A Reader’s Guide I have never let my schooling interfere with my education. – Mark Twain The Student Mathematical Library is aimed at undergraduate students, but our focus is somewhat broader. We may also envision a graduate student looking for a pragmatic view of asymptotic cal- culations. We may also envision a high school student learning new mathematical relationships. The common denominator is a love of mathematics. To the largest degree possible, we have strived to make this work self-contained. The reader should be aware, however, of certain assumptions. Calculus. We do assume a knowledge of first year calculus, as taught in U.S. colleges and, often, high schools. Differentiation and integration is done without proof. The definite integral ∞ −∞ e−x2/2dx = √ 2π is assumed this appears with surprising frequency. We do not use differential equations, nor partial differential equations, nor algebra, nor topology. We do not use material from the course frequently called (in the U.S.) analysis. In particular, all interchanges of limn fn(x)dx and limn fn(x)dx are done from scratch. xiii

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