Problems from the Discrete to the Continuous

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

• 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 book under review consists of ten well-written chapters each devoted to a single topic, or rather a single problem. ... The book is expected to appeal to a wide audience, including graduate and advanced undergraduate students, and can indeed be used for a seminar course in which students may present the lectures. ... Each chapter contains a set of exercises and ends with illuminating historical notes." (M. Hajja, Mathematical Reviews, November, 2015) "The book under review collects a number of problems of discrete nature and with solutions utilizing continuous and analytic tools. ... the book is suitable for undergraduate students to have an excursion on some selected problems and interesting theorems, and also it is suitable for instructors to use it to introduce some good and meaningful examples." (Mehdi Hassani, zbMATH 1311.11002, 2015)