The book includes full discussions of many problems of current interest which are not treated in any extant book, and all these matters are considered with perception and understanding."—S. Chandrasekhar "A tour de force: lucid, straightforward, mathematically rigorous, exacting in the analysis of the theory in its physical aspect."—L. P. Hughston, Times Higher Education Supplement"Truly excellent. . . . A sophisticated text of manageable size that will probably be read by every student of relativity, astrophysics, and field theory for years to come."—James W. York, Physics Today

    Shankar, a well-known physicist and contagiously enthusiastic educator, was among the first to offer a course through the innovative Open Yale Course program. His popular online video lectures on introductory physics have been viewed over a million times. In this concise and self-contained book based on his online Yale course, Shankar explains the fundamental concepts of physics from Galileo’s and Newton’s discoveries to the twentieth-century’s revolutionary ideas on relativity and quantum mechanics.   The book begins at the simplest level, develops the basics, and reinforces fundamentals, ensuring a solid foundation in the principles and methods of physics. It provides an ideal introduction for college-level students of physics, chemistry, and engineering, for motivated AP Physics students, and for general readers interested in advances in the sciences. Instructor resources--including problem sets and sample examinations--and more information about Professor Shankar's course are available at http://oyc.yale.edu/physics/phys-200.

    However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it. If life can grow out of the formal chemical substrate of the cell, if consciousness can emerge out of a formal system of firing neurons, then so too will computers attain human intelligence. Gödel, Escher, Bach is a wonderful exploration of fascinating ideas at the heart of cognitive science: meaning, reduction, recursion, and much more.

    Professor Resnick presents a fundamental and unified development of the subject with unusually clear discussions of the aspects that usually trouble beginners. He includes, for example, a section on the common sense of relativity. His presentation is lively and interspersed with historical, philosophical and special topics (such as the twin paradox) that will arouse and hold the reader's interest. You'll find many unique features that help you grasp the material, such as worked-out examples, summary tables, thought questions and a wealth of excellent problems. The emphasis throughout the book is physical. The experimental background, experimental confirmation of predictions, and the physical interpretation of principles are stressed. The book treats relativistic kinematics, relativistic dynamics, and relativity and electromagnetism and contains special appendices on the geometric representation of space-time and on general relativity. Its organization permits an instructor to vary the length and depth of his treatment and to use the book either with or following classical physics. These features make it an ideal companion for introductory course

    But Shep Doeleman and a global coalition of scientists are on the cusp of doing just that.With exclusive access to the team, journalist Seth Fletcher spent five years following Shep and an extraordinary cast of characters as they assembled the Event Horizon Telescope, a virtual radio observatory the size of the Earth. He witnessed their struggles, setbacks, and breakthroughs, and along the way, he explored the latest thinking on the most profound questions about black holes. Do they represent a limit to our ability to understand reality? Or will they reveal the clues that lead to the long-sought Theory of Everything?Fletcher transforms astrophysics into something exciting, accessible, and immediate, taking us on an incredible adventure to better understand the complexity of our galaxy, the boundaries of human perception and knowledge, and how the messy human endeavor of science really works.Weaving a compelling narrative account of human ingenuity with excursions into cutting-edge science, Einstein’s Shadow is a tale of great minds on a mission to change the way we understand our universe—and our place in it.

    This user-friendly self-study guide is aimed at the general reader who is motivated to tackle that not insignificant challenge. The book is written using straightforward and accessible language, with clear derivations and explanations as well as numerous fully solved problems. For those with minimal mathematical background, the first chapter provides a crash course in foundation mathematics. The reader is then taken gently by the hand and guided through a wide range of fundamental topics, including Newtonian mechanics; the Lorentz transformations; tensor calculus; the Einstein field equations; the Schwarzschild solution (which gives a good approximation of the spacetime of our Solar System); simple black holes and relativistic cosmology. Following the historic 2015 LIGO (Laser Interferometer Gravitational-Wave Observatory) detection, there is now an additional chapter on gravitational waves, ripples in the fabric of spacetime that potentially provide a revolutionary new way to study the universe. Special relativity helps explain a huge range of non-gravitational physical phenomena and has some strangely counter-intuitive consequences. These include time dilation, length contraction, the relativity of simultaneity, mass-energy equivalence and an absolute speed limit. General relativity, the leading theory of gravity, is at the heart of our understanding of cosmology and black holes.Understand even the basics of Einstein's amazing theory and the world will never seem the same again. ContentsPrefaceIntroduction1 Foundation mathematics2 Newtonian mechanics3 Special relativity4 Introducing the manifold5 Scalars, vectors, one-forms and tensors6 More on curvature7 General relativity8 The Newtonian limit9 The Schwarzschild metric10 Schwarzschild black holes11 Cosmology12 Gravitational wavesAppendix: The Riemann curvature tensorBibliographyAcknowledgementsJanuary 2019. This third edition has been revised to make the material even more accessible to the enthusiastic general reader who seeks to understand the mathematics of relativity.

    Who invented zero? Why are there 60 seconds in a minute? Can a butterfly's wings really cause a storm on the far side of the world? In 50 concise essays, Professor Tony Crilly explains the mathematical concepts that allow use to understand and shape the world around us.

