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.

    Their work has uncovered a number of the universe’s more surprising secrets, and many believe further wonders remain hidden within the theory’s tangle of equations, waiting to be exposed. In this sweeping narrative of science and culture, astrophysicist Pedro Ferreira brings general relativity to life through the story of the brilliant physicists, mathematicians, and astronomers who have taken up its challenge. For these scientists, the theory has been both a treasure trove and an enigma, fueling a century of intellectual struggle and triumph.. Einstein’s theory, which explains the relationships among gravity, space, and time, is possibly the most perfect intellectual achievement of modern physics, yet studying it has always been a controversial endeavor. Relativists were the target of persecution in Hitler’s Germany, hounded in Stalin’s Russia, and disdained in 1950s America. Even today, PhD students are warned that specializing in general relativity will make them unemployable. Despite these pitfalls, general relativity has flourished, delivering key insights into our understanding of the origin of time and the evolution of all the stars and galaxies in the cosmos. Its adherents have revealed what lies at the farthest reaches of the universe, shed light on the smallest scales of existence, and explained how the fabric of reality emerges. Dark matter, dark energy, black holes, and string theory are all progeny of Einstein’s theory. We are in the midst of a momentous transformation in modern physics. As scientists look farther and more clearly into space than ever before, The Perfect Theory reveals the greater relevance of general relativity, showing us where it started, where it has led, and where it can still take us.

    His work won him the Nobel Prize in 1922 and his ideas continue to propel physics towards new discoveries. But what is quantum theory? Most of us do not understand even the basics of one of the most significant scientific advances ever made, opening up a whole new field in science, whose ambiguities still challenge scientists around the world.Bohr and Quantum Theory offers an accessible and absorbing account of the man who was both a part of The Manhattan Project but also an advocate of peace.He held the key to understanding such intricate realities as black holes and nuclear energy. Bohr's Big Idea explains complex and crucial ideas in a clear and engaging way, placing quantum theory in the context of a man's life, work and time and examining its important implications for our future.The Big Idea series is a fascinating look at the greatest advances in our scientific history, and at the men and women who made these fundamental breakthroughs.

    Niels Bohr's dictum bears witness to the bewildering impact of quantum theory, flying in the face of classical physics and dramatically transforming scientists' outlook on our relationship with the material world. In this book Paul Davies interviews eight physicists involved in debating and testing the theory, with radically different views of its significance.

    Ever since physics first penetrated the atom, early in this century, what it found there has stood as a radical and unanswered challenge to many of our most cherished conceptions of nature. It has literally been called into question since then whether or not there are always objective matters of fact about the whereabouts of subatomic particles, or about the locations of tables and chairs, or even about the very contents of our thoughts. A new kind of uncertainty has become a principle of science.This book is an original and provocative investigation of that challenge, as well as a novel attempt at writing about science in a style that is simultaneously elementary and deep. It is a lucid and self-contained introduction to the foundations of quantum mechanics, accessible to anyone with a high school mathematics education, and at the same time a rigorous discussion of the most important recent advances in our understanding of that subject, some of which are due to the author himself.

    It defines our experience of the world; it echoes through our every waking hour. Time is the very foundation of conscious experience. Yet as familiar as it is, time is also deeply mysterious. We cannot see, hear, smell, taste, or touch it. Yet we do "feel" it--or at least we "think" we feel it. No wonder poets, writers, philosophers, and scientists have grappled with time for centuries.In his latest book, award-winning science writer Dan Falk chronicles the story of how humans have come to understand time over the millennia, and by drawing from the latest research in physics, psychology, and other fields, Falk shows how that understanding continues to evolve. "In Search of Time" begins with our earliest ancestors' perception of time and the discoveries that led--with much effort--to the Gregorian calendar, atomic clocks, and "leap seconds." Falk examines the workings of memory, the brain's remarkable "bridge across time," and asks whether humans are unique in their ability to recall the past and imagine the future. He explores the possibility of time travel, and the paradoxes it seems to entail. Falk looks at the quest to comprehend the beginning of time and how time--and the universe--may end. Finally, he examines the puzzle of time's "flow," and the remarkable possibility that the passage of time may be an illusion.Entertaining, illuminating, and ultimately thought provoking, "In Search of Time "reveals what some of our most insightful thinkers have had to say about time, from Aristotle to Kant, from Newton to Einstein, and continuing with the brightest minds of today.

