A look at one of the most exciting unsolved problems in mathematics todayElliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics—the Birch and Swinnerton-Dyer Conjecture. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem.The key to the conjecture lies in elliptic curves, which m...

The power and properties of numbers, from basic addition and sums of squares to cutting-edge theoryWe use addition on a daily basis—yet how many of us stop to truly consider the enormous and remarkable ramifications of this mathematical activity? Summing It Up uses addition as a springboard to present a fascinating and accessible look at numbers and number theory, and how we apply beautiful numerical properties to answer math problems. Mathematicians Avner...

The ancient Greeks discovered them, but it wasn't until the nineteenth century that irrational numbers were properly understood and rigorously defined, and even today not all their mysteries have been revealed. In The Irrationals, the first popular and comprehensive book on the subject, Julian Havil tells the story of irrational numbers and the mathematicians who have tackled their challenges, from antiquity to the twenty-first century. Along the way, he explains why irrational nu...

The human brain has some capabilities that the brains of other animals lack. It is to these distinctive capabilities that our species owes its dominant position. Other animals have stronger muscles or sharper claws, but we have cleverer brains. If machine brains one day come to surpass human brains in general intelligence, then this new superintelligence could become very powerful. As the fate of the gorillas now depends more on us humans than on the gorillas themselves, so the fate of our...

**“Witty, compelling, and just plain fun to read . . ." —Evelyn Lamb, Scientific AmericanThe Freakonomics of math—a math-world superstar unveils the hidden beauty and logic of the world and puts its power in our hands**The math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn’t confined to abstract...

Mornings are a madcap time for many of us. We wake up in a haze—often after hitting snooze a few times. Then we rush around to get ready and out the door so we can officially start the day. Before we know it, hours have slipped by without us accomplishing anything beyond downing a cup of coffee, dashing off a few emails, and dishing with our coworkers around the water cooler. By the time the workday wraps up, we’re so exhausted and defeated that any motivation to accomplish something in th...

For more than two thousand years a familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This n...

Calculus Study GuideFEATURES:- Includes both Calculus I and II - Clear and concise explanations - Difficult concepts are explained in simple terms - Illustrated with graphs and diagrams - Search for the words or phrases - Access the guide anytime, anywhere - at home, on the train, in the subway. - Use your down time to prepare for an exam. - Always have the guide available for a quick reference. TABLE OF CONTENTS:Introduction: FunctionsLimits and Continuity: Limit of a Sequence Limit of a ...

A quantity can be made smaller and smaller without it ever vanishing. This fact has profound consequences for science, technology, and even the way we think about numbers. In this book, we will explore this idea by moving at an easy pace through an account of elementary real analysis and, in particular, will focus on numbers, sequences, and series. Almost all textbooks on introductory analysis assume some background in calculus. This book doesn't and, instead, the emphasis is on the applic...

This selection of problems in Group Theory is principally aimed at undergraduate (honours) and postgraduate students of mathematics. Excepting a few, these problems are meant only to supplement the existing ones in standard texts. The comments interspersed in the text help to put the problems in perspective with other problems and with the subject itself. The intention of the book is two-fold: to introduce via problems some concepts not usually taught at the master's level, and reinforce exis...

The book gives a detailed account of the development of the theory of algebraic equations, from its origins in ancient times to its completion by Galois in the nineteenth century. The appropriate parts of works by Cardano, Lagrange, Vandermonde, Gauss, Abel, and Galois are reviewed and placed in their historical perspective, with the aim of conveying to the reader a sense of the way in which the theory of algebraic equations has evolved and has led to such basic mathematical notions as 'gr...