmos—A DVD Review Later Reviewed by John Ewing John Milnor 815 Mathematics Emerging: A Sourcebook 1540– 1900—A Book Review Reviewed by David Pengelley Notices Departments of the American Mathematical Society About the Cover . 819 EDITOR: Steven G. Krantz Crossword Puzzle . 822 ASSOCIATE EDITORS: Mathematics People . 835 Krishnaswami Alladi, David Bailey, Jonathan Borwein, Susanne C. Brenner, Bill Casselman (Graphics Editor), 2011–2012 AMS Centennial Fellowship Awarded, Aschbacher and Robert J. Daverman, Susan Friedlander, Robion Kirby, Putnam Awarded Rolf Schock Prizes, Clay Research Awards, Getz Rafe Mazzeo, Harold Parks, Lisette de Pillis, Peter Sarnak, Mark Saul, Edward Spitznagel, John Swallow and Goresky Awarded 2011 Balaguer Prize, Sloan Fellowships SENIOR WRITER and DEPUTY EDITOR: Awarded, Brenner Awarded Kovalevsky Lectureship, Pelayo Receives Allyn Jackson Rubio de Francia Prize, Eisenbrand and Schröder Awarded Humboldt MANAGING EDITOR: Sandra Frost Professorships, Glynn and Asmussen Awarded John von Neumann CONTRIBUTING WRITER: Elaine Kehoe Theory Prize, Rollo Davidson Prizes Awarded, Putnam Prizes Awarded, CONTRIBUTING EDITOR: Randi D. Ruden Intel Science Talent Search Winners Announced, NSF Graduate Research EDITORIAL ASSISTANT: David M. Collins Fellowships Announced, Jungic Awarded 2011 PIMS Education Prize, PRODUCTION: Kyle Antonevich, Anna Hattoy, Guggenheim Fellowships Awarded, SIAM Fellows Elected, Lalonde Teresa Levy, Mary Medeiros, Stephen Moye, Erin Appointed CRM Director. Murphy, Lori Nero, Karen Ouellette, Donna Salter, Deborah Smith, Peter Sykes, Patricia Zinni Mathematics Opportunities . 840 ADVERTISING SALES: Anne Newcomb NSF Research Training