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 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.

    French women know the intrinsic value of classic basics and integrate their favorite clothes and accessories based upon years of experience perfecting their unique sense of style. French women know how to create a sense of intrigue. And it’s not achieved by wearing a barrage of latest trends or designers. It’s about having the confidence to dress up a simple white button-down, incorporating their signature flair, for a far more interesting and sophisticated look. Most women tend to buy everything that catches their eye. There’s not much discernment, just buying power. And these women have the overstuffed closets to show for it. I must warn you – This book is not just another simplistic buying guide to achieve a French chic look. Nor will I insult you with cliché advice on incorporating scarves into your daily wardrobe. I would like to offer you a different perspective. This book includes advice and insights about making empowering choices when it comes to what is hanging in your closet. The choice to simplify, buy less, and keep only fabulous items. The choice to honor your body first and foremost. And the choice to invest in your wardrobe.

    Nye, this lively book gives readers the background in history and political concepts they need to understand the issues facing our world today: the war in Iraq, the Israeli-Palestinian conflict, nuclear proliferation in North Korea and Iran, and much more. Origins of the Great Twentieth-Century Conflicts; Balance of Power and World War I; The Failure of Collective Security and World War II; The Cold War; Intervention, Institutions, and Regional Conflicts; Interdependence and Globalization; The Information Age; A New World Order? Anyone interested in understanding international relations today.

    But like all adventures, running a nonprofit organization is a real challenge.Nonprofit Kit for Dummies, Second Edition shows you the fun-and-easy way to get your nonprofit up-and-running. It contains savvy advice from the experts on everything from incorporating and managing your nonprofit to unbeatable tactics for raising money and managing public relations. This hands-on, no-nonsense guide is packed with tons of useful information that will give you everything you need to: Plan your nonprofit for the community Write a buy-in guaranteed mission statement Incorporate and apply tax exemption Build your board of directors with the right people Design a volunteer program Have a paid staff run your nonprofit Create budgets and financial reports Craft the perfect fundraising plan Write a great grant proposal Raise money from individuals Included in this must-have resource is a bonus CD-ROM that contains sample grant proposals, over a dozen budget and cash flow projections, multiple fundraising plans to choose from, and a list of indispensable Web resources to keep your nonprofit on track. Nonprofit Kit for Dummies, Second Edition is the ultimate nuts-and-bolts guide to getting your nonprofit off the ground and giving back to your community!

    Simmons advocates a careful approach to the subject, covering such topics as the wave equation, Gauss's hypergeometric function, the gamma function and the basic problems of the calculus of variations in an explanatory fashions - ensuring that students fully understand and appreciate the topics.

    The show combines a surfeit of mad science, some old-school sci-fi flair, and a dash of strawberry-milkshake whimsy to create the challenging, fascinating Pattern that keeps us coming back season after season and universe after universe.Now, in Fringe Science, cutting-edge scientists, science writers, and science fiction authors and historians provide a smart, savvy, and accessible look at the world(s) of Fringe.MIT physics professor Max Tegmark illuminates the real-life possibilities of parallel universesStephen Cass, founding editor of Discover's Science Not Fiction blog and a Senior Editor with Technology Review, unravels Fringe's use of time travelAward-winning science fiction historian Amy H. Sturgis walks us through the show's literary and television ancestors, from the 1800s onTelevision Without Pity staff writer Jacob Clifton looks at the role of the scientist, and scientific redemption, through the ever-shifting role of Massive DynamicGarth Sundem, bestselling author of Brain Candy, explores the mysterious way that memory works, from why Walter forgets to how Olivia remembers And more, from lab cow Gene's scientific résumé to why the Observers should be wearing white lab coats

    To understand algebra is to possess the power to grow your skills and knowledge so you can ace your courses and possibly pursue further study in math. Algebra II For Dummies is the fun and easy way to get a handle on this subject and solve even the trickiest algebra problems. This friendly guide shows you how to get up to speed on exponential functions, laws of logarithms, conic sections, matrices, and other advanced algebra concepts. In no time you'll have the tools you need to:Interpret quadratic functions Find the roots of a polynomial Reason with rational functions Expose exponential and logarithmic functions Cut up conic sections Solve linear and non linear systems of equations Equate inequalities Simplifyy complex numbers Make moves with matrices Sort out sequences and sets This straightforward guide offers plenty of multiplication tricks that only math teachers know. It also profiles special types of numbers, making it easy for you to categorize them and solve any problems without breaking a sweat. When it comes to understanding and working out algebraic equations, Algebra II For Dummies is all you need to succeed!

    Using illustrations and examples from science fiction pulp magazines and comic books, The Amazing Story of Quantum Mechanics explains the fundamental principles of quantum mechanics that underlie the world we live in.Watch a Video

    The new edition provides invitations - not requirements - to use technology, as well as new conceptual problems, and new projects that focus on writing and working in teams.

    If you think of it as staticky transmissions sent by people in the middle of nowhere, think again. Today's ham radio goes beyond wireless to extreme wireless, Operators transmit data and pictures, use the Internet, laser, and microwave transmitters, and travel to places high and low to make contact. In an emergency or natural disaster, ham radio can replace downed traditional communication and save lives. Whether you're just getting turned on to ham radio or already have your license, Ham Radio for Dummies helps you with the terminology, the technology and the talknology. You discover how to:Decipher the jargon and speak the language Buy or upgrade your equipment, including the all-important antennas Build a ham radio shack, complete with the rig, a computer, mobile/base rig, microphones, keys, headphones, antennas, cables and feedlines Study for your license, master Morse code, take the test and get your call sign Understand the basics of ragchews (conversations), nets (organized on-air meetings) and DX-ing (competing in contacts to make contacts) Keeping logs with the vital statistics, including time (in UTC or World Time), frequency, and call sign Written by Ward Silver, an electrical engineer, Certified Amateur Radio License Examiner, and columnist for QST, a monthly magazine for ham operators, Ham Radio for Dummies gives you the info you need to delve into the science or dive into the conversation. It explains how you can:Tune in to the most common types of signals, including Morse Code (CW), single-sideband (SSB), FM, Radioteletype (RTTY), and data signals Break in, introduce yourself, converse, and say or signal goodbye Communicate while traveling (ham radio goes where mobile phones go dead) Register with an emergency organization such as ARES and RACES Help in emergencies such as earthquakes, wildfires, or severe weather Pursue your special interests, including contacting distant stations, participating in contests, exploring the digital modes, using satellites, transmitting images, and more Complete with a glossary and ten pages of additional suggested resources, Ham Radio for Dummies encourages you to touch that dial and take that mike.CUL. (That's Morse Code for "see you later.")

    This entertaining examination of everyday science from the fanciful to the factual covers topics ranging from pesticides and environmental estrogens to lipsticks and garlic.

    Organized alphabetically, coverage extends from the arts to economics, history, linguistics, philosophy, psychology, sociology and on through the hard sciences. Ancient and modern, accepted and discredited, all theories which have relevance in today's world are included. The depth of the terms varies from undergraduate level to the more populist, with theories such as Parkinson's Law and the Peter Principle included.

    Stimulating, illuminating, and always surprising, The Big Questions challenges readers to re-evaluate their most fundamental beliefs and reveals the relationship between the loftiest philosophical quests and our everyday lives.