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 latest generation of titles in this series also feature glossaries and visual elements that complement the classic, familiar format."CliffsNotes on Lord of the Flies" takes you on an exploration of William Golding's novel to the dark side of humanity, the savagery that underlies even the most civilized human beings. Follow Golding's group of young boys from hope to disaster and watch as they attempt to survive their uncivilized, unsupervised, and isolated environment.You can rely on "CliffsNotes on Lord of the Flies" for character analyses, insightful essays, and chapter-by-chapter commentaries to ensure your safe passage through the rich symbolism of this novel. Other features that help you study includeA brief synopsis of the novelA character map to help you see relationships among the charactersA glossary that helps you get the most out of your readingAn interactive quiz to test your knowledgeEssay topics and review questionsClassic literature or modern modern-day treasure -- you'll understand it all with expert information and insight from CliffsNotes study guides.

    Its one downside? For nearly a century, it's been illegal to grow industrial cannabis in the United States-even though Betsy Ross wove the nation's first flag out of hemp fabric, Thomas Jefferson composed the Declaration of Independence on it, and colonists could pay their taxes with it. But as the prohibition on hemp's psychoactive cousin winds down, one of humanity's longest-utilized plants is about to be reincorporated into the American economy. Get ready for the newest billion-dollar industry.In Hemp Bound: Dispatches from the Front Lines of the Next Agricultural Revolution, bestselling author Doug Fine embarks on a humorous yet rigorous journey to meet the men and women who are testing, researching, and pioneering hemp's applications for the twenty-first century. From Denver, where Fine hitches a ride in a hemp-powered limo; to Asheville, North Carolina, where carbon-negative hempcrete-insulated houses are sparking a mini housing boom; to Manitoba where he raps his knuckles on the hood of a hemp tractor; and finally to the fields of east Colorado, where practical farmers are looking toward hemp to restore their agricultural economy--Fine learns how eminently possible it is for this misunderstood plant to help us end dependence on fossil fuels, heal farm soils damaged after a century of growing monocultures, and bring even more taxable revenue into the economy than its smokable relative.Fine's journey will not only leave you wondering why we ever stopped cultivating this miracle crop, it will fire you up to sow a field of it for yourself, for the nation's economy, and for the planet.

    You may find it for free on the web. Purchase of the Kindle edition includes wireless delivery.

    Rousseau was a major Swiss philosopher, writer, and composer of the eighteenth-century Enlightenment, whose political philosophy influenced the French Revolution and the development of modern political and educational thought.This ebook is DRM free and includes an active table of contents.

    Short, clear presentations and lots of opportunity for practice give students the confidence to use new vocabulary. 80 units at each level mean they cover a huge range of topics and everyday situations. Extra practice and interactive activities on CD-ROM.

    Most students worry about what an admissions officer looks for in a writing sample. But that’s the wrong way to approach this vital component, says former college admissions officer Harry Bauld. At Brown and Columbia, he saw what prospective students often did wrong—and now tells you how to do it right.On Writing the College Application Essay is his inside guide to writing a college application essay that will stand out from the pack. Baum advises you on how to avoid platitudes and find your authentic voice, gives you tools and ideas that will spark your imagination, and shows you how to approach themes with originality and panache to make even the most tired topics—the ones most students should stay away from—fresh, such as:The trip (“I had to adjust to a whole new way of life.”)My favorite things (puppy dogs, freedom, and chocolate chip cookies)The pageant contestant (“I think World Peace is the most important issue facing us today.”)The jock (“Through wrestling I have learned to set goals and to work with people.”)The autobiography (“Hello, my name is . . . ”)Tales of my success (“But, finally, when I crossed the finish line . . . ”)Pet death (“As I watched Buttons’s life ebb away, I came to value . . . ”)Getting into the college of your dreams is tough. The competition is fierce. For more than twenty-five years, On Writing the College Application Essay has helped thousands of students improve their chances. Now, let it work for you.

