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.

    Captioned cartoon drawings offering an overview of universal order as they deal with various phenomena are combined with scientific commentary

     This book will provide you an introduction to the history of Buddhism and its teachings and practices. Along with Buddhist philosophies there are many practices to incorporate into your daily life such as meditation and mindfulness to help calm your mind, reduce stress and anxiety. ☆☆“When we meet real tragedy in life, we can react in two ways - either by losing hope and falling into self-destructive habits, or by using the challenge to find our inner strength. Thanks to the teachings of Buddha, I have been able to take this second way.” – The Dalai Lama☆☆ This is a guide to Buddhism for beginners but includes quotes and resources to guide you towards more advanced Buddhist teachings and writing if you wish to develop your own study of Buddhism further. Here Is A Preview Of What’s Included… An introduction to Buddhist Philosophies and Teachings The history of Buddhism and the Life of the Buddha Key Buddhism concepts such as Karma, suffering, Samsara and Nirvana The Four Noble Truths of Buddhism The Eightfold Path, The Five Precepts and The Middle Way Practicing Buddhism in every day life How to practice mindfulness to reduce stress and increase happiness Meditation practices apps, and resources Meditation to obtain calm and clarity over your thoughts Much, Much More! ☆☆ “Worrying doesn’t take away tomorrow’s trouble’s, it takes away today’s peace” – The Buddha ☆☆ KINDLE EDITION: NOTE: You do not need a kindle reader to read this, you can read this on smartphone or in a web browser ☆☆Download This Great Book Today! Available To Read On Your Computer, MAC, Smartphone, Kindle Reader, iPad, or Tablet!☆☆ ☆☆To purchase this book scroll to the top and select Buy now with 1 Click ☆☆ PAPERBACK EDITION: Kindle edition included for free with purchase of paperback To purchase the paper, click paperback at the top of this description to purchase.

    In these essays, Einstein views science as the basis for a "cosmic" religion, embraced by scientists, theologians, and all who share a sense of wonder in the rationality and beauty of the universe. In the course of his career, Einstein wrote more than 300 scientific and 150 nonscientific publications. These essays date from the 1930s and 40s. In direct, everyday language the author develops a coherent view that transcends both the antiquated religion of fear and the modern religion of ethics. His concept of cosmic religion combines science and religion, with science forming the basis for a more enlightened religion. In these essays and aphorisms, Einstein also reflects on pacifism, disarmament, and Zionism. In addition to a brief biography of the author, this volume includes a warm appreciation by George Bernard Shaw.

    In this little book Welsh writer and artist David Wade paints a picture of one of the most elusive and pervasive concepts known to man.

    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.

    They know that whoever successfully creates it will revolutionize our relationship with technology—and make billions of dollars in the process. They call it conversational AI.   Computers that can speak and think like humans may seem like the stuff of science fiction, but they are rapidly moving toward reality. In Talk to Me, veteran tech journalist James Vlahos meets the researchers at Amazon, Google, and Apple who are leading the way. He explores how voice tech will transform every sector of society: handing untold new powers to businesses, overturning traditional notions of privacy, upending how we access information, and fundamentally altering the way we understand human consciousness. And he even tries to understand the significance of the voice-computing revolution first-hand — by building a chatbot version of his terminally ill father.   Vlahos’s research leads him to one fundamental question: What happens when our computers become as articulate, compassionate, and creative as we are?

    Lennox addresses the questions of where humanity is going in terms of technological enhancement, bioengineering, and artificial intelligence. He provides a clear overview of the current capacity of AI, its advantages and disadvantages, as well as the potential future implications, clearly defining the terms associated with this field and delineating between the current scientific facts and more speculative claims. Lennox argues that the worldview, and therefore ethics, with which we approach this area will have serious implications for any future AI and how it interacts with humanity.

    Covert information warfare is being waged by world powers, rogue states—such as Russia, China, Iran, and North Korea—and even terrorist groups like ISIS. This conflict has been designed to defeat and ultimately destroy the United States. This new type of warfare is part of the Information Age that has come to dominate our lives. In iWar, Bill Gertz describes how technology has completely revolutionized modern warfare, how the Obama administration failed to meet this challenge, and what we can and must do to catch up and triumph over this timely and important struggle.

