Cites from the Preface of Concrete Mathematics: A Foundation for Computer Science
One of the present authors had embarked on a series of books called The Art of Computer Programming, and in writing the first volume he (DEK) had found that there were mathematical tools missing from his repertoire; the mathematics he needed for a thorough, well-grounded understanding of computer programs was quite different from what he’d learned as a mathematics major in college.
But what we should ask of educated mathematicians is not what they can speechify about, nor even what they know about the
existing corpus of mathematical knowledge, but rather what can they now do with their learning and whether they can actually solve mathematical problems arising in practice. In short, we look for deeds not words. – John Hammersley
Abstract mathematics was becoming inbred and losing touch with reality; mathematical education needed a concrete counterweight in order to restore a healthy balance.
The heart of mathematics consists of concrete examples and concrete problems. – P. R. Halmos
The material of concrete mathematics may seem at first to be a disparate bag of tricks, but practice makes it into a disciplined set of tools.
It is downright sinful to teach the abstract before the concrete. – Z. A. Melzak
Concrete Mathematics is a bridge to abstract mathematics.
But what exactly is Concrete Mathematics? It is a blend of continuous and discrete mathematics. More concretely, it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems. Once you, the reader, have learned the material in this book, all you will need is a cool head, a large sheet of paper, and fairly decent handwriting in order to evaluate horrendous-looking sums, to solve complex recurrence relations, and to discover subtle patterns in data. You will be so fluent in algebraic techniques that you will often find it easier to obtain exact results
than to settle for approximate answers that are valid only in a limiting sense.
The emphasis is on manipulative technique rather than on existence theorems or combinatorial reasoning; the goal is for each reader to become as familiar with discrete operations (like the greatest-integer function and finite summation) as a student of calculus is familiar with continuous operations (like the absolute-value function and infinite integration).
Concrete mathematics is full of appealing patterns; the manipulations are not always easy, but the answers can be astonishingly attractive.
Mathematics is an ongoing endeavor for people everywhere; many strands are being woven into one rich fabric.