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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 3-6
    3. Martin Aigner, Günter M. Ziegler
      Pages 7-12
    4. Martin Aigner, Günter M. Ziegler
      Pages 13-16
    5. Martin Aigner, Günter M. Ziegler
      Pages 17-22
    6. Martin Aigner, Günter M. Ziegler
      Pages 23-30
    7. Martin Aigner, Günter M. Ziegler
      Pages 31-34
    8. Martin Aigner, Günter M. Ziegler
      Pages 35-41
    9. Martin Aigner, Günter M. Ziegler
      Pages 43-50
  3. Geometry

    1. Front Matter
      Pages 51-51
    2. Martin Aigner, Günter M. Ziegler
      Pages 53-61
    3. Martin Aigner, Günter M. Ziegler
      Pages 63-67
    4. Martin Aigner, Günter M. Ziegler
      Pages 69-73
    5. Martin Aigner, Günter M. Ziegler
      Pages 75-80
    6. Martin Aigner, Günter M. Ziegler
      Pages 81-84
    7. Martin Aigner, Günter M. Ziegler
      Pages 85-88
    8. Martin Aigner, Günter M. Ziegler
      Pages 89-94
    9. Martin Aigner, Günter M. Ziegler
      Pages 95-100
  4. Analysis

    1. Front Matter
      Pages 101-101
    2. Martin Aigner, Günter M. Ziegler
      Pages 103-118
    3. Martin Aigner, Günter M. Ziegler
      Pages 119-125
    4. Martin Aigner, Günter M. Ziegler
      Pages 127-129
    5. Martin Aigner, Günter M. Ziegler
      Pages 131-138
    6. Martin Aigner, Günter M. Ziegler
      Pages 139-144
    7. Martin Aigner, Günter M. Ziegler
      Pages 145-148
    8. Martin Aigner, Günter M. Ziegler
      Pages 149-154
    9. Martin Aigner, Günter M. Ziegler
      Pages 155-158
  5. Combinatorics

    1. Front Matter
      Pages 159-159
    2. Martin Aigner, Günter M. Ziegler
      Pages 161-171
    3. Martin Aigner, Günter M. Ziegler
      Pages 173-177
    4. Martin Aigner, Günter M. Ziegler
      Pages 179-183
    5. Martin Aigner, Günter M. Ziegler
      Pages 185-194
    6. Martin Aigner, Günter M. Ziegler
      Pages 195-200
    7. Martin Aigner, Günter M. Ziegler
      Pages 201-206
    8. Martin Aigner, Günter M. Ziegler
      Pages 207-212
    9. Martin Aigner, Günter M. Ziegler
      Pages 213-218
  6. Graph Theory

    1. Front Matter
      Pages 219-219
    2. Martin Aigner, Günter M. Ziegler
      Pages 221-226
    3. Martin Aigner, Günter M. Ziegler
      Pages 227-230
    4. Martin Aigner, Günter M. Ziegler
      Pages 231-234
    5. Martin Aigner, Günter M. Ziegler
      Pages 235-239
    6. Martin Aigner, Günter M. Ziegler
      Pages 241-250
    7. Martin Aigner, Günter M. Ziegler
      Pages 251-255
    8. Martin Aigner, Günter M. Ziegler
      Pages 257-259
    9. Martin Aigner, Günter M. Ziegler
      Pages 261-268
  7. Back Matter
    Pages 269-274

About this book

Introduction

This revised and enlarged fourth edition of "Proofs from THE BOOK" features five new chapters, which  treat classical results such as the "Fundamental Theorem of Algebra", problems about tilings,  but also quite recent proofs, for example of the Kneser conjecture in graph theory. The new edition also presents further improvements and surprises, among them a new proof for "Hilbert's Third Problem". 

 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. Some of the proofs are classics, but many are new and brilliant proofs of classical results. ...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. Moreover, the exposition makes them transparent. ..." 

LMS Newsletter, January 1999

Keywords

Algebra Counting Finite Identity analysis calculus combinatorics function geometry number theory proof proofs theorem

Authors and affiliations

  • Martin Aigner
    • 1
  • Günter M. Ziegler
    • 1
  1. 1.FU BerlinBerlinGermany

Bibliographic information