The Times called it elegant, discursive, and littered with quotes and allusions from Aquinas via Gershwin to Woolf and The Philadelphia Inquirer praised it as absolutely scintillating. In this delightful new book, Robert Kaplan, writing together with his wife Ellen Kaplan, once again takes us on a witty, literate, and accessible tour of the world of mathematics. Where The Nothing That Is looked at math through the lens of zero, The Art of the Infinite takes infinity, in its countless guises, as a touchstone for understanding mathematical thinking. Tracing a path from Pythagoras, whose great Theorem led inexorably to a discovery that his followers tried in vain to keep secret (the existence of irrational numbers); through Descartes and Leibniz; to the brilliant, haunted Georg Cantor, who proved that infinity can come in different sizes, the Kaplans show how the attempt to grasp the ungraspable embodies the essence of mathematics. The Kaplans guide us through the Republic of Numbers, where we meet both its upstanding citizens and more shadowy dwellers; and we travel across the plane of geometry into the unlikely realm where parallel lines meet. Along the way, deft character studies of great mathematicians (and equally colorful lesser ones) illustrate the opposed yet intertwined modes of mathematical thinking: the intutionist notion that we discover mathematical truth as it exists, and the formalist belief that math is true because we invent consistent rules for it. Less than All, wrote William Blake, cannot satisfy Man. The Art of the Infinite shows us some of the ways that Man has grappled with All, and reveals mathematics as one of the most exhilarating expressions of the human imagination.

    A new foreword by Kip Thorne, the current Richard Feynman Professor of Theoretical Physics at Caltech, discusses the relevance of the new edition to today's readers. This boxed set also includes Feynman's new Tips on Physics—the four previously unpublished lectures that Feynman gave to students preparing for exams at the end of his course. Thus, this 4-volume set is the complete and definitive edition of The Feynman Lectures on Physics. Packaged in a specially designed slipcase, this 4-volume set provides the ultimate legacy of Feynman's extraordinary contribution to students, teachers, researches, and lay readers around the world.

    Yet, each moment of joy is only that: momentary, showing up the rest of our lives to be unsatisfying, somehow lacking and incomplete. On the other hand, Vedanta, the body of knowledge found at the end of the Veda, asserts with breathtaking boldness that one's true nature is completeness and limitlessness. Vedanta also promises that moksa, liberation from all forms of limitations that seem to bind a human being, is possible here and now. In this lucid, lively introduction to Vedanta, Swami Dayananda shows how man's constant struggle to overcome these limitations through the ceaseless pursuit of security and pleasure are predestined to failure for the simple reason that they are misdirected: they stem from a failure in understanding the real nature of the fundamental problem itself. All effort howsoever great or unremitting being limited, the result of such effort is also bound to be equally limited, inadequate. The road to freedom from limitation, then, can scarcely lie that way. Indeed, asserts Vedanta, it is only to be found in the correct knowledge of one's true nature as absolute. This vital first step, a clear understanding of man's fundamental problem of ignorance and error about his real nature. Is what this book is all about.

    . .he believes these ideas to be accessible to the audience he wantsto reach, and he writes so that they are. -- NatureIf you want to encourage anyone's interest in math, get them TheMathematical Universe. * New Scientist

    Even after more than three centuries and the revolutions of Einsteinian relativity and quantum mechanics, Newtonian physics continues to account for many of the phenomena of the observed world, and Newtonian celestial dynamics is used to determine the orbits of our space vehicles.This completely new translation, the first in 270 years, is based on the third (1726) edition, the final revised version approved by Newton; it includes extracts from the earlier editions, corrects errors found in earlier versions, and replaces archaic English with contemporary prose and up-to-date mathematical forms. Newton's principles describe acceleration, deceleration, and inertial movement; fluid dynamics; and the motions of the earth, moon, planets, and comets. A great work in itself, the Principia also revolutionized the methods of scientific investigation. It set forth the fundamental three laws of motion and the law of universal gravity, the physical principles that account for the Copernican system of the world as emended by Kepler, thus effectively ending controversy concerning the Copernican planetary system.The illuminating Guide to the Principia by I. Bernard Cohen, along with his and Anne Whitman's translation, will make this preeminent work truly accessible for today's scientists, scholars, and students.

