| 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.
|
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Graph theory.
|
|
probability.
|
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Combinatorial optimization
|
|
Graph theory
|
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Number theory
|
|
Probabilities
|
| Form |
Electronic book
|
| ISBN |
9783319079653 |
|
3319079654 |
|
3319079646 |
|
9783319079646 |
|
