This is a very old science and its gems have lost their charm for us through everyday use. We have tried in this book to refresh them for you. The main part of the book is made up of problems. The best way to deal with them is: Solve the problem by yourself - compare your solution with the solution in the book (if it exists) - go to the next problem. However, if you have difficulties solving a problem (and some of them are quite difficult), you may read the hint or start to read the solution. If there is no solution in the book for some problem, you may skip it (it is not heavily used in the sequel) and return to it later. The book is divided into sections devoted to different topics. Some of them are very short, others are rather long. Of course, you know arithmetic pretty well. However, we shall go through it once more, starting with easy things. 2 Exchange of terms in addition Let's add 3 and 5: 3+5=8. And now change the order: 5+3=8. We get the same result. Adding three apples to five apples is the same as adding five apples to three - apples do not disappear and we get eight of them in both cases. 3 Exchange of terms in multiplication Multiplication has a similar property. But let us first agree on notation.

    No, hang on, let's make this interesting. Between zero and infinity. Even if you stick to the whole numbers, there are a lot to choose from - an infinite number in fact. Throw in decimal fractions and infinity suddenly gets an awful lot bigger (is that even possible?) And then there are the negative numbers, the imaginary numbers, the irrational numbers like pi which never end. It literally never ends.The world of numbers is indeed strange and beautiful. Among its inhabitants are some really notable characters - pi, e, the "imaginary" number i and the famous golden ratio to name just a few. Prime numbers occupy a special status. Zero is very odd indeed: is it a number, or isn't it?How Numbers Work takes a tour of this mind-blowing but beautiful realm of numbers and the mathematical rules that connect them. Not only that, but take a crash course on the biggest unsolved problems that keep mathematicians up at night, find out about the strange and unexpected ways mathematics influences our everyday lives, and discover the incredible connection between numbers and reality itself. ABOUT THE SERIESNew Scientist Instant Expert books are definitive and accessible entry points to the most important subjects in science; subjects that challenge, attract debate, invite controversy and engage the most enquiring minds. Designed for curious readers who want to know how things work and why, the Instant Expert series explores the topics that really matter and their impact on individuals, society, and the planet, translating the scientific complexities around us into language that's open to everyone, and putting new ideas and discoveries into perspective and context.

    Gardner's array of absorbing puzzles and mind-twisting paradoxes opens mathematics up to the world at large, inspiring people to see past numbers and formulas and experience the application of mathematical principles to the mysterious world around them. With articles on topics ranging from simple algebra to the twisting surfaces of Mobius strips, from an endless game of Bulgarian solitaire to the unreachable dream of time travel, this volume comprises a substantial and definitive monument to Gardner's influence on mathematics, science, and culture.In its twelve sections, The Colossal Book of Math explores a wide range of areas, each startlingly illuminated by Gardner's incisive expertise. Beginning with seemingly simple topics, Gardner expertly guides us through complicated and wondrous worlds: by way of basic algebra we contemplate the mesmerizing, often hilarious, linguistic and numerical possibilities of palindromes; using simple geometry, he dissects the principles of symmetry upon which the renowned mathematical artist M. C. Escher constructs his unique, dizzying universe. Gardner, like few thinkers today, melds a rigorous scientific skepticism with a profound artistic and imaginative impulse. His stunning exploration of "The Church of the Fourth Dimension," for example, bridges the disparate worlds of religion and science by brilliantly imagining the spatial possibility of God's presence in the world as a fourth dimension, at once "everywhere and nowhere."With boundless wisdom and his trademark wit, Gardner allows the reader to further engage challenging topics like probability and game theory which have plagued clever gamblers, and famous mathematicians, for centuries. Whether debunking Pascal's wager with basic probability, making visual music with fractals, or uncoiling a "knotted doughnut" with introductory topology, Gardner continuously displays his fierce intelligence and gentle humor. His articles confront both the comfortingly mundane—"Generalized Ticktacktoe" and "Sprouts and Brussel Sprouts"—and the quakingly abstract—"Hexaflexagons," "Nothing," and "Everything." He navigates these staggeringly obscure topics with a deft intelligence and, with addendums and suggested reading lists, he informs these classic articles with new insight.Admired by scientists and mathematicians, writers and readers alike, Gardner's vast knowledge and burning curiosity reveal themselves on every page. The culmination of a lifelong devotion to the wonders of mathematics, The Colossal Book of Mathematics is the largest and most comprehensive math book ever assembled by Gardner and remains an indispensable volume for the amateur and expert alike.

