Concrete Mathematics: A Foundation for Computer ScienceThis book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline. Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems." The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study. Major topics include:
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a₁ algorithm answer approximation asymptotic b₁ binomial coefficients binomial theorem calculations Chapter closed form compute Concrete Mathematics constant converges convolution defined denominator derivation distribution dominoes equal equation Euler's Euler's summation formula evaluate example exercise factor Fibonacci numbers Find a closed finite formula fraction function gives Gosper's harmonic numbers hence hypergeometric terms identity induction infinite sum look mathematics mean and variance method multiple multiset Newton series nonnegative integer notation parameters Pascal's triangle permutation polynomial positive integer power series prime probability probability generating function probability space problem proof prove random variable rational rational function real numbers recurrence replace sequence side solution solve Stern-Brocot Stern-Brocot tree Stirling numbers Stirling's approximation summation theorem there's zero Σ Σ