Fibonacci and Lucas Numbers with Applications

The first comprehensive survey of mathematics' most fascinating number sequences Fibonacci and Lucas numbers have intrigued amateur and professional mathematicians for centuries. This volume represents the first attempt to compile a definitive history and authoritative analysis of these famous integer sequences, complete with a wealth of exciting applications, enlightening examples, and fun exercises that offer numerous opportunities for exploration and experimentation. The author has assembled a myriad of fascinating properties of both Fibonacci and Lucas numbers-as developed by a wide range of sources-and catalogued their applications in a multitude of widely varied disciplines such as art, stock market investing, engineering, and neurophysiology. Most of the engaging and delightful material here is easily accessible to college and even high school students, though advanced material is included to challenge more sophisticated Fibonacci enthusiasts. A historical survey of the development of Fibonacci and Lucas numbers, biographical sketches of intriguing personalities involved in developing the subject, and illustrative examples round out this thorough and amusing survey. Most chapters conclude with numeric and theoretical exercises that do not rely on long and tedious proofs of theorems. Highlights include: * Balanced blend of theory and real-world applications * Excellent reference material for student reports and projects * User-friendly, informal, and entertaining writing style * Historical interjections and short biographies that add a richer perspective to the topic * Reference sections providing important symbols, problem solutions, and fundamental properties from the theory of numbers and matrices Fibonacci and Lucas Numbers with Applications provides mathematicians with a wealth of reference material in one convenient volume and presents an in-depth and entertaining resource for enthusiasts at every level and from any background.

Praise for the First Edition “ …beautiful and well worth the reading … with many exercises and a good bibliography, this book will fascinate both students and teachers.” Mathematics Teacher Fibonacci and Lucas Numbers with Applications, Volume I, Second Edition provides a user-friendly and historical approach to the many fascinating properties of Fibonacci and Lucas numbers, which have intrigued amateurs and professionals for centuries. Offering an in-depth study of the topic, this book includes exciting applications that provide many opportunities to explore and experiment. In addition, the book includes a historical survey of the development of Fibonacci and Lucas numbers, with biographical sketches of important figures in the field. Each chapter features a wealth of examples, as well as numeric and theoretical exercises that avoid using extensive and time-consuming proofs of theorems. The Second Edition offers new opportunities to illustrate and expand on various problem-solving skills and techniques. In addition, the book features: • A clear, comprehensive introduction to one of the most fascinating topics in mathematics, including links to graph theory, matrices, geometry, the stock market, and the Golden Ratio • Abundant examples, exercises, and properties throughout, with a wide range of difficulty and sophistication • Numeric puzzles based on Fibonacci numbers, as well as popular geometric paradoxes, and a glossary of symbols and fundamental properties from the theory of numbers • A wide range of applications in many disciplines, including architecture, biology, chemistry, electrical engineering, physics, physiology, and neurophysiology The Second Edition is appropriate for upper-undergraduate and graduate-level courses on the history of mathematics, combinatorics, and number theory. The book is also a valuable resource for undergraduate research courses, independent study projects, and senior/graduate theses, as well as a useful resource for computer scientists, physicists, biologists, and electrical engineers. Thomas Koshy, PhD, is Professor Emeritus of Mathematics at Framingham State University in Massachusetts and author of several books and numerous articles on mathematics. His work has been recognized by the Association of American Publishers, and he has received many awards, including the Distinguished Faculty of the Year. Dr. Koshy received his PhD in Algebraic Coding Theory from Boston University. “Anyone who loves mathematical puzzles, number theory, and Fibonacci numbers will treasure this book. Dr. Koshy has compiled Fibonacci lore from diverse sources into one understandable and intriguing volume, [interweaving] a historical flavor into an array of applications.” Marjorie Bicknell-Johnson

