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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 23-26
    7. Martin Aigner, Günter M. Ziegler
      Pages 27-36
  3. Geometry

    1. Front Matter
      Pages 37-37
    2. Martin Aigner, Günter M. Ziegler
      Pages 39-45
    3. Martin Aigner, Günter M. Ziegler
      Pages 47-51
    4. Martin Aigner, Günter M. Ziegler
      Pages 53-57
    5. Martin Aigner, Günter M. Ziegler
      Pages 59-64
    6. Martin Aigner, Günter M. Ziegler
      Pages 65-68
    7. Martin Aigner, Günter M. Ziegler
      Pages 69-72
    8. Martin Aigner, Günter M. Ziegler
      Pages 73-78
    9. Martin Aigner, Günter M. Ziegler
      Pages 79-84
  4. Analysis

    1. Front Matter
      Pages 85-85
    2. Martin Aigner, Günter M. Ziegler
      Pages 87-98
    3. Martin Aigner, Günter M. Ziegler
      Pages 99-105
    4. Martin Aigner, Günter M. Ziegler
      Pages 107-114
    5. Martin Aigner, Günter M. Ziegler
      Pages 115-118
    6. Martin Aigner, Günter M. Ziegler
      Pages 119-124
    7. Martin Aigner, Günter M. Ziegler
      Pages 125-128
  5. Combinatorics

    1. Front Matter
      Pages 129-129
    2. Martin Aigner, Günter M. Ziegler
      Pages 131-141
    3. Martin Aigner, Günter M. Ziegler
      Pages 143-147
    4. Martin Aigner, Günter M. Ziegler
      Pages 149-154
    5. Martin Aigner, Günter M. Ziegler
      Pages 155-160
    6. Martin Aigner, Günter M. Ziegler
      Pages 161-166
    7. Martin Aigner, Günter M. Ziegler
      Pages 167-172
  6. Graph Theory

    1. Front Matter
      Pages 173-173
    2. Martin Aigner, Günter M. Ziegler
      Pages 175-178
    3. Martin Aigner, Günter M. Ziegler
      Pages 179-182
    4. Martin Aigner, Günter M. Ziegler
      Pages 183-187
    5. Martin Aigner, Günter M. Ziegler
      Pages 189-198
    6. Martin Aigner, Günter M. Ziegler
      Pages 199-201
    7. Martin Aigner, Günter M. Ziegler
      Pages 203-211
  7. Back Matter
    Pages 212-215

About this book

Introduction

The (mathematical) heroes of this book are "perfect proofs": brilliant ideas, clever connections and wonderful observations that bring new insight and surprising perspectives on basic and challenging problems from Number Theory, Geometry, Analysis, Combinatorics, and Graph Theory. Thirty beautiful examples are presented here. They are candidates for The Book in which God records the perfect proofs - according to the late Paul Erdös, who himself suggested many of the topics in this collection.
The result is a book which will be fun for everybody with an interest in mathematics, requiring only a very modest (undergraduate) mathematical background. For this revised and expanded second edition several chapters have been revised and expanded, and three new chapters have been added.

Keywords

Combinatorics Lattice Polya Prime analysis calculus differential equation double counting geometry graph theory number theory probability 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/10.1007/978-3-662-04315-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 2001
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-662-04317-2
  • Online ISBN 978-3-662-04315-8
  • Buy this book on publisher's site
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