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.
Encourage children to learn about numbers with these bright, entertaining flashcards. There are 42 cards with numerals or number words on one side and a Stephen Cartwright illustration on the reverse to make learning an enjoyable experience.- Great way to help children learn about numbers- Useful to play matching games and ordering game- Can be used as an introduction to adding and subtracting
An in-depth examination of a powerful new trading strategy «Fischer provides an intriguing and thorough look at blending the Fibonacci series, candlesticks, and 3-point chart patterns to trade securities. Backed by explicit trading rules and numerous examples and illustrations, this book is an invaluable tool for the serious investor. Read it.» –Thomas N. Bulkowski author of Encyclopedia of Chart Patterns and Trading Classic Chart Patterns In this groundbreaking new book, Fibonacci expert Robert Fischer and coauthor Dr. Jens Fischer successfully merge Fibonacci applications with candlestick charting to create an innovative trading strategy that will help you enhance profits and reduce risk. Filled with in-depth insights, helpful charts and graphs, and practical real-world examples, Candlesticks, Fibonacci, and Chart Pattern Trading Tools reveals how correctly combining these different strategies can give you a noticeable edge in challenging market times–regardless of whether you are a short-term or long-term trader–and improve your chances of success under a variety of market conditions. You’ll be introduced to the critical aspects of this synergistic approach through in-depth analysis and detailed explanations of: Core combinations of Fibonacci trading tools with candlesticks and regular 3-point chart patterns The magic figure «three» and its relevance in pattern recognition Fibonacci-related trading strategies, selected candlestick chart patterns, and regular 3-point chart patterns Applications of these trading strategies–double tops, Fibonacci price extensions, PHI-channel applications PHI-ellipses as trading tools And much more Along with the computer technology of the WINPHI charting program included on the companion website, Candlesticks, Fibonacci, and Chart Pattern Trading Tools will help you understand and implement this profitable trading strategy to the best of your ability.
A comprehensive introduction to sampling-based methods in statistical computing The use of computers in mathematics and statistics has opened up a wide range of techniques for studying otherwise intractable problems. Sampling-based simulation techniques are now an invaluable tool for exploring statistical models. This book gives a comprehensive introduction to the exciting area of sampling-based methods. An Introduction to Statistical Computing introduces the classical topics of random number generation and Monte Carlo methods. It also includes some advanced methods such as the reversible jump Markov chain Monte Carlo algorithm and modern methods such as approximate Bayesian computation and multilevel Monte Carlo techniques An Introduction to Statistical Computing: Fully covers the traditional topics of statistical computing. Discusses both practical aspects and the theoretical background. Includes a chapter about continuous-time models. Illustrates all methods using examples and exercises. Provides answers to the exercises (using the statistical computing environment R); the corresponding source code is available online. Includes an introduction to programming in R. This book is mostly self-contained; the only prerequisites are basic knowledge of probability up to the law of large numbers. Careful presentation and examples make this book accessible to a wide range of students and suitable for self-study or as the basis of a taught course
An Introduction to Modern CBT provides an easily accessible introduction to modern theoretical cognitive behavioral therapy models. The text outlines the different techniques, their success in improving specific psychiatric disorders, and important new developments in the field. • Provides an easy-to-read introduction into modern Cognitive Behavioral Therapy approaches with specific case examples and hands-on treatment techniques • Discusses the theoretical models of CBT, outlines the different techniques that have been shown to be successful in improving specific psychiatric disorders, and describes important new developments in the field • Offers useful guidance for therapists in training and is an invaluable reference tool for experienced clinicians
Literary Criticism from Plato to the Present provides a concise and authoritative overview of the development of Western literary criticism and theory from the Classical period to the present day An indispensable and intellectually stimulating introduction to the history of literary criticism and theory Introduces the major movements, figures, and texts of literary criticism Provides historical context and shows the interconnections between various theories An ideal text for all students of literature and criticism
Happy Street is a two-level course for children starting English at the beginning of the school system. Together with songs, chants, games, and listening activities, Happy Street 1 offers an accessible introduction to reading and writing and is suitable for use either as the children's first contact with English or after an oral-aural introduction.
Издание на английском языке.Kleber Will "An introduction to Crystallography", VeB Verlag Technik, Berlin, 1970.Will Kleber is the author of numerous publications among which the book An Introduction to Crystallography takes a prominent place.Книга посвящена кристаллографии.
