Was late antiquity therefore merely a time of decline? In this vibrant and compact introduction, Gillian Clark shedslight on the concept of late antiquity and the events of its time, showing that this was in fact a period of great transformation. Late antiquity saw Roman law codified, Christian creeds formulated, the Talmud compiled, and the Qur'an composed. If the Goths sacked the city of Rome, the Vandalsbuilt churches in Africa and Attila the Hun received an embassy from Constantinople. Anthony of Egypt and Simeon Stylites offered spectacular new models of holiness, while Augustine and Basil and Benedict devised rules for monastic communities. Late antique artists produced the mosaics of Ravennaand the first dome of Hagia Sophia. And it was also the period when emperors Diocletian in the third century and Justinian in the sixth enacted extensive and much-needed reforms of government.

    It is impossible to understand the spread of an epidemic, a computer virus, large-scale blackouts, or massive extinctions without taking into account the network structure that underlies all these phenomena. In this Very Short Introduction, Guido Caldarelli and Michele Catanzaro discuss the nature and variety of networks, using everyday examples from society, technology, nature, and history to explain and understand the science of network theory. They show the ubiquitous role of networks; how networks self-organize; why the rich get richer; and how networks can spontaneously collapse. They conclude by highlighting how the findings of complex network theory have very wide and important applications in genetics, ecology, communications, economics, and sociology.

    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.

      In the past few years, a handful of scientists have been in a race to explain a disturbing aspect of our universe: only 4 percent of it consists of the matter that makes up you, me, our books, and every planet, star, and galaxy. The rest—96 percent of the universe—is completely unknown.   Richard Panek tells the dramatic story of how scientists reached this conclusion, and what they’re doing to find this "dark" matter and an even more bizarre substance called dark energy. Based on in-depth, on-site reporting and hundreds of interviews—with everyone from Berkeley’s feisty Saul Perlmutter and Johns Hopkins’s meticulous Adam Riess to the quietly revolutionary Vera Rubin—the book offers an intimate portrait of the bitter rivalries and fruitful collaborations, the eureka moments and blind alleys, that have fueled their search, redefined science, and reinvented the universe.

    It explains what algorithms do, how they are used, the risks associated with using them, and why governments should be concerned. Important areas arehighlighted, such as Stream Ciphers, block ciphers, public key algorithms, digital signatures, and applications such as e-commerce. This book highlights the explosive impact of cryptography on modern society, with, for example, the evolution of the internet and the introduction of more sophisticatedbanking methods.

    Written by one of the world's leading experimental cosmologists, this short but deeply insightful book describes what scientists are revealing through precise measurements of the faint thermal afterglow of the Big Bang--known as the cosmic microwave background, or CMB--and how their findings are transforming our view of the cosmos.Blending the latest findings in cosmology with essential concepts from physics, Lyman Page first helps readers to grasp the sheer enormity of the universe, explaining how to understand the history of its formation and evolution in space and time. Then he sheds light on how spatial variations in the CMB formed, how they reveal the age, size, and geometry of the universe, and how they offer a blueprint for the formation of cosmic structure.Not only does Page explain current observations and measurements, he describes how they can be woven together into a unified picture to form the Standard Model of Cosmology. Yet much remains unknown, and this incisive book also describes the search for ever deeper knowledge at the field's frontiers--from quests to understand the nature of neutrinos and dark energy to investigations into the physics of the very early universe.

    Language is informal, examples are vivid and lively, and the perspectivie is fresh. Based on lectures delivered to engineering students, this work will also be valued by scientists, engineers, technicians, businessmen, anyone facing energy challenges of the future.

    Having just completed his masterpiece, The General Theory of Relativity—which provided a brand-new theory of gravity and promised a new perspective on the cosmos as a whole—he set out at once to share his excitement with as wide a public as possible in this popular and accessible book.Here published for the first time as a Penguin Classic, this edition of Relativity features a new introduction by bestselling science author Nigel Calder.

