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Compactness and Contradiction
 
Terence Tao University of California, Los Angeles, Los Angeles, CA
Compactness and Contradiction
Compactness and Contradiction
Softcover ISBN:  978-0-8218-9492-7
Product Code:  MBK/81
List Price: $40.00
MAA Member Price: $36.00
AMS Member Price: $32.00
eBook ISBN:  978-1-4704-1611-9
Product Code:  MBK/81.E
List Price: $49.00
MAA Member Price: $44.10
AMS Member Price: $39.20
Softcover ISBN:  978-0-8218-9492-7
eBook: ISBN:  978-1-4704-1611-9
Product Code:  MBK/81.B
List Price: $89.00 $64.50
MAA Member Price: $80.10 $58.05
AMS Member Price: $71.20 $51.60
Compactness and Contradiction
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Compactness and Contradiction
Compactness and Contradiction
Terence Tao University of California, Los Angeles, Los Angeles, CA
Softcover ISBN:  978-0-8218-9492-7
Product Code:  MBK/81
List Price: $40.00
MAA Member Price: $36.00
AMS Member Price: $32.00
eBook ISBN:  978-1-4704-1611-9
Product Code:  MBK/81.E
List Price: $49.00
MAA Member Price: $44.10
AMS Member Price: $39.20
Softcover ISBN:  978-0-8218-9492-7
eBook ISBN:  978-1-4704-1611-9
Product Code:  MBK/81.B
List Price: $89.00 $64.50
MAA Member Price: $80.10 $58.05
AMS Member Price: $71.20 $51.60
  • Book Details
     
     
    2013; 256 pp
    MSC: 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.

    The articles, essays, and notes in this book are derived from the author's mathematical blog in 2010. It contains a broad selection of mathematical expositions, commentary, and self-contained technical notes in many areas of mathematics, such as logic, group theory, analysis, and partial differential equations. The topics range from the foundations of mathematics to discussions of recent mathematical breakthroughs.

    Lecture notes from the author's courses that appeared on the blog have been published separately in the Graduate Studies in Mathematics series.

    Readership

    Graduate students and research mathematicians interested in analysis, logic and foundations, PDEs, algebra, and general topics related to mathematics.

  • Table of Contents
     
     
    • Chapters
    • Chapter 1. Logic and foundations
    • Chapter 2. Group theory
    • Chapter 3. Analysis
    • Chapter 4. Nonstandard analysis
    • Chapter 5. Partial differential equations
    • Chapter 6. Miscellaneous
  • Reviews
     
     
    • Lately, a new generation of experts, some of whom are very powerful researchers, has started disseminating exposition via interactive blogs. Since they receive immediate and continuous international feedback, the interests and needs of their audience inevitably inform the communication. Tao, who---even among Fields medalists---has exceptional intellectual range, writes among the most famous of these blogs, and the present volume contains a selection of redacted content from it. Whereas many textbooks aim to teach lower-division mathematics majors to prove trivial theorems, this book explores very generally how research mathematicians prove nontrivial theorems. But unifying themes aside, Tao has chosen very well as case studies sundry topics from mutually distant branches of mathematics. Those sufficiently elementary demand a healthy stretch, and none will seem overly familiar, even to most experts. The class exhortation 'read the masters' takes on new urgency in an era when the masters return favor. Highly recommended ... [for] all academic and professional library collections.

      D.V. Feldman, CHOICE
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
2013; 256 pp
MSC: 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.

The articles, essays, and notes in this book are derived from the author's mathematical blog in 2010. It contains a broad selection of mathematical expositions, commentary, and self-contained technical notes in many areas of mathematics, such as logic, group theory, analysis, and partial differential equations. The topics range from the foundations of mathematics to discussions of recent mathematical breakthroughs.

Lecture notes from the author's courses that appeared on the blog have been published separately in the Graduate Studies in Mathematics series.

Readership

Graduate students and research mathematicians interested in analysis, logic and foundations, PDEs, algebra, and general topics related to mathematics.

  • Chapters
  • Chapter 1. Logic and foundations
  • Chapter 2. Group theory
  • Chapter 3. Analysis
  • Chapter 4. Nonstandard analysis
  • Chapter 5. Partial differential equations
  • Chapter 6. Miscellaneous
  • Lately, a new generation of experts, some of whom are very powerful researchers, has started disseminating exposition via interactive blogs. Since they receive immediate and continuous international feedback, the interests and needs of their audience inevitably inform the communication. Tao, who---even among Fields medalists---has exceptional intellectual range, writes among the most famous of these blogs, and the present volume contains a selection of redacted content from it. Whereas many textbooks aim to teach lower-division mathematics majors to prove trivial theorems, this book explores very generally how research mathematicians prove nontrivial theorems. But unifying themes aside, Tao has chosen very well as case studies sundry topics from mutually distant branches of mathematics. Those sufficiently elementary demand a healthy stretch, and none will seem overly familiar, even to most experts. The class exhortation 'read the masters' takes on new urgency in an era when the masters return favor. Highly recommended ... [for] all academic and professional library collections.

    D.V. Feldman, CHOICE
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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