Fibonacci and Lucas Numbers with Applications

Author: Thomas Koshy

Publisher: John Wiley & Sons

ISBN: 1118742176

Category: Mathematics

Page: 704

View: 5113

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

Groups and Characters

Author: Larry C. Grove

Publisher: John Wiley & Sons

ISBN: 1118030931

Category: Mathematics

Page: 224

View: 3926

An authoritative, full-year course on both group theory and ordinary character theory--essential tools for mathematics and the physical sciences One of the few treatments available combining both group theory and character theory, Groups and Characters is an effective general textbook on these two fundamentally connected subjects. Presuming only a basic knowledge of abstract algebra as in a first-year graduate course, the text opens with a review of background material and then guides readers carefully through several of the most important aspects of groups and characters, concentrating mainly on finite groups. Challenging yet accessible, Groups and Characters features: * An extensive collection of examples surveying many different types of groups, including Sylow subgroups of symmetric groups, affine groups of fields, the Mathieu groups, and symplectic groups * A thorough, easy-to-follow discussion of Polya-Redfield enumeration, with applications to combinatorics * Inclusive explorations of the transfer function and normal complements, induction and restriction of characters, Clifford theory, characters of symmetric and alternating groups, Frobenius groups, and the Schur index * Illuminating accounts of several computational aspects of group theory, such as the Schreier-Sims algorithm, Todd-Coxeter coset enumeration, and algorithms for generating character tables As valuable as Groups and Characters will prove as a textbook for mathematicians, it has broader applications. With chapters suitable for use as independent review units, along with a full bibliography and index, it will be a dependable general reference for chemists, physicists, and crystallographers.

A Tale of Two Fractals

Author: A.A. Kirillov

Publisher: Springer Science & Business Media

ISBN: 0817683828

Category: Mathematics

Page: 138

View: 8975

Since Benoit Mandelbrot's pioneering work in the late 1970s, scores of research articles and books have been published on the topic of fractals. Despite the volume of literature in the field, the general level of theoretical understanding has remained low; most work is aimed either at too mainstream an audience to achieve any depth or at too specialized a community to achieve widespread use. Written by celebrated mathematician and educator A.A. Kirillov, A Tale of Two Fractals is intended to help bridge this gap, providing an original treatment of fractals that is at once accessible to beginners and sufficiently rigorous for serious mathematicians. The work is designed to give young, non-specialist mathematicians a solid foundation in the theory of fractals, and, in the process, to equip them with exposure to a variety of geometric, analytical, and algebraic tools with applications across other areas.

Convexity and Optimization in Rn

Author: Leonard D. Berkovitz

Publisher: John Wiley & Sons

ISBN: 0471461660

Category: Mathematics

Page: 280

View: 5469

A comprehensive introduction to convexity and optimization in Rn This book presents the mathematics of finite dimensional constrained optimization problems. It provides a basis for the further mathematical study of convexity, of more general optimization problems, and of numerical algorithms for the solution of finite dimensional optimization problems. For readers who do not have the requisite background in real analysis, the author provides a chapter covering this material. The text features abundant exercises and problems designed to lead the reader to a fundamental understanding of the material. Convexity and Optimization in Rn provides detailed discussion of: * Requisite topics in real analysis * Convex sets * Convex functions * Optimization problems * Convex programming and duality * The simplex method A detailed bibliography is included for further study and an index offers quick reference. Suitable as a text for both graduate and undergraduate students in mathematics and engineering, this accessible text is written from extensively class-tested notes.

A History of the Theory of Investments

My Annotated Bibliography

Author: Mark Rubinstein

Publisher: John Wiley & Sons

ISBN: 1118161092

Category: Business & Economics

Page: 384

View: 4340

"This exceptional book provides valuable insights into the evolution of financial economics from the perspective of a major player." -- Robert Litzenberger, Hopkinson Professor Emeritus of Investment Banking, Univ. of Pennsylvania; and retired partner, Goldman Sachs A History of the Theory of Investments is about ideas -- where they come from, how they evolve, and why they are instrumental in preparing the future for new ideas. Author Mark Rubinstein writes history by rewriting history. In unearthing long-forgotten books and journals, he corrects past oversights to assign credit where credit is due and assembles a remarkable history that is unquestionable in its accuracy and unprecedented in its power. Exploring key turning points in the development of investment theory, through the critical prism of award-winning investment theory and asset pricing expert Mark Rubinstein, this groundbreaking resource follows the chronological development of investment theory over centuries, exploring the inner workings of great theoretical breakthroughs while pointing out contributions made by often unsung contributors to some of investment's most influential ideas and models.