    Today, these paradoxes remain on the cutting edge of our investigations into the fabric of space and time. Zeno's Paradox uses the motion paradox as a jumping-off point for an exploration of the twenty-five-hundred-year quest to uncover the true nature of the universe. From Galileo to Einstein to Stephen Hawking, some of the greatest minds in history have tackled the problem and made spectacular breakthroughs, but through it all, the paradox of motion remains.

    It is elegant, clever and rewarding to learn, but it is hard. Even the best students find it challenging, and those who are unprepared often find it incomprehensible at first. This book aims to ensure that no student need be unprepared. It is not like other Analysis books. It is not a textbook containing standard content. Rather, it is designed to be read before arriving at university and/or before starting an Analysis course, or as a companion text once a course is begun. It provides a friendly and readable introduction to the subject by building on the students existing understanding of six key topics: sequences, series, continuity, differentiability, integrability and the real numbers. It explains how mathematicians develop and use sophisticated formal versions of these ideas, and provides a detailed introduction to the central definitions, theorems and proofs, pointing out typical areas of difficulty and confusion and explaining how to overcome these. The book also provides study advice focused on the skills that students need if they are to build on this introduction and learn successfully in their own Analysis courses: it explains how to understand definitions, theorems and proofs by relating them to examples and diagrams, how to think productively about proofs, and how theories are taught in lectures and books on advanced mathematics. It also offers practical guidance on strategies for effective study planning. The advice throughout is research-based and is presented in an engaging style that will be accessible to students who are new to advanced abstract mathematics.

    Few write for the non-specialist as well as Will Durant, and this book is a splendid example of his eminently readable scholarship. Durant’s insight and wit never cease to dazzle; The Story of Philosophy is a key book for anyone who wishes to survey the history and development of philosophical ideas in the Western world.

    Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be reasoned out--from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft--indeed, brilliant--instructions on stripping away irrelevancies and going straight to the heart of the problem.

    A rich source of information for readers of all ages, this book is divided into two sections, first looking at major sources of symbols (basic shapes, colors and numbers, the natural world), then, placing symbols in context of mythologies and religions, the human life cycle, people and culture, and symbol systems. Clear cross-referencing illuminates connections between symbols, while beautiful artwork and photography make this a collector's edition to treasure.

    It reveals the attraction that has drawn leading mathematicians and amateurs alike to number theory over the course of history.

    Its ultimate destination is a plausible, living validation of transcendence. Each of its three parts is like a turn of a spiral, exploring recurring ideas through the prisms of religious myth, truth and belief, respectively. With each turn, the book seeks to convey a more nuanced and complete understanding of the many facets of transcendence. Part I puts forward the controversial notion that many religious myths are actually true; and not just allegorically so. Part II argues that our own inner storytelling plays a surprising role in creating the seeming concreteness of things and the tangibility of history. Part III suggests, in the form of a myth, how deeply ingrained belief systems create the world we live in. The three themes, myth, truth and belief, flow into and interpenetrate each other throughout the book.

    Discovered by an 18th century mathematician and preacher, Bayes' rule is a cornerstone of modern probability theory. In this richly illustrated book, intuitive visual representations of real-world examples are used to show how Bayes' rule is actually a form of commonsense reasoning. The tutorial style of writing, combined with a comprehensive glossary, makes this an ideal primer for novices who wish to gain an intuitive understanding of Bayesian analysis. As an aid to understanding, online computer code (in MatLab, Python and R) reproduces key numerical results and diagrams.Stone's book is renowned for its visually engaging style of presentation, which stems from teaching Bayes' rule to psychology students for over 10 years as a university lecturer.

