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.

    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.

    The key difference is often held to be that the Greeks and Romans practiced a "Western Way of War," in which the aim is an open, decisive battle--won by courage instilled, in part, by discipline. Here, Harry Sidebottom looks at how this Western Way of War was constructed and maintained by the Greeks and Romans and why this concept is so prevalent today. All aspects of ancient warfare are thoroughly examined--from philosophy and strategy to the technical skills needed to fight. Sidebottom examines war in the wider context, showing how wars were able to shape classical society, and how an individual's identity was sometimes constructed by war, as in the case of the Christian soldier fighting in God's name. He also explores the ways in which ancient society thought about conflict: Can a war be just? Why was siege warfare particularly bloody? What role did divine intervention play in the outcome of a battle? Taking fascinating examples from the iliad, Tacitus, and the Persian Wars, Sidebottom uses arresting anecdotes and striking visual images to show that any understanding of ancient war is an ongoing process of interpretation.

    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.

    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.

    This book examines the reasons for those views, and explains why ideologies deserve respect as a major form of political thinking. It investigates the centrality of ideologyboth as a political phenomenon and as an organizing framework of political thought and action. It explores the changing understandings of ideology as a concept, and the arguments of the main ideologies. By employing the latest insights from a range of disciplines, the reader is introduced to thevitality and force of a crucial resource at the disposal of societies, through which sense and purpose is assigned to the political world.

    Echevarria II presents a fascinating account of the "art of the general." Drawing on historical examples, from Hannibal's war against Rome to Napoleon's victory at Austerlitz, from the Allies' campaign to overwhelm Hitler's fortress to the terror attacks of September 11, Echevarria vividly describes the major types of military strategy and their advantages and disadvantages.Clear and engaging, this book shows that military strategy is essential for understanding major events of the past and becomes even more critical today, in a world increasingly threatened by weapons of mass destruction, terrorist attacks, and new dimensions of conflict such as cyberwar and space.

    But how much do these types of entertainment really tell us about recent scientific discoveries and the latest research into the world of the dinosaur?This is the first book explain how scientists have been able to put together a picture of how dinosaurs looked, what they ate, and how they moved and interacted with each other. Taking a new approach to the subject, David Norman combines different areas of science, such as anatomy, genetics, forensics, and engineering design, to piece together the latest evidence of how animal life evolved on earth. Norman engagingly lays out the history of dinosaur research, from the speculation over ancient myths about dragons, to the latest virtual reality animation sequences and engineering design analysis. He also discusses the role that informed speculation and luck has played in many of the major discoveries.This book is a fantastic introduction for those just beginning to take an interest in dinosaurs and a must-read for true dinosaur-lovers who want to know not just the latest theories and discoveries, but how scientists achieved them.

    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 tackles many questions, such as: What accounts for the perpetuation of ethnic and religious conflict in Ireland? Why has armedviolence proven so hard to control? Who are the major figures and issues in the conflict? Can we expect more Northern Irelands in the future?

    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.

    After meeting with Americans on extensive travels in the United States, and intense study of documents and authorities, he authored the landmark Democracy in America, publishing its two volumes in 1835 and 1840. Ever since, this book has been the best source for every serious attempt to understand America and democracy itself. Yet Tocqueville himself remains a mystery behind the elegance of his style. Now one of our leading authorities on Tocqueville explains him in this splendid new entry in Oxford's acclaimed Very Short Introduction series. Harvey Mansfield addresses his subject as a thinker, clearly and incisively exploring Tocqueville's writings--not only his masterpiece, but also his secret Recollections, intended for posterity alone, and his unfinished work on his native France, The Old Regime and the Revolution. Tocqueville was a liberal, Mansfield writes, but not of the usual sort. The many elements of his life found expression in his thought: his aristocratic ancestry, his ventures in politics, his voyages abroad, his hopes and fears for America, and his disappointment with France. All his writings show a passion for political liberty and insistence on human greatness. Perhaps most important, he saw liberty not in theories, but in the practice of self-government in America. Ever an opponent of abstraction, he offered an analysis that forces us to consider what we actually do in our politics--suggesting that theory itself may be an enemy of freedom. And that, Mansfield writes, makes him a vitally important thinker for today. Translator of an authoritative edition of Democracy in America, Harvey Mansfield here offers the fruit of decades of research and reflection in a clear, insightful, and marvelously compact introduction.

    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

    In its heyday during the late 1990s, neoliberalism emerged as the world's dominant economic paradigm, stretching from the Anglo-American heartlands of capitalism to the former communist bloc all the way to the developing regions of the global South. Today, however, neoliberalism has been discredited as the global economy, built on its principles, has been shaken to its core by the worst financial calamity since the 1930s. Is neoliberalism doomed or will it regain its former status? Will the new U.S. President Barack Obama embrace or reject the neoliberal agenda of his predecessors in the White House? And how will his decision impact the current global economic order? Is there a viable alternative to neoliberalism? Exploring the origins, core claims, and various forms of neoliberalism, this Very Short Introduction offers a concise and accessible introduction to one of the most debated "isms" of our time.

    Paul Slack assesses its causes, which have often been disputed and are now being illuminated by microbiologists and archaeologists, and he looks at possible reasons for its periodic disappearance from whole continents. He shows what plague meant for those who suffered from it, and how governments began to fight against it and in doing so invented modern notions of public health. His focus throughout the book is on how people coped with death and disease in epidemic crises.