Book Description
This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its wellknown authors is to provide a solid and relevant base of mathematical skills  the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists  the authors themselves rely heavily on it!  but for serious users of mathematics in virtually every discipline.
Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems." The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for selfstudy.
Major topics include:
Sums
Recurrences
Integer functions
Elementary number theory
Binomial coefficients
Generating functions
Discrete probability
Asymptotic methods
This second edition includes important new material about mechanical summation. In response to the widespread use of the first edition as a reference book, the bibliography and index have also been expanded, and additional nontrivial improvements can be found on almost every page. Readers will appreciate the informal style of Concrete Mathematics. Particularly enjoyable are the marginal graffiti contributed by students who have taken courses based on this material. The authors want to convey not only the importance of the techniques presented, but some of the fun in learning and using them.
Table of Contents
 About This eBook
 Title Page
 Copyright Page
 Dedication Page
 Preface
 A Note on Notation
 Contents
 1. Recurrent Problems
 2. Sums
 3. Integer Functions
 4. Number Theory
 5. Binomial Coefficients
 6. Special Numbers

7. Generating Functions
 7.1 Domino Theory and Change
 7.2 Basic Maneuvers

7.3 Solving Recurrences
 Example 1: Fibonacci numbers revisited.
 Rational Expansion Theorem for Distinct Roots.
 General Expansion Theorem for Rational Generating Functions.
 Example 2: A moreorless random recurrence.
 Example 3: Mutually recursive sequences.
 Example 4: A closed form for change.
 Example 5: A divergent series.
 Example 6: A recurrence that goes all the way back.
 7.4 Special Generating Functions
 7.5 Convolutions
 7.6 Exponential gf’s
 7.7 Dirichlet Generating Functions
 Exercises
 8. Discrete Probability
 9. Asymptotics
 A. Answers to Exercises
 B. Bibliography
 C. Credits for Exercises
 Index
 List of Tables
Product Information
 Title: Concrete Mathematics: A Foundation for Computer Science, Second Edition
 Author(s):
 Release date: February 1994
 Publisher(s): AddisonWesley Professional
 ISBN: 9780134389974