The Art of Proving Binomial Identities
Discrete Mathematics and Its Applications Series
Author: Spivey Michael Z.Language: Anglais
Subjects for The Art of Proving Binomial Identities:
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· 15.6x23.5 cm · Hardback
The book has two goals: (1) Provide a unified treatment of the binomial coefficients, and (2) Bring together much of the undergraduate mathematics curriculum via one theme (the binomial coefficients). The binomial coefficients arise in a variety of areas of mathematics: combinatorics, of course, but also basic algebra (binomial theorem), infinite series (Newton?s binomial series), differentiation (Leibniz?s generalized product rule), special functions (the beta and gamma functions), probability, statistics, number theory, finite difference calculus, algorithm analysis, and even statistical mechanics.
Introducing the Binomial Coefficients. Basic Techniques. Combinatorics. Calculus. Probability. Generating Functions. Recurrence Relations and Finite Differences. Special Numbers. Miscellaneous Techniques. Hints and Solutions to Exercises.