Preface |
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Introduction --- Mathematics, Intuition, and Computers |
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1 | (2) |
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Section I The Realm of the Counterintuitive |
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3 | (66) |
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Chapter 1 The Monty Hall Problem |
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7 | (6) |
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1.1 The Monty Hall Problem |
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7 | (1) |
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1.2 Looking at an Extreme Case |
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8 | (1) |
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1.3 A Trickier Monty Hall Problem |
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9 | (2) |
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11 | (2) |
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Chapter 2 How Probabilistic Entanglement Connects Almost Everything |
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13 | (10) |
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2.1 Is Everything Connected? |
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13 | (1) |
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13 | (1) |
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2.3 Probabilistic Entanglement |
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14 | (1) |
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2.4 Benefitting from a Coin Flip |
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15 | (2) |
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17 | (1) |
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2.6 Multiple Observations from a Single Group |
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17 | (1) |
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2.7 An Odd Number of Trials |
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18 | (2) |
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2.8 Comparing Means of Unrelated Groups |
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20 | (2) |
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2.9 How Fundamental Is Probability? |
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22 | (1) |
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Chapter 3 Blackwell's Bet |
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23 | (10) |
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24 | (1) |
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3.2 Unexpected Expectations |
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25 | (2) |
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3.3 Can Blackwell's Bet Help You Beat the Line at Sports Betting? |
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27 | (1) |
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3.4 Applying Blackwell's Bet to Sample and Population Statistics |
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28 | (5) |
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Chapter 4 A Stop at Willoughby --- Mathematics in the Twilight Zone |
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33 | (10) |
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4.1 Can You Predict the Flip of a Coin? |
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33 | (1) |
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34 | (1) |
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4.3 Next Stop --- Willoughby |
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35 | (1) |
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4.4 An Actual Coin Flip Prediction |
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36 | (2) |
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4.5 A Magical Mystery Tour |
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38 | (2) |
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4.6 Are We Predicting the Future? |
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40 | (3) |
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Chapter 5 The Fate of Schrodinger's Cat |
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43 | (18) |
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5.1 Blackwell's Bet Redux |
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45 | (2) |
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5.2 More About Bernoulli Trials |
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47 | (1) |
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5.3 Creating a Predictable Schrodinger's Cat Experiment |
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48 | (3) |
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5.4 Would This Experiment Fool Erwin Schrodinger? |
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51 | (1) |
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5.5 The Schrodinger Switcheroo |
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52 | (2) |
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5.6 Why Science Is Difficult |
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54 | (1) |
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5.7 The Solar Neutrino Deficit |
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55 | (1) |
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56 | (1) |
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5.9 Non-Predictable Bernoulli Trials |
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57 | (1) |
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5.10 Time Travel and Predictability Paradoxes |
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58 | (1) |
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5.11 Of Time and Third Avenue |
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59 | (1) |
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5.12 Checking Out the Schrodinger's Cat Experiment in Your Home |
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60 | (1) |
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Chapter 6 Coins and Camels |
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61 | (8) |
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6.1 Distinguishing Similar Bernoulli Trials |
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61 | (1) |
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6.2 The Problem of the 17 Camels |
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62 | (1) |
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63 | (3) |
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6.4 A Slightly Different Problem |
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66 | (1) |
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6.5 When One Door Closes --- How Mathematicians Find Problems to Investigate |
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66 | (3) |
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Section II The Monday Morning Quarterback |
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69 | (38) |
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Chapter 7 The Joy of Simulation |
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71 | (14) |
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7.1 Random Number Generators |
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73 | (1) |
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7.2 Chi-Square Tests; Karl Pearson |
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73 | (5) |
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7.3 Simulations in Contemporary Science and Engineering |
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78 | (1) |
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7.4 Simulation in Fantasy Sports |
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79 | (2) |
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7.5 Why Educators Should Teach Simulation Rather than Algebra |
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81 | (1) |
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7.6 Simulation in the Electoral College |
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81 | (1) |
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7.7 Why are Tennis' Big Three so Dominant? |
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82 | (3) |
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Chapter 8 Numbed by Numbers |
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85 | (10) |
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8.1 A Really, Really, REALLY Bad Statistic |
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85 | (3) |
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8.2 The Year of the Unbeatens |
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88 | (2) |
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90 | (3) |
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8.4 Integrating the Real World with Education |
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93 | (2) |
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Chapter 9 Losing the Battle, Winning the War |
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95 | (12) |
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97 | (4) |
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9.2 The Gibbard-Satterthwaite Theorem |
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101 | (3) |
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9.3 Dumping for Future Advantage |
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104 | (3) |
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Section III Getting It Right; A Synergy of Mathematics, Intuition and Computers |
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107 | (24) |
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109 | (8) |
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10.1 Can the "Hot Hand" Be Exploited to Win at Betting Sports? |
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112 | (2) |
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10.2 The "Hot Hand" in a Wider Context |
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114 | (3) |
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Chapter 11 The Bent Coin and the Hot Hand |
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117 | (14) |
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11.1 Binomial Trials and Tribulations |
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117 | (1) |
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11.2 Binomial Trials and Flipping a Coin Just Once |
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118 | (1) |
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11.3 A Different Approach |
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119 | (1) |
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11.4 The Probability of the Probability of Probabilities |
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120 | (4) |
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124 | (1) |
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125 | (2) |
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127 | (1) |
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11.8 Doing Better than Average |
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128 | (3) |
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Section IV The Last Hurrah |
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131 | (8) |
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Chapter 12 Using Combinatorics to Improve Advertising --- For Everyone |
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133 | (6) |
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12.1 A Brief History of Advertising |
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133 | (1) |
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12.2 What We Hate about Advertising |
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133 | (2) |
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12.3 The Element of Surprise |
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135 | (1) |
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12.4 Combinatorial Commercials |
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136 | (3) |
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Appendix --- Basic Probability Theory |
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139 | (8) |
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A.1 Computational Rules for Probability |
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140 | (1) |
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A.2 Conditional Probability |
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141 | (1) |
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141 | (1) |
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A.4 Expected Value (a.k.a. Expectation) |
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142 | (1) |
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143 | (1) |
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144 | (3) |
Annotated Bibliography |
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147 | (10) |
Index |
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157 | |