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.

    But there is one other motive which is as strong as any of these — the search for beauty. Mathematics is an art, and as such affords the pleasures which all the arts afford." In this erudite, entertaining college-level text, Morris Kline, Professor Emeritus of Mathematics at New York University, provides the liberal arts student with a detailed treatment of mathematics in a cultural and historical context. The book can also act as a self-study vehicle for advanced high school students and laymen. Professor Kline begins with an overview, tracing the development of mathematics to the ancient Greeks, and following its evolution through the Middle Ages and the Renaissance to the present day. Subsequent chapters focus on specific subject areas, such as "Logic and Mathematics," "Number: The Fundamental Concept," "Parametric Equations and Curvilinear Motion," "The Differential Calculus," and "The Theory of Probability." Each of these sections offers a step-by-step explanation of concepts and then tests the student's understanding with exercises and problems. At the same time, these concepts are linked to pure and applied science, engineering, philosophy, the social sciences or even the arts.In one section, Professor Kline discusses non-Euclidean geometry, ranking it with evolution as one of the "two concepts which have most profoundly revolutionized our intellectual development since the nineteenth century." His lucid treatment of this difficult subject starts in the 1800s with the pioneering work of Gauss, Lobachevsky, Bolyai and Riemann, and moves forward to the theory of relativity, explaining the mathematical, scientific and philosophical aspects of this pivotal breakthrough. Mathematics for the Nonmathematician exemplifies Morris Kline's rare ability to simplify complex subjects for the nonspecialist.

    It unravels complex central questions such as whether terrorists are criminals, whether terrorism is a kind of war, what kind of threat terrorism represents, how far media publicity sustains terrorism, and whether democracy is especially vulnerable to terrorist attack. It examines the historical ideological and local roots of terrorist violence, and the success of specific terrorist and anti-terrorist campaigns in the more distant as well as the recent past.

    Written expressly for "anyone who believes there are big questions out there, but does not know how to approach them," Think provides a sound framework for exploring the most basic themes of philosophy, and for understanding how major philosophers have tackled the questions that have pressed themselves most forcefully on human consciousness.

    Beginning millions of years ago with ancient “ant odometers” and moving through time to our modern-day quest for new dimensions, it covers 250 milestones in mathematical history. Among the numerous delights readers will learn about as they dip into this inviting anthology: cicada-generated prime numbers, magic squares from centuries ago, the discovery of pi and calculus, and the butterfly effect. Each topic gets a lavishly illustrated spread with stunning color art, along with formulas and concepts, fascinating facts about scientists’ lives, and real-world applications of the theorems.

    Their visionary answers flow from the frontiers of psychology, philosophy, economics, physics, sociology, and more. Surprising and enlightening, these insights will revolutionize the way you think about yourself and the world.Contributors include:Daniel Kahneman on the “focusing illusion”Jonah Lehrer on controlling attentionRichard Dawkins on experimentationAubrey De Grey on conquering our fear of the unknownMartin Seligman on the ingredients of well-beingNicholas Carr on managing “cognitive load”Steven Pinker on win-win negotiatingDaniel Goleman on understanding our connection to the natural worldMatt Ridley on tapping collective intelligenceLisa Randall on effective theorizingBrian Eno on “ecological vision”J. Craig Venter on the multiple possible origins of life  Helen Fisher on temperamentSam Harris on the flow of thoughtLawrence Krauss on living with uncertainty

    This Very Short Introduction offers an indispensable starting point for anyone who needs to quickly know the themes and controversies that have shaped modern China. Prize-winning author and scholar Rana Mitter examines the modern history, politics, economy, and thriving cultural scene of contemporary China, and its relations with the wider world. This lively guide covers a range of social issues from the decline of footbinding and the position of women in society, to the influence of television and film, and the role of the overseas Chinese diaspora. It covers many prominent figures as well, such as the Communist leaders, the last emperors, and prominent writers and artists throughout China's history.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

    Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be reasoned out--from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft--indeed, brilliant--instructions on stripping away irrelevancies and going straight to the heart of the problem.

