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.

    But as Morris Rossabi reveals in this VeryShort Introduction, within two generations of their bloody conquests, the Mongols evolved from conquerors and predators to wise rulers who devised policies to foster the economies of the lands they had subjugated. By adopting political and economic institutions familiar to the local populations andrecruiting native officials, they won over many of their non-Mongol subjects. In addition, Mongol nobles were ardent patrons of art and culture, supporting the production of Chinese porcelains and textiles, Iranian tiles and illustrated manuscripts, and Russian metalwork. Perhaps most important, thepeace imposed by the Mongols on much of Asia and their promotion of trade resulted in considerable interaction among merchants, scientists, artists, and missionaries of different ethnic groups--including Europeans. Modern Eurasian and perhaps global history starts with the Mongol empire.

    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.

    The book describes dramatic breakthroughs in our knowledge of how sleep occurs, what it does, and what happens to our health if we do not have enough. The authors consider the impact of modern society, examining the relationship between sleep and our 24/7 culture.

    However, their impact has not been limited to debates about geology and evolution: attempts to explain their existence has shaken religion at its very roots, and they have remained a subject of ceaseless fascination for people of all ages and backgrounds. In this readable and wide-ranging book, Keith Thomson provides a remarkably all-encompassing explanation of fossils as a phenomenon. How did Darwin use fossils to support his theory of evolution? What are living fossils? What fossils will we leave behind for future generations to examine? Beyond the scientific aspects, Thomson highlights the impact of fossils on philosophy and mythology, our concept of time, and today's popular culture. From the black market to the Piltdown Man, and from mythological dragons to living dinosaurs, fossils hold a permanent place in the popular imagination.

    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.

    Supreme Court and its justices as a correspondent for the New York Times. In this Very Short Introduction, she draws on her deep knowledge of the court's history and of its written and unwritten rules to show readers how the Supreme Court really works.Greenhouse offers a fascinating institutional biography of a place and its people--men and women who exercise great power but whose names and faces are unrecognized by many Americans and whose work often appears cloaked in mystery. How do cases get to the Supreme Court? How do the justices go about deciding them? What special role does the chief justice play? What do the law clerks do? How does the court relate to the other branches of government? Greenhouse answers these questions by depicting the justices as they confront deep constitutional issues or wrestle with the meaning of confusing federal statutes. Throughout, the author examines many individual Supreme Court cases to illustrate points under discussion, ranging from Marbury v. Madison, the seminal case which established judicial review, to the recent District of Columbia v. Heller (2008), which struck down the District of Columbia's gun-control statute and which was, surprisingly, the first time in its history that the Court issued an authoritative interpretation of the Second Amendment. To add perspective, Greenhouse also compares the Court to foreign courts, revealing interesting differences. For instance, no other country in the world has chosen to bestow life tenure on its judges.A superb overview packed with telling details, this volume offers a matchless introduction to one of the pillars of American government.

    Indeed it could be said that all history is colonial history, if one takes a broad enough definition and goes far enough back. And although the great historic imperial systems--the land-based Russian one as well as the seaborneempires of western European powers--have collapsed during the past half century, their legacies shape almost every aspect of life on a global scale. Meanwhile there is fierce argument, and much speculation, about what has replaced the old territorial empires in world politics. Do the United Statesand its allies, transnational companies, financial and media institutions, or more broadly the forces of globalization, constitute a new imperial system?Stephen Howe interprets the meaning of the idea of empire through the ages, disentangling the multiple uses and abuses of the labels empire and colonialism, etc., and examines the aftermath of imperialism on the contemporary world.

