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＜電子ブック＞
Problems from the Discrete to the Continuous : Probability, Number Theory, Graph Theory, and Combinatorics / by Ross G. Pinsky
(Universitext. ISSN:21916675)

版	1st ed. 2014.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2014
本文言語	英語
大きさ	XIII, 154 p. 8 illus. in color : online resource
著者標目	*Pinsky, Ross G author SpringerLink (Online service)
件　名	LCSH:Probabilities LCSH:Graph theory LCSH:Number theory LCSH:Discrete mathematics FREE:Probability Theory FREE:Graph Theory FREE:Number Theory FREE:Discrete Mathematics
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-319-07965-3

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