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Notes on Introductory Combinatorics

  • George Pólya
  • Robert E. Tarjan
  • Donald R. Woods

Part of the Modern Birkhäuser Classics book series

Table of contents

  1. Front Matter
    Pages i-ix
  2. George Pólya, Robert E. Tarjan, Donald R. Woods
    Pages 1-1
  3. George Pólya, Robert E. Tarjan, Donald R. Woods
    Pages 2-10
  4. George Pólya, Robert E. Tarjan, Donald R. Woods
    Pages 11-31
  5. George Pólya, Robert E. Tarjan, Donald R. Woods
    Pages 32-40
  6. George Pólya, Robert E. Tarjan, Donald R. Woods
    Pages 41-54
  7. George Pólya, Robert E. Tarjan, Donald R. Woods
    Pages 55-85
  8. George Pólya, Robert E. Tarjan, Donald R. Woods
    Pages 86-94
  9. George Pólya, Robert E. Tarjan, Donald R. Woods
    Pages 95-115
  10. George Pólya, Robert E. Tarjan, Donald R. Woods
    Pages 116-127
  11. George Pólya, Robert E. Tarjan, Donald R. Woods
    Pages 128-134
  12. George Pólya, Robert E. Tarjan, Donald R. Woods
    Pages 135-151
  13. George Pólya, Robert E. Tarjan, Donald R. Woods
    Pages 152-156
  14. George Pólya, Robert E. Tarjan, Donald R. Woods
    Pages 157-168
  15. George Pólya, Robert E. Tarjan, Donald R. Woods
    Pages 169-181
  16. George Pólya, Robert E. Tarjan, Donald R. Woods
    Pages 182-190
  17. George Pólya, Robert E. Tarjan, Donald R. Woods
    Pages 191-192

About this book

Introduction

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)

Keywords

Computer Counting Eulerian paths Hamiltonian paths Pólya's theory of counting Ramsey theory Stirling numbers algorithms combinations computer science function generating functions mathematics permutations theorem

Authors and affiliations

  • George Pólya
    • 1
  • Robert E. Tarjan
    • 2
  • Donald R. Woods
    • 3
  1. 1.Dept. MathematicsStanford UniversityStanfordU.S.A.
  2. 2.Dept. Computer SciencePrinceton UniversityPrincetonU.S.A.
  3. 3.Google, Inc.Mountain ViewU.S.A.

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