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.

    Now, in Lincoln: A Very Short Introduction, the award-winning Lincoln authority Allen C. Guelzo offers a penetrating look into the mind of one of our greatest presidents. If Lincoln was famous for reading aloud from joke books, Guelzo shows that he also plunged deeply into the mainstream of nineteenth-century liberal democratic thought. Guelzo takes us on a wide-ranging exploration of problems that confronted Lincoln and liberal democracy--equality, opportunity, the rule of law, slavery, freedom, peace, and his legacy. The book sets these problems and Lincoln's responses against the larger world of American and trans-Atlantic liberal democracy in the 19th century, comparing Lincoln not just to Andrew Jackson or John Calhoun, but to British thinkers such as Richard Cobden, Jeremy Bentham, and John Bright, and to French observers Alexis de Tocqueville and Fran ois Guizot. The Lincoln we meet here is an Enlightenment figure who struggled to create a common ground between a people focused on individual rights and a society eager to establish a certain moral, philosophical, and intellectual bedrock. Lincoln insisted that liberal democracy had a higher purpose, which was the realization of a morally right political order. But how to interject that sense of moral order into a system that values personal self-satisfaction--"the pursuit of happiness"--remains a fundamental dilemma even today. Abraham Lincoln was a man who, according to his friend and biographer William Henry Herndon, "lived in the mind." Guelzo paints a marvelous portrait of this Lincoln--Lincoln the man of ideas--providing new insights into one of the giants of American history.

    From randomized clinical trials in medical research, to statistical models of risk in banking and hedge fund industries, to the statistical tools used to probe vast astronomical databases, the field of statistics has become centrally important to how we understand our world. But the discipline underlying all these is not the dull statistics of the popular imagination. Long gone are the days of manual arithmetic manipulation. Nowadays statistics is a dynamic discipline, revolutionized by the computer, which uses advanced software tools to probe numerical data, seeking structures, patterns, and relationships. This Very Short Introduction sets the study of statistics in context, describing its history and giving examples of its impact, summarizes methods of gathering and evaluating data, and explains the role played by the science of chance, of probability, in statistical methods. The book also explores deep philosophical issues of induction--how we use statistics to discern the true nature of reality from the limited observations we necessarily must make.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.

    Insights are drawn from psychology, neuroscience, genetics, epidemiology and clinical trials. Providing a fascinating illustration of the discussion are two interviews conducted specifically for the book, with the actor, writer and director Michael Palin and former England football manager Graham Taylor.

    In this Very Short Introduction, Robert C. Allen shows how the interplay of geography, globalization, technological change, and economic policy has determined the wealth and poverty of nations. Allen shows how the industrial revolution was Britain's path-breaking response to the challenge of globalization. Western Europe and North America joined Britain to form a club of rich nations, pursuing four polices--creating a national market by abolishing internal tariffs and investing in transportation, erecting an external tariff to protect their fledgling industries from British competition, creating banks to stabilize the currency and mobilize domestic savings for investment, and promoting mass education to prepare people for industrial work. Together these countries pioneered new technologies that have made them ever richer. A few countries--Japan, Soviet Russia, South Korea, Taiwan, and perhaps China--have caught up with the West through creative responses to the technological challenge and with Big Push industrialization that has achieved rapid growth through coordinated investment.

    This book describes what schizophrenia is really like, how the illness progresses, and the treatments that have been applied. It also summarizes the most up-to-date knowledge available about the biological bases of this disorder. Finally it attempts to give some idea of what it is like to have schizophrenia and what this disorder tells us about the relationship between mind and brain.

    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.

    Short, clear discussions on the mechanical workings of the brain are offered and the details of brain science are covered in an accessible style. Explanations of the more familiar implications of the brain's actions, such as memories, perceptions, and motor control are integrated throughout the book. It has chapters on brain processes and the causes of "altered mental states," as well as a final chapter that discusses possible future developments in neuroscience, touching on artificial intelligence, gene therapy, the importance of the Human Genome Project, drugs by design, and transplants. Up-to-date coverage of the newest developments in brain research and suggestions for future research on the brain are also included. 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.

