Advertisement

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 23-26
    7. Martin Aigner, Günter M. Ziegler
      Pages 27-33
    8. Martin Aigner, Günter M. Ziegler
      Pages 35-42
  3. Geometry

    1. Front Matter
      Pages 43-43
    2. Martin Aigner, Günter M. Ziegler
      Pages 45-51
    3. Martin Aigner, Günter M. Ziegler
      Pages 53-57
    4. Martin Aigner, Günter M. Ziegler
      Pages 59-63
    5. Martin Aigner, Günter M. Ziegler
      Pages 65-70
    6. Martin Aigner, Günter M. Ziegler
      Pages 71-74
    7. Martin Aigner, Günter M. Ziegler
      Pages 75-78
    8. Martin Aigner, Günter M. Ziegler
      Pages 79-84
    9. Martin Aigner, Günter M. Ziegler
      Pages 85-90
  4. Analysis

    1. Front Matter
      Pages 91-91
    2. Martin Aigner, Günter M. Ziegler
      Pages 93-108
    3. Martin Aigner, Günter M. Ziegler
      Pages 109-115
    4. Martin Aigner, Günter M. Ziegler
      Pages 117-122
    5. Martin Aigner, Günter M. Ziegler
      Pages 123-126
    6. Martin Aigner, Günter M. Ziegler
      Pages 127-132
    7. Martin Aigner, Günter M. Ziegler
      Pages 133-136
  5. Combinatorics

    1. Front Matter
      Pages 137-137
    2. Martin Aigner, Günter M. Ziegler
      Pages 139-149
    3. Martin Aigner, Günter M. Ziegler
      Pages 151-155
    4. Martin Aigner, Günter M. Ziegler
      Pages 157-166
    5. Martin Aigner, Günter M. Ziegler
      Pages 167-172
    6. Martin Aigner, Günter M. Ziegler
      Pages 173-178
    7. Martin Aigner, Günter M. Ziegler
      Pages 179-184
    8. Martin Aigner, Günter M. Ziegler
      Pages 185-190
    9. Martin Aigner, Günter M. Ziegler
      Pages 191-196
  6. Graph Theory

    1. Front Matter
      Pages 197-197
    2. Martin Aigner, Günter M. Ziegler
      Pages 199-202
    3. Martin Aigner, Günter M. Ziegler
      Pages 203-206
    4. Martin Aigner, Günter M. Ziegler
      Pages 207-211
    5. Martin Aigner, Günter M. Ziegler
      Pages 213-222
    6. Martin Aigner, Günter M. Ziegler
      Pages 223-225
    7. Martin Aigner, Günter M. Ziegler
      Pages 227-235
  7. Back Matter
    Pages 236-239

About this book

Introduction

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

This third edition offers two new chapters, on partition identities, and on card shuffling. Three proofs of Euler's most famous infinite series appear in a separate chapter. There is also a number of other improvements, such an exciting new way to "enumerate the rationals."

Keywords

Finite Identity Partition analysis combinatorics geometry number theory proof proofs

Authors and affiliations

  • Martin Aigner
    • 1
  • Günter M. Ziegler
    • 2
  1. 1.Institut für Mathematik II (WE2)Freie Universität BerlinBerlinGermany
  2. 2.Institut für Mathematik, MA 6-2Technische Universität BerlinBerlinGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-05412-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 2004
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-662-05414-7
  • Online ISBN 978-3-662-05412-3
  • Buy this book on publisher's site
Industry Sectors
Pharma
Automotive
Finance, Business & Banking
Consumer Packaged Goods
Aerospace
Oil, Gas & Geosciences