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Author Pinsky, Ross G., author

Title Problems from the discrete to the continuous : probability, number theory, graph theory, and combinatorics / Ross G. Pinsky
Published Cham : Springer, 2014
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Description 1 online resource (xiii, 154 pages) : color illustrations
Series Universitext, 0172-5939
Universitext. 0172-5939
Contents Partitions With Restricted Summands or "The Money Changing Problem" -- The Asymptotic Density of Relatively Prime Pairs and of Square-Free Numbers -- A One-Dimensional Probabilistic Packing Problem -- The Arcsine Laws for the One-Dimensional Simple Symmetric Random Walk -- The Distribution of Cycles in Random Permutations -- Chebyshev's Theorem on the Asymptotic Density of the Primes -- Mertens' Theorems on the Asymptotic Behavior of the Primes -- The Hardy-Ramanujan Theorem on the Number of Distinct Prime Divisors -- The Largest Clique in a Random Graph and Applications to Tampering Detection and Ramsey Theory -- The Phase Transition Concerning the Giant Component in a Sparse Random Graph-a Theorem of Erdős and Rényi
Summary The primary intent of the book is to introduce an array of beautiful problems in a variety of subjects quickly, pithily and completely rigorously to graduate students and advanced undergraduates. The book takes a number of specific problems and solves them, the needed tools developed along the way in the context of the particular problems. It treats a mélange of topics from combinatorial probability theory, number theory, random graph theory and combinatorics. The problems in this book involve the asymptotic analysis of a discrete construct as some natural parameter of the system tends to infinity. Besides bridging discrete mathematics and mathematical analysis, the book makes a modest attempt at bridging disciplines. The problems were selected with an eye toward accessibility to a wide audience, including advanced undergraduate students. The book could be used for a seminar course in which students present the lectures
Bibliography Includes bibliographical references and index
Notes Online resource; title from PDF title page (SpringerLink, viewed August 20, 2014)
Subject Combinatorial optimization.
Probabilities.
Number theory.
Graph theory.
Form Electronic book
ISBN 3319079646 (print)
3319079654 (electronic bk.)
9783319079646 (print)
9783319079653 (electronic bk.)