Numerical Solution of Ordinary Differential Equations

Author: Kendall Atkinson,Weimin Han,David E. Stewart

Publisher: John Wiley & Sons

ISBN: 1118164520

Category: Mathematics

Page: 272

View: 7793

A concise introduction to numerical methodsand the mathematical framework neededto understand their performance Numerical Solution of Ordinary Differential Equations presents a complete and easy-to-follow introduction to classical topics in the numerical solution of ordinary differential equations. The book's approach not only explains the presented mathematics, but also helps readers understand how these numerical methods are used to solve real-world problems. Unifying perspectives are provided throughout the text, bringing together and categorizing different types of problems in order to help readers comprehend the applications of ordinary differential equations. In addition, the authors' collective academic experience ensures a coherent and accessible discussion of key topics, including: Euler's method Taylor and Runge-Kutta methods General error analysis for multi-step methods Stiff differential equations Differential algebraic equations Two-point boundary value problems Volterra integral equations Each chapter features problem sets that enable readers to test and build their knowledge of the presented methods, and a related Web site features MATLAB® programs that facilitate the exploration of numerical methods in greater depth. Detailed references outline additional literature on both analytical and numerical aspects of ordinary differential equations for further exploration of individual topics. Numerical Solution of Ordinary Differential Equations is an excellent textbook for courses on the numerical solution of differential equations at the upper-undergraduate and beginning graduate levels. It also serves as a valuable reference for researchers in the fields of mathematics and engineering.

Fibonacci and Lucas Numbers, and the Golden Section

Theory and Applications

Author: Steven Vajda

Publisher: Courier Corporation

ISBN: 0486462765

Category: Mathematics

Page: 189

View: 9199

This survey of the use of Fibonacci and Lucas numbers and the ancient principle of the Golden Section covers areas relevant to operational research, statistics, and computational mathematics. 1989 edition.

Fibonacci and Catalan Numbers

An Introduction

Author: Ralph Grimaldi

Publisher: John Wiley & Sons

ISBN: 1118159764

Category: Mathematics

Page: 448

View: 477

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.

Excel Essential Skills

Author: A. S. Kalra

Publisher: Pascal Press

ISBN: 9781740200431

Category: Fractions

Page: 96

View: 6210

The Excel Problem Solving Workbook for Year 7 is specifically written for the Year 7 Australian Curriculum Mathematics Course. This book aims to give Year 7 Mathematics students a step-by-step process for both the Problem Solving and Reasoning proficiency strands of the new curriculum.

The Craft of Probabilistic Modelling

A Collection of Personal Accounts

Author: J. Gani

Publisher: Springer Science & Business Media

ISBN: 1461386314

Category: Mathematics

Page: 313

View: 1811

This book brings together the personal accounts and reflections of nineteen mathematical model-builders, whose specialty is probabilistic modelling. The reader may well wonder why, apart from personal interest, one should commission and edit such a collection of articles. There are, of course, many reasons, but perhaps the three most relevant are: (i) a philosophicaJ interest in conceptual models; this is an interest shared by everyone who has ever puzzled over the relationship between thought and reality; (ii) a conviction, not unsupported by empirical evidence, that probabilistic modelling has an important contribution to make to scientific research; and finally (iii) a curiosity, historical in its nature, about the complex interplay between personal events and the development of a field of mathematical research, namely applied probability. Let me discuss each of these in turn. Philosophical Abstraction, the formation of concepts, and the construction of conceptual models present us with complex philosophical problems which date back to Democritus, Plato and Aristotle. We have all, at one time or another, wondered just how we think; are our thoughts, concepts and models of reality approxim&tions to the truth, or are they simply functional constructs helping us to master our environment? Nowhere are these problems more apparent than in mathematical model ling, where idealized concepts and constructions replace the imperfect realities for which they stand.

Complexity and the Arrow of Time

Author: Charles H. Lineweaver,Paul C. W. Davies,Michael Ruse

Publisher: Cambridge University Press

ISBN: 1107276632

Category: Science

Page: N.A

View: 3208

There is a widespread assumption that the universe in general, and life in particular, is 'getting more complex with time'. This book brings together a wide range of experts in science, philosophy and theology and unveils their joint effort in exploring this idea. They confront essential problems behind the theory of complexity and the role of life within it: what is complexity? When does it increase, and why? Is the universe evolving towards states of ever greater complexity and diversity? If so, what is the source of this universal enrichment? This book addresses those difficult questions, and offers a unique cross-disciplinary perspective on some of the most profound issues at the heart of science and philosophy. Readers will gain insights in complexity that reach deep into key areas of physics, biology, complexity science, philosophy and religion.

