Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics? Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts.Brought up to date with a new chapter by Ian Stewart, What is Mathematics? Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.Formal mathematics is like spelling and grammar - a matter of the correct application of local rules. Meaningful mathematics is like journalism - it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature - it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature - it opens a window onto the world of mathematics for anyone interested to view.

    The first full-scale history of cognitive science, this work addresses a central issue: What is the nature of knowledge?

    His public advocacy of the Copernican over the Aristotelian system of the universe flew directly in the face of biblical authority and ecclesiastical tradition. Condemned and placed under house arrest by the Inquisition, Galileo nonetheless devoted his last years to the completion of his Dialogues Concerning Two New Sciences, which deals with motion and the resistance of solids. The Two New Sciences, which Galileo called his most important work, may be regarded as the summary statement of a life devoted to scientific experimentation and free inquiry untrammeled by tradition and authority.

    These bloody events echoed an older political rift in Egypt and the Middle East: the splitting of nationalists and Islamists during the rule of Egyptian president and Arab nationalist leader Gamal Abdel Nasser. In Making the Arab World, Fawaz Gerges, one of the world's leading authorities on the Middle East, tells how the clash between pan-Arab nationalism and pan-Islamism has shaped the history of the region from the 1920s to the present. Gerges tells this story through an unprecedented dual biography of Nasser and another of the twentieth-century Arab world's most influential figures--Sayyid Qutb, a leading member of the Muslim Brotherhood and the father of many branches of radical political Islam. Their deeply intertwined lives embody and dramatize the divide between Arabism and Islamism. Yet, as Gerges shows, beyond the ideological and existential rhetoric, this is a struggle over the state, its role, and its power. Based on a decade of research, including in-depth interviews with many leading figures in the story, Making the Arab World is essential reading for anyone who wants to understand the roots of the turmoil engulfing the Middle East, from civil wars to the rise of Al-Qaeda and ISIS.

    Like you, the elements have lives: personalities and attitudes, talents and shortcomings, stories rich with meaning. You may think of them as the inscrutable letters of the periodic table but you know them much better than you realise. Welcome to a dazzling tour through history and literature, science and art. Here you'll meet iron that rains from the heavens and noble gases that light the way to vice. You'll learn how lead can tell your future while zinc may one day line your coffin. You'll discover what connects the bones in your body with the Whitehouse in Washington, the glow of a streetlamp with the salt on your dinner table. From ancient civilisations to contemporary culture, from the oxygen of publicity to the phosphorus in your pee, the elements are near and far and all around us. Unlocking their astonishing secrets and colourful pasts, Periodic Tales will take you on a voyage of wonder and discovery, excitement and novelty, beauty and truth. Along the way, you'll find that their stories are our stories, and their lives are inextricable from our own.

    Ask them the meaning of 'relativity' and few of them will be able to tell you what it is.The basic principles of relativity have not changed since Russell first published his lucid guide for the general reader. The ABC of Relativity is Bertrand Russell's most brilliant work of scientific popularisation. With marvellous lucidity he steers the reader who has no knowledge of maths or physics through the subtleties of Einstein's thinking. In easy, assimilable steps, he explains the theories of special and general relativity and describes their practical application to, amongst much else, discoveries about gravitation and the invention of the hydrogen bomb.

    Conventional wisdom has long claimed that economic change is the prime mover of political change, whether in the age of industry or the Internet. In our own time Paul Kennedy has claimed that economics provided the key to international power, while Francis Fukuyama and others have argued that capitalism doomed socialism and ensured the victory of democracy. Small wonder politicians are obsessed with the economy: the Clinton campaign motto-"It's the economy stupid" -sums up a central tenet of modern life. But is it the economy? Ferguson thinks it is high time we re-examined the link-the "nexus," to use Thomas Carlyle's term-between economics and politics, in the aftermath not only of the failure of socialism but also of the apparent triumph of American-style capitalism. His central argument is that the conflicting impulses of sex, violence, and power are together more powerful than money. In particular, political events and institutions have often dominated economic development. A bold synthesis of political history and modern economic theory, Cash Nexus will transform the landscape of modern history and draw challenging and unsettling conclusions about the prospects of both capitalism and democracy.

    In one of modern history’s most miraculous occurrences, communism imploded–and not with a bang, but with a whimper. Now two of the foremost scholars of East European and Soviet affairs, Stephen Kotkin and Jan T. Gross, drawing upon two decades of reflection, revisit this crash. In a crisp, concise, unsentimental narrative, they employ three case studies–East Germany, Romania, and Poland–to illuminate what led Communist regimes to surrender, or to be swept away in political bank runs. This is less a story of dissidents, so-called civil society, than of the bankruptcy of a ruling class–communism’s establishment, or “uncivil society.” The Communists borrowed from the West like drunken sailors to buy mass consumer goods, then were unable to pay back the hard-currency debts and so borrowed even more. In Eastern Europe, communism came to resemble a Ponzi scheme, one whose implosion carries enduring lessons. From East Germany’s pseudotechnocracy to Romania’s megalomaniacal dystopia, from Communist Poland’s cult of Mary to the Kremlin’s surprise restraint, Kotkin and Gross pull back the curtain on the fraud and decadence that cashiered the would-be alternative to the market and democracy, an outcome that opened up to a deeper global integration that has proved destabilizing.

