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.

    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.

    In this account of his life and work A. C. Grayling introduces both his technical contributions to logic and philosophy, and his wide-ranging views on education, politics, war, and sexual morality. Russell is credited with being one of the prime movers of Analytic Philosophy, and with having played a part in the revolution in social attitudes witnessed throughout the twentieth-century world. This introduction gives a clear survey of Russell's achievements across a wide ange.

    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.

    How then did it come to be that there was a Second World War causing twiceas much loss of life and more destruction than any other previous conflict? In this Very Short Introduction, Gerhard L. Weinberg provides an introduction to the origins, course, and impact of the war on those who fought and the ordinary citizens who lived through it. Starting by looking at the inter-war years and the German invasion of Poland in September 1939, he examines how the war progressed by examining a number of key events, including the war in the West in 1940, Barbarossa, the German Invasion of the Soviet Union, the expansion of Japan's war with China, developments on the home front, and the Allied victory from 1944-45. Exploring the costs and effects of the war, Weinberg concludes by considering the long-lasting mark World War II has left on society today. 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.

    As humans, we decipher the meaning of newspaper articles, books, legal matters, religious texts, political speeches, emails, and even dinner conversations every day . But how is knowledge mediated through these forms? What constitutes the process of interpretation? And how do we draw meaning from the world around us so that we might understand ourposition in it?In this Very Short Introduction Jens Zimmermann traces the history of hermeneutic theory, setting out its key elements, and demonstrating how they can be applied to a broad range of disciplines: theology; literature; law; and natural and social sciences. Demonstrating the longstanding and wide-ranging necessity of interpretation, Zimmermann reveals its significance in our current social and political landscape.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.

    Then they came to Earth and amnesia set in: they forgot they were from different planets.Based on years of successful counseling of couples and individuals, Men Are from Mars, Women Are from Venus has helped millions of couples transform their relationships. Now viewed as a modern classic, this phenomenal book has helped men and women realize how different they really are and how to communicate their needs in such a way that conflict doesn't arise and intimacy is given every chance to grow!!!!

    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

    The first great works of this repertory were written in the twelfth century in northern France, and now, at the beginning of the twenty-first century, this literature includes authors writing in many parts of the world, ranging from the Caribbean to Western Africa. This Very Short Introduction gives the reader a basic orientation to this lively literary world by focusing on texts (epics, novels, plays, poems, screenplays) that concern protagonists whose adventures and conflicts reveal shifts in literary and social practices. From the hero of the medieval Song of Roland to the Caribbean heroines of I, Tituba, Black Witch of Salem or the European expatriate in Japan in Fear and Trembling, these problematic protagonists allow us to understand what interests writers and readers across the wide world of French literature.

    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.

    From deserts to jungles, from deep caves to mountain tops, from pebble tools to satellite photographs, from excavation to abstract theory, archaeology interacts with nearly every other discipline in its attempts to reconstruct the past.

    Yet, the science underpinning this technology is less visible and little understood outside the professional computer science community. As a scientific discipline, computer science stands alongside the likes of molecular biology and cognitive science as one of the most significant new sciences of the post Second World War era.In this Very Short Introduction, Subrata Dasgupta sheds light on these lesser known areas and considers the conceptual basis of computer science. Discussing algorithms, programming, and sequential and parallel processing, he considers emerging modern ideas such as biological computing and cognitive modelling, challenging the idea of computer science as a science of the artificial.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.

    It is also one of the most controversial. It clashes, or is widely thought to clash, with many conventional moral views, and with human rights when they are seen as inviolable. Would it, for example, be right to torture a suspected terrorist in order to prevent an attack that could kill and injure a large number of innocent people? In this Very Short Introduction Peter Singer and Katarzyna de Lazari-Radek provide an authoritative account of the nature of utilitarianism, from its nineteenth-century origins, to its justification and its varieties. Considering how utilitarians can respond to objections that are often regarded as devastating, they explore the utilitarian answer to the question of whether torture can ever be justified. They also discuss what it is that utilitarians should seek to maximize, paying special attention to the classical utilitarian view that only pleasure or happiness is of intrinsic value.Singer and de Lazari-Radek conclude by analyzing the continuing importance of utilitarianism in the world, indicating how it is a force for new thinking on contemporary moral challenges like global poverty, the treatment of animals, climate change, reducing the risk of human extinction, end-of-life decisions for terminally-ill patients, and the shift towards assessing the success of government policies in terms of their impact on happiness.

    Growing understanding of the immune system, and especially the creation of immune memory (long lasting protection), which can be harnessed in the design of vaccines, have been major breakthroughs in medicine.In this Very Short Introduction, Paul Klenerman describes the immune system, and how it works in health and disease. In particular he focuses on the human immune system, considering how it evolved, the basic rules that govern its behavior, and the major health threats where it is important. Theimmune system comprises a series of organs, cells and chemical messengers which work together as a team to provide defence against infection. Klenerman discusses these components, the critical signals that trigger them and how they exert their protective effects, including so-called innate immuneresponses, which react very fast to infection, and adaptive immune responses, which have huge diversity and a capacity to recognize and defend against a massive array of micro-organisms. Klenerman also considers what happens when our immune systems fail to be activated effectively, leading toserious infections, problems with inherited diseases, and also HIV/AIDS. At the opposite extreme, as Klenerman shows, an over-exaggerated immune response leads to inflammatory diseases such as Multiple Sclerosis and Rheumatoid Arthritis, as well as allergy and asthma. Finally he looks at the Immunesystem v2.o - how immune therapies and vaccines can be advanced to protect us against the major diseases of the 21st century.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.

    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.