Problems from the Discrete to the Continuous : Probability, Number Theory, Graph Theory, and Combinatorics / by Ross G. Pinsky.
Material type: TextSeries: UniversitextPublication details: Cham : Springer International Publishing : Imprint: Springer, 2014Description: XIII, 154 p.: ill.; 23 cmISBN: 9783319709550 (pbk)Subject(s): Mathematics | Combinatorial analysis | Number theory | Distribution (Probability theory)Genre/Form: Electronic books.Additional physical formats: Printed edition:: No titleDDC classification: 519.2 LOC classification: QA274-274.9Online resources: Full text available from Springer Mathematics and Statistics eBooks 2014 English/InternationalItem type | Current library | Call number | Copy number | Status | Date due | Barcode | Item holds |
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Books | Namal Library Mathematics | 519.2 PIN-P 2019 10909 (Browse shelf (Opens below)) | 1 | Available | 0010909 |
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.
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.
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