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## Catalan Numbers with Applications (Hardback)"Catalan numbers crop up in chess boards, computer programs, and even train tracks. This comprehensive text presents a clear introduction to one of the truly fascinating topics in mathematics." — From the back cover ## $21.25 |

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Please contact us if you've got questions about this product.## Condition

**VERY GOOD:** This book is in very good condition, showing some use on the slightly bent cover corners. The pages are free of writing and the book still “crackles” when opened. The book was printed on acid-free paper.

## Description

From the back cover: “Catalan numbers are named after the Belgian mathematician Eugene Charles Catalan, who ‘discovered’ them in 1838 (though he was not the first person actually to discover them). The book includes descriptions of the mathematics and history behind Catalan numbers as well as short biographies of the prominent mathematicians who have worked with the numbers, including that of the Swiss mathematician Leonhard Euler who did, in fact, first discover them a century before Catalan. Koshy as brings together, for the first time, the extensive research that has been done on Catalan numbers, which until now has been scattered in a variety of sources.

“Teachers and professors can use Catalan numbers to generate excitement among students for exploration, to spur their intellectual curiosity, and to sharpen a variety of mathematical skills and tools, such as pattern recognition, conjecturing, and proof- and problem-solving techniques. This book is intended not only for mathematicians but also for mathematics and science teachers, computer scientists, and those amateurs with a modicum of mathematical curiosity. An invaluable resource book, it contains an intriguing array of applications to computer science, abstract algebra, combinatorics, geometry, graph theory, and chess.”

**BRIEF CONTENTS**

**Chapters**

- Binomial Coefficients
- The Central Binomial Coefficient
- The Central Binomial Coefficient Revisited
- Binomial Coefficients Revisited
- Catalan Numbers
- The Ubiquity of Catalan Numbers I
- The Ubiquity of Catalan Numbers II
- Trees and Catalan Numbers
- Lattice Paths and Catalan Numbers
- Partitions and Catalan Numbers
- Partitions and Catalan Numbers
- Algebra, Sports, and Catalan Numbers
- Pascal’s Triangle and Catalan Numbers
- Divisibility Properties
- A Catalan Triangle
- A Family of Binary Words
- Tribinomial Coefficients
- Generalized Catalan Numbers

**Appendices**

- Appendix A
- Bijections
- Fundamental Counting Principles
- Recursion
- Generating Functions
- Congruences
- Mathematical Induction
- Extended Binomial Coefficients
- Maclaurin’s Series
- A Definition of [(p/q over r)]
- Appendix B: The First 100 Catalan Numbers

The book ends with References, Index of Mathematicians, and Index.

## Details

- SKU:
- 2245
- Author:
- Koshy, Thomas
- Publisher:
- Oxford University Press
- Publish Date:
- 2009 (First Printing)
- Format:
- Hardback
- Weight (pounds):
- 1.61
- Dimensions (W”xL”xH”):
- 6.35″x9.5″x1″
- ISBN-13:
- 9780195334548
- ISBN-10:
- 019533454X

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