This is a text that defines "the number of ways there are of doing some well-defined operation." Covers permutations and combinations associated with elementary algebra, generating functions, the principle of inclusion and exclusion, the cycles of permutations, the theory of distributions, partitions, compositions, trees, and linear graphs; and permutations with restricted position. Includes problems. 1958 edition.
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Most Helpful Customer Reviews
6 of 6 people found the following review helpful:
5.0 out of 5 stars
A Classic Text in the Subject,
By Math Geek (Oro Valley, AZ USA) - See all my reviews
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This review is from: Introduction to Combinatorial Analysis (Dover Books on Mathematics) (Paperback)
This is a text which, while considered an introduction and perhaps a bit dated nowadays, requires some of the closest attention I have ever had to pay to a mathematical work. If I may call this book a mathematical gold mine, I must also say that in parts the digging is arduous and rewarding and the rock can be of high density. The section in chapter 2, on derivatives of composite functions (essentially Bell Polynomials, after the famous Eric Temple Bell), is an example.This is at least my third pass through the book and this time I decided not to slough over some of the details on these polynomials. I found myself bewildered for a couple of days, as the author gives no assistance to the reader--no doubt to help the reader develop some of that mathematical maturity mentioned in the preface--and found gold thereby. Statements made apparently as an aside, such as "completely determined..." had not been paid adequate attention by me. Also, it was not pointed out by the author that certain constants evaluated in the examples were found by setting the variable to zero, and so on. This is all left to the reader to dig out. In a span of two or three pages in this section there are hours of profitable work left to the reader. This is not a complaint, but rather a statement of the level of audience addressed by this book. It is not a text for readers who require hand-holding. However, anyone who is prepared to dig will experience the "joy of finding things out", if I may humbly steal a favored phrase of the late, great Richard P. Feynman.
2 of 2 people found the following review helpful:
4.0 out of 5 stars
A very good old text,
By R. Bagula "Roger L. Bagula" (Lakeside, Ca United States) - See all my reviews (VINE VOICE) (REAL NAME)
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This review is from: Introduction to Combinatorial Analysis (Dover Books on Mathematics) (Paperback)
The thing that borthers me is the archadic notation used in parts of this book and notation used with no reference that I can find.I really learned a lot in reading this book and intend to try to get more out of it in the future, but I really wouldn't use this as an introductory text as some of the theorems an problems are graduate or post graduate level. It is a useful and helpful book for those intent on understanding combinatorial theory.
2 of 2 people found the following review helpful:
5.0 out of 5 stars
Dated, but excellent,
By PST "A Reader from Germany" (Eislingen Deutschland) - See all my reviews
This review is from: Introduction to Combinatorial Analysis (Dover Books on Mathematics) (Paperback)
As a "hobby mathematician", I had had exposure to this subject while studying related topics (e.g. random graphs), but this was the first book I studied, which was dedicated ot combinatorics only. The book seems easy reading, but I have a feel, a real mathematician will find a lot of depth in this book. Generating functions are explained in great detail.It is obviously written in the older style, not in the Definition-Theorem-Proof style, which I find easier to read. Still, it is a simple yet rigorous introduction into the field of combinatorics
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86
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cite this book:
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- Gian-Carlo Rota on Combinatorics: Introductory Papers and Commentaries (Contemporary Mathematicians) by Joseph P.S. Kung on page 72, page 260, and page 276
- The Theory of Partitions (Encyclopedia of Mathematics and its Applications) by George E. Andrews in Front Matter, page 15, and page 211
- Advances in Combinatorial Methods and Applications to Probability and Statistics (Statistics for Industry and Technology) by N. Balakrishnan on page 273, and page 480
- Combinatorics: Topics, Techniques, Algorithms by Peter J. Cameron on page 335, and Back Matter
- Probability, Stochastic Processes, and Queueing Theory: The Mathematics of Computer Performance Modeling by Randolph Nelson in Back Matter (1), and Back Matter (2)
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