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.

    It was a sea in name only. It was actually a bone dry, ancient dusty basin pockmarked with craters and littered with rocks and boulders. Somewhere in that 500 mile diameter basin, the astronauts would attempt to make Mankind’s first landing on the Moon. Neil Armstrong would pilot the Lunar Module “Eagle” during its twelve minute descent from orbit down to a landing. Col. Edwin “Buzz” Aldrin would assist him. On the way down they would encounter a host of problems, any one of which could have potentially caused them to have to call off the landing, or, even worse, die making the attempt. The problems were all technical-communications problems, computer problems, guidance problems, sensor problems. Armstrong and Aldrin faced the very real risk of dying by the very same technical sword that they had to live by in order to accomplish the enormous task of landing on the Moon for the first time. Yet the human skills Armstrong and Aldrin employed would be more than equal to the task. Armstrong’s formidable skills as an aviator, honed from the time he was a young boy, would serve him well as he piloted Eagle down amidst a continuing series of systems problems that might have fatally distracted a lesser aviator. Armstrong’s brilliant piloting was complemented by Aldrin’s equally remarkable discipline and calmness as he stoically provided a running commentary on altitude and descent rate while handling systems problems that threatened the landing. Finally, after a harrowing twelve and a half minutes, Armstrong gently landed Eagle at “Tranquility Base”, a name he had personally chosen to denote the location of the first Moon landing. In “Landing Eagle-Inside the Cockpit During the First Moon Landing”, author Mike Engle gives a minute by minute account of the events that occurred throughout Eagle’s descent and landing on the Moon. Engle, a retired NASA engineer and Mission Control flight controller, uses NASA audio files of actual voice recordings made inside Eagle’s cockpit during landing to give the reader an “inside the cockpit” perspective on the first Moon landing. Engle’s transcripts of these recordings, along with background material on the history and technical details behind the enormous effort to accomplish the first Moon landing, give a new and fascinating insight into the events that occurred on that remarkable day fifty years ago.

    It deals with one powerful obsession that preoccupied Escher: what he called "the regular division of the plane," the puzzlelike interlocking of birds, fish, lizards, and other natural forms in continuous patterns. Schattschneider asks, "How did he do it?" She answers the question by analyzing Escher's notebooks." Visions of Symmetry includes many of Escher's masterworks, as well as hundreds of lesser-known examples of his work. This new edition also features a foreward and an illustrated epilogue that reveals new information about Escher's inspiration and shows how his ideas of symmetry have influenced mathematicians, computer scientists, and contemporary artists.

    His influence on 20th-century thinking and issues is arguably unparalleled, affecting attitudes on sex, religion, art, culture, and more. Written for the layperson, Freud for Beginners explains the doctor's dogma with wit and clarity, all in a contemporary context.

    When research suggests how to harness brain evolution, a hunt ensues for a missing link―one that allows to design humans with skills that prodigies of old would have envied.As germline engineering and biological enhancement have become routine, ancient doubts have emerged under new guises: Who are we? Is there a purpose to life? Why is there so much suffering? When faith and science fail to answer these questions, personal greed and national interest quickly fill the void. But gene selection is expensive, and many are excluded from its benefits. The stage is set for tribalism and social discontent on a scale without precedent, and those caught in the fray, whether by choice or by chance, must play roles not always to their liking in the struggle of all creatures against the arbitrariness of existence.

    Even after more than three centuries and the revolutions of Einsteinian relativity and quantum mechanics, Newtonian physics continues to account for many of the phenomena of the observed world, and Newtonian celestial dynamics is used to determine the orbits of our space vehicles.This completely new translation, the first in 270 years, is based on the third (1726) edition, the final revised version approved by Newton; it includes extracts from the earlier editions, corrects errors found in earlier versions, and replaces archaic English with contemporary prose and up-to-date mathematical forms. Newton's principles describe acceleration, deceleration, and inertial movement; fluid dynamics; and the motions of the earth, moon, planets, and comets. A great work in itself, the Principia also revolutionized the methods of scientific investigation. It set forth the fundamental three laws of motion and the law of universal gravity, the physical principles that account for the Copernican system of the world as emended by Kepler, thus effectively ending controversy concerning the Copernican planetary system.The illuminating Guide to the Principia by I. Bernard Cohen, along with his and Anne Whitman's translation, will make this preeminent work truly accessible for today's scientists, scholars, and students.