Statistics Essentials For Dummies

Author: Deborah Rumsey

Publisher: John Wiley & Sons

ISBN: 0470618396

Category: Mathematics

Page: 192

View: 2418

Statistics Essentials For Dummies not only provides students enrolled in Statistics I with an excellent high-level overview of key concepts, but it also serves as a reference or refresher for students in upper-level statistics courses. Free of review and ramp-up material, Statistics Essentials For Dummies sticks to the point, with content focused on key course topics only. It provides discrete explanations of essential concepts taught in a typical first semester college-level statistics course, from odds and error margins to confidence intervals and conclusions. This guide is also a perfect reference for parents who need to review critical statistics concepts as they help high school students with homework assignments, as well as for adult learners headed back into the classroom who just need a refresher of the core concepts. The Essentials For Dummies Series Dummies is proud to present our new series, The Essentials For Dummies. Now students who are prepping for exams, preparing to study new material, or who just need a refresher can have a concise, easy-to-understand review guide that covers an entire course by concentrating solely on the most important concepts. From algebra and chemistry to grammar and Spanish, our expert authors focus on the skills students most need to succeed in a subject.

Time-Dependent Problems and Difference Methods

Author: Bertil Gustafsson,Heinz-Otto Kreiss,Joseph Oliger

Publisher: John Wiley & Sons

ISBN: 1118548523

Category: Mathematics

Page: 528

View: 2185

Praise for the First Edition ". . . fills a considerable gap in the numerical analysis literature by providing a self-contained treatment . . . this is an important work written in a clear style . . . warmly recommended to any graduate student or researcher in the field of the numerical solution of partial differential equations." —SIAM Review Time-Dependent Problems and Difference Methods, Second Edition continues to provide guidance for the analysis of difference methods for computing approximate solutions to partial differential equations for time-dependent problems. The book treats differential equations and difference methods with a parallel development, thus achieving a more useful analysis of numerical methods. The Second Edition presents hyperbolic equations in great detail as well as new coverage on second-order systems of wave equations including acoustic waves, elastic waves, and Einstein equations. Compared to first-order hyperbolic systems, initial-boundary value problems for such systems contain new properties that must be taken into account when analyzing stability. Featuring the latest material in partial differential equations with new theorems, examples, and illustrations,Time-Dependent Problems and Difference Methods, Second Edition also includes: High order methods on staggered grids Extended treatment of Summation By Parts operators and their application to second-order derivatives Simplified presentation of certain parts and proofs Time-Dependent Problems and Difference Methods, Second Edition is an ideal reference for physical scientists, engineers, numerical analysts, and mathematical modelers who use numerical experiments to test designs and to predict and investigate physical phenomena. The book is also excellent for graduate-level courses in applied mathematics and scientific computations.

Math Instruction for Students with Learning Problems

Author: Susan Perry Gurganus

Publisher: Routledge

ISBN: 1317409329

Category: Education

Page: 448

View: 5433

Math Instruction for Students with Learning Problems, Second Edition provides a research-based approach to mathematics instruction designed to build confidence and competence in pre- and in-service PreK–12 teachers. This core textbook addresses teacher and student attitudes toward mathematics, as well as language issues, specific mathematics disabilities, prior experiences, and cognitive and metacognitive factors. The material is rich with opportunities for class activities and field extensions, and the second edition has been fully updated to reference both NCTM and CCSSM standards throughout the text and includes an entirely new chapter on measurement and data analysis.

Breakthrough Strategies for Predicting Any Market

Charting Elliott Wave, Lucas, Fibonacci, Gann, and Time for Profit

Author: Jeff Greenblatt

Publisher: John Wiley & Sons

ISBN: 1118716019

Category: Business & Economics

Page: 432

View: 8466

The revised and updated edition of the book that changed the way you think about trading In the Second Edition of this groundbreaking book by star trader Jeff Greenblatt, he continues to shares his hard-won lessons on what it takes to be a professional trader, while detailing his proven techniques for mastering market timing. With the help of numerous case studies and charts, Greenblatt develops his original high-probability pattern recognition system which, once mastered, endows its user with a deeper understanding of how the markets really work and boosts the efficiency of any trading methodology. Following in the footsteps of the great W.D. Gann, Jeff Greenblatt helps investors gain greater precision with any instrument they trade, during any time frame. Shows how to combine a variety of technical indicators to pinpoint turning points in the financial markets Makes even the most complex subject matter easy to understand with crystal-clear explanations and step-by-step guidance on all concepts, terms, processes, and techniques Reveals how to use Elliott Wave Analysis, Fibonacci, candlesticks, and momentum indicators to interpret market movements Breakthrough Strategies for Predicting Any Market shares fascinating and enlightening personal anecdotes from Jeff Greenblatt's career along with his candid reflection on developing and maintaining the mental discipline of a successful trader.

