Published by: honhungoc (Karma: 8660.27) on 12 March 2011 | Views: 3729
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Table of Contents 7 Introduction 9 Games with numbers 9 An historical note 11 A first curiosity 12 Fibonacci numbers 14 A curious calculating device: the abacus 20 The origins of algebra 21 Games with algebra 23 Odds and evens 24 The successor of a number 24 A shortcut in calculations 25 How much money is in your pocket? 25 How to guess a birth date 26 Guessing age and size of shoes 26 Where is the error? 27 Positional notation of numbers 28 One rotten apple can spoil the whole basket 29 Ordinary language and mathematical language 33 Games with geometrical figures 33 Geometry and optical illusions 41 Games with matches 42 Lo shu, an ancient Chinese figure 42 Magic squares: their history and mathematical features 44 More intricate magic squares 47 Diabolic squares 48 Magic stars 51 More about squares 51 An extraordinary surface 52 The bridges of Kdnigsberg 55 Elementary theory of graphs 57 Save the goat and the cabbage 58 The jealous husbands 61 Interchanging knights 62 A wide range of applications 63 Topology, or the geometry of distortion 70 Topological labyrinths 73 The Mobius ring 76 Games with topological knots 77 The four-colour theorem 84 Rubik's cube 91 Paradoxes and antinomies 91 The role of paradoxes in the development of mathematical thought 94 Geometrical representation of numbers 94 A tragic Pythagorean paradox: the odd equals the even 96 Unthinkable numbers 97 Zeno of Elea 98 Zeno's paradoxes 100 Theoretical significance and solution of Zeno's paradoxes 101 The part equals the whole 102 Sets, an antinomic concept 103 A postman and barber in trouble 104 Russell's paradox 105 A great game: mathematical logic 105 A special chessboard 105 What is a logical argument? 106 Logic and ordinary language 107 An ingenious idea of Leibniz 108 Logic: the science of correct reasoning 112 Logical variables 113 George Boole and the origins of propositional calculus 113 The logical calculus 114 Negation 115 Explanation of symbols 115 Conjunction and the empty set 116 The empty set 117 Disjunction 118 Implication 119 Who has drunk the brandy? 120 The multiplication tables of propositional calculus: truth-tables 125 Another solution to the problem of the brandy drinkers 126 Who is the liar? 129 How to argue by diagram 135 A practical application: logic circuits 143 Games with probability 143 The reality of chance and uncertainty 144 Cards, dice, games of chance and bets: historical origins of the calculus of probability 144 Chance phenomena 145 A clarification 146 Sample space 148 The measure of probability 148 Horse races 149 The concept of function 149 The algebra of events and probability games 150 The complementary event and its probability measure 150 The probability of the union of two events 151 The probability of the intersection of two events 152 The probability of a choice 153 Drawing a card from a pack 154 Joint throw of coin and die 154 Dependent events 156 Independent events 159 What is the probability that George and Bob speak the truth? 160 Probability and empirical science 160 Probability and statistics 160 Sample and population 161 Guess the vintage 161 Conclusion n symbols used 179 Bibliograph163 Appendix: games with logic and probability 163 Note 164 Games with logic 167 Games with probability 177 List of maiy 181 Index
