Download Concrete Mathematics: A Foundation for Computer Science (1st by Donald E. Knuth, Ronald L. Graham, Oren Patashnik PDF

By Donald E. Knuth, Ronald L. Graham, Oren Patashnik

This e-book introduces the math that help complicated machine programming and the research of algorithms. The book's basic goal is to supply a fantastic and suitable base of mathematical talents. it truly is an critical textual content and reference for laptop scientists and severe programmers in almost each self-discipline.

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Additional info for Concrete Mathematics: A Foundation for Computer Science (1st Edition)

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The h4gm ‘t 1 All horses are the same color; we can prove this by induction on the number of horses in a given set. Here’s how: “If there’s just one horse then it’s the same color as itself, so the basis is trivial. For the induction step, assume that there are n horses numbered 1 to n. By the induction hypothesis, horses 1 through n - 1 are the same color, and similarly horses 2 through n are the same color. But the middle horses, 2 through n - 1, can’t change color when they’re in different groups; these are horses, not chameleons.

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Here s g(x) dx, the indefinite integral of g(x), is the class of functions whose derivative is g(x). Analogously, A has as an inverse, the anti-difference (or summation) operator x; and there’s another Fundamental Theorem: g(x) = Af(xl if and only if xg(x)bx = f(x)+C. 46) Here x g(x) 6x, the indefinite sum of g(x), is the class of functions whose diflerence is g(x). ) The “C” for indefinite integrals is an arbitrary constant; the “C” for indefinite sums is any function p(x) such that p(x + 1) = p(x).

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