Concrete Mathematics

Concrete Mathematics

Concrete Mathematics: A Foundation for Computer Science, by Ronald Graham, Donald Knuth, and Oren Patashnik, is a textbook that is widely used in computer-science departments. It provides mathematical knowledge and skills for computer science, especially for the analysis of algorithms. According to the preface, the topics in Concrete Mathematics are "a blend of CONtinuous and disCRETE mathematics." Calculus is frequently used in the explanations and exercises. The term "concrete mathematics" also denotes a complement to "abstract mathematics".

The book is based on a course begun in 1970 by Knuth at Stanford University. The book expands on the material in the "Mathematical Preliminaries" section of Knuth's The Art of Computer Programming. Consequently, some readers use it as an introduction to that famous series of books.

Concrete Mathematics has an informal and often humorous style. The authors reject what they see as the dry style of most mathematics textbooks. The margins contain "mathematical graffiti", comments submitted by the text's first editors: Knuth and Patashnik's students at Stanford.

As with many of Knuth's books, readers are invited to claim a reward for any error found in the book—in this case, whether an error is "technically, historically, typographically, or politically incorrect."

The book has popularized a lot of mathematical notation. This includes Iverson bracket, Floor and ceiling functions and notation for rising and falling factorials.

Read more about Concrete Mathematics:  Typography, Chapter Outline, Editions

Famous quotes containing the words concrete and/or mathematics:

    A doctor, like anyone else who has to deal with human beings, each of them unique, cannot be a scientist; he is either, like the surgeon, a craftsman, or, like the physician and the psychologist, an artist.... This means that in order to be a good doctor a man must also have a good character, that is to say, whatever weaknesses and foibles he may have, he must love his fellow human beings in the concrete and desire their good before his own.
    —W.H. (Wystan Hugh)

    Why does man freeze to death trying to reach the North Pole? Why does man drive himself to suffer the steam and heat of the Amazon? Why does he stagger his mind with the mathematics of the sky? Once the question mark has arisen in the human brain the answer must be found, if it takes a hundred years. A thousand years.
    Walter Reisch (1903–1963)