    The catalogue of current classical CDs runs to more than two and half thousand tightly packed pages, and lists nearly three hundred composers before reaching the second letter of the alphabet. An average month sees some four hundred recordings and re-issues added to the pile. The Rough Guide to Classical Music attempts to make sense of this overwhelming volume of music, giving you the information that's essential whether you're starting from the beginning or have already begun exploring. As well as being a buyer's guide to CDs, this book is a who's who of classical music, ranging from Hildegard of Bingen, one of the great figures of eleventh-century European culture, to Thomas Adès, born in London in 1971. Of course we've had to be selective, both with the composers and with their output - Domenico Scarlatti, for example, was a fascinating musician, but no book of this scope could do justice to each of his five hundred keyboard sonatas. Gaetano Donizetti wrote more than seventy operas, but you wouldn't want to listen to all of them. We've gone for what we think are the best works by the most interesting composers, mixing some underrated people with the big names, and highlighting some we think you should keep an eye on. When it comes to CDs the situation requires even greater ruthlessness. Beethoven may have written only nine symphonies, but there are more than one hundred versions of the fifth in the catalogue, and scores of recordings of all the others. Several of these CDs should never have been issued - they are there simply because any up-and-coming conductor has to make a Beethoven recording as a kind of calling card, regardless of any aptitude for the music. However, a fair proportion of the Beethoven CDs are worth listening to, because a piece of music as complex as a Beethoven symphony will bear as many different readings as a Shakespeare play. Although there are recordings that stand head and shoulders above the competition, no performance can be described as definitive, which is one reason why we have often recommended more than one account of a work. Whereas all our first-choice CDs make persuasive cases for the music, some of the additional recommendations are included because they make provocative counter-arguments. Where price is a consideration, we've also listed a lower-cost alternative whenever appropriate - thus we might suggest a mid-price boxed set of symphonies as an alternative to buying them as full-price individual CDs. Finally, in many instances we've picked an outstanding pre-stereo performance as a complement to a modern recording. These `historic' reissues are the one reliable growth area in the classical music industry, and their success is not due to mere nostalgia. There are some great musicians around today, but there's also a lot of hype in the business, with many soloists owing their success more to the way they look than to the way they play - and conversely, many superlative musicians who remain obscure because they don't project the requisite glamour. It's in the area of orchestral music and opera that the situation is especially bad, notwithstanding the technically immaculate quality of many digital recordings. Orchestral musicians are now trained to a very high standard, but only a few of the top-class orchestras enjoy the sort of long-term relationship with an individual conductor that can mould a distinctive identity. The same goes for opera companies, which used to have a stable core of singers and musicians working under the same conductor for years. Now there's a system based on jet-setting stars, who might be performing in London one night, New York the next, then in the recording studio for a few days to record something with people they hadn't met until the day the session started. You don't necessarily get a good football team by paying millions for a miscellaneous batch of top-flight players, and you don't build a good musical team that way either. Musically, then, new is not always best. And don't assume that a recording made more than thirty years ago will sound terrible. Sound quality won't match that of digital CDs, but you'll be surprised at how good it can be - indeed, many people prefer the warmth of the old analogue sound to the often chilly precision produced by modern studios. (We've warned you if surface noise or tinny quality might be a hindrance to enjoyment.) In short, you'll be missing a lot if you insist on hi-tech - few recent releases can match Vladimir Horowitz's 1940 account of Tchaikovsky's Piano Concerto No. 1, for instance, or Josef Hofmann's versions of the Chopin piano concertos from the 1930s.

    As exciting as any action/adventure novel, this is actually the story of incredible individuals and engrossing tales behind the most profound, enduring mathematical theorems.Archimedes famously ran naked through the streets shouting, “Eureka, eureka!” after finding a method for measuring the volume of an irregular-shaped object. René Descartes was not only a great French mathematician, philosopher, physicist, and natural scientist; he was also an expert swordsman who traveled with European armies from town to town, dressed in green taffeta and accompanied by a valet. Georg Cantor grappled with mental illness as he explored the highly counterintuitive, bizarre properties of infinite sets and numbers. Emmy Noether struggled to find employment as she laid the mathematical groundwork for modern theoretical physics. And Alexander Grothendieck taught himself mathematics while interned in Nazi concentration camps, only to disappear into the Pyrenees at the zenith of his career.These are just a few stories recounted in this absorbing narrative. In probing the lives of the preeminent mathematicians in history, a Strange Wilderness will leave you entertained and enlightened, with a newfound appreciation of the tenacity, complexity, and brilliance of the mathematical genius.