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eBook ISBN:  9781470416027 
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Softcover ISBN:  9780821848852 
eBook: ISBN:  9781470416027 
Product Code:  MBK/67.B 
List Price:  $94.00 $71.50 
MAA Member Price:  $84.60 $64.35 
AMS Member Price:  $75.20 $57.20 
Softcover ISBN:  9780821848852 
Product Code:  MBK/67 
List Price:  $49.00 
MAA Member Price:  $44.10 
AMS Member Price:  $39.20 
eBook ISBN:  9781470416027 
Product Code:  MBK/67.E 
List Price:  $45.00 
MAA Member Price:  $40.50 
AMS Member Price:  $36.00 
Softcover ISBN:  9780821848852 
eBook ISBN:  9781470416027 
Product Code:  MBK/67.B 
List Price:  $94.00 $71.50 
MAA Member Price:  $84.60 $64.35 
AMS Member Price:  $75.20 $57.20 

Book Details2009; 292 ppMSC: Primary 00
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 Black–Scholes 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.
ReadershipGraduate students and research mathematicians interested in mathematics in general with a focus on geometry, topology, and partial differential equations.

Table of Contents

Chapters

Chapter 1. Expository articles

Chapter 2. The Poincaré conjecture


Additional Material

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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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 Black–Scholes 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.
Graduate students and research mathematicians interested in mathematics in general with a focus on geometry, topology, and partial differential equations.

Chapters

Chapter 1. Expository articles

Chapter 2. The Poincaré conjecture

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