    Michael Guillen, known to millions as the science editor of ABC's Good Morning America, tells the fascinating stories behind five mathematical equations. As a regular contributor to daytime's most popular morning news show and an instructor at Harvard University, Dr. Michael Guillen has earned the respect of millions as a clear and entertaining guide to the exhilarating world of science and mathematics. Now Dr. Guillen unravels the equations that have led to the inventions and events that characterize the modern world, one of which -- Albert Einstein's famous energy equation, E=mc2 -- enabled the creation of the nuclear bomb. Also revealed are the mathematical foundations for the moon landing, airplane travel, the electric generator -- and even life itself. Praised by Publishers Weekly as "a wholly accessible, beautifully written exploration of the potent mathematical imagination," and named a Best Nonfiction Book of 1995, the stories behind The Five Equations That Changed the World, as told by Dr. Guillen, are not only chronicles of science, but also gripping dramas of jealousy, fame, war, and discovery. Dr. Michael Guillen is Instructor of Physics and Mathematics in the Core Curriculum Program at Harvard University.

    No other telescope combines instant name recognition with the production of consistently spectacular images. Yet few people outside of the astronomy community realize that Hubble is now at the apex of its imaging capabilities. A collection of stunningly detailed pictures, made possible by the new Wide Field Camera 3, has yet to be incorporated into a popular-level book. Until now. Hubble's Universe will be the premier venue for the Hubble Telescope's most recent visual splendors. Bestselling astronomy writer Terence Dickinson showcases extraordinary late-breaking pictures, many of which have yet to receive wide distribution as news stories or in publications outside scientific papers, and presents a breathtaking portfolio drawn from an archive of over 500,000 existing Hubble images.The accompanying text balances accuracy with accessibility, Dickinson's hallmark. And thanks to the author's familiarity with Hubble's history and discoveries and his access to top Hubble scientists for insight and accuracy, the text includes facts and tidbits not found in any other book. Combined with hundreds of brilliant images, the clear, succinct and illuminating narrative brings to life the fascinating forces at work in the universe.

    From stars, planets and galaxies, to black holes, the Big Bang and life in space, this title has been making it easy for beginners to quickly grasp the basic concepts of astronomy for over 25 years. Updated with the latest discoveries in astronomy and astrophysics, this newest edition of Dinah Moche's classic guide now includes many Web site addresses for spectacular images and news. And like all previous editions, it is packed with valuable tables, charts, star and moon maps and features simple activities that reinforce readers' grasp of basic concepts at their own pace, as well as objectives, reviews, and self-tests to monitor their progress. Dinah L. Moche, PhD (Rye, NY), is an award-winning author, educator, and lecturer. Her books have sold over nine million copies in seven languages.

    Yet recent theories suggest that there is far more to the universe than what our instruments record--in fact, it could be infinite. Colossal flows of galaxies, large empty regions called voids, and other unexplained phenomena offer clues that our own "bubble universe" could be part of a greater realm called the multiverse. How big is the observable universe? What it is made of? What lies beyond it? Was there a time before the Big Bang? Could space have unseen dimensions? In this book, physicist and science writer Paul Halpern explains what we know--and what we hope to soon find out--about our extraordinary cosmos.Explains what we know about the Big Bang, the accelerating universe, dark energy, dark flow, and dark matter to examine some of the theories about the content of the universe and why its edge is getting farther away from us fasterExplores the idea that the observable universe could be a hologram and that everything that happens within it might be written on its edgeWritten by physicist and popular science writer Paul Halpern, whose other books include "Collider: The Search for the World's Smallest Particles," and "What's Science Ever Done For Us: What the Simpsons Can Teach Us About Physics, Robots, Life, and the Universe"

    C. Cole. Once again, acclaimed science writer K. C. Cole brings the arcane and academic down to the level of armchair scientists in The Hole in the Universe, an entertaining and edifying search for nothing at all. Open the newspaper on any given day and you will read of a newly discovered planet, star, and so on. Yet scientists and mathematicians have spent generations searching the far reaches of the universe for that one elusive state—nothingness. Although this may sound like a simple task, every time the absolute void appears within reach, something new is discovered in its place: a black hole, an undulating string, an additional dimension of space or time—even another universe. A fascinating and literary tour de force, The Hole in the Universe is a virtual romp into the unknown that you never knew wasn't there.

    Organized around the central concept of a vector space, the book includes numerous physical applications in the body of the text as well as many problems of a physical nature. It is also one of the purposes of this book to introduce the physicist to the language and style of mathematics as well as the content of those particular subjects with contemporary relevance in physics.Chapters 1 and 2 are devoted to the mathematics of classical physics. Chapters 3, 4 and 5 — the backbone of the book — cover the theory of vector spaces. Chapter 6 covers analytic function theory. In chapters 7, 8, and 9 the authors take up several important techniques of theoretical physics — the Green's function method of solving differential and partial differential equations, and the theory of integral equations. Chapter 10 introduces the theory of groups. The authors have included a large selection of problems at the end of each chapter, some illustrating or extending mathematical points, others stressing physical application of techniques developed in the text.Essentially self-contained, the book assumes only the standard undergraduate preparation in physics and mathematics, i.e. intermediate mechanics, electricity and magnetism, introductory quantum mechanics, advanced calculus and differential equations. The text may be easily adapted for a one-semester course at the graduate or advanced undergraduate level.

    He went on to become a twentieth-century icon-a man whose name and face are synonymous with "genius." Now, at last, ordinary readers can explore Einstein's life and work in this new For Dummies guide. Physicist Carlos Calle chronicles Einstein's career and explains his work-including the theories of special and general relativity-in language that anyone can understand. He shows how Einstein's discoveries affected everything from the development of the atom bomb to the theory of quantum mechanics. He sheds light on Einstein's personal life and beliefs, including his views on religion and politics. And he shows how Einstein's work continues to affect our world today, from nuclear power to space travel to artificial intelligence.