Historian Jacqueline Stedall shows that mathematical ideas are far from being fixed, but are adapted and changed by their passage across periods and cultures. The book illuminates some of the varied contexts in which people have learned, used, and handed on mathematics, drawing on fascinating case studies from a range of times and places, including early imperial China, the medieval Islamic world, and nineteenth-century Britain. By drawing out some common threads, Stedall provides an introduction not only to the mathematics of the past but to the history of mathematics as a modern academic discipline.

    Allan Hobson provides a new and increasingly complete picture of how dreaming is created by the brain. Focusing on dreaming to explain the mechanisms of sleep, this book explores how the new science of dreaming is affecting theories in psychoanalysis, and how it is helping our understanding of the causes of mental illness.J. Allan Hobson investigates his own dreams to illustrate and explain some of the fascinating discoveries of modern sleep science, while challenging some of the traditionally accepted theories about the meaning of dreams. He reveals how dreaming maintains and develops the mind, why we go crazy in our dreams in order to avoid doing so when we are awake, and why sleep is not just good for health but essential for life.

    Here, Timothy Lim explores the cultural and historical background of the scrolls, and examines their significance for our understanding of the Old Testament and the origins of Christianity and Judaism. Lim tells the fascinating story of the scrolls since their discouvery; their cultural context through the archaeology and history of the Dead Sea region. He explains the science behind their deciphering and dating, and does not omit the cast of characters, scandals, and controversies that have hastened the scrolls' rise to the status of cultrual icon.Beginning with their discovery in the 1940s, through the political, legal, and scholary controversies that still persist today, public interest in the Dead Sea Scrolls has remained exceptionally high. This is an accessible and well-written mini-history that will appeal to anyone interested in the true history of these fascinating documents.

    The most fundamental differences are philosophical, and readers of this book will emerge with a clearer understandingof paradoxical-sounding concepts such as infinity, curved space, and imaginary numbers. The first few chapters are about general aspects of mathematical thought. These are followed by discussions of more specific topics, and the book closes with a chapter answering common sociological questionsabout the mathematical community (such as Is it true that mathematicians burn out at the age of 25?) It is the ideal introduction for anyone who wishes to deepen their understanding of mathematics.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.

    This Very Short Introduction presents a succinct guide to the key episodes in that story - from the very origins of life four million years ago to the extraordinary diversity of species around the globe today.Beginning with an explanation of the controversies surrounding the birth of life itself, each following chapter tells of a major breakthrough that made new forms of life possible: including sex and multicellularity, hard skeletons, and the move to land. Along the way, we witness the greatest mass extinction, the first forests, the rise of modern ecosystems, and, most recently, conscious humans.Introducing ideas from a range of scientific disciplines, from evolutionary biology and earth history, to geochemistry, palaeontology, and systematics, Michael Benton explains how modern science pieces the evidence in this vast evolutionary puzzle together, to build up an accessible and up-to-date picture of the key developments in the history of life on earth.

    In this Very Short Introduction, Peter M. Higgins, a renowned popular-science writer, unravels the world of numbers, demonstrating its richness and providing an overview of all the number types that feature in modern science and mathematics. Indeed, Higgins paints a crystal-clear picture of the number world, showing how the modern number system matured over many centuries, and introducing key concepts such as integers, fractions, real and imaginary numbers, and complex numbers. Higgins sheds light on such fascinating topics as the series of primes, describing how primes are now used to encrypt confidential data on the internet. He also explores the infinite nature of number collections and explains how the so-called real numbers knit together to form the continuum of the number line. Written in the fashion of Higgins' highly popular science paperbacks, Numbers accurately explains the nature of numbers and how so-called complex numbers and number systems are used in calculations that arise in real problems.

    Indeed, for all the effort to reduce nuclear stockpiles to zero and to keep other nations (such as Iran) from developing nuclear capability, it seems that the Bomb is here to stay. In this gripping Very Short Introduction, Joseph M. Siracusa, an internationally respected authority on nuclear arms, provides a comprehensive, accessible, and at times chilling overview of the most deadly weapon ever invented. Siracusa explains the history of the arms race and the politics of the bomb, ranging from the technology of nuclear weapons, to the revolutionary implications of the H-bomb and the politics of nuclear deterrence. The issues are set against a backdrop of the changing international landscape, from the early days of development, through the Cold War, to the present-day controversy over George W. Bush's National Missile Defense, and the role of nuclear weapons in an Age of Terror. Providing an accessible and eye-opening backdrop to one of the most unsettling aspects of the modern world, this compact introduction is must reading.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.

