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Martin Aigner Günter M. Ziegler Pr
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Prof. Dr. Martin Aigner FB Mathemat
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VI Preface to the Fourth Edition Wh
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VIII Table of Contents 21. A theore
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Six proofs of the infinity of prime
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Six proofs of the infinity of prime
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Bertrand’s postulate Chapter 2 We
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Bertrand’s postulate 9 times. Her
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Bertrand’s postulate 11 by compar
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Binomial coefficients are (almost)
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Binomial coefficients are (almost)
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Representing numbers as sums of two
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Representing numbers as sums of two
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Representing numbers as sums of two
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The law of quadratic reciprocity Ch
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The law of quadratic reciprocity 25
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The law of quadratic reciprocity 27
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The law of quadratic reciprocity 29
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Every finite division ring is a fie
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Every finite division ring is a fie
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Some irrational numbers Chapter 7
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Some irrational numbers 37 and this
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Some irrational numbers 39 F(x) may
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Some irrational numbers 41 Now assu
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44 Three times π 2 /6 v 1 1 2 y v
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46 Three times π 2 /6 For m = 1, 2
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48 Three times π 2 /6 1 f(t) = 1 t
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50 Three times π 2 /6 (3) It has b
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Hilbert’s third problem: decompos
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Hilbert’s third problem: decompos
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Hilbert’s third problem: decompos
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Hilbert’s third problem: decompos
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Hilbert’s third problem: decompos
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64 Lines in the plane, and decompos
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66 Lines in the plane, and decompos
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The slope problem Chapter 11 Try fo
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The slope problem 71 • Every move
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The slope problem 73 For the second
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76 Three applications of Euler’s
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78 Three applications of Euler’s
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80 Three applications of Euler’s
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82 Cauchy’s rigidity theorem Q: Q
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84 Cauchy’s rigidity theorem A be
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86 Touching simplices l l l ′ Pr
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88 Touching simplices For our examp
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90 Every large point set has an obt
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92 Every large point set has an obt
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94 Every large point set has an obt
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96 Borsuk’s conjecture Theorem. L
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98 Borsuk’s conjecture On the oth
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100 Borsuk’s conjecture To obtain
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Sets, functions, and the continuum
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Sets, functions, and the continuum
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Sets, functions, and the continuum
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Sets, functions, and the continuum
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Sets, functions, and the continuum
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Sets, functions, and the continuum
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Sets, functions, and the continuum
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Sets, functions, and the continuum
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In praise of inequalities Chapter 1
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In praise of inequalities 121 where
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In praise of inequalities 123 Proo
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In praise of inequalities 125 Seco
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128 The fundamental theorem of alge
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One square and an odd number of tri
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One square and an odd number of tri
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One square and an odd number of tri
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One square and an odd number of tri
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A theorem of Pólya on polynomials
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A theorem of Pólya on polynomials
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A theorem of Pólya on polynomials
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On a lemma of Littlewood and Offord
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On a lemma of Littlewood and Offord
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Cotangent and the Herglotz trick Ch
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Cotangent and the Herglotz trick 15
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Cotangent and the Herglotz trick 15
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Buffon’s needle problem Chapter 2
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Buffon’s needle problem 157 The c
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Combinatorics 25 Pigeon-hole and do
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162 Pigeon-hole and double counting
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164 Pigeon-hole and double counting
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166 Pigeon-hole and double counting
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168 Pigeon-hole and double counting
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170 Pigeon-hole and double counting
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Tiling rectangles Chapter 26 Some m
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Tiling rectangles 175 Third proof.
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Tiling rectangles 177 References [1
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180 Three famous theorems on finite
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- Page 194 and 195: Shuffling cards Chapter 28 How ofte
- Page 196 and 197: Shuffling cards 187 Indeed, if A i
- Page 198 and 199: Shuffling cards 189 Let T be the nu
- Page 200 and 201: Shuffling cards 191 Theorem 1. Let
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- Page 204 and 205: Lattice paths and determinants Chap
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- Page 216 and 217: Identities versus bijections Chapte
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- Page 222 and 223: Completing Latin squares Chapter 32
- Page 224 and 225: Completing Latin squares 215 Proof
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- Page 228: Graph Theory 33 The Dinitz problem
- Page 231 and 232: 222 The Dinitz problem In 1976 Vizi
- Page 233 and 234: 224 The Dinitz problem X A bipartit
- Page 235 and 236: 226 The Dinitz problem G : L(G) : a
- Page 237 and 238: 228 Five-coloring plane graphs From
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- Page 245 and 246: 236 Turán’s graph theorem Let us
- Page 247 and 248: 238 Turán’s graph theorem Thus b
- Page 250 and 251: Communicating without errors Chapte
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- Page 254 and 255: Communicating without errors 245 Le
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- Page 260 and 261: The chromatic number of Kneser grap
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- Page 267 and 268: 258 Of friends and politicians w 1
- Page 270 and 271: Probability makes counting (sometim
- Page 272 and 273: Probability makes counting (sometim
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- Page 278 and 279: Proofs from THE BOOK 269
- Page 280 and 281: Index acyclic directed graph, 196 a
- Page 282 and 283: Index 273 matrix-tree theorem, 203