Triangular Arrays with Applications

Erscheinungsjahr 2011
ISBN: 978-0-19-974294-3
Verlag: Oxford University Press

Buch, Englisch, 438 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 819 g

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.

Zielgruppe

Mathematicians as well as computer scientists, math and science teachers, advanced high school students, and those with mathematical curiosity and maturity.

Autoren/Hrsg.

Koshy, Thomas

Fachgebiete

• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik

Inhaltsverzeichnis

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

Über Autor(innen)

Koshy, Thomas
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.