Description 
1 online resource (xiii, 154 pages) : color illustrations 
Series 
Universitext, 01725939 

Universitext. 01725939

Contents 
Partitions With Restricted Summands or "The Money Changing Problem"  The Asymptotic Density of Relatively Prime Pairs and of SquareFree Numbers  A OneDimensional Probabilistic Packing Problem  The Arcsine Laws for the OneDimensional 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 HardyRamanujan 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 Grapha 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.) 