    Includes expert coverage of new topics: Turbocodes, Turboequalization, Antenna Arrays, Digital Cellular Systems, and Iterative Detection. Convenient, sequential organization begins with a look at the historyo and classification of channel models and builds from there.

    For centuries, the power of zero savored of the demonic; once harnessed, it became the most important tool in mathematics. Zero follows this number from its birth as an Eastern philosophical concept to its struggle for acceptance in Europe and its apotheosis as the mystery of the black hole. Today, zero lies at the heart of one of the biggest scientific controversies of all time, the quest for the theory of everything. Elegant, witty, and enlightening, Zero is a compelling look at the strangest number in the universe and one of the greatest paradoxes of human thought.

    This book will teach you the basic poker mathematics you need to know in order to improve and outplay your opponents, and focuses on foundational poker mathematics - the ones you’ll use day in and day out at the poker table; and probably the ones your opponents neglect.

    Get ready to amaze your friends—and yourself—with incredible calculations you never thought you could master, as renowned “mathemagician” Arthur Benjamin shares his techniques for lightning-quick calculations and amazing number tricks. This book will teach you to do math in your head faster than you ever thought possible, dramatically improve your memory for numbers, and—maybe for the first time—make mathematics fun.Yes, even you can learn to do seemingly complex equations in your head; all you need to learn are a few tricks. You’ll be able to quickly multiply and divide triple digits, compute with fractions, and determine squares, cubes, and roots without blinking an eye. No matter what your age or current math ability, Secrets of Mental Math will allow you to perform fantastic feats of the mind effortlessly. This is the math they never taught you in school.Also available as an eBook

    In this collection of landmark mathematical works, editor Stephen Hawking has assembled the greatest feats humans have ever accomplished using just numbers and their brains.

    Along the way she considers how to use a chessboard to plan a worldwide dinner party, how to make a chicken-sandwich sandwich, and how to create infinite cookies from a finite ball of dough. Beyond Infinity shows how this little symbol holds the biggest idea of all. "Beyond Infinity is a spirited and friendly guide--appealingly down to earth about math that's extremely far out." --Jordan Ellenberg, author of How Not to Be Wrong "Dr. Cheng . . . has a knack for brushing aside conventions and edicts, like so many pie crumbs from a cutting board." --Natalie Angier, New York Times

    New co-authors--Irl Bivens and Stephen Davis--from Davidson College; both distinguished educators and writers.* More emphasis on graphing calculators in exercises and examples, including CAS capabilities of graphing calculators.* More problems using tabular data and more emphasis on mathematical modeling.

    In Intentional Talk: How to Structure and Lead Productive Mathematical Discussions , authors Elham Kazemi and Allison Hintz provide teachers with a framework for planning and facilitating purposeful math talks that move group discussions to the next level while achieving a mathematical goal.Through detailed vignettes from both primary and upper elementary classrooms, the authors provide a window into how teachers lead discussions and make important pedagogical decisions along the way. By creating equitable opportunities to share ideas, teachers can orient students to one another while enforcing that all students are sense makers and their ideas are valued. They examine students’ roles as both listeners and talkers, offering numerous strategies for improving student participation. Intentional Talk includes a collection of lesson planning templates in the appendix to help teachers apply the right structure to discussions in their own classrooms.

    Topics covered include matrix multiplication, row reduction, matrix inverse, orthogonality and computation. The self-teaching book is loaded with examples and graphics and provides a wide array of probing problems, accompanying solutions, and a glossary. Chapter 1: Introduction to Vectors; Chapter 2: Solving Linear Equations; Chapter 3: Vector Spaces and Subspaces; Chapter 4: Orthogonality; Chapter 5: Determinants; Chapter 6: Eigenvalues and Eigenvectors; Chapter 7: Linear Transformations; Chapter 8: Applications; Chapter 9: Numerical Linear Algebra; Chapter 10: Complex Vectors and Matrices; Solutions to Selected Exercises; Final Exam. Matrix Factorizations. Conceptual Questions for Review. Glossary: A Dictionary for Linear Algebra Index Teaching Codes Linear Algebra in a Nutshell.

    In addition to being the most up-to-date communications text available, Simon Haykin has added MATLAB computer experiments.

    This edition features new material on Controls, Computer-Aided Design and Manufacturing, and Off-Line Programming Systems.

    He sifts through over 30,000 survey submissions to uncover the world’s favourite number, and meets a mathematician who looks for universes in his garage. He attends the World Mathematical Congress in India, and visits the engineer who designed the first roller-coaster loop. Get hooked on math as Alex delves deep into humankind’s turbulent relationship with numbers, and reveals how they have shaped the world we live in.