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

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Ross G. Pinsky

Problems from the Discrete to the Continuous

Probability, Number Theory, Graph Theory, and Combinatorics

Ross G. Pinsky

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English

Springer International Publishing AG
25 August 2014

Discrete mathematics; Number theory; Probability & statistics; Combinatorics & graph theory; Stochastics

Series: Universitext

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 melange 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.

By: Ross G. Pinsky
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: 2014 ed.
Dimensions: Height: 235mm, Width: 155mm, Spine: 9mm
Weight: 2.642kg
ISBN: 9783319079646
ISBN 10: 3319079646
Series: Universitext
Pages: 154
Publication Date: 25 August 2014
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

"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."

Ross Pinsky is a Professor in the Department of Mathematics at Technion-Israel Institute of Technology.

Reviews for Problems from the Discrete to the Continuous: Probability, Number Theory, Graph Theory, and Combinatorics

The book under review collects a number of problems of discrete nature and with solutions utilizing continuous and analytic tools. ... the book is suitable for undergraduate students to have an excursion on some selected problems and interesting theorems, and also it is suitable for instructors to use it to introduce some good and meaningful examples. (Mehdi Hassani, zbMATH 1311.11002, 2015)