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.
To succeed in Algebra II, start practicing now Algebra II builds on your Algebra I skills to prepare you for trigonometry, calculus, and a of myriad STEM topics. Working through practice problems helps students better ingest and retain lesson content, creating a solid foundation to build on for future success. Algebra II Workbook For Dummies, 2nd Edition helps you learn Algebra II by doing Algebra II. Author and math professor Mary Jane Sterling walks you through the entire course, showing you how to approach and solve the problems you encounter in class. You'll begin by refreshing your Algebra I skills, because you'll need a strong foundation to build upon. From there, you'll work through practice problems to clarify concepts and improve understanding and retention. Revisit quadratic equations, inequalities, radicals, and basic graphs Master quadratic, exponential, and logarithmic functions Tackle conic sections, as well as linear and nonlinear systems Grasp the concepts of matrices, sequences, and imaginary numbers Algebra II Workbook For Dummies, 2nd Edition includes sections on graphing and special sequences to familiarize you with the key concepts that will follow you to trigonometry and beyond. Don't waste any time getting started. Algebra II Workbook For Dummies, 2nd Edition is your complete guide to success.
An exciting approach to the history and mathematics of number theory “. . . the author’s style is totally lucid and very easy to read . . .the result is indeed a wonderful story.” —Mathematical Reviews Written in a unique and accessible style for readers of varied mathematical backgrounds, the Second Edition of Primes of the Form p = x2+ ny2 details the history behind how Pierre de Fermat’s work ultimately gave birth to quadratic reciprocity and the genus theory of quadratic forms. The book also illustrates how results of Euler and Gauss can be fully understood only in the context of class field theory, and in addition, explores a selection of the magnificent formulas of complex multiplication. Primes of the Form p = x2 + ny2, Second Edition focuses on addressing the question of when a prime p is of the form x2 + ny2, which serves as the basis for further discussion of various mathematical topics. This updated edition has several new notable features, including: • A well-motivated introduction to the classical formulation of class field theory • Illustrations of explicit numerical examples to demonstrate the power of basic theorems in various situations • An elementary treatment of quadratic forms and genus theory • Simultaneous treatment of elementary and advanced aspects of number theory • New coverage of the Shimura reciprocity law and a selection of recent work in an updated bibliography Primes of the Form p = x2 + ny2, Second Edition is both a useful reference for number theory theorists and an excellent text for undergraduate and graduate-level courses in number and Galois theory.
The laminated flashcards in this pack are ideal for teachers, parents and carers to teach the numbers 0 to 50 to children aged 3+ and to teach sums to young school children. The cards have the number on one side and the word on the other. The plus, minus, multiply, divide and equals signs are included. Notes provide handy suggestions for a variety of games and activities with the cards._x000D__x000D_• Clear, easy-to-read numbers and words_x000D_• Ideal for learning numbers and sums_x000D_• Helpful notes for teachers, parents and carers_x000D_• Durable laminated cards
Fields of vision is a comprehensive, flexible, user-friendly anthology of Literature in the English language from the origins to contemporary times. It aims to instill in students a love of Literature and involve them actively in the learning experience through. The course promotes communication, develops learning and language skills to give students a deeper understanding of English Literature and widen their fields of vision.
Predictably Irrational meets Moneyball in ESPN veteran writer and statistical analyst Keith Law's iconoclastic look at the numbers game of baseball, proving why some of the most trusted stats are surprisingly wrong, explaining what numbers actually work, and exploring what the rise of Big Data means for the future of the sport. For decades, statistics such as batting average, saves recorded, and pitching won-lost records have been used to measure individual players' and teams' potential and success. But in the past fifteen years, a revolutionary new standard of measurement—sabermetrics—has been embraced by front offices in Major League Baseball and among fantasy baseball enthusiasts. But while sabermetrics is recognized as being smarter and more accurate, traditionalists, including journalists, fans, and managers, stubbornly believe that the "old" way—a combination of outdated numbers and "gut" instinct—is still the best way. Baseball, they argue, should be run by people, not by numbers.? In this informative and provocative book, the renowned ESPN analyst and senior baseball writer demolishes a century's worth of accepted wisdom, making the definitive case against the long-established view. Armed with concrete examples from different eras of baseball history, logic, a little math, and lively commentary, he shows how the allegiance to these numbers—dating back to the beginning of the professional game—is firmly rooted not in accuracy or success, but in baseball's irrational adherence to tradition. While Law gores sacred cows, from clutch performers to RBIs to the infamous save rule, he also demystifies sabermetrics, explaining what these "new" numbers really are and why they're vital. He also considers the game's future, examining how teams are using Data—from PhDs to sophisticated statistical databases—to build future rosters; changes that will transform baseball and all of professional sports.