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.

    Readers will find an enlightening history of the vacuum: how the efforts to make a better vacuum led to the discovery of the electron; the ideas of Newton, Mach, and Einstein on the nature of space and time; the mysterious aether and how Einstein did away with it; and the latest ideas that the vacuum is filled with the Higgs field. The story ranges from the absolute zero of temperature and the seething vacuum of virtual particles and anti-particles that fills space, to the extreme heat and energy of the early universe. 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.

    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.

    Bill Gates. George W. Bush. Osama bin Laden. Leaders and leadership are perennial topics of debate. What is leadership? How does one become a leader? Do we actually need leaders? In this Very Short Introduction, Keith Grint offers provocative answers to these questions, prompting readers to rethink their assumptions about what leadership is. Indeed, Grint argues that leadership is a very elusive quality, and that there are few definitive answers to be found, which explains why most books on leadership produce so much heat and so little light. But there are important questions to ask, questions which shed light on why leadership so resists definition. Grint looks at the way leadership has evolved from its earliest manifestations in ancient societies, highlights the early ideas about leadership found in Plato, Sun Tzu, Machiavelli and others, considers how social, economic, and political forces can undermine particular modes of leadership, and discusses the practice of management, its history, future, and influence on all aspects of society.

    Negotiations for the accession of six new states have begun, and membership, which already covers almost all of Western Europe, will soon extend to most of Central and Eastern Europe. The Union's institutions have been reformed, and its powers may soon reach beyond the economy and the environment into the fields of foreign policy and defense. This thorough yet succinct introduction has been completely updated to take the many recent developments into account. John Pinder provides a detailed and coherent view of the evolution of the European Union, and investigates its future as Europe thrives in the new millennium.

    This Very Short Introduction, addresses a variety of questions, including what a black hole actually is, how they are characterized and discovered, and what would happen if you came too close to one. Professor Katherine Blundell looks at the seemingly paradoxical, mysterious, and intriguing phenomena of black holes. Outlining their nature and characteristics, both those resulting from the spectacular collapse of heavy stars, and the giant black holes found at the centres of galaxies, she separates scientific fact from science fiction, and demonstrates the important role they play in the cosmos. 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.

    This book gives a lucid, exciting, and accessible account of the surprising and counterintuitive ideas that shape our understanding of the sub-atomic world. It does not disguise the problems of interpretation that still remain unsettled 75 years after the initial discoveries. The main text makes no use of equations, but there is a Mathematical Appendix for those desiring stronger fare. Uncertainty, probabilistic physics, complementarity, the problematic character of measurement, and decoherence are among the many topics discussed. This volume offers the reader access to one of the greatest discoveries in the history of physics and one of the outstanding intellectual achievements of the twentieth century.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.

    Once access to the Internet became a reality for large swathes of the world's population, the amount of data generated each day became huge, and continues to grow exponentially. It includes all our uploaded documents, video, and photos, all our social media traffic, our online shopping, even the GPS data from our cars."Big Data" represents a qualitative change, not simply a quantitative one. The term refers both to the new technologies involved, and to the way it can be used by business and government. Dawn E. Holmes uses a variety of case studies to explain how data is stored, analyzed, and exploited by a variety of bodies from big companies to organizations concerned with disease control. Big data is transforming the way businesses operate, and the way medical research can be carried out. At the same time, it raises important ethical issues; Holmes discusses cases such as the Snowden affair, data security, and domestic smart devices which can be hijacked by hackers.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.

    Each chapter addresses a central scientific issue but does so in a way that is lively and completely accessible. Issues discussed include whether there are several different types of intelligence, whether intelligence differences are caused by genes or the environment, the biological basis of intelligence levels, and whether intelligence declines as we grow older. 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 Mary, Queen of Scots, trapped by her own code, to the Navajo Code Talkers who helped the Allies win World War II, to the incredible (and incredibly simple) logisitical breakthrough that made Internet commerce secure, The Code Book tells the story of the most powerful intellectual weapon ever known: secrecy.Throughout the text are clear technical and mathematical explanations, and portraits of the remarkable personalities who wrote and broke the world’s most difficult codes. Accessible, compelling, and remarkably far-reaching, this book will forever alter your view of history and what drives it. It will also make you wonder how private that e-mail you just sent really is.

    First, geologists realized that the continents themselves were drifting across the surface of the globe and that oceans were being created and destroyed. Secondly, pictures of the entire planet were returned from space. Suddenly, the Earth began to be viewed as a single entity; a dynamic, interacting whole, controlled by complex processes we scarcely understood. This Introduction explores emerging geological research and explains how new advances in the understanding of plate tectonics, seismology, and satellite imagery have enabled us to begin to see the Earth as it actually is: dynamic and ever changing.

    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.

    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.

    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.