This book discusses a number of selected results and methods, mostly from the areas of combinatorics and graph theory. The authors develop most topics to the extent that they can describe the discrete mathematics behind an important application of mathematics such as optimization problems, cryptography, and coding to name a few. Another feature that is not covered in other discrete mathematics books is the use of ESTIMATES (How many digits does 100! have? or Which is larger: 2^100 or 100!?). There are questions posed in the text and problems at the end of each chapter with solutions for many of them at the end of the book.

László Lovász is a Senior Researcher in the Theory Group at Microsoft Corporation. He is a recipient of the 1999 Wolf Prize and the Gödel Prize for the top paper in Computer Science. József Pelikán is Professor of Mathematics in the Department of Algebra and Number Theory at Eötvös Loránd University, Hungary. In 2002, he was elected Chairman of the Advisory Board of the International Mathematical Olympiad. Katalin Vesztergombi is Senior Lecturer in the Department of Mathematics at the University of Washington.

Aimed at undergraduate mathematics and computer science students, this book is an excellent introduction to a lot of problems of discrete mathematics. It discusses a number of selected results and methods, mostly from areas of combinatorics and graph theory, and it uses proofs and problem solving to help students understand the solutions to problems. Numerous examples, figures, and exercises are spread throughout the book.

* Preface * Let us count! * Combinatorial tools * Binomial Coefficients and Pascal's Triangle * Fibonacci numbers * Combinatorial probability * Integers, divisors, and primes * Graphs * Trees * Finding the optimum * Matchings in graphs * Combinatorics in geometry * Euler's formula * Coloring maps and graphs * Finite geometries, codes, Latin squares, and other pretty creatures * A glimpse of complexity and cryptography * Answers to exercises