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.

    From the ancient Romans to the present day, their real nature has been obscured by a tangled web of preconceived ideas and stereotypes.Barry Cunliffe seeks to reveal this fascinating people for the first time, using an impressive range of evidence, and exploring subjects such as trade, migration, and the evolution of Celtic traditions. Along the way, he exposes the way in which society's needs have shaped our visions of the Celts, and examines such colorful characters as St. Patrick, Cu Chulainn, and Boudica.

    Short, clear discussions on the mechanical workings of the brain are offered and the details of brain science are covered in an accessible style. Explanations of the more familiar implications of the brain's actions, such as memories, perceptions, and motor control are integrated throughout the book. It has chapters on brain processes and the causes of "altered mental states," as well as a final chapter that discusses possible future developments in neuroscience, touching on artificial intelligence, gene therapy, the importance of the Human Genome Project, drugs by design, and transplants. Up-to-date coverage of the newest developments in brain research and suggestions for future research on the brain are also included. 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 this Very Short Introduction, Michael Cook provides a lucid and direct account of the significance of the Koran both in the modern world and inthat of traditional Islam. He gives vivid accounts of its role in Muslim civilization, illustrates the diversity of interpretations championed by traditional and modern commentators, discusses the processes by which the book took shape, and compares it to other scriptures and classics of thehistoric cultures of Eurasia.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.

    But why did it last so long? And what impact did it have on the United States, the Soviet Union, Europe, and the Third World? Finally, how did it affect the broader history of the second half of the twentieth century--what were the human and financial costs? This Very Short Introduction provides a clear and stimulating interpretive overview of the Cold War, one that will both invite debate and encourage deeper investigation.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.

    But sometimes the solutions are not as interesting as the beautiful symmetric patterns that lead to them. Written in a friendly style for a general audience, Fearless Symmetry is the first popular math book to discuss these elegant and mysterious patterns and the ingenious techniques mathematicians use to uncover them.Hidden symmetries were first discovered nearly two hundred years ago by French mathematician �variste Galois. They have been used extensively in the oldest and largest branch of mathematics--number theory--for such diverse applications as acoustics, radar, and codes and ciphers. They have also been employed in the study of Fibonacci numbers and to attack well-known problems such as Fermat's Last Theorem, Pythagorean Triples, and the ever-elusive Riemann Hypothesis. Mathematicians are still devising techniques for teasing out these mysterious patterns, and their uses are limited only by the imagination.The first popular book to address representation theory and reciprocity laws, Fearless Symmetry focuses on how mathematicians solve equations and prove theorems. It discusses rules of math and why they are just as important as those in any games one might play. The book starts with basic properties of integers and permutations and reaches current research in number theory. Along the way, it takes delightful historical and philosophical digressions. Required reading for all math buffs, the book will appeal to anyone curious about popular mathematics and its myriad contributions to everyday life.

    This fascinating Very Short Introduction discusses all the aspects of psychology that are relevant to the legal and criminal process as a whole. It includes explanations of criminal behavior and criminality, including the role of mental disorder in crime, and it reveals how forensic psychology contributes to helping investigate the crime and catching the perpetrators. David Canter also explains how psychologists provide guidance to all those involved in civil and criminal court proceedings, including both the police and the accused, and what expert testimony can be provided by a psychologist about the offender at the trial. Finally, Canter describes how forensic psychology is used, particularly in prisons, to help in the management, treatment and rehabilitation of offenders, once they have been convicted.

    Would you believe that these five pieces can be reassembled in such a fashion so as to create two apples equal in shape and size to the original? Would you believe that you could make something as large as the sun by breaking a pea into a finite number of pieces and putting it back together again? Neither did Leonard Wapner, author of The Pea and the Sun, when he was first introduced to the Banach-Tarski paradox, which asserts exactly such a notion. Written in an engaging style, The Pea and the Sun catalogues the people, events, and mathematics that contributed to the discovery of Banach and Tarski's magical paradox. Wapner makes one of the most interesting problems of advanced mathematics accessible to the non-mathematician.