    States failed, governments became predators, and citizens took up arms. In When Things Fell Apart, Robert H. Bates advances an explanation of state failure in Africa. In so doing, he not only plumbs the depths of the continent's late-century tragedy, but also the logic of political order and the foundations of the state. This book covers a wide range of territory by drawing on materials from Rwanda, Sudan, Liberia, and Congo. Written to be accessible to the general reader, it is nonetheless a must-read for scholars and policy makers concerned with political conflict and state failure.

    These truly remarkable South American people are one of the few primitive sovereign tribal societies left on earth. This new edition includes events and changes that have occurred since 1992, including a recent trip by the author to the Brazilian Yanomamo in 1995.

    O’Malley, SJ, provides essential historical background from the founder Ignatius of Loyola through the present. The book tells the story of the Jesuits’ great successes as missionaries, educators, scientists, cartographers, polemicists, theologians, poets, patrons of the arts, and confessors to kings. It tells the story of their failures and of the calamity that struck them in 1773 when Pope Clement XIV suppressed them worldwide. It tells how a subsequent pope restored them to life and how they have fared to this day in virtually every country in the world. Along the way it introduces readers to key figures in Jesuit history, such as Matteo Ricci and Pedro Arrupe, and important Jesuit writings, such as the Spiritual Exercises.Concise and compelling, The Jesuits is an accessible introduction for anyone interested in world or church history. In addition to the narrative, the book provides a timeline, a list of significant figures, photos of important figures and locations, recommendations for additional reading, and

    It remains the one of the most widely read books about science to come out of the twentieth century.(Note: the book was first published in 1934, in German, with the title Logik der Forschung. It was "reformulated" into English in 1959. See Wikipedia for details.)

    You may find it for free on the web. Purchase of the Kindle edition includes wireless delivery.

    As a military aide to George Washington, forceful critic of the Articles of Confederation, persuasive proponent of ratification of the Constitution, first Secretary of the Treasury, and leader of the Federalist party, Hamilton devoted himself to the creation of a militarily and economically powerful American nation guided by a strong republican government. His public and private writings demonstrate the perceptive intelligence, confident advocacy, driving ambition, and profound concern for honor and reputation that contributed both to his rise to fame and to his tragic early death.Arranged chronologically, Writings contains more than 170 letters, speeches, essays, reports, and memoranda written between 1769 and 1804. Included are all 51 of Hamilton's contributions to The Federalist, as well as subsequent writing calling for a broad construction of federal power under the Constitution; his famous speech to the Constitutional Convention, which gave rise to accusations that he favored monarchy; early writings supporting the Revolutionary cause and a stronger central government; his visionary reports as Treasury secretary on the public credit, a national bank, and the encouragement of American manufactures; a detailed confession of adultery made by Hamilton in order to defend himself against charges of official misconduct; and his self-destructive attack on John Adams during the 1800 campaign. An extensive selection of private letters illuminates Hamilton's complex relationship with George Washington, his deep affection for his wife andchildren, his mounting fears during the 1790s regarding the Jeffersonian opposition and the French Revolution, and his profound distrust of Aaron Burr. Included in an appendix are conflicting eyewitness accounts of the Hamilton-Burr duel.

    After the Limited Test Ban Treaty between the United States and the Soviet Union in 1963, nuclear testing went underground. It became literally invisible—but more frequent: the United States conducted a further 723 underground tests, the last in 1992. 100 Suns documents the era of visible nuclear testing, the atmospheric era, with one hundred photographs drawn by Michael Light from the archives at Los Alamos National Laboratory and the U.S. National Archives in Maryland. It includes previously classified material from the clandestine Lookout Mountain Air Force Station based in Hollywood, whose film directors, cameramen and still photographers were sworn to secrecy.The title, 100 Suns, refers to the response by J.Robert Oppenheimer to the world’s first nuclear explosion in New Mexico when he quoted a passage from the Bhagavad Gita, the classic Vedic text: “If the radiance of a thousand suns were to burst forth at once in the sky, that would be like the splendor of the Mighty One . . . I am become Death, the destroyer of worlds.” This was Oppenheimer’s attempt to describe the otherwise indescribable. 100 Suns likewise confronts the indescribable by presenting without embellishment the stark evidence of the tests at the moment of detonation. Since the tests were conducted either in Nevada or the Pacific the book is simply divided between the desert and the ocean. Each photograph is presented with the name of the test, its explosive yield in kilotons or megatons, the date and the location. The enormity of the events recorded is contrasted with the understated neutrality of bare data. Interspersed within the sequence of explosions are pictures of the awestruck witnesses. The evidence of these photographs is terrifying in its implication while at same time profoundly disconcerting as a spectacle. The visual grandeur of such imagery is balanced by the chilling facts provided at the end of the book in the detailed captions, a chronology of the development of nuclear weaponry and an extensive bibliography. A dramatic sequel to Michael Light’s Full Moon, 100 Suns forms an unprecedented historical document.