- Concrete Mathematics
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Concrete Mathematics: A Foundation for Computer Science 
The cover displays the mathematical symbol for summation, ∑, inscribed in concrete.Author(s) Ronald Graham, Donald Knuth, and Oren Patashnik Country United States Language English Genre(s) Mathematics
Computer sciencePublisher Addison–Wesley Publication date 1994 Media type Print (Hardcover) Pages 657 pp (second edition) ISBN 0201558025 OCLC Number 29357079 Dewey Decimal 510 20 LC Classification QA39.2 .G733 1994 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."[1]
The book has popularized a lot of mathematical notation. This includes Iverson bracket, Floor and ceiling functions and notation for rising and falling factorials.
Contents
Typography
Donald Knuth used the first edition of Concrete Mathematics as a test case for the AMS Euler typeface and Concrete Roman font.[2]
Chapter outline
- Recurrent Problems
- Summation
- Integer Functions
- Number Theory
- Binomial Coefficients
- Special Numbers
- Generating Functions
- Discrete Probability
- Asymptotics
Editions
- 1st edition: September 1988 (ISBN 0-201-14236-8): Graham, Ronald L.; Knuth, Donald E.; Patashnik, Oren (1989). Concrete Mathematics. Advanced Book Program (first ed.). Reading, MA: Addison-Wesley Publishing Company. pp. xiv+625. ISBN 0-201-14236-8. MR1001562.
- 2nd edition: January 1994 (ISBN 0-201-55802-5): Graham, Ronald L.; Knuth, Donald E.; Patashnik, Oren (1994). Concrete Mathematics (second ed.). Reading, MA: Addison-Wesley Publishing Company. pp. xiv+657. ISBN 0-201-55802-5. MR1397498.
Notes
- ^ Graham, Knuth, and Patashnik: Concrete Mathematics
- ^ Donald E. Knuth. Typesetting Concrete Mathematics, TUGboat 10 (1989), 31–36, 342. Reprinted as chapter 18 of the book Digital Typography.
External links
Donald Knuth Publications The Art of Computer Programming • "The Complexity of Songs" • Computers and Typesetting • Concrete Mathematics • Surreal Numbers • Things a Computer Scientist Rarely Talks About • Selected papers seriesSoftware Fonts Literate programming Algorithms Knuth's Algorithm X • Knuth–Bendix completion algorithm • Knuth–Morris–Pratt algorithm • Knuth shuffle • Robinson–Schensted–Knuth correspondence • Trabb Pardo–Knuth algorithmOther Categories:- 1988 books
- Mathematics books
- Books by Donald Knuth
- Computer science books
- Addison-Wesley books
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