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.

    Not only are galaxies fascinatingastronomical structures in themselves, but their study has revealed much of what we know today about the cosmos, providing a window on the Big Bang and the origins of the Universe. Gribben looks at our own Milky Way Galaxy in detail, from the different kinds of stars that are born within it, tothe origins of its magnificent spiral structure. Perhaps most interesting, Gribben describes the many exciting discoveries have been made about our own galaxy and about those beyond: how a supermassive black hole lurks at the center of every galaxy, how enormous forces are released when galaxiescollide, how distant galaxies provide a window on the early Universe, and how the formation of young galaxies shed needed light on the mysteries of Cold Dark Matter.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.

    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.

    Moreover, groundbreaking research on genes, and especially key families of genes such as the Homeobox genes which controlthe development of body plans, has led to radical changes in the classification of animals. In this Very Short Introduction, Peter Holland presents a cutting-edge tour of the animal kingdom, providing an authoritative summary of the modern view of animal life, its origins, and the new classificationresulting from DNA studies. Beginning with the definition of animals (not obvious in biological terms), Holland takes the reader through the revolutionary new high-level groupings of animals (phyla) based on evolutionary relationships and ancestry. Ranging from corals and sponges to nematodes, seasquirts, and vertebrates, and illuminating many key topics in zoology, this fascinating, brief overview will be of great value to all students of the life sciences as well as providing a concise summary for the interested lay reader.

    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.

    The book discusses environmental issues including pollution control, reducing environmental damage, global climate change policies, questions about how we should balance environmental and economic considerations, and what form government policies should take. In recent years, Smith reveals, many economists have argued for greater use of incentives such as pollution charges and emissions trading rather than more traditional direct regulation of polluters. Including many illustrative case studies, this book offers an illuminating introduction to an exciting field of economics.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.

    Scerri looks at the trends in properties of elements that led to the construction of the periodic table, and how the deeper meaning of its structure gradually became apparent with the development of atomic theory and quantum mechanics, so that physics arguably came to colonize an entirely different science, chemistry.

    The relics of their power, in traditions and behavior, in architecture and the arts, are still all around us. This engaging Very Short Introduction shows how ideas of aristocracy originated in ancient times, were transformed in the middle ages, and have only fallen apart over the last two centuries, following the outbreak of the American and French Revolutions. William Doyle, an authority on eighteen-century European history, here strips away the myths in which aristocracies have always sought to shroud themselves, but he also astutely delineates the true sources of their enduring power. Their outlook and behavior affected the rest of society in innumerable and sometimes surprising ways, but perhaps most surprising was the way in which the centuries-old aristocratic hegemony crumbled away. In this Very Short Introduction William Doyle considers why this happened and what is left today.

    Featuring many striking photos, this Very Short Introduction offers a fascinating portrait of the unique world of each planet as well as an illuminating discussion of moons, asteroids, and Trans-Neptunian objects. Leading planetary scientist David A. Rothery, who has chaired the European Space Agency's Mercury surface and composition working group since 2007, gives a stimulating overview of the origin, nature, and evolution of our Solar System, including the controversial issues of what qualifies as a planet, and what conditions are required for a planetary body to support life. He explains how the surfaces of planets and moons have been sculpted by geology, weather, and impacts by meteors and asteroids. Rothery shows how our knowledge has advanced over the centuries, and how it has expanded at a dramatic rate in recent years, going far beyond our Solar System to explore planets orbiting distant stars.

    In addition, the author discusses the development of the Big Bang theory, and more speculative modern issues like quantum cosmology, superstrings, and dark matter.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.

    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.

    It traces the history and cultural impact of the elements on humankind, and examines why people have long sought to identify thesubstances around them. The book includes chapters on particular elements such as gold, iron, and oxygen, showing how they shaped culture and technology. Looking beyond the Periodic Table, the author examines our relationship with matter, from the uncomplicated vision of the Greek philosophers, whobelieved there were four elements--earth, air, fire, and water--to the work of modern-day scientists in creating elements such as hassium and meitnerium. Packed with anecdotes, The Elements is a highly engaging and entertaining exploration of the fundamental question: what is the world made from?

    While pure mathematics is mostly interested in abstract structures, applied mathematics sits at the interface between this abstract world and the world inwhich we live. This area of mathematics takes its nourishment from society and science and, in turn, provides a unified way to understand problems arising in diverse fields.This Very Short Introduction presents a compact yet comprehensive view of the field of applied mathematics, and explores its relationships with (pure) mathematics, science, and engineering. Explaining the nature of applied mathematics, Alain Goriely discusses its early achievements in physics andengineering, and its development as a separate field after World War II. Using historical examples, current applications, and challenges, Goriely illustrates the particular role that mathematics plays in the modern sciences today and its far-reaching potential.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, andenthusiasm to make interesting and challenging topics highly readable.

    And while research into cancer is bringing huge improvements in the range of options available to cancer patients, these new therapies bring with them massive challenges for healthcare systems struggling to find the huge sums of money for the large numbers of patients involved. This Very Short Introduction explores the facts underlying these figures, starting with the basic facts about the disease before moving on to the bigger picture of the economics and politics of cancer care. Nick James, founder of the CancerHelp UK website, examines the trends in diagnosis of the disease and the constant improvements in treatment techniques that result in better cure rates and increased quality and quantity of life for cancer patients. The book also considers issues surrounding expensive drug development, highlights what can be done to reduce the risk of developing cancer, and discusses the use of complementary and alternative therapies.

    Lyman Sargent discusses the role of utopianism in literature, and in the development of colonies and in immigration. The idea of utopia has become commonplace in social and political thought, both negatively and positively. Some thinkers see a trajectory from utopia to totalitarianism with violence an inevitable part of the mix. Others see utopia directly connected to freedom and as a necessary element in the fight against totalitarianism. In Christianity utopia is labelled as both heretical and as a fundamental part of Christian belief, and such debates are also central to such fields as architecture, town and city planning, and sociology among many othersSargent introduces and summarizes the debates over the utopia in literature, communal studies, social and political theory, and theology.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.