Triangular Arrays with Applications

Hardcover | February 20, 2011

byThomas Koshy

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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-solvingtechniques.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 comprehensiveintroduction 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 tribinomialcoefficients 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 scienceteachers, advanced high school students, and those with mathematical curiosity and maturity.

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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-solvingtechniques.While a good deal of research exists concer...

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.

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Format:HardcoverDimensions:408 pages, 9.25 × 6.12 × 0.98 inPublished:February 20, 2011Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199742944

ISBN - 13:9780199742943

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Table of Contents

Preface1. Fundamentals2. Binomial Coefficients3. The Binomial Theorem4. Binomial Congruences5. Binomial Coefficients Revisited6. Pascal's Triangle7. Pascal's Triangle Revisited8. Pascal's m-ary Triangles9. Pascal Graphs10. Maclaurin's Series11. Fibonacci and Lucas Numbers12. Pascal's Triangle and Generating Functions13. Pascal-like Triangles14. Fibonacci Triangles15. Josef 's Triangle16. Lucas Triangles17. Catalan Numbers and Pascal's Triangle18. Catalan's Parenthesization Problem Revisited19. Leibniz's Harmonic Triangle20. Stirling's Triangles21. Bell's Triangles22. Euler's Triangles23. Lah's Triangle24. Fibonacci Convolution Triangles25. Tartaglia's Arrays26. Miscellaneous Arrays27. Tribinomial Triangles28. Fibonomial Triangles29. Multinomial Arrays