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ISSN 0002-9920 Notices of the American Mathematical Society AMERICAN MATHEMATICAL SOCIETY Graduate Studies in Mathematics Series The volumes in the GSM series are specifically designed as graduate studies texts, but are also suitable for recommended and/or supplemental course reading. With appeal to both students and professors, these texts make ideal independent study resources. The breadth and depth of the series’ coverage make it an ideal acquisition for all academic libraries that of the American Mathematical Society support mathematics programs. al January 2010 Volume 57, Number 1 Training Manual Optimal Control of Partial on Transport Differential Equations and Fluids Theory, Methods and Applications John C. Neu FROM THE GSM SERIES... Fredi Tro˝ltzsch NEW Graduate Studies Graduate Studies in Mathematics in Mathematics Volume 109 Manifolds and Differential Geometry Volume 112 ocietty American Mathematical Society Jeffrey M. Lee, Texas Tech University, Lubbock, American Mathematical Society TX Volume 107; 2009; 671 pages; Hardcover; ISBN: 978-0-8218- 4815-9; List US$89; AMS members US$71; Order code GSM/107 Differential Algebraic Topology From Stratifolds to Exotic Spheres Mapping Degree Theory Matthias Kreck, Hausdorff Research Institute for Enrique Outerelo and Jesús M. Ruiz, Mathematics, Bonn, Germany Universidad Complutense de Madrid, Spain Volume 110; 2010; approximately 215 pages; Hardcover; A co-publication of the AMS and Real Sociedad Matemática ISBN: 978-0-8218-4898-2; List US$55; AMS members US$44; Española (RSME). Order code GSM/110 Volume 108; 2009; 244 pages; Hardcover; ISBN: 978-0-8218- 4915-6; List US$62; AMS members US$50; Ricci Flow and the Sphere Theorem The Art of Order code GSM/108 Simon Brendle, Stanford University, CA Mathematics Volume 111; 2010; 176 pages; Hardcover; ISBN: 978-0-8218- page 8 Training Manual on Transport 4938-5; List US$47; AMS members US$38; and Fluids Order code GSM/111 John C. Neu, University of California, Berkeley, The Life and Survival CA Optimal Control of Partial of Mathematical Volume 109; 2010; 265 pages; Hardcover; ISBN: 978-0-8218- Differential Equations Ideas 4083-2; List US$59; AMS members US$47; Theory, Methods and Applications Order code GSM/109 page 10 Fredi Tröltzsch, Technische Universität Berlin, Germany Envisioning the 2010 Translated by Jürgen Sprekels Volume 57, Number 1, Pages 1–200, January 2010 San Francisco, CA January 13–16, 2010 Volume 112; 2010; approximately 408 pages; Hardcover; Invisible Visit the AMS Book ISBN: 978-0-8218-4904-0; List US$69; AMS members US$55; page 24 Exhibit at JMM 2010: Order code GSM/112 • UpU tot 25% off all AMS books Music: Broken • Free Shipping and Handling Symmetry, • No California Sales Tax* *The AMS will pay your California sales tax on all on-site AMS purchases Geometry, and Complexity page 30 TEXTBOOKS FROM THE AMS Lexington Meeting www.ams.org/bookstore www.ams.org/bookstore page 95 Creativity Issue (see page 57) Trim: 8.25" x 10.75" 200 pages on 40 lb Velocity • Spine: 7/32" • Print Cover on 9pt Carolina ,!4%8 ,!4%8 ,!4%8 TEXTBOOKS FROM THE AMS PureUndergraduate and Applied Texts Series The volumes in this series are intended for undergraduate post-calculus courses and, in some cases, will provide applications in engineering and applied mathematics. The books are characterized by excellent exposition and maintain the highest standards of scholarship. This series was founded by the highly respected mathematician and educator, Paul J. Sally, Jr. (ISSN 1943-9334). ◗ Instructor’s Manual Available ◗ Instructor’s Manual Available Introduction to Analysis Advanced Calculus Geometry for Fifth Edition Second Edition College Students Edward D. Gaughan, New Mexico Patrick M. Fitzpatrick, University of I. Martin Isaacs, University of State University, Las Cruces, NM Maryland, College Park, MD Wisconsin, Madison, WI Volume 1; 1998; 240 pages; Hardcover; Volume 5; 2006; 590 pages; Hardcover; Volume 8; 2001; 222 pages; Hardcover; ISBN: 978-0-8218-4787-9; List US$62; ISBN: 978-0-8218-4791-6; List US$82; ISBN: 978-0-8218-4794-7; List US$62; AMS members US$50; Order code AMSTEXT/1 AMS members US$66; Order code AMSTEXT/5 AMS members US$50; Order code AMSTEXT/8 ◗ Instructor’s Manual Available ◗ Instructor’s Manual Available ◗ Student Manual Available Numerical Analysis Abstract Algebra Probability: The Science Mathematics of Scientific Ronald Solomon, Ohio State Computing, Third Edition of Uncertainty University, Columbus, OH with Applications to Investments, David Kincaid and Ward Cheney, Volume 9; 2003; 227 pages; Hardcover; Insurance, and Engineering University of Texas at Austin, TX ISBN: 978-0-8218-4795-4; List US$62; AMS members US$50; Order code AMSTEXT/9 Volume 2; 2002; 788 pages; Hardcover; I Michael A. Bean SBN: 978-0-8218-4788-6; List US$89; Volume 6; 2001; 448 pages; Hardcover; AMS members US$71; Order code AMSTEXT/2 ISBN: 978-0-8218-4792-3; List US$72; AMS members US$58; Order code AMSTEXT/6 Beginning Topology ◗ Instructor’s