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.

    In 1905 an unknown 26-year-old clerk at the Swiss Patent Office, who had supposedly failed math in school, burst on to the scientific scene and swept away the hidebound theories of the day. The clerk, Albert Einstein, introduced a new and unexpected understanding of the universe and launched the two great revolutions of twentieth-century physics, relativity and quantum mechanics. The obscure origin and wide-ranging brilliance of the work recalled Isaac Newton’s “annus mirabilis” (miracle year) of 1666, when as a 23-year-old seeking safety at his family manor from an outbreak of the plague, he invented calculus and laid the foundations for his theory of gravity. Like Newton, Einstein quickly became a scientific icon--the image of genius and, according to Time magazine, the Person of the Century.The actual story is much more interesting. Einstein himself once remarked that “science as something coming into being ... is just as subjectively, psychologically conditioned as are all other human endeavors.” In this profile, the historian of science L. Randles Lagerstrom takes you behind the myth and into the very human life of the young Einstein. From family rifts and girlfriend troubles to financial hardships and jobless anxieties, Einstein’s early years were typical of many young persons. And yet in the midst of it all, he also saw his way through to profound scientific insights. Drawing upon correspondence from Einstein, his family, and his friends, Lagerstrom brings to life the young Einstein and enables the reader to come away with a fuller and more appreciative understanding of Einstein the person and the origins of his revolutionary ideas.About the cover image: While walking to work six days a week as a patent clerk in Bern, Switzerland, Einstein would pass by the famous "Zytglogge" tower and its astronomical clocks. The daily juxtaposition was fitting, as the relative nature of time and clock synchronization would be one of his revolutionary discoveries in the miracle year of 1905.

    As recently as 1918, a pandemic of influenza claimed over 50 million lives worldwide. The advent of drugs and vaccines led to an era of hope when we thought our battles with infectious disease were won, but our optimism has been eroded by the recognition that many pathogens have the capacity to transform themselves and escape our efforts to eradicate them. Are we now facing an inevitable repeat of a calamity such as the 1918 influenza pandemic or the Black Death? Can we anticipate and thwart such an event, or are we wilfully creating the conditions that would promote the emergence of new and highly virulent human infectious disease?Sunetra Gupta is Professor of Theoretical Epidemiology at the University of Oxford specialising in infectious diseases. She holds a bachelor's degree from Princeton University and a Ph.D. from the University of London. She has been awarded the Scientific Medal by the Zoological Society of London and the Royal Society Rosalind Franklin Award for her scientific research. She is also a novelist whose books have been awarded the Sahitya Akademi Award, the Southern Arts Literature Prize, shortlisted for the Crossword Award, and longlisted for the DSC and Orange Prizes.

    To reach this unique audience, Whitlock and Schluter motivate learning with interesting biological and medical examples; they emphasize intuitive understanding; and they focus on real data. The book covers basic topics in introductory statistics, including graphs, confidence intervals, hypothesis testing, comparison of means, regression, and designing experiments. It also introduces the principles behind such modern topics as likelihood, linear models, meta-analysis and computer-intensive methods. Instructors and students consistently praise the book's clear and engaging writing, strong visualization techniques, and its variety of fascinating and relevant biological examples.

    His Incompleteness Theorem turned not only mathematics but also the whole world of science and philosophy on its head. Equally legendary were Gö's eccentricities, his close friendship with Albert Einstein, and his paranoid fear of germs that eventually led to his death from self-starvation. Now, in the first popular biography of this strange and brilliant thinker, John Casti and Werner DePauli bring the legend to life. After describing his childhood in the Moravian capital of Brno, the authors trace the arc of Gö's remarkable career, from the famed Vienna Circle, where philosophers and scientists debated notions of truth, to the Institute for Advanced Study in Princeton, New Jersey, where he lived and worked until his death in 1978. In the process, they shed light on Gö's contributions to mathematics, philosophy, computer science, artificial intelligence -- even cosmology -- in an entertaining and accessible way.

    New co-authors--Irl Bivens and Stephen Davis--from Davidson College; both distinguished educators and writers.* More emphasis on graphing calculators in exercises and examples, including CAS capabilities of graphing calculators.* More problems using tabular data and more emphasis on mathematical modeling.

    Each chapter contains integrated worked examples and chapter tests. This edition has the ancillary ATLAST computer exercise guide and new MATLAB and Maple guides.