    --Carlo Rovelli, author of Seven Brief Lessons on Physics and Helgoland You've got questions: about space, time, gravity, and the odds of meeting your older self inside a wormhole. All the answers you need are right here.As a species, we may not agree on much, but one thing brings us all together: a need to know. We all wonder, and deep down we all have the same big questions. Why can't I travel back in time? Where did the universe come from? What's inside a black hole? Can I rearrange the particles in my cat and turn it into a dog?Researcher-turned-cartoonist Jorge Cham and physics professor Daniel Whiteson are experts at explaining science in ways we can all understand, in their books and on their popular podcast, Daniel and Jorge Explain the Universe. With their signature blend of humor and oh-now-I-get-it clarity, Jorge and Daniel offer short, accessible, and lighthearted answers to some of the most common, most outrageous, and most profound questions about the universe they've received.This witty, entertaining, and fully illustrated book is an essential troubleshooting guide for the perplexing aspects of reality, big and small, from the invisible particles that make up your body to the identical version of you currently reading this exact sentence in the corner of some other galaxy. If the universe came with an FAQ, this would be it.

    In this guide for students, each equation is the subject of an entire chapter, with detailed, plain-language explanations of the physical meaning of each symbol in the equation, for both the integral and differential forms. The final chapter shows how Maxwell's equations may be combined to produce the wave equation, the basis for the electromagnetic theory of light. This book is a wonderful resource for undergraduate and graduate courses in electromagnetism and electromagnetics. A website hosted by the author at www.cambridge.org/9780521701471 contains interactive solutions to every problem in the text as well as audio podcasts to walk students through each chapter.

    The book also provides a balanced presentation of time-varying and static fields, preparingstudents for employment in today's industrial and manufacturing sectors. Streamlined to facilitate student understanding, this edition features worked examples in every chapter that explain how to use the theory presented in the text to solve different kinds of problems. Numerical methods, including MATLAB and vector analysis, are also included to help students analyzesituations that they are likely to encounter in industry practice. Elements of Electromagnetics, Fifth Edition, is designed for introductory undergraduate courses in electromagnetics.

    Using Everett's unpublished papers (recently discovered in his son's basement) and dozens of interviews with his friends, colleagues, and surviving family members, Byrne paints, for the general reader, a detailed portrait of the genius who invented an astonishing way of describing our complex universe from the inside. Everett's mathematical model (called the "universal wave function") treats all possible events as "equally real," and concludes that countless copies of every person and thing exist in all possible configurations spread over an infinity of universes: many worlds. Afflicted by depression and addictions, Everett strove to bring rational order to the professional realms in which he played historically significant roles. In addition to his famous interpretation of quantum mechanics, Everett wrote a classic paper in game theory; created computer algorithms that revolutionized military operations research; and performed pioneering work in artificial intelligence for top secret government projects. He wrote the original software for targeting cities in a nuclear hot war; and he was one of the first scientists to recognize the danger of nuclear winter. As a Cold Warrior, he designed logical systems that modeled "rational" human and machine behaviors, and yet he was largely oblivious to the emotional damage his irrational personal behavior inflicted upon his family, lovers, and business partners. He died young, but left behind a fascinating record of his life, including correspondence with such philosophically inclined physicists as Niels Bohr, Norbert Wiener, and John Wheeler. These remarkable letters illuminate the long and often bitter struggle to explain the paradox of measurement at the heart of quantum physics. In recent years, Everett's solution to this mysterious problem-the existence of a universe of universes-has gained considerable traction in scientific circles, not as science fiction, but as an explanation of physical reality.

