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

• Κύριος συγγραφέας: Pinsky, Ross G. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2014.
• Σειρά: Universitext,
• Θέματα: Mathematics.; Number theory.; Probabilities.; Combinatorics.; Graph theory.; Probability Theory and Stochastic Processes.; Graph Theory.; Number Theory.

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...

Πίνακας περιεχομένων:

• 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.