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Triangular Arrays with Applications

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Triangular Arrays with Applications Cover

 

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Synopses & Reviews

Publisher Comments:

Triangular arrays are a unifying thread throughout various areas of discrete mathematics such as number theory and combinatorics. They can be used to sharpen a variety of mathematical skills and tools, such as pattern recognition, conjecturing, proof-techniques, and problem-solving techniques.

While a good deal of research exists concerning triangular arrays and their applications, the information is scattered in various journals and is inaccessible to many mathematicians. This is the first text that will collect and organize the information and present it in a clear and comprehensive introduction to the topic. An invaluable resource book, it gives a historical introduction to Pascal's triangle and covers application topics such as binomial coefficients, figurate numbers, Fibonacci and Lucas numbers, Pell and Pell-Lucas numbers, graph theory, Fibonomial and tribinomial coefficients and Fibonacci and Lucas polynomials, amongst others. The book also features the historical development of triangular arrays, including short biographies of prominent mathematicians, along with the name and affiliation of every discoverer and year of discovery. The book is intended for mathematicians as well as computer scientists, math and science teachers, advanced high school students, and those with mathematical curiosity and maturity.

About the Author

Thomas Koshy, Ph.D., is Professor of Mathematics at Framingham State College, Framingham, Massachusetts. His Fibonacci and Lucas Numbers with Applications , published by Wiley, won the Association of American Publishers' new book award in 2001. He published Catalan Numbers with OUP USA in 2008.

Table of Contents

Contents:

Preface

1. Fundamentals

2. Binomial Coefficients

3. The Binomial Theorem

4. Binomial Congruences

5. Binomial Coefficients Revisited

6. Pascal's Triangle

7. Pascal's Triangle Revisited

8. Pascal's m-ary Triangles

9. Pascal Graphs

10. Maclaurin's Series

11. Fibonacci and Lucas Numbers

12. Pascal's Triangle and Generating Functions

13. Pascal-like Triangles

14. Fibonacci Triangles

15. Josef 's Triangle

16. Lucas Triangles

17. Catalan Numbers and Pascal's Triangle

18. Catalan's Parenthesization Problem Revisited

19. Leibniz's Harmonic Triangle

20. Stirling's Triangles

21. Bell's Triangles

22. Euler's Triangles

23. Lah's Triangle

24. Fibonacci Convolution Triangles

25. Tartaglia's Arrays

26. Miscellaneous Arrays

27. Tribinomial Triangles

28. Fibonomial Triangles

29. Multinomial Arrays

Product Details

ISBN:
9780199742943
Author:
Koshy, Thomas
Publisher:
Oxford University Press, USA
Author:
null, Thomas
Subject:
Discrete Mathematics
Subject:
Applied
Subject:
Computer Science
Subject:
Mathematics | Applied Mathematics
Subject:
Mathematics - Advanced
Publication Date:
20110231
Binding:
HARDCOVER
Grade Level:
Professional and scholarly
Language:
English
Pages:
438
Dimensions:
6.4 x 9.3 x 1.1 in 1.65 lb

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