Proofs from THE BOOK

  • Martin Aigner
  • Günter M. Ziegler

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Number Theory

    1. Front Matter
      Pages 1-1
    2. Martin Aigner, Günter M. Ziegler
      Pages 3-8
    3. Martin Aigner, Günter M. Ziegler
      Pages 9-14
    4. Martin Aigner, Günter M. Ziegler
      Pages 15-18
    5. Martin Aigner, Günter M. Ziegler
      Pages 19-24
    6. Martin Aigner, Günter M. Ziegler
      Pages 25-32
    7. Martin Aigner, Günter M. Ziegler
      Pages 33-36
    8. Martin Aigner, Günter M. Ziegler
      Pages 37-44
    9. Martin Aigner, Günter M. Ziegler
      Pages 45-51
    10. Martin Aigner, Günter M. Ziegler
      Pages 53-60
  3. Geometry

    1. Front Matter
      Pages 61-61
    2. Martin Aigner, Günter M. Ziegler
      Pages 63-71
    3. Martin Aigner, Günter M. Ziegler
      Pages 73-78
    4. Martin Aigner, Günter M. Ziegler
      Pages 79-83
    5. Martin Aigner, Günter M. Ziegler
      Pages 85-90
    6. Martin Aigner, Günter M. Ziegler
      Pages 91-94
    7. Martin Aigner, Günter M. Ziegler
      Pages 95-102
    8. Martin Aigner, Günter M. Ziegler
      Pages 103-106
    9. Martin Aigner, Günter M. Ziegler
      Pages 107-112

About this book

Introduction

This revised and enlarged fifth edition features four new chapters, which contain highly original and delightful proofs for classics such as the spectral theorem from linear algebra, some more recent jewels like the non-existence of the Borromean rings and other surprises.

From the Reviews

"... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. ... Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... "

Notices of the AMS, August 1999

"... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures, and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately, and the proofs are brilliant. ..."

LMS Newsletter, January 1999

"Martin Aigner and Günter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erdös. The theorems are so fundamental, their proofs so elegant, and the remaining open questions so intriguing that every ma

thematician, regardless of speciality, can benefit from reading this book. ... "

SIGACT News, December 2011

Keywords

algebra analysis calculus combinatorics counting finite geometry number theory proof theorem

Authors and affiliations

  • Martin Aigner
    • 1
  • Günter M. Ziegler
    • 2
  1. 1.Institut für MathematikFreie Universität BerlinBerlinGermany
  2. 2.Institut für MathematikFreie Universität BerlinBerlinGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-44205-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 2014
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-662-44204-3
  • Online ISBN 978-3-662-44205-0
  • About this book