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What'S Happening In The Mathematical Sciences,Used
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The AMS series What's Happening in the Mathematical Sciences distills the amazingly rich brew of current research in mathematics down to a few choice samples. This volume leads off with an update on the Poincar Conjecture, a hundredyearold problem that has apparently been solved by Grigory Perelman of St. Petersburg, Russia. So what did topologists do when the oldest and most famous problem about closed manifolds was vanquished? As the second chapter describes, they confronted a suite of problems concerning the 'ends' of open manifolds ... and solved those, too. Not to be outdone, number theorists accomplished several unexpected feats in the first five years of the new century, from computing a trillion digits of pi to finding arbitrarily long equallyspaced sequences of prime numbers. Undergraduates made key discoveries, as explained in the chapters on Venn diagrams and primality testing. In applied mathematics, the NavierStokes equations of fluid mechanics continued to stir up interest. One team proved new theorems about the longterm evolution of vortices, while others explored the surprising ways that insects use vortices to move around. The random jittering of Brownian motion became a little less mysterious. Finally, an old and trusted algorithm of computer science had its trustworthiness explained in a novel way. Barry Cipra explains these new developments in his wry and witty style, familiar to readers of Volumes 15, and is joined in this volume by Dana Mackenzie. Volume 6 of What's Happening will convey to all readersfrom mathematical novices to expertsthe beauty and wonder that is mathematics.
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