    Backed by years of serious research, "Managing the Millennials" provides managers of all ages with specific recommendations and tools for engaging this burgeoning demographic-some 78 million strong. Each chapter shares relevant interviews, case studies, and offers research-backed ideas and best practices to help any organization and their leaders address the challenges generational diversity presents.Answering the perplexing question of how does one lead and manage younger employees, this book Offers research-based guidance on getting the most from twenty-something employees Answers common questions and outlines practical solutions for building better relationships between the younger workers and the people who manage them Includes a Special Offer with immediate benefit to readers: access to the authors' Generational Rapport Inventory (GRI), a tool that measures a managers competencies and identifies strengths and weaknesses in dealing with Millennials. Accompanied by an associate web site, leadingthemillennials.com, offering a weekly blog addressing generational diversity issues in the workplaceInsightful and practical, "Managing the Millennials" is a valuable tool for millions of managers globally whose job it is to manage and motivate their twenty-something workers.

    Jobs in the geosciences are expected to increase over the next decade, which will increase geology-related jobs well above average projection for all occupations in the coming years."Geology For Dummies" is the most accessible book on the market for anyone who needs to get a handle on the subject, whether you?re looking to supplement classroom learning or are simply interested in earth sciences. Presented in a straightforward, trusted format, it features a thorough introduction to the study of the earth, its materials, and its processes.Tracks to a typical college-level introductory geology courseAn 8-page color insert includes photos of rocks, minerals, and geologic marvelsCovers geological processes; rock records and geologic times; matter, minerals, and rock; and more"Geology For Dummies" is an excellent classroom supplement for all students who enroll in introductory geology courses, from geology majors to those who choose earth science courses as electives.

    Dr Chambers contends that researchers, scientists, administrators and fieldworkers rarely appreciate the richness and validity of rural people's knowledge or the hidden nature of rural poverty. This is a challenging book for all concerned with rural development, as practitioners, academics, students or researchers.

    Donald Logan's successful book examines the Vikings and their critical role in history.The author uses archaeological, literary and historical evidence to analyze the Vikings' overseas expeditions and their transformation from raiders to settlers. Focusing on the period from 800-1050, it studies the Vikings across the world, from Denmark and Sweden right across to the British Isles, the North Atlantic and the New World.This edition includes:a new epilogue explaining the aims of the book updated further reading sections maps and photographs.By taking this new archaeological and primary research into account, the author provides a vital text for history students and researchers of this fascinating people.

    After more than fifty years of national pacifism and isolation including the "lost decade" of the 1990s, Japan is quietly, stealthily awakening. As Japan prepares to become a major player in the strategic struggles of the 21st century, critical questions arise about its motivations. What are the driving forces that influence how Japan will act in the international system? Are there recurrent patterns that will help explain how Japan will respond to the emerging environment of world politics? American understanding of Japanese character and purpose has been tenuous at best. We have repeatedly underestimated Japan in the realm of foreign policy. Now as Japan shows signs of vitality and international engagement, it is more important than ever that we understand the forces that drive Japan. In Japan Rising, renowned expert Kenneth Pyle identities the common threads that bind the divergent strategies of modern Japan, providing essential reading for anyone seeking to understand how Japan arrived at this moment--and what to expect in the future.

    This book is significant because it is not only thoughtfully developed and based on careful reading of the extensive literature on leadership and governance, but it is also deliberately intended to enable the author to bridge the gap between theories of organization, on one hand, and practical application, on the other. --Journal of Higher Education

    Discussing philosophy's ability to clarifyour thoughts, he explains why such clarification depends on the development of philosophical theories, and how those theories can be tested by imaginative thought experiments, and compared against each other by standards similar to those used in the natural and social sciences. He also shows howlogical rigor can be understood as a way of enhancing the explanatory power of philosophical theories.Drawing on the history of philosophy to provide a track record of philosophical thinking's successes and failures, Williams overturns widely held dogmas about the distinctive nature of philosophy in comparison to the sciences, demystifies its methods, and considers the future of the discipline. Fromthought experiments, to deduction, to theories, this little book will cause you to totally rethink what philosophy is.

    Not a standard textbook, Core Concepts in Cultural Anthropology functions as a thorough annotated bibliography of the terms and concepts that anthropologists use in their work; its conceptual framework prepares students to read ethnography more effectively, with less misunderstanding.