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

• Autore: Pinsky Ross G
• Pubblicazione: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2014
• Edizione: 1st ed. 2014.
• Descrizione fisica: 1 online resource (XIII, 154 p. 8 illus. in color.)
• Disciplina: 519.64
• Soggetto topico: Probabilities; Graph theory; Number theory; Combinatorics; Probability Theory and Stochastic Processes; Graph Theory; Number Theory
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di contenuto: 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.
• Sommario/riassunto: 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.
• Titolo autorizzato: Problems from the discrete to the continuous
• ISBN: 3-319-07965-4
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910299978703321
• Lo trovi qui: Univ. Federico II
• Serie: Universitext, . 0172-5939