“Concrete Mathematics”的意思、由来-开放百科全书

词条

Concrete Mathematics

释义

Contents and history
Typography
Chapter outline
Editions
References
External links

{{Infobox book
| name = Concrete Mathematics: A Foundation for Computer Science
| title_orig =
| translator =
| image = Concrete Mathematics - Cover.png
| caption = The cover displays the mathematical symbol for summation, ∑, inscribed in concrete.
| author = Ronald Graham, Donald Knuth, and Oren Patashnik
| illustrator =
| cover_artist =
| country = United States
| language = English
| series =
| subject =
| genre = Mathematics
Computer science
| publisher = Addison–Wesley
| pub_date = 1994
| media_type = Print (Hardcover)
| pages = 657 pp (Second Edition)
| isbn = 0-201-55802-5
| dewey = 510 20
| congress = QA39.2 .G733 1994
| oclc = 29357079
| preceded_by =
| followed_by =
}}

Concrete Mathematics: A Foundation for Computer Science, by Ronald Graham, Donald Knuth, and Oren Patashnik, first published in 1989, is a textbook that is widely used in computer-science departments as a substantive but light-hearted treatment of the analysis of algorithms.

Contents and history

The book 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.

Typography

Donald Knuth used the first edition of Concrete Mathematics as a test case for the AMS Euler typeface and Concrete Roman font.

Chapter outline

Recurrent Problems
Summation
Integer Functions
Number Theory
Binomial Coefficients
Special Numbers
Generating Functions
Discrete Probability
Asymptotics

Editions

{{cite book |author-last1=Graham |author-first1=Ronald L. |author-link1=Ronald L. Graham |author-last2=Knuth |author-first2=Donald E. |author-link2=Donald E. Knuth |author-last3=Patashnik |author-first3=Oren |author-link3=Oren Patashnik |title=Concrete Mathematics - A foundation for computer science |edition=1st |series=Advanced Book Program |publisher=Addison-Wesley Publishing Company |location=Reading, MA, USA |date=1989 |pages=xiv+625 |isbn=0-201-14236-8 |mr=1001562}}
{{cite book |author-last1=Graham |author-first1=Ronald L. |author-link1=Ronald L. Graham |author-last2=Knuth |author-first2=Donald E. |author-link2=Donald E. Knuth |author-last3=Patashnik |author-first3=Oren |author-link3=Oren Patashnik |title=Concrete Mathematics - A foundation for computer science |edition=2nd |publisher=Addison-Wesley Professional |location=Reading, MA, USA |date=February 1994 |pages=xiv+657 |isbn=0-201-55802-5 |mr=1397498}} Errata: (1994), (January 1998), (27th printing, May 2013)

References

External links

ToC and blurb for Concrete Mathematics: A Foundation for Computer Science", 2nd ed.
Preface for Concrete Mathematics: A Foundation for Computer Science, 2nd ed.

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