Problems from the Discrete to the Continuous: Probability, Number Theory, Graph Theory, and Combinatorics by Ross G. PinskyProblems from the Discrete to the Continuous: Probability, Number Theory, Graph Theory, and Combinatorics by Ross G. Pinsky

Problems from the Discrete to the Continuous: Probability, Number Theory, Graph Theory, and…

byRoss G. Pinsky

Paperback | August 22, 2014

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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.

Ross Pinsky is a Professor in the Department of Mathematics at Technion-Israel Institute of Technology.
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Title:Problems from the Discrete to the Continuous: Probability, Number Theory, Graph Theory, and…Format:PaperbackDimensions:154 pages, 23.5 × 15.5 × 0.01 inPublished:August 22, 2014Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3319079646

ISBN - 13:9783319079646

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Table of 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 ErdÅs and Rényi.