    But, Alex Bellos says, "math can be inspiring and brilliantly creative. Mathematical thought is one of the great achievements of the human race, and arguably the foundation of all human progress. The world of mathematics is a remarkable place."Bellos has traveled all around the globe and has plunged into history to uncover fascinating stories of mathematical achievement, from the breakthroughs of Euclid, the greatest mathematician of all time, to the creations of the Zen master of origami, one of the hottest areas of mathematical work today. Taking us into the wilds of the Amazon, he tells the story of a tribe there who can count only to five and reports on the latest findings about the math instinct--including the revelation that ants can actually count how many steps they've taken. Journeying to the Bay of Bengal, he interviews a Hindu sage about the brilliant mathematical insights of the Buddha, while in Japan he visits the godfather of Sudoku and introduces the brainteasing delights of mathematical games.Exploring the mysteries of randomness, he explains why it is impossible for our iPods to truly randomly select songs. In probing the many intrigues of that most beloved of numbers, pi, he visits with two brothers so obsessed with the elusive number that they built a supercomputer in their Manhattan apartment to study it. Throughout, the journey is enhanced with a wealth of intriguing illustrations, such as of the clever puzzles known as tangrams and the crochet creation of an American math professor who suddenly realized one day that she could knit a representation of higher dimensional space that no one had been able to visualize. Whether writing about how algebra solved Swedish traffic problems, visiting the Mental Calculation World Cup to disclose the secrets of lightning calculation, or exploring the links between pineapples and beautiful teeth, Bellos is a wonderfully engaging guide who never fails to delight even as he edifies. "Here's Looking at Euclid "is a rare gem that brings the beauty of math to life.

    Writing with her customary charm and erudition, Dent offers a wonderfully readable and endlessly entertaining exploration of language, answering 101 of the most intriguing questions about the English language, from word origins and spelling to grammar and usage. Dent ranges far and wide in her search for the oddities of language, pondering the ancient origin of the word tragedy (which originally meant goat song in Greek) as well as the modern meaning of the word donk in the Blackout Crew's song title Put a Donk in It. And throughout, the book brims with fascinating tales. Readers learn, for instance, that the word bankrupt comes from the Italian banca rotta or broken bench and the word broke (meaning out of funds) has the same origin. Dent explains that in the sixteenth century, money lenders conducted their business on benches outdoors and the usual Italian word for bench was banca (hence today's bank). The author also provides an entertaining account of the origin of the term white elephant (meaning a useless, burdensome possession) that dates back to ancient Siam, where rare white elephants were always given to the king. But since by law white elephants couldn't be worked (and earn money) or even be ridden, the king often re-gifted these worthless burdens to courtiers whom he didn't like. Sparkling with insight and linguistic curiosity, this delightful compendium will be irresistible to anyone fascinated with language--the perfect gift for word lovers everywhere.

    This wonderfully accessible book illuminates the professional and personal paths that led him to this remarkable conclusion.All interactions between particles in the universe, Lloyd explains, convey not only energy but also information—in other words, particles not only collide, they compute. And what is the entire universe computing, ultimately? “Its own dynamical evolution,” he says. “As the computation proceeds, reality unfolds.”To elucidate his theory, Lloyd examines the history of the cosmos, posing questions that in other hands might seem unfathomably complex: How much information is there in the universe? What information existed at the moment of the Big Bang and what happened to it? How do quantum mechanics and chaos theory interact to create our world? Could we attempt to re-create it on a giant quantum computer? Programming the Universe presents an original and compelling vision of reality, revealing our world in an entirely new light.

    Based on a course of lectures delivered by the author at Columbia University, the text is elementary in treatment and remarkable for its clarity and organization. Although it is assumed that the reader is familiar with the fundamental facts of thermometry and calorimetry, no advanced mathematics beyond calculus is assumed.Partial contents: thermodynamic systems, the first law of thermodynamics (application, adiabatic transformations), the second law of thermodynamics (Carnot cycle, absolute thermodynamic temperature, thermal engines), the entropy (properties of cycles, entropy of a system whose states can be represented on a (V, p) diagram, Clapeyron and Van der Waals equations), thermodynamic potentials (free energy, thermodynamic potential at constant pressure, the phase rule, thermodynamics of the reversible electric cell), gaseous reactions (chemical equilibria in gases, Van't Hoff reaction box, another proof of the equation of gaseous equilibria, principle of Le Chatelier), the thermodynamics of dilute solutions (osmotic pressure, chemical equilibria in solutions, the distribution of a solute between 2 phases vapor pressure, boiling and freezing points), the entropy constant (Nernst's theorem, thermal ionization of a gas, thermionic effect, etc.).

    In this richly illustrated book, accessible examples are used to show how information theory can be understood in terms of everyday games like '20 Questions', and the simple MatLab programs provided give hands-on experience of information theory in action. Written in a tutorial style, with a comprehensive glossary, this text represents an ideal primer for novices who wish to become familiar with the basic principles of information theory.Download chapter 1 from http://jim-stone.staff.shef.ac.uk/Boo...