xiv A Reader’s Guide Probability. A number of basic distributions are considered in this work. These include the binomial, the Poisson, and the Gauss- ian distributions. We have defined these when they appear. Still, some prior knowledge of the notions of random variable, expectation, variance, and independence would be helpful to the student. Graph Theory. We do not assume a knowledge of graph theory. Still, some prior knowledge of what a graph is, as a set of vertices and edges, would be helpful. We examine the random graph G(n, p). Again, a prior familiarity would be helpful but not necessary. Number Theory. We expect the reader to know what prime numbers are and to know the unique factorization of positive integers into primes. Otherwise, our presentation of number theory is self- contained. Algorithms. The mathematical analysis of algorithms is a fas- cinating subject. Here we give some glimpses into the analyses, but our study of algorithms is self-contained. Certainly, no actual pro- gramming is needed. Our final chapter, Really Big Numbers!, is different in flavor. This author has always been fascinated with big numbers. This chapter is basically a paper written for the American Mathematical Monthly three decades ago. Some of the material uses ordinal numbers, like ωω, which may be new to the reader. We sometimes skirt a topic, pulling from it only some asymptotic aspects. This is particularly noticeable in Ramsey theory, one of our favorite topics. Certain sections are technically quite complicated and are labelled as such. They may be skipped without losing the thread of the argu- ment. Facility with logarithms is assumed throughout. We use ln x for natural logarithm and lg x for the logarithm to the base two. Asymptopia is a beautiful world. Enjoy!
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