Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics? Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts.Brought up to date with a new chapter by Ian Stewart, What is Mathematics? Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.Formal mathematics is like spelling and grammar - a matter of the correct application of local rules. Meaningful mathematics is like journalism - it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature - it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature - it opens a window onto the world of mathematics for anyone interested to view.

    Unfortunately, the subject has gained a notorious reputation for difficulty, with forbidding looking mathematics and a peculiar diagrammatic language described in an array of unforgiving, weighty textbooks aimed firmly at aspiring professionals. However, quantum field theory is too important, too beautiful, and too engaging to be restricted to the professionals. This book on quantum field theory is designed to be different. It is written by experimental physicists and aims to provide the interested amateur with a bridge from undergraduate physics to quantum field theory. The imagined reader is a gifted amateur, possessing a curious and adaptable mind, looking to be told an entertaining and intellectually stimulating story, but who will not feel patronised if a few mathematical niceties are spelled out in detail. Using numerous worked examples, diagrams, and careful physically motivated explanations, this book will smooth the path towards understanding the radically different and revolutionary view of the physical world that quantum field theory provides, and which all physicists should have the opportunity to experience.To request a copy of the Solutions Manual, visit http: //global.oup.com/uk/academic/physics/ad....

    Elefteriades, one of Men’s Health magazine’s ten best doctors in America, shares moving patient stories and lessons about the human heart. The human heart is a paradox, incredibly strong yet surprisingly fragile. And while stories that reveal its symbolic characteristics abound, there are far fewer that laud its physical capabilities, which are perhaps even more profound. Dr. Elefteriades, one of the most respected cardiac surgeons in America, has treated more than 10,000 patients in his distinguished career. Now, for the first time, he shares fascinating stories of his most memorable patients and cases—patients who have challenged him technically and moved him emotionally, patients who have enriched his life and expanded his horizons while he cared for their hearts. By detailing heart conditions and cardiac reparative procedures with specific yet accessible medical narratives, Dr. Elefteriades encapsulates the beauty, complexity, and majesty of the human heart. But there is far more to this organ—and these stories—than a collection of veins, arteries, and valves. These are stories of courage, miracles, and the bravery of patients (some famous and others not) and their families when facing nearly insurmountable challenges, offering a thought-provoking, informative, and at times heart-wrenching study of the resilience of both the human body and spirit.

    Illustrating his text with maps, graphics, and photographs, David offers inside information about how the United States, allies and competitors, as well as key private corporations like Moon Express and Jeff Bezos's Blue Origin, plan to reach, inhabit, and even harvest the moon in the decades to come.Spurred on by the Google Lunar XPRIZE--$20 million for the first to get to the moon and send images home--the 21st-century space race back to the moon has become more urgent, and more timely, than ever. Accounts of these new strategies are set against past efforts, including stories never before told about the Apollo missions and Cold War plans for military surveillance and missile launches from the moon. Timely and fascinating, this book sheds new light on our constant lunar companion, offering reasons to gaze up and see it in a different way than ever before.

    Maudlin explains special relativity using a geometrical approach, emphasizing intrinsic space-time structure rather than coordinate systems or reference frames. He gives readers enough detail about special relativity to solve concrete physical problems while presenting general relativity in a more qualitative way, with an informative discussion of the geometrization of gravity, the bending of light, and black holes. Additional topics include the Twins Paradox, the physical aspects of the Lorentz-FitzGerald contraction, the constancy of the speed of light, time travel, the direction of time, and more.Introduces nonphysicists to the philosophical foundations of space-time theoryProvides a broad historical overview, from Aristotle to EinsteinExplains special relativity geometrically, emphasizing the intrinsic structure of space-timeCovers the Twins Paradox, Galilean relativity, time travel, and moreRequires only basic algebra and no formal knowledge of physicsTim Maudlin is professor of philosophy at New York University. His books include The Metaphysics within Physics and Quantum Non-Locality and Relativity.

    In this compelling memoir, his first wife, Jane Hawking, relates the inside story of their extraordinary marriage. As Stephen's academic renown soared, his body was collapsing under the assaults of a motor neuron disease. Jane's candid account of trying to balance his 24-hour care with the needs of their growing family reveals the inner strength of the author, while the self-evident character and achievements of her husband make for an incredible tale presented with unflinching honesty. Jane's candor is no less apparent when the marriage finally ends in a high-profile meltdown, with Stephen leaving Jane for one of his nurses and Jane marrying an old family friend. In this exceptionally open, moving, and often funny memoir, Jane Hawking confronts not only the acutely complicated and painful dilemmas of her first marriage, but also the relationship's fault lines exposed by the pervasive effects of fame and wealth. The result is a book about optimism, love, and change that will resonate with readers everywhere.

