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Proofs from THE BOOK

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Cover of 'Proofs from THE BOOK'

Table of Contents

  1. Altmetric Badge
    Book Overview
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    Chapter 1 Six proofs of the infinity of primes
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    Chapter 2 Bertrand’s postulate
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    Chapter 3 Binomial coefficients are (almost) never powers
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    Chapter 4 Representing numbers as sums of two squares
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    Chapter 5 Every finite division ring is a field
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    Chapter 6 Some irrational numbers
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    Chapter 7 Hilbert’s third problem: decomposing polyhedra
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    Chapter 8 Lines in the plane and decompositions of graphs
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    Chapter 9 The slope problem
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    Chapter 10 Three applications of Euler’s formula
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    Chapter 11 Cauchy’s rigidity theorem
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    Chapter 12 The problem of the thirteen spheres
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    Chapter 13 Touching simplices
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    Chapter 14 Every large point set has an obtuse angle
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    Chapter 15 Borsuk’s conjecture
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    Chapter 16 Sets, functions, and the continuum hypothesis
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    Chapter 17 In praise of inequalities
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    Chapter 18 A theorem of Pólya on polynomials
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    Chapter 19 On a lemma of Littlewood and Offord
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    Chapter 20 Pigeon-hole and double counting
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    Chapter 21 Three famous theorems on finite sets
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    Chapter 22 Cayley’s formula for the number of trees
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    Chapter 23 Completing Latin squares
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    Chapter 24 The Dinitz problem
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    Chapter 25 Five-coloring plane graphs
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    Chapter 26 How to guard a museum
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    Chapter 27 Turán’s graph theorem
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    Chapter 28 Communicating without errors
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    Chapter 29 Of friends and politicians
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    Chapter 30 Probability makes counting (sometimes) easy
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Title
Proofs from THE BOOK
Published by
Springer Berlin Heidelberg, June 2013
DOI 10.1007/978-3-662-22343-7
ISBNs
978-3-66-222345-1, 978-3-66-222343-7
Authors

Aigner, Martin, Ziegler, Günter M.