Discover the properties and real-world applications of the Fibonacci and the Catalan numbers With clear explanations and easy-to-follow examples, Fibonacci and Catalan Numbers: An Introduction offers a fascinating overview of these topics that is accessible to a broad range of readers. Beginning with a historical development of each topic, the book guides readers through the essential properties of the Fibonacci numbers, offering many introductory-level examples. The author explains the relationship of the Fibonacci numbers to compositions and palindromes, tilings, graph theory, and the Lucas numbers. The book proceeds to explore the Catalan numbers, with the author drawing from their history to provide a solid foundation of the underlying properties. The relationship of the Catalan numbers to various concepts is then presented in examples dealing with partial orders, total orders, topological sorting, graph theory, rooted-ordered binary trees, pattern avoidance, and the Narayana numbers. The book features various aids and insights that allow readers to develop a complete understanding of the presented topics, including: Real-world examples that demonstrate the application of the Fibonacci and the Catalan numbers to such fields as sports, botany, chemistry, physics, and computer science More than 300 exercises that enable readers to explore many of the presented examples in greater depth Illustrations that clarify and simplify the concepts Fibonacci and Catalan Numbers is an excellent book for courses on discrete mathematics, combinatorics, and number theory, especially at the undergraduate level. Undergraduates will find the book to be an excellent source for independent study, as well as a source of topics for research. Further, a great deal of the material can also be used for enrichment in high school courses.

There are many books covering Fibonacci from an artistic and historical point of view and almost as many suggesting that Fibonacci retracements and numbers can be successfully applied to financial market time series. What is missing is a book that addresses the common errors in using screen based Fibonacci (and Gann and other tools). The book is a critical exploration of Fibonacci numbers, retracements, projections, timeframes and fanlines and their current usage within the financial markets by technical analysts. Although they can be extremely effective analytical tools when used appropriately, mistakes in usage can be extremely costly from a financial and credibility viewpoint. George MacLean takes a brief look at the history of Fibonacci and Gann, before providing a full account of their applications in financial markets, including fixed income, equity, foreign exchange, commodities and indexes. In particular, he draws attention to the overuse and misuse of easily applied computer packages available to professional and amateur traders.

Expert practical and theoretical coverage of runs and scans This volume presents both theoretical and applied aspects of runs and scans, and illustrates their important role in reliability analysis through various applications from science and engineering. Runs and Scans with Applications presents new and exciting content in a systematic and cohesive way in a single comprehensive volume, complete with relevant approximations and explanations of some limit theorems. The authors provide detailed discussions of both classical and current problems, such as: * Sooner and later waiting time * Consecutive systems * Start-up demonstration testing in life-testing experiments * Learning and memory models * «Match» in genetic codes Runs and Scans with Applications offers broad coverage of the subject in the context of reliability and life-testing settings and serves as an authoritative reference for students and professionals alike.

This new work by Wilfred Kaplan, the distinguished author of influential mathematics and engineering texts, is destined to become a classic. Timely, concise, and content-driven, it provides an intermediate-level treatment of maxima, minima, and optimization. Assuming only a background in calculus and some linear algebra, Professor Kaplan presents topics in order of difficulty. In four short chapters, he describes basic concepts and geometric aspects of maxima and minima, progresses to problems with side conditions, introduces optimization and programming, and concludes with an in-depth discussion of research topics involving the duality theorems of Fenchel and Rockafellar. Throughout the text, the subject of convexity is gradually developed-from its theoretical underpinnings to problems, and finally, to its role in applications. Other features include: * A strong emphasis on practical applications of maxima and minima * An impressive array of supporting topics such as numerical analysis * An ample number of examples and problems * More than 60 illustrations highlighting the text * Algorithms to reinforce concepts * An appendix reviewing the prerequisite linear algebra Maxima and Minima with Applications is an ideal text for upper-undergraduate and graduate students taking courses in operations research, management, general engineering, and applied mathematics. It can also be used to supplement courses on linear and nonlinear optimization. This volume's broad scope makes it an excellent reference for professionals wishing to learn more about cutting-edge topics in optimization and mathematical programming.