Manual Available ◗ Student Manual Available ◗ Instructor’s Manual Available Sue E. Goodman, University of North Carolina, Chapel Hill, NC A Discrete Transition to The Mathematics of Finance Volume 10; 2005; 236 pages; Hardcover; Advanced Mathematics Modeling and Hedging ISBN: 978-0-8218-4796-1; List US$62; AMS members US$50; Order code AMSTEXT/10 Bettina Richmond and Thomas Victor Goodman and Joseph Richmond, Western Kentucky Stampfli, Indiana University, University, Bowling Green, KY Bloomington, IN Volume 3; 2004; 424 pages; Hardcover; Volume 7; 2001; 250 pages; Hardcover; ISBN: 978-0-8218-4789-3; List US$72; ISBN: 978-0-8218-4793-0; List US$62; AMS members US$58; Order code AMSTEXT/3 AMS members US$50; Order code AMSTEXT/7 Fourier Analysis and Its Applications TEXTBOOKS The AMS publishes many high-quality Gerald B. Folland, University of FROM THE AMS books for use in the classroom. To Washington, Seattle, WA view a comprehensive list of our best- Volume 4; 1992; 433 pages; Hardcover; selling textbooks, please visit www.ams.org/bookstore/textbooks. ISBN: 978-0-8218-4790-9; List US$72; Most of the titles are designed as undergraduate or graduate texts but AMS members US$58; Order code AMSTEXT/4 are also suitable for recommended and/or supplemental course reading. Request a desk or exam copy by visiting www.ams.org/bookstore/ exam-desk-request. www.ams.org/bookstore 1-800-321-4AMS (4267), in the U. S. and Canada, or 1-401-455-4000 (worldwide); fax:1-401-455-4046; email: [email protected]. American Mathematical Society, 201 Charles Street, Providence, RI 02904-2294 USA “ME, MYSELF & WEBASSIGN.” WELCOME TO THE NEW ECONOMICS OF TEACHING. The new economics of teaching will test the resourcefulness of every instructor and administrator, from the smallest private college to the ivy league. There will be fewer resources and even fewer assistants and supporting staff. Oh, and you’ll be expected to teach more courses to more students. Which is why, more than ever, you need WebAssign. With WebAssign, it’s like having two of you to go around. That’s because WebAssign helps you do more, more effectively, with less. Our large enrollment course features allow a single person to easily administer multiple sections. Automated features eliminate administrative tasks such as grading, so fewer graders are needed. Departments can even sell their own text materials and eLabs online, providing new revenue streams. All of which explains why WebAssign users are 3 million strong and growing. So, what will it take to survive, even thrive, in the new economics of teaching? Three things: You. Yourself. And WebAssign. Visit www.webassign.net to sign up for your free faculty account today. Notices of the American Mathematical Society January 2010 Communications 24 50 WHAT IS…an Oka Manifold? Finnur Lárusson 56 Kalman Receives National Medal of Science Allyn Jackson Commentary 30 10 5 Opinion: Mathematicians and the Tower of Babel The theme of this issue of the Notices of the American John Wermer Mathematical Society is “Mathematics and the Arts”. Even in 7 Letters to the Editor the time of the ancient Greeks it was generally recognized that mathematics and art are inextricably intertwined. 53 Tools of American The symbiosis has continued through the ages. Today, Mathematics Teaching, with computer graphics and many new artistic media, this 1800–2000—A Book Review Reviewed by Andrew G. interplay has taken startling and enlightening new forms. Bennett We have selected here four articles to showcase different aspects of mathematics and art. We hope that this collec- tion will lead to stimulating discussions and perhaps future contributions to the Notices of the AMS. —Steven G. Krantz Editor Features 8 The Art of Mathematics Michael Atiyah 10 The Life and Survival of Mathematical Ideas Michael F. Barnsley 24 Envisioning the Invisible Tim Chartier 30 Music: Broken Symmetry, Geometry, and Complexity Gary W. Don, Karyn K. Muir, Gordon B. Volk, and James S. Walker Notices Departments of the American Mathematical Society About the Cover . 57 EDITOR: Steven G. Krantz Mathematics People . 58 ASSOCIATE EDITORS: Mahadevan Receives MacArthur Fellowship, Bringmann Awarded 2009 Krishnaswami Alladi, David Bailey, Jonathan Borwein, SASTRA Ramanujan Prize, Lytchak Awarded von Kaven Prize, NSF Susanne C. Brenner, Bill Casselman (Graphics Editor), Robert J. Daverman, Susan Friedlander, Robion Kirby, Postdoctoral Fellowships Awarded. Rafe Mazzeo, Harold Parks, Lisette de Pillis, Peter Sarnak, Mark Saul, Edward Spitznagel, John Swallow Mathematics Opportunities . 61 SENIOR WRITER and DEPUTY EDITOR: Proposal Due Dates at the DMS, NDSEG Fellowships, National Allyn Jackson Academies Research Associateship Programs, AMS-AAAS Mass MANAGING EDITOR: Sandra Frost Media Summer Fellowship, AWM Essay Contest, Departments Again CONTRIBUTING WRITER: Elaine Kehoe Coordinate Job Offer Deadlines, News from the Fields Institute, PIMS CONTRIBUTING EDITOR: Randi D. Ruden IGTC Fellowship for 2010–2011.
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