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An Epsilon of Room, I: Real Analysis: pages from year three of a mathematical blog
 
Terence Tao University of California, Los Angeles, Los Angeles, CA
An Epsilon of Room, I: Real Analysis
Softcover ISBN:  978-1-4704-7161-3
Product Code:  GSM/117.S
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
Sale Price: $57.85
eBook ISBN:  978-1-4704-1179-4
Product Code:  GSM/117.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Sale Price: $55.25
Softcover ISBN:  978-1-4704-7161-3
eBook: ISBN:  978-1-4704-1179-4
Product Code:  GSM/117.S.B
List Price: $174.00 $131.50
MAA Member Price: $156.60 $118.35
AMS Member Price: $139.20 $105.20
An Epsilon of Room, I: Real Analysis
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An Epsilon of Room, I: Real Analysis: pages from year three of a mathematical blog
Terence Tao University of California, Los Angeles, Los Angeles, CA
Softcover ISBN:  978-1-4704-7161-3
Product Code:  GSM/117.S
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
Sale Price: $57.85
eBook ISBN:  978-1-4704-1179-4
Product Code:  GSM/117.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Sale Price: $55.25
Softcover ISBN:  978-1-4704-7161-3
eBook ISBN:  978-1-4704-1179-4
Product Code:  GSM/117.S.B
List Price: $174.00 $131.50
MAA Member Price: $156.60 $118.35
AMS Member Price: $139.20 $105.20
  • Book Details
     
     
    Graduate Studies in Mathematics
    Volume: 1172010; 349 pp
    MSC: Primary 42; 46;

    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 first two years of the blog have already been published by the American Mathematical Society. The posts from the third year are being published in two volumes. The present volume consists of a second course in real analysis, together with related material from the blog.

    The real analysis course assumes some familiarity with general measure theory, as well as fundamental notions from undergraduate analysis. The text then covers more advanced topics in measure theory, notably the Lebesgue-Radon-Nikodym theorem and the Riesz representation theorem, topics in functional analysis, such as Hilbert spaces and Banach spaces, and the study of spaces of distributions and key function spaces, including Lebesgue's \(L^p\) spaces and Sobolev spaces. There is also a discussion of the general theory of the Fourier transform.

    The second part of the book addresses a number of auxiliary topics, such as Zorn's lemma, the Carathéodory extension theorem, and the Banach-Tarski paradox. Tao also discusses the epsilon regularisation argument—a fundamental trick from soft analysis, from which the book gets its title. Taken together, the book presents more than enough material for a second graduate course in real analysis.

    The second volume consists of technical and expository articles on a variety of topics and can be read independently.

    Readership

    Graduate students interested in analysis.

  • Table of Contents
     
     
    • Chapters
    • Chapter 1. Real analysis
    • Chapter 2. Related articles
  • Reviews
     
     
    • It is a nice contribution to the current literature by one of the leading mathematicians in the world and can only be warmly recommended to everybody interested in these topics.

      Monatshafte für Mathematik
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1172010; 349 pp
MSC: Primary 42; 46;

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 first two years of the blog have already been published by the American Mathematical Society. The posts from the third year are being published in two volumes. The present volume consists of a second course in real analysis, together with related material from the blog.

The real analysis course assumes some familiarity with general measure theory, as well as fundamental notions from undergraduate analysis. The text then covers more advanced topics in measure theory, notably the Lebesgue-Radon-Nikodym theorem and the Riesz representation theorem, topics in functional analysis, such as Hilbert spaces and Banach spaces, and the study of spaces of distributions and key function spaces, including Lebesgue's \(L^p\) spaces and Sobolev spaces. There is also a discussion of the general theory of the Fourier transform.

The second part of the book addresses a number of auxiliary topics, such as Zorn's lemma, the Carathéodory extension theorem, and the Banach-Tarski paradox. Tao also discusses the epsilon regularisation argument—a fundamental trick from soft analysis, from which the book gets its title. Taken together, the book presents more than enough material for a second graduate course in real analysis.

The second volume consists of technical and expository articles on a variety of topics and can be read independently.

Readership

Graduate students interested in analysis.

  • Chapters
  • Chapter 1. Real analysis
  • Chapter 2. Related articles
  • It is a nice contribution to the current literature by one of the leading mathematicians in the world and can only be warmly recommended to everybody interested in these topics.

    Monatshafte für Mathematik
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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