Fibonacci and Lucas Numbers with Applications

<p>Volume II provides an advanced approach to the extended gibonacci family, which includes Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas, Vieta, Vieta-Lucas, and Chebyshev polynomials of both kinds. This volume offers a uniquely unified, extensive, and historical approach that will appeal to both students and professional mathematicians. </p> <p>As in Volume I, Volume II focuses on problem-solving techniques such as pattern recognition; conjecturing; proof-techniques, and applications. It offers a wealth of delightful opportunities to explore and experiment, as well as plentiful material for group discussions, seminars, presentations, and collaboration.<br /><br />In addition, the material covered in this book promotes intellectual curiosity, creativity, and ingenuity.</p> <p>Volume II features: </p> <ul> <li>A wealth of examples, applications, and exercises of varying degrees of difficulty and sophistication.</li> <li>Numerous combinatorial and graph-theoretic proofs and techniques.</li> <li>A uniquely thorough discussion of gibonacci subfamilies, and the fascinating relationships that link them.</li> <li>Examples of the beauty, power, and ubiquity of the extended gibonacci family.</li> <li>An introduction to tribonacci polynomials and numbers, and their combinatorial and graph-theoretic models.</li> <li>Abbreviated solutions provided for all odd-numbered exercises.</li> <li>Extensive references for further study.</li> </ul> <p>This volume will be a valuable resource for upper-level undergraduates and graduate students, as well as for independent study projects, undergraduate and graduate theses. It is the most comprehensive work available, a welcome addition for gibonacci enthusiasts in computer science, electrical engineering, and physics, as well as for creative and curious amateurs.</p>