    Written By Two Of Today'S Most Respected Computer Science Educators, Nell Dale And John Lewis, The Text Provides A Broad Overview Of The Many Aspects Of The Discipline From A Generic View Point. Separate Program Language Chapters Are Available As Bundle Items For Those Instructors Who Would Like To Explore A Particular Programming Language With Their Students. The Many Layers Of Computing Are Thoroughly Explained Beginning With The Information Layer, Working Through The Hardware, Programming, Operating Systems, Application, And Communication Layers, And Ending With A Discussion On The Limitations Of Computing. Perfect For Introductory Computing And Computer Science Courses, Computer Science Illuminated, Third Edition's Thorough Presentation Of Computing Systems Provides Computer Science Majors With A Solid Foundation For Further Study, And Offers Non-Majors A Comprehensive And Complete Introduction To Computing.

    Twitter may be the most powerful business and personal networking platform ever created but it remains a frustrating, strange world for most people. The Tao of Twitter is a path, a majestic random synergy with the potential to change your business and your life forever -- if you know the way! This is a book designed for busy people who can't spend hours in experimentation and research trying to find success. In one hour you will know enough strategies, tactics, and time-savers to create an effective presence on Twitter that will result in meaningful and measurable benefits. Through colorful examples and easy-to-follow, non-technical language, college educator and renowned marketing expert Mark Schaefer teaches you: > Secrets to building influence on Twitter > The formula behind every Twitter success > Applying Twitter for competititve advantage > A daily Twitter regimen > Specific business and personal benefits > 15 Ways to attract targeted followers ... plus hundreds of fresh ideas that will make Twitter fun and profitable. Jump-start your journey toward social media success by learning the Tao of Twitter!

    The author provides a succinct but lucid outline of the ways in which language has been defined, described, and explored, and guides readers towards further exploration of their own.

    In this new, innovative overview textbook, the authors put special emphasis on the deep ideas of mathematics, and present the subject through lively and entertaining examples, anecdotes, challenges and illustrations, all of which are designed to excite the student's interest. The underlying ideas include topics from number theory, infinity, geometry, topology, probability and chaos theory. Throughout the text, the authors stress that mathematics is an analytical way of thinking, one that can be brought to bear on problem solving and effective thinking in any field of study.

    The cat lives in an opaque box with a fiendish device that randomly feeds it either food, allowing it to live, or poison, which kills it. But in the quantum world, all possibilities coexist and have a reality of their own, and they ensure that the cat is both alive and dead, simultaneously.Who's Afraid of Schrvdinger's Cat? is a clear, concise explanation of the new sciences of quantum mechanics, chaos and complexity theory, relativity, new theories of mind, and the new cosmology. It studies worlds beyond the realm of common sense, and the new kinds of thinking that we need to understand ourselves, our minds, and our human place in the larger scheme of things.

    Biological processes do not create consciousness. This conceptual breakthrough turns traditional scientific thinking upside down. In An End to Upside Down Thinking, Mark Gober traces his journey - he explores compelling scientific evidence from a diverse set of disciplines, ranging from psychic phenomena, to near-death experiences, to quantum physics. With cutting-edge thinkers like two-time Nobel Peace Prize nominee Dr. Ervin Laszlo, Chief Scientist at the Institute of Noetic Sciences Dr. Dean Radin, and New York Times bestselling author Larry Dossey, MD supporting this thesis, this book will rock the scientific community and mainstream generalists interested in understanding the true nature of reality. Today's disarray around the globe can be linked, at its core, to a fundamental misunderstanding of our reality. This book aims to shift our collective outlook, reshaping our view of human potential and how we treat one another. The book's implications encourage much-needed revisions in science, technology, and medicine. General readers will find comfort in the implied worldview, which will impact their happiness and everyday decisions related to business, health and politics. Stephen Hawking's A Brief History of Time meets Eckhart Tolle's The Power of Now.