Applied and Computational Matrix Analysis

MAT-TRIAD, Coimbra, Portugal, September 2015 Selected, Revised Contributions

Author: Natália Bebiano

Publisher: Springer

ISBN: 331949984X

Category: Mathematics

Page: 347

View: 2967

This volume presents recent advances in the field of matrix analysis based on contributions at the MAT-TRIAD 2015 conference. Topics covered include interval linear algebra and computational complexity, Birkhoff polynomial basis, tensors, graphs, linear pencils, K-theory and statistic inference, showing the ubiquity of matrices in different mathematical areas. With a particular focus on matrix and operator theory, statistical models and computation, the International Conference on Matrix Analysis and its Applications 2015, held in Coimbra, Portugal, was the sixth in a series of conferences. Applied and Computational Matrix Analysis will appeal to graduate students and researchers in theoretical and applied mathematics, physics and engineering who are seeking an overview of recent problems and methods in matrix analysis.

Topics for mathematics clubs

Author: LeRoy C. Dalton,Henry D. Snyder,National Council of Teachers of Mathematics

Publisher: Natl Council of Teachers of


Category: Mathematics

Page: 106

View: 1489


The Trouble With Testosterone

And Other Essays On The Biology Of The Human Predi

Author: Robert M. Sapolsky

Publisher: Simon and Schuster

ISBN: 1439125058

Category: Science

Page: 288

View: 2491

Finalist for the Los Angeles Times Book Prize From the man who Oliver Sacks hailed as “one of the best scientist/writers of our time,” a collection of sharply observed, uproariously funny essays on the biology of human culture and behavior. In the tradition of Stephen Jay Gould and Oliver Sacks, Robert Sapolsky offers a sparkling and erudite collection of essays about science, the world, and our relation to both. “The Trouble with Testosterone” explores the influence of that notorious hormone on male aggression. “Curious George’s Pharmacy” reexamines recent exciting claims that wild primates know how to medicate themselves with forest plants. “Junk Food Monkeys” relates the adventures of a troop of baboons who stumble upon a tourist garbage dump. And “Circling the Blanket for God” examines the neurobiological roots underlying religious belief. Drawing on his career as an evolutionary biologist and neurobiologist, Robert Sapolsky writes about the natural world vividly and insightfully. With candor, humor, and rich observations, these essays marry cutting-edge science with humanity, illuminating the interconnectedness of the world’s inhabitants with skill and flair.

Hot-Wiring Your Creative Process

Strategies for print and new media designers

Author: Curt Cloninger

Publisher: New Riders

ISBN: 9780132798228

Category: Computers

Page: 264

View: 7451

Design philosophies can be useful, but inspiration, creative strategies, and efficient work habits are what really get the job done. Designer, instructor, and author Curt Cloninger provides a multitude of strategies, tools, and practices that readers can use to inject a big dose of creativity into just about any design project. With illustrations drawn from 20th-century French philosophy, medieval manuscripts, punkrock posters, and more, Curt’s innovative text introduces readers to his personal toolkit for hot-wiring the creative process. You’ll learn strategies to: • Recognize and believe in your creative powers • Develop effective methods for evaluating your own work • Draw inspiration from the past • Use standard software in experimental ways, and find nonstandard applications to create new effects • Maintain a personal design playground • Mine your subconscious with the Oblique Strategies Cards, developed by Brian Eno and Peter Schmidt • Un-stick your imagination by “blitz-designing” mock-ups Curt Cloninger is an artist, designer, author, and instructor in Multimedia Arts & Sciences at the University of North Carolina at Asheville. His book Fresh Styles for Web Designers: Eye Candy from the U nderground (New Riders, 2002) is an industry standard on creative Web design solutions. Curt’s art and design work has been featured in I.D. Magazine, HOW Magazine, The New York Times, Desktop Magazine, and at digital arts festivals from Korea to Brazil. He regularly speaks at international events such as HOW Design, South by Southwest, Web Design World, and FILE. His pirate signal broadcasts from to facilitate lively dialog.