Problems from the Discrete to the Continuous Probability, Number Theory, Graph Theory, and Combinatorics
Başlık:
Problems from the Discrete to the Continuous Probability, Number Theory, Graph Theory, and Combinatorics
ISBN:
9783319079653
Personal Author:
Edition:
1st ed. 2014.
Yayın Bilgileri:
Cham : Springer International Publishing : Imprint: Springer, 2014.
Fiziksel Tanımlama:
XIII, 154 p. 8 illus. in color. online resource.
Series:
Universitext,
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.
Abstract:
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.
Ek Kurum Yazarı:
Dil:
English