Problems from the Discrete to the Continuous

Probability, Number Theory, Graph Theory, and Combinatorics
2014
ISBN: 978-3-319-07964-6
Verlag: Springer International Publishing

Buch, Englisch, 154 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 2642 g

Reihe: Universitext

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 melange 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.

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Pinsky, Ross G.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Operations Research Graphentheorie
• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung

Inhaltsverzeichnis

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 Erdos and Rényi.

Über Autor(innen)

Ross Pinsky is a Professor in the Department of Mathematics at Technion-Israel Institute of Technology.