Notes on introductory combinatorics
Author(s)
Bibliographic Information
Notes on introductory combinatorics
（Progress in computer science, no. 4）
Birkhäuser, 1983
- : us
- : us : pbk
- : sz
- : sz : pbk
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science数学
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Note
Bibliography: p. [191]
Description and Table of Contents
- Volume
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: us ISBN 9780817631239
Description
"This is a delightful little paperback which presents a day-by-day transcription of a course taught jointly by Polya and Tarjan at Stanford University...One can count on [Polya and Tarjan] for new insights and a fresh outlook. Both instructors taught by presenting a succession of examples rather than by presenting a body of theory...[The book] is very well suited as supplementary material for any introductory class on combinatorics; as such, it is very highly recommended. Finally, for all of us who like the topic and delight in observing skilled professionals at work, this book is entertaining and, yes, instructive, reading." Mathematical Reviews (Review of the original hardcover edition) "The mathematical community welcomes this book as a final contribution to honour the teacher G. Polya." Zentralblatt MATH (Review of the original hardcover edition)"
- Volume
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: us : pbk ISBN 9780817631703
Description
In the winter of 1978, Professor George P61ya and I jointly taught Stanford University's introductory combinatorics course. This was a great opportunity for me, as I had known of Professor P61ya since having read his classic book, How to Solve It, as a teenager. Working with P6lya, who *was over ninety years old at the time, was every bit as rewarding as I had hoped it would be. His creativity, intelligence, warmth and generosity of spirit, and wonderful gift for teaching continue to be an inspiration to me. Combinatorics is one of the branches of mathematics that play a crucial role in computer sCience, since digital computers manipulate discrete, finite objects. Combinatorics impinges on computing in two ways. First, the properties of graphs and other combinatorial objects lead directly to algorithms for solving graph-theoretic problems, which have widespread application in non-numerical as well as in numerical computing. Second, combinatorial methods provide many analytical tools that can be used for determining the worst-case and expected performance of computer algorithms. A knowledge of combinatorics will serve the computer scientist well. Combinatorics can be classified into three types: enumerative, eXistential, and constructive. Enumerative combinatorics deals with the counting of combinatorial objects. Existential combinatorics studies the existence or nonexistence of combinatorial configurations.
Table of Contents
1. Introduction.- 2. Combinations and Permutations.- 3. Generating Functions.- 4. Principle of Inclusion and Exclusion.- 5. Stirling Numbers.- 6. Polya's Theory of Counting.- 7. Outlook.- 8. Midterm Examination.- 9. Ramsey Theory.- 10. Matchings (Stable Marriages).- 11. Matchings (Maximum Matchings).- 12. Network Flow.- 13. Hamiltonian and Eulerian Paths.- 14. Planarity and the Four-Color Theorem.- 15. Final Examination.- 16. Bibliography.
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