Koshy, Thomas
2015, XXIII, 431 p. 139 illus., 1 illus. in color.
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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.
Content Level » Upper undergraduate
Keywords » Chebyshev Polynomials - Pell Fibonacci - Pell Triangle - Pell numbers - Pell–Lucas numbers - Pell’s Equation - Pythagorean Triples - Triangular Numbers
Related subjects » History of Mathematical Sciences - Mathematics - Number Theory and Discrete Mathematics
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