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.