    Robots have taken their first steps into homes and hospitals, and have seen spectacular success in planetary exploration. Yet despite these successes, robots have failed to live up to the predictions of the 1950s and 60s, when it was widely thought--by scientists as well as the public--that we would have, by now, intelligent robots as butlers, companions, or co-workers. This Very Short Introduction explains how it is that robotics can be both a success story and a disappointment, and how robots can be both ordinary and remarkable. Alan Winfield introduces the subject by looking at the parts that together make a robot. Not surprisingly, these parts each have a biological equivalent: a robot's camera is like an animal's eyes, a robot's microcomputer is equivalent to an animal's brain, and so on. By introducing robots in this way this book builds a conceptual, non-technical picture of what a robot is, how it works, and how "intelligent" it is.

    There are deep connections between stars and atoms, between the cosmos and the microworld. Just six numbers, imprinted in the "big bang," determine the essential features of our entire physical world. Moreover, cosmic evolution is astonishingly sensitive to the values of these numbers. If any one of them were "untuned," there could be no stars and no life. This realization offers a radically new perspective on our universe, our place in it, and the nature of physical laws.

    What is communism? Where did the idea come from and what attracted people to it? Is there a future for communism? This Very Short Introduction considers these questions and more in the search to explore and understand this controversial political force.Explaining the theory behind its ideology, and examining the history and mindset behind its political, economic and social structures, Leslie Holmes considers the evolution of communism from Marx's time, to its practice in the Bolshevik Revolution, to its collapse in 1989-91. Holmes highlights theinner dynamics, crises, and demise of communism as a global system, and introduces the major players in the communist world, including Marx, Lenin, Stalin, and Mao.About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundredsof key topics, from philosophy to Freud, quantum theory to Islam.

    But when did this essential part of our lives begin? Why do we all write differently and how did writing evolve into what we use today? All of these questions are answered in this Very Short Introduction. Andrew Robinson tells the fascinating story of the history of writing, shedding light on its development and examining the enormous variety of writing and scripts we use today. Starting with the origins of writing five thousand years ago, with cuneiform and Egyptian hieroglyphs, Robinson explains how these early forms developed into hundreds of scripts, including the Roman alphabet and Chinese characters. He reveals how the modern writing symbols and abbreviations we take for granted today--including airport signage and text messaging--resemble ancient ones much more closely than we might think. The book also includes a chronology of events from 3300 BC to AD 2000, a list of titles for further reading, and an index.About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundreds of key topics, from philosophy to Freud, quantum theory to Islam.

    Now, in this Very Short Introduction, Lee provides a magnificent look at the genre in which she is an undisputed master--the art of biography. Here Lee considers the cultural and historical background of different types of biographies, looks at the factors that affect biographers, and asks whether there are different strategies, ethics, and principles required for writing about one person compared to another. She also discusses contemporary biographical publications and considers what kind of lives are the most popular and in demand. And along the way, she answers such questions as why do certain people and historical events arouse so much interest? How can biographies be compared with history and works of fiction? Does a biography need to be true? Is it acceptable to omit or conceal things? Does the biographer need to personally know the subject? Must a biographer be subjective?About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundreds of key topics, from philosophy to Freud, quantum theory to Islam.

    Starting once again with fossils, he turns his gaze skyward, showing us how the entirety of the universe’s fourteen-billion-year history can be seen in our bodies. As he moves from our very molecular composition (a result of stellar events at the origin of our solar system) through the workings of our eyes, Shubin makes clear how the evolution of the cosmos has profoundly marked our own bodies. Fully illustrated with black and white drawings.

    In the book, Sagan explores 15 billion years of cosmic evolution and the development of science and civilization. Cosmos traces the origins of knowledge and the scientific method, mixing science and philosophy, and speculates to the future of science. The book also discusses the underlying premises of science by providing biographical anecdotes about many prominent scientists throughout history, placing their contributions into the broader context of the development of modern science.The book covers a broad range of topics, comprising Sagan's reflections on anthropological, cosmological, biological, historical, and astronomical matters from antiquity to contemporary times. Sagan reiterates his position on extraterrestrial life—that the magnitude of the universe permits the existence of thousands of alien civilizations, but no credible evidence exists to demonstrate that such life has ever visited earth.