    A criminal case can often hinge on a piece of evidence such as a hair, a blood trace, a bit of saliva on a cigarette butt, or the telltale mark of a tire tread. High profile cases have stoked this interest in recent years and some of the most popular shows on television--such as CSI: Crime Scene Investigation and its raft of spin-offs--attest to the enduring popularity of forensic science as a form of grisly entertainment. This Very Short Introduction looks at the nature of forensic science, examining what forensic science is, how it is used in the investigation of crime, how crime scenes are managed, how forensic scientists work, the different techniques used to recover evidence, and the range of methods available for analysis. It also considers how forensic science serves the criminal justice system and the challenges of communicating complex scientific evidence in a court of law.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.

    After painting Hegel's life and times in broad strokes, Peter Singer goes on to tackle some of the more challenging aspects of Hegel's philosophy. Offering a broad discussion of Hegel'sideas and an account of his major works, Singer explains what have often been considered abstruse and obscure ideas in a clear and inviting manner.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

    A lecture class taught by Wittgenstein, however, hardly resembled a lecture. He sat on a chair in the middle of the room, with some of the class sitting in chairs, some on the floor. He never used notes. He paused frequently, sometimes for several minutes, while he puzzled out a problem. He often asked his listeners questions and reacted to their replies. Many meetings were largely conversation. These lectures were attended by, among others, D. A. T. Gasking, J. N. Findlay, Stephen Toulmin, Alan Turing, G. H. von Wright, R. G. Bosanquet, Norman Malcolm, Rush Rhees, and Yorick Smythies. Notes taken by these last four are the basis for the thirty-one lectures in this book. The lectures covered such topics as the nature of mathematics, the distinctions between mathematical and everyday languages, the truth of mathematical propositions, consistency and contradiction in formal systems, the logicism of Frege and Russell, Platonism, identity, negation, and necessary truth. The mathematical examples used are nearly always elementary.

    For real.If you're like most people, geometry is a sterile and dimly remembered exercise you gladly left behind in the dust of ninth grade, along with your braces and active romantic interest in pop singers. If you recall any of it, it's plodding through a series of miniscule steps only to prove some fact about triangles that was obvious to you in the first place. That's not geometry. Okay, it is geometry, but only a tiny part, which has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel.Shape reveals the geometry underneath some of the most important scientific, political, and philosophical problems we face. Geometry asks: Where are things? Which things are near each other? How can you get from one thing to another thing? Those are important questions. The word "geometry," from the Greek for "measuring the world." If anything, that's an undersell. Geometry doesn't just measure the world—it explains it. Shape shows us how.

    Reynolds provides a general overview of the history of the subject as it has developed in English, at the same time introducing key debates, developments, and figures in the field. Reynolds demonstrates how writing for children--whether on page or screen--has helped in shaping ideas about culture, society and childhood. She also raises questions about the future of children's literature generally and discusses the shape that it might take.

    New co-authors--Irl Bivens and Stephen Davis--from Davidson College; both distinguished educators and writers.* More emphasis on graphing calculators in exercises and examples, including CAS capabilities of graphing calculators.* More problems using tabular data and more emphasis on mathematical modeling.

     According to MSNBC, having a child makes you stupid. You actually lose IQ points. Good Morning America has announced that natural blondes will be extinct within two hundred years. Pundits estimated that there were more than a million demonstrators at a tea party rally in Washington, D.C., even though roughly sixty thousand were there. Numbers have peculiar powers-they can disarm skeptics, befuddle journalists, and hoodwink the public into believing almost anything. "Proofiness," as Charles Seife explains in this eye-opening book, is the art of using pure mathematics for impure ends, and he reminds readers that bad mathematics has a dark side. It is used to bring down beloved government officials and to appoint undeserving ones (both Democratic and Republican), to convict the innocent and acquit the guilty, to ruin our economy, and to fix the outcomes of future elections. This penetrating look at the intersection of math and society will appeal to readers of Freakonomics and the books of Malcolm Gladwell.