Learn all the basics of C# 3.0 from Beginning C# 3.0: An Introduction to Object Oriented Programming, a book that presents introductory information in an intuitive format. If you have no prior programming experience but want a thorough, easy-to-understand introduction to C# and Object Oriented Programming, this book is an ideal guide. Using the tutorials and hands-on coding examples, you can discover tried and true tricks of the trade, understand design concepts, employ debugging aids, and design and write C# programs that are functional and that embody safe programming practices.
A modern approach to mathematical modeling, featuring unique applications from the field of mechanics An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical models that form the foundations of modern science and incorporates examples that illustrate how the most successful models arise from basic principles in modern and classical mathematical physics. Written by a world authority on mathematical theory and computational mechanics, the book presents an account of continuum mechanics, electromagnetic field theory, quantum mechanics, and statistical mechanics for readers with varied backgrounds in engineering, computer science, mathematics, and physics. The author streamlines a comprehensive understanding of the topic in three clearly organized sections: Nonlinear Continuum Mechanics introduces kinematics as well as force and stress in deformable bodies; mass and momentum; balance of linear and angular momentum; conservation of energy; and constitutive equations Electromagnetic Field Theory and Quantum Mechanics contains a brief account of electromagnetic wave theory and Maxwell's equations as well as an introductory account of quantum mechanics with related topics including ab initio methods and Spin and Pauli's principles Statistical Mechanics presents an introduction to statistical mechanics of systems in thermodynamic equilibrium as well as continuum mechanics, quantum mechanics, and molecular dynamics Each part of the book concludes with exercise sets that allow readers to test their understanding of the presented material. Key theorems and fundamental equations are highlighted throughout, and an extensive bibliography outlines resources for further study. Extensively class-tested to ensure an accessible presentation, An Introduction to Mathematical Modeling is an excellent book for courses on introductory mathematical modeling and statistical mechanics at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for professionals working in the areas of modeling and simulation, physics, and computational engineering.
Bayesian Networks: An Introduction provides a self-contained introduction to the theory and applications of Bayesian networks, a topic of interest and importance for statisticians, computer scientists and those involved in modelling complex data sets. The material has been extensively tested in classroom teaching and assumes a basic knowledge of probability, statistics and mathematics. All notions are carefully explained and feature exercises throughout. Features include: An introduction to Dirichlet Distribution, Exponential Families and their applications. A detailed description of learning algorithms and Conditional Gaussian Distributions using Junction Tree methods. A discussion of Pearl's intervention calculus, with an introduction to the notion of see and do conditioning. All concepts are clearly defined and illustrated with examples and exercises. Solutions are provided online. This book will prove a valuable resource for postgraduate students of statistics, computer engineering, mathematics, data mining, artificial intelligence, and biology. Researchers and users of comparable modelling or statistical techniques such as neural networks will also find this book of interest.
Learn the Chinese numbers from 1 to 100 with this amusing and innovative game.Play at home or in class with useful and interesting cards, designed to help you memorise the numbers.A comprehensive Instruction Booklet complete with suggestions for exercises, games and activities, and interesting facts about numbers, makes Playing with Numbers an essential part of the Chinese lesson.• 2 packs of 50 cards• 36 individual cards• Instruction Booklet.Instruction Booklet available in:EnglishFrancaisDeutschEspanolItaliano.
An invaluable introduction to nanomaterials and their applications Offering the unique approach of applying traditional physics concepts to explain new phenomena, Introduction to Nanomaterials and Devices provides readers with a solid foundation on the subject of quantum mechanics and introduces the basic concepts of nanomaterials and the devices fabricated from them. Discussion begins with the basis for understanding the basic properties of semiconductors and gradually evolves to cover quantum structures—including single, multiple, and quantum wells—and the properties of nanomaterial systems, such as quantum wires and dots. Written by a renowned specialist in the field, this book features: An introduction to the growth of bulk semiconductors, semiconductor thin films, and semiconductor nanomaterials Information on the application of quantum mechanics to nanomaterial structures and quantum transport Extensive coverage of Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein stastistics An in-depth look at optical, electrical, and transport properties Coverage of electronic devices and optoelectronic devices Calculations of the energy levels in periodic potentials, quantum wells, and quantum dots Introduction to Nanomaterials and Devices provides essential groundwork for understanding the behavior and growth of nanomaterials and is a valuable resource for students and practitioners in a field full of possibilities for innovation and invention.