Contents Preface ix A Reader’s Guide xiii Chapter 0. An Infinity of Primes 1 Chapter 1. Stirling’s Formula 5 §1.1. Asymptotic Estimation of an Integral 5 §1.2. Approximating Sums by Trapezoids 13 §1.3. Combining Forces to Estimate the Error 16 §1.4. Estimating the Integral More Accurately 18 §1.5. An Application to Random Walks 21 Chapter 2. Big Oh, Little Oh, and All That 27 §2.1. The Language of Asymptotics 28 §2.2. . . . and How to Use It 29 §2.3. Little Oh One 31 §2.4. Little Fleas and Littler Fleas: The Strange Hierarchy of Asymptopia 31 §2.5. Little Oh One in the Exponent 33 §2.6. Inverting Functions 34 §2.7. Taylor Series 35 v
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