    Explaining the nature of genetic variation in the human population, how hereditary factors were identified as molecules of DNA, and how certain specific mutations can lead to disease, Slack highlights how DNA variants are used to trace human ancestry and migration, and can also be used by forensic scientists to identify individuals in crime. Slack also explores issues such as the role of genetic heritability and IQ as well as the changes that occur in the genes of populations during evolution. An ideal guide for anyone curious about what genes are and how genetics can be put to use, this Very Short Introduction demonstrates the ways in which the gene concept has been understood and used by molecular biologists, population biologists, and social scientists around the world. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

    Travel fast enough and you could weigh as much as a jumbo jet, be flattened thinner than a CD without feeling a thing-and live forever! As for the angles of a triangle, they do not always have to add up to 180 degrees. And then, of course, there are black holes. These are but a few of the extraordinary consequences of Einstein's theory of relativity. It is now over a hundred years since he made these discoveries, and yet the general public is still largely unaware of them. Filled with illuminating anecdotes and fascinating accounts of experiments, this book aims to introduce the interested lay person to the subject of relativity in a way which is accessible and engaging and at the same time scientifically rigorous. With relatively few mathematical equations--nothing more complicated than the Pythagoras's Theorem--this VSI packs a lot time into very little space, and for anyone who has felt intimidated by Einstein's groundbreaking theory, it offers the perfect place to start. 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 has been explained as a combination of romance, science and prophecy; as a genre based on an imagined alternative to the reader's environment; and as a form of fantastic fiction and historical literature. It has also been argued that science fiction narratives are the most engaged, socially relevant, and responsive to the modern technological environment. This Very Short Introduction doesn't offer a history of science fiction, but instead ties examples of science fiction to different historical moments, in order to demonstrate how science fiction has evolved over time. David Seed looks not only at literature, but also at drama and poetry, as well as film. Examining recurrent themes in science fiction he looks at voyages into space, the concept of the alien and alternative social identities, the role of technology in science fiction, and its relation to time - in the past, present, and future.

    These, along with the introduction of the oral contraceptive, have altered all of our lives. There has also been an increase in the recreational use and abuse of drugs in the Western world. This Very Short Introduction gives a non-technical account of how drugs act on the body and how therapeutic drugs are developed and tested, then goes on to review both legal (prescription, alcohol, nicotine, and caffeine) and illegal drugs, and discuss current ideas about why some drugs are addictive, and whether drug laws need reform.

    As a concept and a practice, it has attracted the attention of theologians, anthropologists, psychologists, sociologists, artists, and historians over the centuries. This Very Short Introduction explains why. Magic has been defined in terms of the false religions of others, as an evolutionary stage in human thought, a universal state of mind, and a liberating expression of the imagination. For hundreds of millions of people today, no matter their religious persuasion, magic is a real force that helps them to overcome misfortune, poverty, and illness. Indeed, with magic as relevant today as it ever was, it raises questions about the meaning of human progress.

    In this Very Short Introduction, renowned evolutionary scholar Bernard Wood traces the history of paleoanthropology from its beginnings inthe eighteenth century to today's latest fossil finds. Along the way we are introduced to the lively cast of characters, past and present, involved in evolutionary research. Although concentrating on the fossil evidence for human evolution, the book also covers the latest genetic evidence aboutregional variations in the modern human genome that relate to our evolutionary history. Wood draws on over thirty years of experience to provide an insiders view of the field, and demonstrates that our understanding of human evolution is critically dependent on advances in related sciences such aspaleoclimatology, geochronology, systematics, genetics, and developmental biology. This is an ideal introduction for anyone interested in the origins and development of humankind.

    Readers meet a people highly skilled in sculpture, astronomy, city planning, poetry, and philosophy, who were also profoundly committed tocosmic regeneration through the thrust of the ceremonial knife and through warfare. Dav�d Carrasco looks beyond Spanish accounts that have colored much of the Western narrative to let Aztec voices speak about their origin stories, the cosmic significance of their capital city, their methods of childrearing, and the contributions women made to daily life and the empire. Carrasco discusses the arrival of the Spaniards, contrasts Aztec mythical traditions about the origins of their city with actual urban life in Mesoamerica, and outlines the rise of the Aztec empire. He also explores Aztecreligion, which provided both justification for and alternatives to warfare, sacrifice, and imperialism, and he sheds light on Aztec poetry, philosophy, painting, and especially monumental sculpture and architecture. He concludes by looking at how the Aztecs have been portrayed in Western thought, art, film, and literature as well as in Latino culture and arts.