Pell and Pell–Lucas Numbers with Applications

  • Thomas Koshy

Table of contents

  1. Front Matter
    Pages i-xxiii
  2. Thomas Koshy
    Pages 1-30
  3. Thomas Koshy
    Pages 31-55
  4. Thomas Koshy
    Pages 57-78
  5. Thomas Koshy
    Pages 79-85
  6. Thomas Koshy
    Pages 87-100
  7. Thomas Koshy
    Pages 101-114
  8. Thomas Koshy
    Pages 115-149
  9. Thomas Koshy
    Pages 151-172
  10. Thomas Koshy
    Pages 173-192
  11. Thomas Koshy
    Pages 193-205
  12. Thomas Koshy
    Pages 207-225
  13. Thomas Koshy
    Pages 227-246
  14. Thomas Koshy
    Pages 247-253
  15. Thomas Koshy
    Pages 255-281
  16. Thomas Koshy
    Pages 283-301
  17. Thomas Koshy
    Pages 303-323
  18. Thomas Koshy
    Pages 325-361
  19. Thomas Koshy
    Pages 363-369
  20. Thomas Koshy
    Pages 371-394

About this book

Introduction

Pell and Pell–Lucas Numbers has been carefully crafted as an undergraduate/graduate textbook; the level of which depends on the college/university and the instructor’s preference. The exposition moves from the basics to more advanced topics in a systematic rigorous fashion, motivating  the reader with numerous examples, figures, and exercises. Only a strong foundation in precalculus, plus a good background in matrices, determinants, congruences, and combinatorics is required. The text may be used in a variety of number theory courses, as well as in seminars, workshops, and other capstone experiences for teachers in-training and instructors at all levels.

 

A number of  key features  on the Pell family surrounds the historical flavor that is interwoven into an extensive, in-depth coverage of this unique text on the subject. Pell and Pell-Lucas numbers, like the well-known Fibonacci and Catalan numbers, continue to intrigue the mathematical community with their beauty and applicability. Beyond  the classroom setting, the professional mathematician, computer scientist, and other university faculty will greatly benefit from exposure to a range of mathematical skills involving pattern recognition, conjecturing, and problem-solving techniques; these insights and tools are presented in an array of applications to combinatorics, graph theory, geometry, and various other areas of discrete mathematics.

 

Pell and Pell-Lucas Numbers provides

a powerful tool for extracting numerous interesting properties of a vast array of number sequences. It is a fascinating book, offering boundless opportunities for experimentation and exploration for the mathematically curious, from   student, to  the professional, amateur number theory enthusiast, and  talented high schooler.

 

About the author: Thomas Koshy is Professor Emeritus of Mathematics at Framingham State University in Framingham, Massachusetts. In 2007, he received the Faculty of the Year Award and his publication Fibonacci and Lucas numbers with Applications won the Association of American Publishers' new book award in 2001. Professor Koshy has also authored numerous articles on a wide spectrum of topics and more than  seven books, among them,  Elementary Number Theory with Applications, second edition; Catalan Numbers with Applications;  Triangular Arrays with Applications; and  Discrete Mathematics with Applications.

Keywords

Chebyshev Polynomials Pell Fibonacci Pell Triangle Pell numbers Pell–Lucas numbers Pell’s Equation Pythagorean Triples Triangular Numbers

Authors and affiliations

  • Thomas Koshy
    • 1
  1. 1.Framingham State UniversityFraminghamUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-8489-9
  • Copyright Information Springer Science+Business Media New York 2014
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-8488-2
  • Online ISBN 978-1-4614-8489-9
  • About this book
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