# Notes on Introductory Combinatorics

## George Polya; Robert E. Tarjan; Donald R. Woods

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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.

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From the Back Cover:

Developed from the authors’ introductory combinatorics course, this book focuses on a branch of mathematics which plays a crucial role in computer science. Combinatorial methods provide many analytical tools used for determining the expected performance of computer algorithms. Elementary subjects such as combinations and permutations, and mathematical tools such as generating functions and Pólya’s Theory of Counting, are covered, as are analyses of specific problems such as Ramsey Theory, matchings, and Hamiltonian and Eulerian paths.

This introduction will provide students with a solid foundation in the subject.

----

"This is a delightful little paperback which presents a day-by-day transcription of a course taught jointly by Pólya and Tarjan at Stanford University. Woods, the teaching assistant for the class, did a very good job of merging class notes into an interesting mini-textbook; he also included the exercises, homework, and tests assigned in the class (a very helpful addition for other instructors in the field). The notes are very well illustrated throughout and Woods and the Birkhäuser publishers produced a very pleasant text.

One can count on [Pólya 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. Pólya."

―Zentralblatt MATH (Review of the original hardcover edition)

Review:

From the reviews:

“The purpose of this re-publication was to make modern classics books like this one remain accessible to new generations of students, scholars and researchers.” (Zentralblatt MATH, Vol. 1195, 2010)

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## 1.Notes on Introductory Combinatorics (Paperback)

Editore: Birkhauser Boston, Germany (1990)
ISBN 10: 0817631704 ISBN 13: 9780817631703
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Descrizione libro Birkhauser Boston, Germany, 1990. Paperback. Condizione libro: New. 2nd Revised edition. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. Brand New Book. 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. Codice libro della libreria LIE9780817631703

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## 2.Notes on Introductory Combinatorics

Editore: BirkhÃ¤user (1990)
ISBN 10: 0817631704 ISBN 13: 9780817631703
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Descrizione libro BirkhÃ¤user, 1990. Paperback. Condizione libro: NEW. 9780817631703 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Codice libro della libreria HTANDREE0736917

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## 3.Notes on Introductory Combinatorics (Progress in Computer Science and Applied Logic)

Editore: Birkhäuser (1990)
ISBN 10: 0817631704 ISBN 13: 9780817631703
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Descrizione libro Birkhäuser, 1990. Condizione libro: New. This item is printed on demand for shipment within 3 working days. Codice libro della libreria LP9780817631703

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## 4.Notes on Introductory Combinatorics

Editore: Birkhäuser
ISBN 10: 0817631704 ISBN 13: 9780817631703
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Descrizione libro Birkhäuser. PAPERBACK. Condizione libro: New. 0817631704 New Condition. Codice libro della libreria NEW6.0504126

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## 5.Notes on Introductory Combinatorics (Progress in Computer Science and Applied Logic (PCS))

Editore: Birkhäuser Boston (1990)
ISBN 10: 0817631704 ISBN 13: 9780817631703
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Descrizione libro Birkhäuser Boston, 1990. Paperback. Condizione libro: New. Codice libro della libreria DADAX0817631704

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## 6.Notes on Introductory Combinatorics

Editore: Birkhäuser (1990)
ISBN 10: 0817631704 ISBN 13: 9780817631703
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Descrizione libro Birkhäuser, 1990. Paperback. Condizione libro: New. book. Codice libro della libreria 0817631704

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## 7.Notes on Introductory Combinatorics

Editore: Birkhauser (1984)
ISBN 10: 0817631704 ISBN 13: 9780817631703
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Descrizione libro Birkhauser, 1984. Paperback. Condizione libro: Brand New. 1st edition. 212 pages. 9.00x6.00x0.50 inches. In Stock. Codice libro della libreria zk0817631704

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