Emerson offers timeless meditations on the value of individual greatness, reconnecting readers with the everyday virtues of his “Representative Men”: Plato, in whose writings are contained “the culture of nations”; Emanuel Swedenborg, a “rich discoverer” who strove to unite the scientific and spiritual planes; Michel de Montaigne, “the frankest and honestest of all writers”; William Shakespeare, who “wrote the text of modern life”; Napoleon Bonaparte, who had the “virtues and vices” of common men writ large; and Johann Wolfgang von Goethe, who “in conversation, in calamity…finds new materials.”This Modern Library Paperback Classic reflects the author’s corrections for an 1876 reprinting.

    Augustine equate nothingness with the Devil? What tortuous means did 17th-century scientists employ in their attempts to create a vacuum? And why do contemporary quantum physicists believe that the void is actually seething with subatomic activity? You’ll find the answers in this dizzyingly erudite and elegantly explained book by the English cosmologist John D. Barrow.Ranging through mathematics, theology, philosophy, literature, particle physics, and cosmology, The Book of Nothing explores the enduring hold that vacuity has exercised on the human imagination. Combining high-wire speculation with a wealth of reference that takes in Freddy Mercury and Shakespeare alongside Isaac Newton, Albert Einstein, and Stephen Hawking, the result is a fascinating excursion to the vanishing point of our knowledge.

    SIR: THESE thoughts concerning education, which now come abroad into the world, do of right belong to you, being written several years since for your sake, and are no other than what you have already by you in my letters. I have so little vary'd any thing, but only the order of what was sent you at different times, and on several occasions, that the reader will easily find, in the familiarity and fashion of the stile, that they were rather the private conversation of two friends, than a discourse design'd for publick view.

    E. Lendon surveys a millennium of warfare to discover how militaries change—and don’t change—and how an army’s greatness depends on its use of the past. Noting this was an age that witnessed few technological advances, J. E. Lendon shows us that the most successful armies were those that made the most effective use of cultural tradition. Ancient combat moved forward by looking backward for inspiration—the Greeks, to Homer; the Romans, to the Greeks and to their own heroic past. The best ancient armies recruited soldiers from societies with strong competitive traditions; and the best ancient leaders, from Alexander to Julius Caesar, called upon those traditions to encourage ferocious competition at every rank.Ranging from the Battle of Champions between Sparta and Argos in 550 B.C. through Julian’s invasion of Persia in A.D. 363, Soldiers and Ghosts brings to life the most decisive military contests of ancient Greece and Rome. Lendon places these battles, and the methods by which they were fought, in a sweeping narrative of ancient military history. On every battlefield, living soldiers fought alongside the ghosts of tradition—ghosts that would inspire greatness for almost a millennium before ultimately coming to stifle it.

    His Epigrams can be affectionate or cruel, elegiac or playful; they target every element of Roman society, from slaves to schoolmasters to, above all, the aristocratic elite. With wit and wisdom, Martial evokes not “the grandeur that was Rome,” but rather the timeless themes of urban life and society.

    As a member of the Los Alamos National Laboratory from 1944 on, Ulam helped to precipitate some of the most dramatic changes of the postwar world. He was among the first to use and advocate computers for scientific research, originated ideas for the nuclear propulsion of space vehicles, and made fundamental contributions to many of today's most challenging mathematical projects. With his wide-ranging interests, Ulam never emphasized the importance of his contributions to the research that resulted in the hydrogen bomb. Now Daniel Hirsch and William Mathews reveal the true story of Ulam's pivotal role in the making of the "Super," in their historical introduction to this behind-the-scenes look at the minds and ideas that ushered in the nuclear age. An epilogue by Françoise Ulam and Jan Mycielski sheds new light on Ulam's character and mathematical originality.

    But while this epic struggle forms the core of his work, Herodotus' natural curiosity frequently gives rise to colorful digressions - a description of the natural wonders of Egypt; an account of European lake-dwellers; and far-fetched accounts of dog-headed men and gold-digging ants. With its kaleidoscopic blend of fact and legend, the "Histories" offers a compelling Greek view of the world of the fifth century BC.

    With a new introduction, three new chapters, modernized language and methods throughout, and an appendix of challenging and enjoyable practice problems, Calculus Made Easy has been thoroughly updated for the modern reader.

