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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
    10. Martin Aigner, Günter M. Ziegler
      Pages 113-119
  4. Analysis

    1. Front Matter
      Pages 121-121
    2. Martin Aigner, Günter M. Ziegler
      Pages 123-138
    3. Martin Aigner, Günter M. Ziegler
      Pages 139-146
    4. Martin Aigner, Günter M. Ziegler
      Pages 147-149
    5. Martin Aigner, Günter M. Ziegler
      Pages 151-158
    6. Martin Aigner, Günter M. Ziegler
      Pages 159-164
    7. Martin Aigner, Günter M. Ziegler
      Pages 165-168
    8. Martin Aigner, Günter M. Ziegler
      Pages 169-174
    9. Martin Aigner, Günter M. Ziegler
      Pages 175-178
  5. Combinatorics

    1. Front Matter
      Pages 179-179
    2. Martin Aigner, Günter M. Ziegler
      Pages 181-191
    3. Martin Aigner, Günter M. Ziegler
      Pages 193-197
    4. Martin Aigner, Günter M. Ziegler
      Pages 199-203
    5. Martin Aigner, Günter M. Ziegler
      Pages 205-214
    6. Martin Aigner, Günter M. Ziegler
      Pages 215-220
    7. Martin Aigner, Günter M. Ziegler
      Pages 221-226
    8. Martin Aigner, Günter M. Ziegler
      Pages 227-232
    9. Martin Aigner, Günter M. Ziegler
      Pages 233-237
    10. Martin Aigner, Günter M. Ziegler
      Pages 239-244
  6. Graph Theory

    1. Front Matter
      Pages 245-245
    2. Martin Aigner, Günter M. Ziegler
      Pages 247-252
    3. Martin Aigner, Günter M. Ziegler
      Pages 253-260
    4. Martin Aigner, Günter M. Ziegler
      Pages 261-264
    5. Martin Aigner, Günter M. Ziegler
      Pages 265-268
    6. Martin Aigner, Günter M. Ziegler
      Pages 269-273
    7. Martin Aigner, Günter M. Ziegler
      Pages 275-284
    8. Martin Aigner, Günter M. Ziegler
      Pages 285-289
    9. Martin Aigner, Günter M. Ziegler
      Pages 291-293
    10. Martin Aigner, Günter M. Ziegler
      Pages 295-302

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