Concrete Mathematics
Encyclopedia
Concrete Mathematics: A Foundation for Computer Science, by Ronald Graham
, Donald Knuth
, and Oren Patashnik
, is a mathematical 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 of Concrete Mathematics form "a blend of CONtinuous and disCRETE mathematics." In particular, 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, and 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.
typeface and Concrete Roman
font.
Ronald Graham
Ronald Lewis Graham is a mathematician credited by the American Mathematical Society as being "one of the principal architects of the rapid development worldwide of discrete mathematics in recent years"...
, Donald Knuth
Donald Knuth
Donald Ervin Knuth is a computer scientist and Professor Emeritus at Stanford University.He is the author of the seminal multi-volume work The Art of Computer Programming. Knuth has been called the "father" of the analysis of algorithms...
, and Oren Patashnik
Oren Patashnik
Oren Patashnik is a computer scientist. He is notable for co-creating BibTeX, and co-writing Concrete Mathematics: A Foundation for Computer Science...
, is a mathematical 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 of Concrete Mathematics form "a blend of CONtinuous and disCRETE mathematics." In particular, calculus
Calculus
Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...
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
Stanford University
The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is a private research university on an campus located near Palo Alto, California. It is situated in the northwestern Santa Clara Valley on the San Francisco Peninsula, approximately northwest of San...
. The book expands on the material in the "Mathematical Preliminaries" section of Knuth's The Art of Computer Programming
The Art of Computer Programming
The Art of Computer Programming is a comprehensive monograph written by Donald Knuth that covers many kinds of programming algorithms and their analysis....
. 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, and the margins contain "mathematical graffiti
Graffiti
Graffiti is the name for images or lettering scratched, scrawled, painted or marked in any manner on property....
," 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
Knuth reward check
Knuth reward checks are awarded by computer scientist Donald Knuth for finding mistakes in, or making suggestions for, his publications. In the preface of each of his books and on his website, Knuth offers a reward of $2.56 to the first person to find each error in his published books, whether it...
for any error found in the book—in this case, whether an error is "technically, historically, typographically, or politically incorrect
Politically incorrect
The phrase "politically incorrect" may refer to:* Someone or something which does not meet a standard of political correctness* Politically Incorrect, a late-night U.S. political talk show* Politically Incorrect, a German political blog...
."
The book has popularized a lot of mathematical notation. This includes Iverson bracket, Floor and ceiling functions and notation for rising and falling factorials.
Typography
Donald Knuth used the first edition of Concrete Mathematics as a test case for the AMS EulerAMS Euler
AMS Euler is an upright cursive typeface, commissioned by the American Mathematical Society and designed and created by Hermann Zapf with the assistance of Donald Knuth. It tries to emulate a mathematician's style of handwriting mathematical entities on a blackboard, which is upright rather than...
typeface and Concrete Roman
Concrete Roman
Concrete Roman is a slab serif typeface designed by Donald Knuth using his METAFONT program. It was intended to accompany the Euler mathematical font which it partners in Knuth's book Concrete Mathematics. It is has a darker appearance than its more famous sibling, Computer Modern...
font.
Editions
- 1st edition: September 1988 (ISBN 0-201-14236-8):
- 2nd edition: January 1994 (ISBN 0-201-55802-5):