    In addition to being the most up-to-date communications text available, Simon Haykin has added MATLAB computer experiments.

    Not anymore. The best-selling author of The Complete Idiot's Guide® to Calculus has taken what appears to be a typical calculus workbook, chock full of solved calculus problems, and made legible notes in the margins, adding missing steps and simplifying solutions. Finally, everything is made perfectly clear. Students will be prepared to solve those obscure problems that were never discussed in class but always seem to find their way onto exams.--Includes 1,000 problems with comprehensive solutions--Annotated notes throughout the text clarify what's being asked in each problem and fill in missing steps--Kelley is a former award-winning calculus teacher

    David Peat explains the development and meaning of this Superstring Theory in a thoroughly readable, dramatic manner accessible to lay readers with no knowledge of mathematics. The consequences of the Superstring Theory are nothing less than astonishing.

     99.99% of the world’s mysteries are yet to be discovered and/or solved. Why not… It’s time for you to rediscover science? One of the most compelling draws of the sciences for many people is the potential of discovering something that was not known before. Whether someone’s doing it for fame, for fortune, or just for the fun of it, discovering something new, leaving your own personal mark for the rest of humanity’s time in the universe, is a tempting prospect for many. How would you feel about naming a star, and for others to know that you named it? That star would be visible in the sky for the rest of your lifetime, and more than likely for your great-great-great-grandchildren’s lifetimes. Your discovery would be immortalized above for the life of the star. Inside this book you will discover: -String theory and how it came about -Black holes and quantum gravity -If Schrödinger’s Cat is really a cat? -Disagreements between Einstein and Bohr -The double slit experiment Attention! Quantum Physics is NOT for everyone! This book is not for people: -Who doesn’t want to impress their girl with science -Who are not curious about the universe -Who isn’t inspired to name their own science theory If you are ready to learn about quantum physics, Scroll Up And Click On The “BUY NOW” Button Now!

    You’ll find it fun to read too - written in simple, everyday language.And, if you’re like most people, you’ll find that learning “why” the law of attraction works will pour rocket fuel into your belief in it. And attaining such a level of belief will allow you to unleash the law of attraction more powerfully than you’ve done previously. Why Quantum Physicists Create More Abundance removes your barriers of doubt and resistance concerning the law of attraction. It can be a very powerful tool for you, helping you soar past previous frustrations and manifesting a life much more closely aligned with your dreams and desires.

    It's extremely selfish to think we are the only existing intelligent life. Science and religion are on the verge of discovering the truth. Super ancient societies and their archaeological evidence uncovered to this day is a vault of stored information waiting to be unlocked. All we need to do is find the key. Help us uncover the truth by learning about Ancient Earth Mysteries.

    This includes further education, adult and community learning, work-based learning, the forces and offender learning and skills. It is easy to read with plenty of practical activities and examples throughout and the content is fully linked to the Teacher Training Standards. Please note: This book has since been updated to reflect the new title of the qualification: The Award in Education and Training.The qualification unit content contained in the appendices has since changed, and some legislation mentioned in the book has been updated.

    As was the case with Gore's first movie (An Inconvenient Truth), the movie is bursting with bad science, bad policy and some outright falsehoods. The storm events Gore addresses occur naturally, and there is little or no evidence they are being made worse from human activities: sea level is rising at the same rate it was before humans started burning fossil fuels; in Miami Beach the natural rise is magnified because buildings and streets were constructed on reclaimed swampland that has been sinking; the 9/11 memorial was not flooded by sea level rise from melting ice sheets, but a storm surge at high tide, which would have happened anyway and was not predicted by Gore in his first movie, as he claims; the Greenland ice sheet undergoes melt every summer, which was large in 2012 but then unusually weak in 2017; glaciers advance and retreat naturally, as evidenced by 1,000 to 2,000 year old tree stumps being uncovered in Alaska; rain gauge measurements reveal the conflict in Syria was not caused by reduced rainfall hurting farming there, and in fact the Middle East is greening from increasing CO2 in the atmosphere; agricultural yields in China have been rising, not falling as claimed by Gore. The renewable energy sources touted by Gore (wind and solar), while a laudable goal for our future, are currently very expensive: their federal subsidies per kilowatt-hour of energy produced are huge compared to coal, natural gas, and nuclear power. These costs are hidden from the public in increased federal and state tax rates. Gore is correct that "it is right to save humanity", but what we might need saving from the most are bad decisions that reduce prosperity and hurt the poor.