The Art of Proving Binomial Identities: 1st Edition (Hardback) book cover

The Art of Proving Binomial Identities

1st Edition

By Michael Z. Spivey

Chapman and Hall/CRC

384 pages | 29 B/W Illus.

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Hardback: 9780815379423
pub: 2019-06-06
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Description

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.

Table of Contents

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.

About the Author

Michael Z. Spivey is Professor of Mathematics at the University of Puget Sound, where he currently serves as chair of the Department of Mathematics and Computer Science. He earned his PhD in operations research from Princeton University. He has authored more than 25 mathematics papers, most of which are on optimization, combinatorics, or the binomial coeffcients.

About the Series

Discrete Mathematics and Its Applications

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Subject Categories

BISAC Subject Codes/Headings:
MAT028000
MATHEMATICS / Set Theory
MAT036000
MATHEMATICS / Combinatorics