    In this unconventional introduction, physicist Leonard Susskind and hacker-scientist George Hrabovsky offer a first course in physics and associated math for the ardent amateur. Unlike most popular physics books—which give readers a taste of what physicists know but shy away from equations or math—Susskind and Hrabovsky actually teach the skills you need to do physics, beginning with classical mechanics, yourself. Based on Susskind's enormously popular Stanford University-based (and YouTube-featured) continuing-education course, the authors cover the minimum—the theoretical minimum of the title—that readers need to master to study more advanced topics.An alternative to the conventional go-to-college method, The Theoretical Minimum provides a tool kit for amateur scientists to learn physics at their own pace.

    Rucker acquaints us with Godel's rotating universe, in which it is theoretically possible to travel into the past, and explains an interpretation of quantum mechanics in which billions of parallel worlds are produced every microsecond. It is in the realm of infinity, he maintains, that mathematics, science, and logic merge with the fantastic. By closely examining the paradoxes that arise from this merging, we can learn a great deal about the human mind, its powers, and its limitations.Using cartoons, puzzles, and quotations to enliven his text, Rucker guides us through such topics as the paradoxes of set theory, the possibilities of physical infinities, and the results of Godel's incompleteness theorems. His personal encounters with Godel the mathematician and philosopher provide a rare glimpse at genius and reveal what very few mathematicians have dared to admit: the transcendent implications of Platonic realism.

    This book can be cut, drawn in, folded into shapes and will even take you to the fourth dimension. So join stand-up mathematician Matt Parker on a journey through narcissistic numbers, optimal dating algorithms, at least two different kinds of infinity and more.

    Turing Mathematician Alan Turing invented an imaginary computer known as the Turing Machine; in an age before computers, he explored the concept of what it meant to be "computable," creating the field of computability theory in the process, a foundation of present-day computer programming.The book expands Turing's original 36-page paper with additional background chapters and extensive annotations; the author elaborates on and clarifies many of Turing's statements, making the original difficult-to-read document accessible to present day programmers, computer science majors, math geeks, and others.Interwoven into the narrative are the highlights of Turing's own life: his years at Cambridge and Princeton, his secret work in cryptanalysis during World War II, his involvement in seminal computer projects, his speculations about artificial intelligence, his arrest and prosecution for the crime of "gross indecency," and his early death by apparent suicide at the age of 41.

    Includes many examples and figures. GENERAL TOPOLOGY. Set Theory and Logic. Topological Spaces and Continuous Functions. Connectedness and Compactness. Countability and Separation Axioms. The Tychonoff Theorem. Metrization Theorems and paracompactness. Complete Metric Spaces and Function Spaces. Baire Spaces and Dimension Theory. ALGEBRAIC TOPOLOGY. The Fundamental Group. Separation Theorems. The Seifert-van Kampen Theorem. Classification of Surfaces. Classification of Covering Spaces. Applications to Group Theory. For anyone needing a basic, thorough, introduction to general and algebraic topology and its applications.

    As much as anyone in the modern era, he changed human thought, and his influence is still felt in virtually all aspects of our lives. This new edition, larger and more varied than the previous ones, includes more of Darwin's own work and also presents the most recent research and scholarship on all aspects of Darwin’s legacy. The biological sciences, as well as social thought, philosophy, ethics, religion, and literature, have all been shaped and reshaped by evolutionary concepts.Excerpts from the most important books and articles of recent years confirm this Darwinian heritage. New work by Richard Dawkins, Edward O. Wilson, Kevin Padian, Eugene C. Scott, Steven Pinker, Daniel Dennett, Michael Ruse, Frans de Waal, Noretta Koertge, George C. Williams, George Levine, Stephen Jay Gould, Gillian Beer, Ernst Mayr, and many others illuminates this exciting intellectual history. A wide-ranging new introduction by the editor provides context and coherence to this rich body of engaging material, much of which will be shaping human thought well into the new century.This collection of Darwin's writing, those of his critics and those of his intellectual descendants, includes:- The Voyage of the Beagle (1845): Ch. I, XVII- On the Tendency of Species to Form Varieties; And on the Perpetuation of Varieties and Species by Natural Means of Selection (1858): Ch. I-II- An Historical Sketch of the Progress of Opinion on the Origin of Species Previously to the Publication of this Work (1861) The Origin of Species (1859): Introduction, Ch. I-IV, VI, IX, XIII-XIV- The Descent of Man (1871): Introduction, Ch. I-III, VI, VIII, XIX-XXI

    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.