
Preface  Table of Contents  Supplementary Material 
2009; 293 pp; softcover ISBN10: 0821848836 ISBN13: 9780821848838 List Price: US$41 Member Price: US$32.80 Order Code: MBK/66 See also: Structure and Randomness: pages from year one of a mathematical blog  Terence Tao Poincaré's Legacies, Part II: 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 I of the secondyear posts, focusing on ergodic theory, combinatorics, and number theory. Chapter 2 consists of lecture notes from Tao's course on topological dynamics and ergodic theory. By means of various correspondence principles, recurrence theorems about dynamical systems are used to prove some deep theorems in combinatorics and other areas of mathematics. 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, ranging from recent developments in additive prime number theory to expository articles on individual mathematical topics such as the law of large numbers and the LucasLehmer test for Mersenne primes. 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 ergodic theory, combinatorics, and number theory. Reviews "Tao's mathematical knowledge has an extraordinary combination of breadth and depth: he can write confidently and authoritatively on topics ... Reading these extended discussions in book form will, for many people at least, be easier than reading them on the blog."  Mathematical Reviews "[This book] is demanding, entertaining, provides you with the big picture behind the sometimes technical results, and certainly gives you your money's worth. ... Armed with a minimal background in number theory, these lectures can be read with profit by advanced undergraduates."  Zentralblatt MATH 


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