A guide to modern optimization applications and techniques in newly emerging areas spanning optimization, data science, machine intelligence, engineering, and computer sciences Optimization Techniques and Applications with Examples introduces the fundamentals of all the commonly used techniques in optimization that encompass the broadness and diversity of the methods (traditional and new) and algorithms. The author—a noted expert in the field—covers a wide range of topics including mathematical foundations, optimization formulation, optimality conditions, algorithmic complexity, linear programming, convex optimization, and integer programming. In addition, the book discusses artificial neural network, clustering and classifications, constraint-handling, queueing theory, support vector machine and multi-objective optimization, evolutionary computation, nature-inspired algorithms and many other topics. Designed as a practical resource, all topics are explained in detail with step-by-step examples to show how each method works. The book’s exercises test the acquired knowledge that can be potentially applied to real problem solving. By taking an informal approach to the subject, the author helps readers to rapidly acquire the basic knowledge in optimization, operational research, and applied data mining. This important resource: Offers an accessible and state-of-the-art introduction to the main optimization techniques Contains both traditional optimization techniques and the most current algorithms and swarm intelligence-based techniques Presents a balance of theory, algorithms, and implementation Includes more than 100 worked examples with step-by-step explanations Written for upper undergraduates and graduates in a standard course on optimization, operations research and data mining, Optimization Techniques and Applications with Examples is a highly accessible guide to understanding the fundamentals of all the commonly used techniques in optimization.

Expert coverage of the design and implementation of state estimation algorithms for tracking and navigation Estimation with Applications to Tracking and Navigation treats the estimation of various quantities from inherently inaccurate remote observations. It explains state estimator design using a balanced combination of linear systems, probability, and statistics. The authors provide a review of the necessary background mathematical techniques and offer an overview of the basic concepts in estimation. They then provide detailed treatments of all the major issues in estimation with a focus on applying these techniques to real systems. Other features include: Problems that apply theoretical material to real-world applications In-depth coverage of the Interacting Multiple Model (IMM) estimator Companion DynaEst(TM) software for MATLAB(TM) implementation of Kalman filters and IMM estimators Design guidelines for tracking filters Suitable for graduate engineering students and engineers working in remote sensors and tracking, Estimation with Applications to Tracking and Navigation provides expert coverage of this important area.

The essential guide to grammars with context conditions This advanced computer science book systematically and compactly summarizes the current knowledge about grammars with context conditions-an important area of formal language theory. According to the types of context conditions, this self-contained reference classifies them into grammars with context conditions placed on the domains of grammatical derivations, the use of grammatical productions, and the neighborhood of the rewritten symbols. The focus is on grammatical generative power, important properties, simplification, reduction, implementation, and applications, most of which are related to microbiology. The text features: * Up-to-date coverage of grammatical concepts based on context conditions * Self-contained explanations without assumption of any previous knowledge * Clear definitions and exact proofs preceded by intuitive explanations * Numerous easy-to-implement grammatical transformations * Realistic applications * Relation to mathematics, linguistics, and biology * Additional material and information about the book available on accompanying Web site (see preface for details) Practitioners and advanced students in theoretical computer science and related areas- including mathematics, linguistics, and molecular biology-will find Grammars with Context Conditions and Their Applications an essential reference for this cutting-edge area of formal language theory.

A self-contained introduction to microprocessor theory and applications This book presents the fundamental concepts of assembly language programming and system design associated with typical microprocessors, such as the Motorola MC68000/68020 and Intel? Pentium?. It begins with an overview of microprocessors–including anexplanation of terms, the evolution of the microprocessor, and typical applications–and goes on to systematically cover: Microcomputer architecture Microprocessor memory organization Microprocessor Input/Output (I/O) Microprocessor programming concepts Assembly language programming with the 68000 68000 hardware and interfacing Assembly language programming with the 68020 68020 hardware and interfacing Assembly language programming with Pentium Pentium hardware and interfacing The author assumes a background in basic digital logic, and all chapters conclude with a Questions and Problems section, with selected answers provided at the back of the book. Microprocessor Theory and Applications with 68000/68020 and Pentium is an ideal textbook for undergraduate- and graduate-level courses in electrical engineering, computer engineering, and computer science. (An instructor's manual is available upon request.) It is also appropriate for practitioners in microprocessor system design who are looking for simplified explanations and clear examples on the subject. Additionally, the accompanying CD-ROM, which contains step-by-step procedures for installing and using Ide 68k21 (68000/68020) and MASM32 / Olly Debugger (Pentium) software, provides valuable simulation results via screen shots.