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.

    It examines a distinctive stage in the development of capitalism that began in the 1980s, in order to understand where we are now and how capitalism has evolved since. The book discusses the crisis tendencies of capitalism--including the S.E. Asian banking crisis, the collapse of the Russian economy, and the 1997-1998 global financial crisis--asking whether capitalism is doomed to fail. In the end, the author ruminates on a possible alternative to capitalism, discussing socialism, communal and cooperative experiments, and alternatives proposed by environmentalists.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.

    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.

    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.

    In this accessible and stimulating Very Short Introduction, Martin Bunton illuminates the history of the problem, reducing it to its very essence. Adopting a fresh and original approach, Bunton explores the Palestinian-Israeli dispute in twenty-year segments, to highlight the historical complexity of the conflict throughout successive decades. Each chapter starts with an examination of the relationships among people and events that marked particular years as historical stepping stones in the evolution of the conflict, including the 1897 Basle Congress, the 1917 Balfour Declaration and British occupation of Palestine, and the 1947 UN Partition Plan and the war for Palestine.Providing a clear and fair exploration of the main issues, Bunton explores not only the historical basis of the conflict, but also looks at how and why partition has been so difficult and how efforts to restore peace continue today.About the Series:Oxford's Very Short Introductions series offers concise and original introductions to a wide range of subjects--from Islam to Sociology, Politics to Classics, Literary Theory to History, and Archaeology to the Bible. Not simply a textbook of definitions, each volume in this series provides trenchant and provocative--yet always balanced and complete--discussions of the central issues in a given discipline or field. Every Very Short Introduction gives a readable evolution of the subject in question, demonstrating how the subject has developed and how it has influenced society. Eventually, the series will encompass every major academic discipline, offering all students an accessible and abundant reference library. Whatever the area of study that one deems important or appealing, whatever the topic that fascinates the general reader, the Very Short Introductions series has a handy and affordable guide that will likely prove indispensable.

    "This is the story of England's birth. A great story, beautifully told." (Bernard Cornwell, author of The Pale Horseman)Alfred was England's first kin, and his rule spanned troubled times. As his shores sat under constant threat from Viking marauders, his life was similarly imperiled by conspiracies in his own court. He was an extraordinary character - a soldier, scholar, and statesman like no other in English history - and out of adversity he forged a new kind of nation. Justin Pollard's enthralling account strips back centuries of myth to reveal the individual behind the legend. He offers a radical new interpretation of what inspired Alfred to create England and how it how it has colored the nation's history to the present day.

    Insights are drawn from psychology, neuroscience, genetics, epidemiology and clinical trials. Providing a fascinating illustration of the discussion are two interviews conducted specifically for the book, with the actor, writer and director Michael Palin and former England football manager Graham Taylor.

    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.

    His teachings had a profound effect on Medieval scholarship, Renaissance humanism, and the religious controversies of both the Reformation and the Counter-Reformation. Here, Henry Chadwick places Augustine in his philosophical and religious context and traces the history of his influence on Western thought, both within and beyond the Christian tradition. A handy account to one of the greatest religious thinkers, this Very Short Introduction is both a useful guide for the one who seeks to know Augustine and a fine companion for the one who wishes to know him better.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.

    Edward's controversial match brought his queen's large family to court and into the thick of the Wars of the Roses. This is the story of the family whose fates would be inextricably intertwined with the fall of the Plantagenets and the rise of the Tudors: Richard, the squire whose marriage to a duchess would one day cost him his head; Jacquetta, mother to the queen and accused witch; Elizabeth, the commoner whose royal destiny would cost her three of her sons; Anthony, the scholar and jouster who was one of Richard III's first victims; and Edward, whose military exploits would win him the admiration of Ferdinand and Isabella. This history includes little-known material such as private letters and wills.

    Was the Battle of Hastings a French victory?Non! William the Conqueror was Norman and hated the French.Were the Brits really responsible for the death of Joan of Arc?Non! The French sentenced her to death for wearing trousers.Was the guillotine a French invention?Non! It was invented in Yorkshire.Ten centuries' worth of French historical 'facts' bite the dust as Stephen Clarke looks at what has really been going on since 1066 ...