    Even the simplest system of cause and effect can be subject to chaos, denying us accurate predictions of its behaviour, and sometimes giving rise to astonishing structures of large-scale order. Our growing understanding of Chaos Theory is having fascinating applications in the real world - from technology to global warming, politics, human behaviour, and even gambling on the stock market. Leonard Smith shows that we all have an intuitive understanding of chaotic systems. He uses accessible maths and physics (replacing complex equations with simple examples like pendulums, railway lines, and tossing coins) to explain the theory, and points to numerous examples in philosophy and literature (Edgar Allen Poe, Chang-Tzu, Arthur Conan Doyle) that illuminate the problems. The beauty of fractal patterns and their relation to chaos, as well as the history of chaos, and its uses in the real world and implications for the philosophy of science are all discussed in this Very Short Introduction.

    It requires, in short, an understanding of probability. In this Very Short Introduction, John Haigh introduces the ideas of probability--and the different philosophical approaches to probability--and gives a brief account of the history of development of probability theory, from Galileo and Pascal to Bayes, Laplace, Poisson, and Markov. He describes the basic probability distributions and discusses a wide range of applications in science, economics, and a variety of other contexts such as games and betting. He concludes with an intriguing discussion of coincidences and some curious paradoxes.

    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

    In this concise, crisply written guide, Patricia Aufderheide takes readers along the diverse paths of documentary history and charts the lively, often fierce debates among filmmakers and scholars about the best ways to represent reality and to tell the truths worth telling.Beginning with an overview of the central issues of documentary filmmaking--its definitions and purposes, its forms and founders--Aufderheide focuses on several of its key subgenres, including public affairs films, government propaganda (particularly the works produced during World War II), historical documentaries, and nature films. Her thematic approach allows readers to enter the subject matter through the kinds of films that first attracted them to documentaries, and it permits her to make connections between eras, as well as revealing the ongoing nature of documentary's corecontroversies involving objectivity, advocacy, and bias. Interwoven throughout are discussions of the ethical and practical considerations that arise with every aspect of documentary production. A particularly useful feature of the book is an appended list of 100 great documentaries that anyonewith a serious interest in the genre should see.Drawing on the author's four decades of experience as a film scholar and critic, this book is the perfect introduction not just for teachers and students but also for all thoughtful filmgoers and for those who aspire to make documentaries themselves.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.

    Considering the remarkable achievements chemistry has made, he presents a fascinating, clear, and rigorous exploration of the world of chemistry - its structure, core concepts, and contributions to the material comfort and culture of the modern world.

    Nearly every regime today claims to be democratic, but not all democracies allow free politics, and free politics existed long before democratic franchises. This book is a short account of the history of the doctrine and practice of democracy, from ancient Greece and Rome through the American, French, and Russian revolutions, and of the usages and practices associated with it in the modern world. It argues that democracy is a necessary but not asufficient condition for good government, and that ideas of the rule of law, and of human rights, should in some situations limit democratic claims.

    The author illustrates important aspects of Africa's history with a range of fascinating historical examples, drawn from over 5 millennia across this vast continent. The multitude of topics that the reader will learn about in this succinct work include the unity and diversity of African cultures, slavery, religion, colonial conquest, the diaspora, and the importance of history in understanding contemporary Africa. The book examines questions such as: Who invented the idea of "Africa"? How is African history pieced together, given such a lack of documentary evidence? How did Africa interact with the world 1,000 years ago? Africa has been known as 'the cradle of mankind', and its recoverable history stretches back to the Pharaohs. But the idea of studying African history is itself new, and the authors show why it is still contested and controversial. This VSI, the first concise work of its kind, will prove essential reading for anyone interested in the African continent and the diversity of human history.

    They haunt us, we cherish them, and in our lives we collect more of them with each new experience. Without memory, you would not be able to maintain a relationship, drive your car, talk to your children, read a poem, watch television, or do much ofanything at all. Memory: A Very Short Introduction explores the fascinating intricacies of human memory. Is it one thing or many? Why does it seem to work well sometimes and not others? What happens when it goes wrong? Can it be improved or manipulated through techniques such as mnemonic rhymes orbrain implants? How does memory change as we age? And what about so-called recovered memories--can they be relied upon as a record of what actually happened in our personal past? This book brings together our most recent knowledge to address (in a scientifically rigorous but highly accessible way)these and many other important questions about how memory works, and why we can't live without it.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.