    He shows that the scientists of ancient and medieval times not only did not understand what we understand about the world—they did not understand what there is to understand, or how to understand it. Yet over the centuries, through the struggle to solve such mysteries as the curious backward movement of the planets and the rise and fall of the tides, the modern discipline of science eventually emerged. Along the way, Weinberg examines historic clashes and collaborations between science and the competing spheres of religion, technology, poetry, mathematics, and philosophy.An illuminating exploration of the way we consider and analyze the world around us, To Explain the World is a sweeping, ambitious account of how difficult it was to discover the goals and methods of modern science, and the impact of this discovery on human knowledge and development.

    From this starting point, and assuming no previous knowledge of logic, Wilfrid Hodges takes the reader through the whole gamut of logical expressions in a simple and lively way. Readers who are more mathematically adventurous will find optional sections introducing rather more challenging material. 'A lively and stimulating book' Philosophy

    It invites both introductory and advanced students to appreciate the roots and limits of American exceptionalism, and to recognize the profound importance of current debates over the government's role in our everyday lives.

    If I am still alivewhen the events foretold in these pages occur, then I hope that you will find me before it is too late.Roberta Ann SparrowOctober, 1944"

    Indeed, if God knows everything, why do we need to learn through pain and suffering? If God is omnipotent, why are we needed to do good? If the universe is fundamentally good, why are wars, crime, and injustice all around us? In modern society, orthodox science takes the rational high-ground and tackles these contradictions by denying the very need for, and the existence of, meaning. Indeed, many of us implicitly accept the notion that rationality somehow contradicts spirituality. That is a modern human tragedy, not only for its insidiousness, but for the fact that it is simply not true. In this book, the author constructs a coherent and logical argument for the meaning of existence, informed by science itself. A framework is laid out wherein all aspects of human existence have a logical, coherent reason and role, including the ones often perceived as negative. The powerful logic of this framework inescapably leads to insightful and inspiring guidelines for living a purposeful and meaningful life.

    Set in the early 5th century AD, the events and personalities of that important turning point in Western Civilization are presented in great mystical detail. There is a great lesson portrayed in the book and it is about to be repeated in our time.Large format paper back for easy reading. Historical epic concerning the Ancient Egyptian philosopher, from the author of The Water Babies.

    It is a collection of 150 brain teasing math riddles and puzzles. Their purpose is to make children think and stretch the mind. They are designed to test logic, lateral thinking as well as memory and to engage the brain in seeing patterns and connections between different things and circumstances. They are laid out in three chapters which get more difficult as you go through the book, in the author’s opinion at least. The answers are at the back of the book if all else fails. These are more difficult riddles and are designed to be attempted by children from 10 years onwards, as well as participation from the rest of the family. Tags: Riddles and brain teasers, riddles and trick questions, riddles book, riddles book for kids, riddles for kids, riddles for kids aged 9-12, riddles and puzzles, jokes and riddles, jokes book, jokes book for kids, jokes children, jokes for kids, jokes kids, puzzle book

    It remains the one of the most widely read books about science to come out of the twentieth century.(Note: the book was first published in 1934, in German, with the title Logik der Forschung. It was "reformulated" into English in 1959. See Wikipedia for details.)

    However, rather than resting on that reputation, the new edition of this text marks a significant advance in the already excellent quality of the book. While preserving concise language, state of the art educational pedagogy, and top-notch worked examples, the Eighth Edition features a unified art design as well as streamlined and carefully reorganized problem sets that enhance the thoughtful instruction for which Raymond A. Serway and John W. Jewett, Jr. earned their reputations. Likewise, PHYSICS FOR SCIENTISTS AND ENGINEERS, will continue to accompany Enhanced WebAssign in the most integrated text-technology offering available today. In an environment where new Physics texts have appeared with challenging and novel means to teach students, this book exceeds all modern standards of education from the most solid foundation in the Physics market today.