. . intellectual and religious history of late medieval and Reformation Europe.”—Christianity Today"A learned, humane, and expressive book."—Gerald Strauss, Renaissance Quarterly The seeds of the swift and sweeping religious movement that reshaped European thought in the 1500s were sown in the late Middle Ages. In this book, Steven Ozment traces the growth and dissemination of dissenting intellectual trends through three centuries to their explosive burgeoning in the Reformations—both Protestant and Catholic—of the sixteenth century. He elucidates with great clarity the complex philosophical and theological issues that inspired antagonistic schools, traditions, and movements from Aquinas to Calvin. This masterly synthesis of the intellectual and religious history of the period illuminates the impact of late medieval ideas on early modern society.

    But a dispute over its discovery sowed the seeds of discontent between two of the greatest scientific giants of all time - Sir Isaac Newton and Gottfried Wilhelm Leibniz." "Today Newton and Leibniz are generally considered the twin independent inventors of calculus. They are both credited with giving mathematics its greatest push forward since the time of the Greeks. Had they known each other under different circumstances, they might have been friends. But in their own lifetimes, the joint glory of calculus was not enough for either and each declared war against the other, openly and in secret." This long and bitter dispute has been swept under the carpet by historians - perhaps because it reveals Newton and Leibniz in their worst light - but The Calculus Wars tells the full story in narrative form for the first time. This history ultimately exposes how these twin mathematical giants were brilliant, proud, at times mad, and in the end completely human.

    The best history of the Latter-day Saints addressed to a general audience now includes a new preface, an epilogue, and a bibliographical after-word.

    A Treatise In Three Parts.

    Louis are all intimately connected with the mysterious number e. In this informal and engaging history, Eli Maor portrays the curious characters and the elegant mathematics that lie behind the number. Designed for a reader with only a modest mathematical background, this biography brings out the central importance of e to mathematics and illuminates a golden era in the age of science.

    xn + yn = zn, where n represents 3, 4, 5, ...no solution"I have discovered a truly marvelous demonstration of this proposition which this margin is too narrow to contain."With these words, the seventeenth-century French mathematician Pierre de Fermat threw down the gauntlet to future generations.  What came to be known as Fermat's Last Theorem looked simple; proving it, however, became the Holy Grail of mathematics, baffling its finest minds for more than 350 years.  In Fermat's Enigma--based on the author's award-winning documentary film, which aired on PBS's "Nova"--Simon Singh tells the astonishingly entertaining story of the pursuit of that grail, and the lives that were devoted to, sacrificed for, and saved by it.  Here is a mesmerizing tale of heartbreak and mastery that will forever change your feelings about mathematics.

    Neither poor enough to evoke Africa’s moral crusade, nor as explosively booming as India and China, it has largely been overlooked by the West. Yet this vast continent, home to half a billion people, the world’s largest reserves of arable land, and 8.5 percent of global oil, is busily transforming its political and economic landscape. This book argues that rather than failing the test, Latin America’s efforts to build fairer and more prosperous societies make it one of the world’s most vigorous laboratories for capitalist democracy. In many countries—including Brazil, Chile and Mexico—democratic leaders are laying the foundations for faster economic growth and more inclusive politics, as well as tackling deep-rooted problems of poverty, inequality, and social injustice. They face a new challenge from Hugo Chávez’s oil-fuelled populism, and much is at stake. Failure will increase the flow of drugs and illegal immigrants to the United States and Europe, jeopardize stability in a region rich in oil and other strategic commodities, and threaten some of the world's most majestic natural environments. Drawing on Michael Reid’s many years of reporting from inside Latin America’s cities, presidential palaces, and shantytowns, the book provides a vivid, immediate, and informed account of a dynamic continent and its struggle to compete in a globalized world.

    But ask what it means, and the result will be a brawl. For a century, most physicists have followed Niels Bohr's Copenhagen interpretation and dismissed questions about the reality underlying quantum physics as meaningless. A mishmash of solipsism and poor reasoning, Copenhagen endured, as Bohr's students vigorously protected his legacy, and the physics community favored practical experiments over philosophical arguments. As a result, questioning the status quo long meant professional ruin. And yet, from the 1920s to today, physicists like John Bell, David Bohm, and Hugh Everett persisted in seeking the true meaning of quantum mechanics. What Is Real? is the gripping story of this battle of ideas and of the courageous scientists who dared to stand up for truth.

    That is a well-known period in history, when titans like Andrew Carnegie, John D. Rockefeller, and J. P. Morgan walked the earth.But as Charles R. Morris shows us, the platform for that spectacular growth spurt was built in the first half of the century. By the 1820s, America was already the world's most productive manufacturer and the most intensely commercialized society in history. The War of 1812 jump-started the great New England cotton mills, the iron centers in Connecticut and Pennsylvania, and the forges around the Great Lakes. In the decade after the War, the Midwest was opened by entrepreneurs. In this book, Morris paints a vivid panorama of a new nation buzzing with the work of creation. He also points out the parallels and differences in the nineteenth century American/British standoff and that between China and America today.

