Contents vii §7.4. Computations for R(k, k) 96 §7.5. Asymmetrical Ramsey Numbers 98 §7.6. Application to R(3,l) 100 Chapter 8. Large Deviations 103 §8.1. The Chernoff Bound 103 §8.2. The Gaussian Tail 105 §8.3. The Gaussian Paradigm I 105 §8.4. Heads Minus Tails 107 §8.5. . . . and the Central Limit Theorem 109 §8.6. The Binomial Distribution 109 §8.7. The Gaussian Paradigm II 111 Chapter 9. Primes 115 §9.1. Fun with Primes 116 §9.2. Prime Number Theorem—Lower Bound 118 §9.3. Prime Number Theorem—Upper Bound 119 §9.4. Prime Number Theorem with Constant 120 §9.5. Telescoping 123 Chapter 10. Asymptotic Geometry 125 §10.1. Small Triangles 125 §10.2. The Convex Hull of n Random Points 129 Chapter 11. Algorithms 137 §11.1. Recurrences 137 §11.2. Multiplying Large Numbers 141 §11.3. Multiplying Large Matrices 142 §11.4. Merge Sort 144 §11.5. The Sorting Game 145 §11.6. Quicksort 148 Chapter 12. Potpourri 151 §12.1. The Law of the Iterated Logarithm 151
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