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.

    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.

    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.

    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.

    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.

    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 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.

    Indeed, without religion, our lives are left without meaning and are likely to degenerate into moral chaos. In this Very Short Introduction, philosopher Stephen Law explains why these claims are false and why humanism--though a rejection of religion--nevertheless provides both a moral basis and a meaning for our lives. Indeed, Law shows that humanism is a quite positive alternative to religion. The humanist is not simply one who denies the truth of religious belief, but one who believes we can enjoy meaningful, purposeful, and good lives without religion. And far from embracing moral nihilism, humanists are often deeply committed people, to be found at the forefront of many important ethical campaigns. Law goes on to show how the term humanism is used in a variety of ways. Marx described himself as a humanist but the Pope has also expressed support for what he calls humanism. Law argues for humanism as it is most commonly understood--as a positive, moral form of atheism.

    Jan Westerhoff shows that the question "what is real?" is not some esoteric puzzle that only philosophers ponder. Scientists also ask this question when they investigate whether candidates for the fundamental constituents of matter are actually "out there" or just a mere abstraction from a successful theory and cognitive scientists ask it when trying to find out which set of the bewildering array of data processed by our brain could constitute the basis for the self.

    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.

    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.

    Allen and Cowling start with the simple "prokaryotic" cell--cells with no nucleus--and show how the bodies of more complex plants and animals consist of billions of "eukaryotic" cells, of varying kinds, adapted to fill different roles--red blood cells, muscle cells, branched neurons. The authors also show that each cell is an astonishingly complex chemical factory, the activities of which we have only begun to unravel in the past fifty years.

    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?

    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.

    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.