Notes on Introductory Combinatorics

✍ Scribed by George Pólya, Robert E. Tarjan, Donald R. Woods (auth.)

• Publisher: Birkhäuser Basel
• Year: 2010
• Tongue: English
• Leaves: 201
• Series: Modern Birkhäuser Classics / Progress in Computer Science 4
• Edition: 1
• Category: Library

✦ Synopsis

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)

✦ Table of Contents

Front Matter....Pages i-ix
Introduction....Pages 1-1
Combinations and Permutations....Pages 2-10
Generating Functions....Pages 11-31
Principle of Inclusion and Exclusion....Pages 32-40
Stirling Numbers....Pages 41-54
Pólya’s Theory of Counting....Pages 55-85
Outlook....Pages 86-94
Midterm Examination....Pages 95-115
Ramsey Theory....Pages 116-127
Matchings (Stable Marriages)....Pages 128-134
Matchings (Maximum Matchings)....Pages 135-151
Network Flow....Pages 152-156
Hamiltonian and Eulerian Paths....Pages 157-168
Planarity and the Four-Color Theorem....Pages 169-181
Final Examination....Pages 182-190
Bibliography....Pages 191-192

✦ Subjects

Combinatorics; Algorithms; Algorithm Analysis and Problem Complexity; Computational Mathematics and Numerical Analysis; Numeric Computing