TY - BOOK AU - Pinsky,Ross G. TI - Problems from the discrete to the continuous: probability, number theory, graph theory, and combinatorics T2 - Universitext SN - 9783319079646 U1 - 519.3 23 PY - 2014/// CY - Switzerland PB - Springer KW - Combinatorial optimization. KW - Probabilities KW - Number theory N1 - Includes bibliographical references and index; 1. Partitions With Restricted Summands or "The Money Changing Problem" -- 2. The Asymptotic Density of Relatively Prime Pairs and of Square-Free Numbers -- 3. A One-Dimensional Probabilistic Packing Problem -- 4. The Arcsine Laws for the One-Dimensional Simple Symmetric Random Walk -- 5. The Distribution of Cycles in Random Permutations -- 6. Chebyshev's Theorem on the Asymptotic Density of the Primes -- 7. Mertens' Theorems on the Asymptotic Behavior of the Primes -- 8. The Hardy-Ramanujan Theorem on the Number of Distinct Prime Divisors -- 9. The Largest Clique in a Random Graph and Applications to Tampering Detection and Ramsey Theory -- 10. The Phase Transition Concerning the Giant Component in a Sparse Random Graph-a Theorem of Erdos and Renyi-- Appendices-- References-- Index N2 - 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. ER -