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.

    The foxes change shapes as quick as a wink, from rabbits to dogs to squirrels and geese. But their game turns dangerous when a hunter raises his bow. . . .Originally published in 1990, Grandfather Tang's Story will continue to delight new readers as the wonder of the tangram puzzle--and an endearing game between a grandfather and his granddaughter--reveals a story of magic, clever animals, and, ultimately, true friendship.An NCSS-CBC Notable Children's Trade Book in the Field of Social Studies An NCTE Notable Children's Trade Book in the Language Arts"Ingenious." --The Bulletin of the Center for Children's Books

    And, it's true, many of them do. But Paul Erdos never followed the usual path. At the age of four, he could ask you when you were born and then calculate the number of seconds you had been alive in his head. But he didn't learn to butter his own bread until he turned twenty. Instead, he traveled around the world, from one mathematician to the next, collaborating on an astonishing number of publications. With a simple, lyrical text and richly layered illustrations, this is a beautiful introduction to the world of math and a fascinating look at the unique character traits that made "Uncle Paul" a great man.

    Meet Polygon and Plane, Reflection and Rotation, Odd Number and his buddy Even Number and the three amigos Sine, Cosine and Tangent. Discover the secrets of their world and how they like to throw their numbers about. Bringing his charming manga-style artwork and tongue-and-cheek approach to explaining the basics, Basher brings a whole new spin to the world of higher math.

    The Fourth Edition builds on this strength with new examples, additional applications and increased cryptology coverage. Up-to-date information on the latest discoveries is included.Elementary Number Theory and Its Applications provides a diverse group of exercises, including basic exercises designed to help students develop skills, challenging exercises and computer projects. In addition to years of use and professor feedback, the fourth edition of this text has been thoroughly accuracy checked to ensure the quality of the mathematical content and the exercises.

    Zip. Zilch. Nada. That's what all the other numbers think of Zero. He doesn't add anything in addition. He's of no use in division. And don't even ask what he does in multiplication. (Hint: Poof!) But Zero knows he's worth a lot, and when the other numbers get into trouble, he swoops in to prove that his talents are innumerable.

    Higgins as he dashes from hall--'twenty minutes past four'--up to attic--'twenty-three minutes past four'--down two flights to kitchen--'twenty-five minutes past four'--and up one to bedroom--'twenty-six minutes past four.'"--Kirkus Reviews, pointered review. Full color.

    

    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.

    Look at all the bricks!Grab a hard hat and all your tools, and get ready for a construction adventure in counting! This clever, rhyming picture book leads readers through a day in the life of a construction crew building with bricks. A brick may seem like just a simple block, but in groupings of ten, twenty, and more, it can create many impressive structures, from hotels to schools to skyscrapers. This is a terrific introduction to counting in quantities for children.A Christy Ottaviano Book

    By doing so, he's able to get six different dinners every night! He also answers to six names, sleeps in six beds, and maintains six different personalities.All is perfect for Sid - until the day he catches a dreadful cough. Then it is off to the vet not once, but six times! Inga Moore's humorous illustrations capture Sid's sly nature.

    Hop along to the Field and follow Lonely and Chalk Rabbit through a year as they try to cope with their fast expanding brood and handle a different seasonal challenge each month, from the cold of February to the wet of April and the heat of July.

    Do you see more than five jelly beans? Less than a million? This unique book will show you how to train your eyes and your mind to make really great estimations—by making estimating into a game. Jelly beans are just the beginning! This title has Common Core connections.Great Estimations is a 2007 Bank Street - Best Children's Book of the Year.

    Children learn to count to 100 with various classroom activities.

    How many stars were in the sky? A million? A billion? Maybe the number was as big as infinity. I started to feel very, very small. How could I even think about something as big as infinity? Uma can't help feeling small when she peers up at the night sky. She begins to wonder about infinity. Is infinity a number that grows forever? Is it an endless racetrack? Could infinity be in an ice cream cone? Uma soon finds that the ways to think about this big idea may just be . . . infinite.