    Italian investigative journalist Paola Leopizzi Harris and French-born information scientist Dr. Jacques F. Vallée have teamed up to uncover the details of a New Mexico crash in 1945, fully two years before the well-known incident at Roswell and the famous sighting by pilot Kenneth Arnold in 1947.Over several site investigation surveys Harris and Vallée reconstructed the historic observations by three witnesses, two of whom are still living, who described to them the circumstances of the crash, with details of the recovery of a nearly-intact flying vehicle and its occupants by an Army detachment. Combining their long experience in field research around the world, the authors have documented the step-by-step efforts by the military to remove the object, an avocado-shaped craft weighting several tons, from the property where it crash-landed during a storm.Surprisingly, the literature of the field only includes a few passing mentions about the case, and only one (foreign) TV documentary has mentioned it, but the correlation between the crash of the extraordinary object and the explosion of the first atom bomb at White Sands, less than 20 miles away, has been missed. Harris and Vallée suggest that the correlation is significant for physical, geographic and biological reasons, quite apart from the obvious strategic implications.The witnesses were able to observe not only the actual crash of the object on their property but every step of the military efforts to lift it and take it away. Fearing retaliation, they remained silent for some 60 years about what they had seen and done over those nine days at the site while the recovery was proceeding. When placed in the context of the history of chemical and physical analysis of retrieved UFO debris--an area where Harris and Vallée have long collaborated—the devices observed by the witnesses raise a number of very important scientific questions.The Honorable Paul Hellyer, former Minister of National Defence of Canada, has stated: “Paola Harris and Jacques Vallée have spent much effort doing field research on location (…) It is now time that their discovery be revealed to the world.”Christopher Mellon, former deputy Assistant Secretary of Defense, called the data “fresh reason to believe that our government is concealing physical proof of alien technology. Read the book, and if persuaded, join the millions of other Americans seeking a straight answer.”And Professor Paul Hynek added that the research “reveals a new UFO history.”

    

    The information presented includes: definitions, names, historical background, coordinates, classifications, physical descriptions, maps, charts, sketches, and observing guides. All told in an engaging manner.The series became an instant success with amateur astronomers, and remained so for decades. While it is now dated, it is still a popular source of information.Volume One lists the constellations from Andromeda to Cetus.

    The book is designed for advanced undergraduates or beginning graduate students and assumes no prior knowledge of general relativity. An emphasis is placed on developing the readers' physical insight rather than losing them with complex math. An approachable writing style and wealth of fresh and imaginative analogies from "everyday" physics are used to make the concepts of cosmology more accessible. The book is unique in that it not only includes recent major developments in cosmology, like the cosmological constant and accelerating universe, but also anticipates key developments expected in the next few years, such as detailed results on the cosmic microwave background.

    With the Big Bang, it went from a state of unimaginable density to an all-encompassing cosmic fireball to a simmering fluid of matter and energy, laying down the seeds for everything from dark matter to black holes to one rocky planet orbiting a star near the edge of a spiral galaxy that happened to develop life. But what happens at the end of the story? In billions of years, humanity could still exist in some unrecognizable form, venturing out to distant space, finding new homes and building new civilizations. But the death of the universe is final. What might such a cataclysm look like? And what does it mean for us? Dr. Katie Mack has been contemplating these questions since she was eighteen, when her astronomy professor first informed her the universe could end at any moment, setting her on the path toward theoretical astrophysics. Now, with lively wit and humor, she unpacks them in The End of Everything, taking us on a mind-bending tour through each of the cosmos’ possible finales: the Big Crunch; the Heat Death; Vacuum Decay; the Big Rip; and the Bounce. In the tradition of Neil DeGrasse’s bestseller Astrophysics for People in a Hurry, Mack guides us through major concepts in quantum mechanics, cosmology, string theory, and much more, in a wildly fun, surprisingly upbeat ride to the farthest reaches of everything we know.

    The boy who became a famous naturalist was never again to see the spectacle except in his imagination. That childhood event contributed to the profound sense of time and space that marks The Invisible Pyramid. This collection of essays, first published shortly after Americans landed on the moon, explores inner and outer space, the vastness of the cosmos, and the limits of what can be known. Bringing poetic insight to scientific discipline, Eiseley makes connections between civilizations past and present, multiple universes, humankind, and nature.

    These include applications drawn from important new areas of technology such as optical fibers, radome design, satellite communication, and microstrip lines. There is also added coverage of several new topics, including Hall effect, radar equation and scattering cross section, transients in transmission lines, waveguides and circular cavity resonators, wave propagation in the ionosphere, and helical antennas. New exercises, new problems, and many worked-out examples make this complex material more accessible to students.

    Written by two of the field's true pioneers, Spacetime Physics can extend and enhance coverage of specialty relativity in the classroom. This thoroughly up-to-date, highly accessible overview covers microgravity, collider accelerators, satellite probes, neutron detectors, radioastronomy, and pulsars.  The chapter on general relativity with new material on gravity waves, black holes, and cosmology.

    Every technology we rely on today was created by the human mind, seeking to understand the universe around us. Scientific knowledge is our most precious possession, and our future will be shaped by the breakthroughs to come. In this personal and fascinating work, Neil Turok, Director of the Perimeter Institute for Theoretical Physics, explores the transformative scientific discoveries of the past three centuries -- from classical mechanics, to the nature of light, to the bizarre world of the quantum, and the evolution of the cosmos. Each new discovery has, over time, yielded new technologies causing paradigm shifts in the organization of society. Now, he argues, we are on the cusp of another major transformation: the coming quantum revolution that will supplant our current, dissatisfying digital age. Facing this brave new world, Turok calls for creatively re-inventing the way advanced knowledge is developed and shared, and opening access to the vast, untapped pools of intellectual talent in the developing world. Scientific research, training, and outreach are vital to our future economy, as well as powerful forces for peaceful global progress.