    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.

    Offering the first brief introduction to Machiavelli's thought to appear in twenty-five years, Skinner focuses on his three major works, The Prince, Discourses, and The History of Florence. He discusses the influence of Roman moral thought on Machiavelli, concentrating on the extent to which Machiavelli's teachings represent a reaction against this tradition. Placing Machiavelli in the proper social and intellectual context, Skinner reveals the extraordinary originality of his attack on the prevailing moral and political assumptions of his age. 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.

    Many new exercises introduced in this edition help supplement and support explanations, aid in review, and make the book visually stimulating. This edition also includes a revised Logic tutorial on CD-Rom--further simplifying the study of logic. Includes many fascinating illustrations taken from the history of science as well as from contemporary research in the physical and biological sciences, plus introduces an abundance of new exercises throughout, complete with solutions for the first exercise in a set. Appropriate for those in business, education, political, or psychology careers.

    In the aftermath, Harris discovered that most people - from religious fundamentalists to non-believing scientists - agree on one point: science has nothing to say on the subject of human values. Indeed, our failure to address questions of meaning and morality through science has now become the most common justification for religious faith. It is also the primary reason why so many secularists and religious moderates feel obligated to "respect" the hardened superstitions of their more devout neighbors.In this explosive new book, Sam Harris tears down the wall between scientific facts and human values, arguing that most people are simply mistaken about the relationship between morality and the rest of human knowledge. Harris urges us to think about morality in terms of human and animal well-being, viewing the experiences of conscious creatures as peaks and valleys on a "moral landscape." Because there are definite facts to be known about where we fall on this landscape, Harris foresees a time when science will no longer limit itself to merely describing what people do in the name of "morality"; in principle, science should be able to tell us what we ought to do to live the best lives possible.Bringing a fresh perspective to age-old questions of right and wrong and good and evil, Harris demonstrates that we already know enough about the human brain and its relationship to events in the world to say that there are right and wrong answers to the most pressing questions of human life. Because such answers exist, moral relativism is simply false - and comes at increasing cost to humanity. And the intrusions of religion into the sphere of human values can be finally repelled: for just as there is no such thing as Christian physics or Muslim algebra, there can be no Christian or Muslim morality.Using his expertise in philosophy and neuroscience, along with his experience on the front lines of our "culture wars," Harris delivers a game-changing book about the future of science and about the real basis of human cooperation.

    It remains the one of the most widely read books about science to come out of the twentieth century.(Note: the book was first published in 1934, in German, with the title Logik der Forschung. It was "reformulated" into English in 1959. See Wikipedia for details.)

    Indeed, from childhood most of us develop some mental image of a witch--usually an old woman, mysterious and malignant. But why do witches still feature so heavily in our cultures and consciousness? From Halloween superstitions to literary references such as Faust and, of course, Harry Potter, witches seem ever-present in our lives. In this Very Short Introduction, Malcolm Gaskill takes a long historical perspective, from the ancient world to contemporary paganism. This is a book about the strangeness of the past, and about contrasts and change; but it's also about affinity and continuity. He reveals that witchcraft is multi-faceted, that it has always meant different things to different people, and that in every age it has raised questions about the distinction between fantasy and reality, faith and proof. Delving into court records, telling anecdotes, and challenging myths, Gaskill re-examines received wisdom, especially concerning the European witch-hunts of the sixteenth and seventeenth centuries. He also explores the modern memory and reinvention of witchcraft--as history, religion, fiction, and metaphor.

    The material is arranged chronologically beginning with archaic origins and covers Egyptian, Mesopotamian, Greek, Chinese, Indian, Arabic and European contributions done to the nineteenth century and present day. There are revised references and bibliographies and revised and expanded chapters on the nineteeth and twentieth centuries.