Free download Concrete Mathematics Book in PDF written by Ronal L. Graham (AT & T Bell Laboratories), Donald E. Knuth (Stanford University), Oren Patashnik (Stanford University) and published by Addison-Wesley Publishing Company.
According to the Authors, “This book is based on a course of the same name that has been taught annually at Stanford University since 1970. About fifty students have taken it each year-juniors and seniors, but mostly graduate students-and alumni of these classes have begun to spawn similar courses elsewhere. Thus the time seems ripe to present the material to a wider audience (including sophomores).
The course title “Concrete Mathematics” was originally intended as an antidote to “Abstract Mathematics,” since concrete classical results were rapidly being swept out of the modern mathematical curriculum by a new wave of abstract ideas popularly called the “New Math!’ Abstract mathematics is a wonderful subject, and there’s nothing wrong with it: It’s beautiful, general, and useful. But its adherents had become deluded that the rest of mathematics was inferior and no longer worthy of attention. The goal of generalization had become so fashionable that a generation of mathematicians had become unable to relish beauty in the particular, to enjoy the challenge of solving quantitative problems, or to appreciate the value of technique. Abstract mathematics was becoming inbred and losing touch with reality; mathematical education needed a concrete counterweight in order to restore a healthy balance.
This book contains more than 500 exercises, divided into six categories:
- Warmups are exercises that every reader should try to do when first reading the material.
- Basics are exercises to develop facts that are best learned by trying
one’s own derivation rather than by reading somebody else’s, - Homework exercises are problems intended to deepen an understanding of material in the current chapter.
- Exam problems typically involve ideas from two or more chapters simultaneously; they are generally intended for use in take-home exams (not for in-class exams under time pressure).
- Bonus problems go beyond what an average student of concrete mathematics is expected to handle while taking a course based on this book; they extend the text in interesting ways.
- Research problems may or may not be humanly solvable, but the ones
presented here seem to be worth a try (without time pressure).
Table of Contents
- Recurrent Problems
- Sums
- Integer Functions
- Number Theory
- Binomial Coefficients
- Special Numbers
- Generating Functions
- Discrete Probability
- Asymptotics
A. Answers to Exercises
B. Bibliography
C. Credits for Exercises
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