| |
|
|
|
|
|
|
|
|
1. |
Record Nr. |
UNINA9910299978703321 |
|
|
Autore |
Pinsky Ross G |
|
|
Titolo |
Problems from the Discrete to the Continuous : Probability, Number Theory, Graph Theory, and Combinatorics / / by Ross G. Pinsky |
|
|
|
|
|
|
|
Pubbl/distr/stampa |
|
|
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2014 |
|
|
|
|
|
|
|
|
|
ISBN |
|
|
|
|
|
|
Edizione |
[1st ed. 2014.] |
|
|
|
|
|
Descrizione fisica |
|
1 online resource (XIII, 154 p. 8 illus. in color.) |
|
|
|
|
|
|
Collana |
|
Universitext, , 0172-5939 |
|
|
|
|
|
|
Disciplina |
|
|
|
|
|
|
Soggetti |
|
Probabilities |
Graph theory |
Number theory |
Combinatorics |
Probability Theory and Stochastic Processes |
Graph Theory |
Number Theory |
|
|
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
Formato |
Materiale a stampa |
|
|
|
|
|
Livello bibliografico |
Monografia |
|
|
|
|
|
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. |
|
|
|
|
|
| |