    Full of insights, arguments and philosophical perspectives, the book covers an amazing array of topics. Beginning in antiquity with Democritus, it progresses through logic and set theory, computability and complexity theory, quantum computing, cryptography, the information content of quantum states and the interpretation of quantum mechanics. There are also extended discussions about time travel, Newcomb's Paradox, the anthropic principle and the views of Roger Penrose. Aaronson's informal style makes this fascinating book accessible to readers with scientific backgrounds, as well as students and researchers working in physics, computer science, mathematics and philosophy.

    No German tank better represents that thundering power than the infamous Tiger, and Otto Carius was one of the most successful commanders to ever take a Tiger into battle, destroying well over 150 enemy tanks during his incredible career.

    This is a new view of mathematics, not the one we learned at school but a comprehensive guide to the patterns that recur through the universe and underlie human affairs. A Beginner's Guide to Constructing, the Universe shows you: Why cans, pizza, and manhole covers are round.Why one and two weren't considered numbers by the ancient Greeks.Why squares show up so often in goddess art and board games.What property makes the spiral the most widespread shape in nature, from embryos and hair curls to hurricanes and galaxies. How the human body shares the design of a bean plant and the solar system. How a snowflake is like Stonehenge, and a beehive like a calendar. How our ten fingers hold the secrets of both a lobster a cathedral, and much more.

    Vilfredo Pareto's long essay from the turn of the century on The Rise and Fall of the Elites marks his giant step from econometrics into sociology. Here in brief outline is the major sociological ideas for which he later became famous. This essay is more readable and disciplined than most of his later elaborations and serves exceedingly well as a first introduction to his political sociology. Translation of Un applicazione di teorie sociologiche, published in Revista Italiana di sociologia, 1901. Bibliography and notes: p. [103]-120. Introd. by Hans L. Zetterberg.

    As we enter the year 2000, zero is once again making its presence felt. Nothing itself, it makes possible a myriad of calculations. Indeed, without zero mathematicsas we know it would not exist. And without mathematics our understanding of the universe would be vastly impoverished. But where did this nothing, this hollow circle, come from? Who created it? And what, exactly, does it mean? Robert Kaplan's The Nothing That Is: A Natural History of Zero begins as a mystery story, taking us back to Sumerian times, and then to Greece and India, piecing together the way the idea of a symbol for nothing evolved. Kaplan shows us just how handicapped our ancestors were in trying to figurelarge sums without the aid of the zero. (Try multiplying CLXIV by XXIV). Remarkably, even the Greeks, mathematically brilliant as they were, didn't have a zero--or did they? We follow the trail to the East where, a millennium or two ago, Indian mathematicians took another crucial step. By treatingzero for the first time like any other number, instead of a unique symbol, they allowed huge new leaps forward in computation, and also in our understanding of how mathematics itself works. In the Middle Ages, this mathematical knowledge swept across western Europe via Arab traders. At first it was called dangerous Saracen magic and considered the Devil's work, but it wasn't long before merchants and bankers saw how handy this magic was, and used it to develop tools likedouble-entry bookkeeping. Zero quickly became an essential part of increasingly sophisticated equations, and with the invention of calculus, one could say it was a linchpin of the scientific revolution. And now even deeper layers of this thing that is nothing are coming to light: our computers speakonly in zeros and ones, and modern mathematics shows that zero alone can be made to generate everything.Robert Kaplan serves up all this history with immense zest and humor; his writing is full of anecdotes and asides, and quotations from Shakespeare to Wallace Stevens extend the book's context far beyond the scope of scientific specialists. For Kaplan, the history of zero is a lens for looking notonly into the evolution of mathematics but into very nature of human thought. He points out how the history of mathematics is a process of recursive abstraction: how once a symbol is created to represent an idea, that symbol itself gives rise to new operations that in turn lead to new ideas. Thebeauty of mathematics is that even though we invent it, we seem to be discovering something that already exists.The joy of that discovery shines from Kaplan's pages, as he ranges from Archimedes to Einstein, making fascinating connections between mathematical insights from every age and culture. A tour de force of science history, The Nothing That Is takes us through the hollow circle that leads to infinity.

    This recreational math book takes the reader on a fantastic voyage into the world of natural numbers. From the earliest discoveries of the ancient Greeks to various fundamental characteristics of the natural number sequence, Clawson explains fascinating mathematical mysteries in clear and easy prose. He delves into the heart of number theory to see and understand the exquisite relationships among natural numbers, and ends by exploring the ultimate mystery of mathematics: the Riemann hypothesis, which says that through a point in a plane, no line can be drawn parallel to a given line.While a professional mathematician's treatment of number theory involves the most sophisticated analytical tools, its basic ideas are surprisingly easy to comprehend. By concentrating on the meaning behind various equations and proofs and avoiding technical refinements, Mathematical Mysteries lets the common reader catch a glimpse of this wonderful and exotic world.