Notes on Introductory Combinatorics

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Springer Science & Business Media, Nov 17, 2009 - Mathematics - 192 pages

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.

 

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"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)

 

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Contents

Introduction
1
Combinations and Permutations
2
Generating Functions
11
Principle of Inclusion and Exclusion
32
Stirling Numbers
41
Pólyas Theory of Counting
55
Outlook
86
Midterm Examination
95
Ramsey Theory
116
Matchings Stable Marriages
128
Matchings Maximum Matchings
135
Hamiltonian and Eulerian Paths
157
Planarity and the FourColor Theorem
169
Final Examination
182
Bibliography
191
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