    This Very Short Introduction provides an accessible, thoughtful and thought-provoking introduction to major debates around sexuality in the modern world, highlighting the social and political aspects of sexuality. It critically explores different ways of defining and thinking about sexuality and shows that many of our assumptions about what is "natural" in the sexual domain have, in reality, varied greatly in different historical or cultural contexts. The volume also examines ways in which governments have tried to regulate citizens' sexualities in the past-through policies and laws concerning public health, HIV/Aids, prostitution, and sex education-paying special attention to the particular zeal with which women's sexuality has been policed. The volume concludes by discussing political activism around sexuality more widely, focusing on the ways in which feminists, lesbians and gay men, as well as religious fundamentalists have transformed our ways of thinking about sexuality in the past few decades. 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.

    Despite this, and perhaps in part because of its prevalence in the media, it is often denigrated as trivial and superficial, as a sign of vanity and narcissism. Written by a highly regarded authority on twentieth-century fashion, this Very Short Introduction offer a wide-ranging and revealing look at fashion that discusses everything from production and design, to couture and retailing, to the wider role of fashion in society. This lively book illuminates the structure of the fashion industry and the range of professionals involved in its creation, and it provides cogent insight into its historical, social and cultural contexts. It also sheds light on how fashion has developed, while raising questions about its ethical and controversial aspects, such as the use of fur, exploitative trading, and poor working conditions for laborers.

    In this Very Short Introduction, Michael Wood offers a wealth of insight into the nature of film, considering its role and impact on society as well as its future in the digital age. As Wood notes, film is many things, but it has become above all a means of telling stories through images and sounds. The stories are often quite false, frankly and beautifully fantastic, and they are sometimes insistently said to be true. Indeed, many condemn movies as an instrument of illusion, an emphatic way of seeing what is not there. And others celebrate the reverse: that film brings us closest to the world as it actually is. "Photography is truth," a character says in a film by Jean-Luc Godard. "And cinema is the truth twenty-four times per second." But they are stories in either case, and there are very few films, Wood observes, even in avant-garde art, that don't imply or quietly slip into narrative.

    A criminal case can often hinge on a piece of evidence such as a hair, a blood trace, a bit of saliva on a cigarette butt, or the telltale mark of a tire tread. High profile cases have stoked this interest in recent years and some of the most popular shows on television--such as CSI: Crime Scene Investigation and its raft of spin-offs--attest to the enduring popularity of forensic science as a form of grisly entertainment. This Very Short Introduction looks at the nature of forensic science, examining what forensic science is, how it is used in the investigation of crime, how crime scenes are managed, how forensic scientists work, the different techniques used to recover evidence, and the range of methods available for analysis. It also considers how forensic science serves the criminal justice system and the challenges of communicating complex scientific evidence in a court of law.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.

    In this Very Short Introduction, Michael Cook provides a lucid and direct account of the significance of the Koran both in the modern world and inthat of traditional Islam. He gives vivid accounts of its role in Muslim civilization, illustrates the diversity of interpretations championed by traditional and modern commentators, discusses the processes by which the book took shape, and compares it to other scriptures and classics of thehistoric cultures of Eurasia.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 short and accessible introduction provides an invaluable tool with which to think about the ethical values that lie at the heart of medicine.Tony Hope deals with thorny moral issues, including euthanasia and the morality of killing. He also explores political questions, such as how we can make sure health care resources are distributed fairly. Each chapter in the book considers a different issue, for example, genetics, modern reproductive technologies, resource allocation, mental health, and medical research. Each section also discusses controversial questions such as: Who should have access to reproductive technology? Is it right to fund expensive drug treatment for individuals? Should treatment for mental illness be imposed on patients without their consent? Considering a wide range of questions of medical ethics, this Very Short Introduction will help to explain some of the confusing issues facing the field of medicine today.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.

    It is a word with which we are universally familiar, and a condition that haunts the human imagination. In this Very Short Introduction, Andrew Scull provides a provocative and entertaining examination of the social, cultural, medical, and artistic responses to mental disturbance across more than two millennia, concluding with some observations on the contemporary accounts of mental illness. He shows that through the centuries, in poetry and in prose, in drama and in the visual arts, madness has been on display for all to see. He also describes how a whole industry has grown up, devoted to its management and suppression. Perhaps most important, he conveys how madness profoundly disturbs our common sense assumptions; threatens the social order, both symbolically and practically; creates almost unbearable disruptions in the texture of daily living; and turns our experience and our expectations upside down. Throughout this fascinating history, many fascinating and arresting pictures illuminate the overall portrait of madness in its various contexts.