Problems from the Discrete to the Continuous Probability, Number Theory, Graph Theory, and Combinatorics /

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 i...

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Détails bibliographiques
Cote:Libro Electrónico
Auteur principal: Pinsky, Ross G. (Auteur)
Collectivité auteur: SpringerLink (Online service)
Format: Électronique eBook
Langue:Inglés
Publié: Cham : Springer International Publishing : Imprint: Springer, 2014.
Édition:1st ed. 2014.
Collection:Universitext,
Sujets:
Probabilities.
Graph theory.
Number theory.
Discrete mathematics.
Probability Theory.
Graph Theory.
Number Theory.
Discrete Mathematics.
Accès en ligne:Texto Completo
Table des matières:
  • 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.

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