The Clay Mathematics Institute is offering a prize of $1 million to anyone who can discover a general solution to the problem. 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 are cubic equations in two variables. These equations may appear simple, yet they arise from some very deep--and often very mystifying--mathematical ideas. Using only basic algebra and calculus while presenting numerous eye-opening examples, Ash and Gross make these ideas accessible to general readers, and in the process venture to the very frontiers of modern mathematics. Along the way, they give an informative and entertaining introduction to some of the most profound discoveries of the last three centuries in algebraic geometry, abstract algebra, and number theory. They demonstrate how mathematics grows more abstract to tackle ever more challenging problems, and how each new generation of mathematicians builds on the accomplishments of those who preceded them. Ash and Gross fully explain how the Birch and Swinnerton-Dyer Conjecture sheds light on the number theory of elliptic curves, and how it provides a beautiful and startling connection between two very different objects arising from an elliptic curve, one based on calculus, the other on algebra.

    Harris.Elephant has a bucket of blocks and wants to build something tall. Something as tall as Elephant. But will it stay up? CRASH! BOOM! Not this time. Build it again? One block. Two blocks? Four blocks? It's still not as tall as Elephant. More blocks! Now will it stay up? Now will it be as tall as Elephant? Build, balance, count -- question, estimate, measure -- predict, crash, and build again! Young children will happily follow along as Elephant goes through the ups and downs of creating something new and finally celebrates the joy and pride of success.

    Steve Olson followed the six 2001 contestants from the intense tryouts to the Olympiad’s nail-biting final rounds to discover not only what drives these extraordinary kids but what makes them both unique and typical. In the process he provides fascinating insights into the science of intelligence and learning and, finally, the nature of genius. Brilliant, but defying all the math-nerd stereotypes, these teens want to excel in whatever piques their curiosity, and they are curious about almost everything — music, games, politics, sports, literature. One team member is ardent about both water polo and creative writing. Another plays four musical instruments. For fun and entertainment during breaks, the Olympians invent games of mind-boggling difficulty. Though driven by the glory of winning this ultimate math contest, they are in many ways not so different from other teenagers, finding pure joy in indulging their personal passions. Beyond the the Olympiad, Olson sheds light on many questions, from why Americans feel so queasy about math, to why so few girls compete in the subject, to whether or not talent is innate. Inside the cavernous gym where the competition takes place, Count Down uncovers a fascinating subculture and its engaging, driven inhabitants.

    When a hungry nightingale threatens to eat him for breakfast unless he can measure her song, the inchworm calls on his craft and skill to creatively solve the dilemma.

    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.

    Unlike party puzzles or brain teasers, many paradoxes are serious in that they raise serious philosophical problems, and are associated with crises of thought and revolutionary advances. To grapple with them is not merely to engage in an intellectual game, but to come to grips with issues of real import. The second, revised edition of this intriguing book expands and updates the text to take account of new work on the subject. It provides a valuable and accessible introduction to a range of paradoxes and their possible solutions, with questions designed to engage the reader with the arguments and full bibliographical references to both classic and current literature on the topic.

    Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings. It is a revolutionary work, astounding in its foresight and contemporaneity. The University of Illinois Press is pleased and honored to issue this commemorative reprinting of a classic.

    Missile trajectories. Cornering dynamics in speeding cars. By applying the laws of physics, you can realistically model nearly everything in games that bounces around, flies, rolls, slides, or isn't sitting still, to create compelling, believable content for computer games, simulations, and animation. "Physics for Game Developers" serves as the starting point for those who want to enrich games with physics-based realism.Part one is a mechanics primer that reviews basic concepts and addresses aspects of rigid body dynamics, including kinematics, force, and kinetics. Part two applies these concepts to specific real-world problems, such as projectiles, boats, airplanes, and cars. Part three introduces real-time simulations and shows how they apply to computer games. Many specific game elements stand to benefit from the use of real physics, including: The trajectory of rockets and missiles, including the effects of fuel burn offThe collision of objects such as billiard ballsThe stability of cars racing around tight curvesThe dynamics of boats and other waterborne vehiclesThe flight path of a baseball after being struck by a batThe flight characteristics of airplanesYou don't need to be a physics expert to learn from "Physics for Game Developers, " but the author does assume you know basic college-level classical physics. You should also be proficient in trigonometry, vector and matrix math (reference formulas and identities are included in the appendixes), and college-level calculus, including integration and differentiation of explicit functions. Although the thrust of the book involves physics principles and algorithms, it should be noted that the examples are written in standard C and use Windows API functions.

    It is intended to provide the essential primary texts for students of logic, metaphysics and philosophy of language.It contains, in particular, Frege's four essays 'Function and Concept', 'On Sinn and Bedeutung', 'On Concept and Object' and 'Thought', and new translations of key parts of the Begriffschrift, Grundlagen and Grundgesetze. Additional selections have also been made from his Collected Papers, Posthumous Writings and Correspondence. The editor's introduction provides an overview of the development and significance of Frege's philosophy, highlighting some of the main issues of interpretation. Footnotes, appendices and other editorial material have been supplied to facilitate understanding of the works of one of the central figures in modern philosophy.

    

    Stewart's Calculus is successful throughout the world because he explains the material in a way that makes sense to a wide variety of readers. His explanations make ideas come alive, and his problems challenge, to reveal the beauty of calculus. Stewart's examples stand out because they are not just models for problem solving or a means of demonstrating techniques--they also encourage readers to develp an analytic view of the subject. This edition includes new problems, examples, and projects.

    This is done in a way that is not only easy to understand, but is actually fun! Professors and engineers, with high school and college students following closely, comprise the largest percentage of our readers. It is a must-have for anyone interested in music, mathematics, physics, engineering, or complex science. Dr. Yoichiro Nambu, 2008 Nobel Prize Winner in Physics, served as a senior adviser to the English version of Who is Fourier? A Mathematical Adventure.

    Drawing on examples from many fields, it explains how scientists analyze and choose their working facts, and it explores the nature of experimentation, theory, and the mind. 1914 edition.

    Somebody must be putting extra water in the bath. Is it Kangaroo? Or is it Goat or Wombat?Whoever it is, Mr Archimedes is going to find out.AWARDSCommended - 1981 Children's Book Council Book of the Year Awards

    This book can be cut, drawn in, folded into shapes and will even take you to the fourth dimension. So join stand-up mathematician Matt Parker on a journey through narcissistic numbers, optimal dating algorithms, at least two different kinds of infinity and more.