
Preface  Table of Contents  Supplementary Material 
2009; 292 pp; softcover ISBN10: 0821848852 ISBN13: 9780821848852 List Price: US$39 Member Price: US$31.20 Order Code: MBK/67 See also: Structure and Randomness: pages from year one of a mathematical blog  Terence Tao Poincaré's Legacies, Part I: pages from year two of a mathematical blog  Terence Tao An Epsilon of Room, II: pages from year three of a mathematical blog  Terence Tao An Epsilon of Room, I: Real Analysis: pages from year three of a mathematical blog  Terence Tao The Scientific Legacy of Poincaré  Eric Charpentier, Etienne Ghys and Annick Lesne  There are many bits and pieces of folklore in mathematics that are passed down from advisor to student, or from collaborator to collaborator, but which are too fuzzy and nonrigorous to be discussed in the formal literature. Traditionally, it was a matter of luck and location as to who learned such folklore mathematics. But today, such bits and pieces can be communicated effectively and efficiently via the semiformal medium of research blogging. This book grew from such a blog. In 2007, Terry Tao began a mathematical blog to cover a variety of topics, ranging from his own research and other recent developments in mathematics, to lecture notes for his classes, to nontechnical puzzles and expository articles. The articles from the first year of that blog have already been published by the AMS. The posts from 2008 are being published in two volumes. This book is Part II of the secondyear posts, focusing on geometry, topology, and partial differential equations. The major part of the book consists of lecture notes from Tao's course on the Poincaré conjecture and its recent spectacular solution by Perelman. The course incorporates a review of many of the basic concepts and results needed from Riemannian geometry and, to a lesser extent, from parabolic PDE. The aim is to cover in detail the highlevel features of the argument, along with selected specific components of that argument, while sketching the remaining elements, with ample references to more complete treatments. The lectures are as selfcontained as possible, focusing more on the "big picture" than on technical details. In addition to these lectures, a variety of other topics are discussed, including expository articles on topics such as gauge theory, the Kakeya needle problem, and the BlackScholes equation. Some selected comments and feedback from blog readers have also been incorporated into the articles. The book is suitable for graduate students and research mathematicians interested in broad exposure to mathematical topics. Readership Graduate students and research mathematicians interested in mathematics in general with a focus on geometry, topology, and partial differential equations. Reviews "Most of [the articles] are connected in one way or another with Tao's research interests, so if you have research interests that overlap with those of Tao, then it is a great pleasure to read ... Given how broad Tao's research interests are, that applies to just about everyone."  Mathematical Reviews 


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