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.

    An indignant, outrageous, witty, deeply felt collection of reviews, essays, and speeches, this is a window not only into Vonnegut’s mind but also into his heart.

    He shows that the scientists of ancient and medieval times not only did not understand what we understand about the world—they did not understand what there is to understand, or how to understand it. Yet over the centuries, through the struggle to solve such mysteries as the curious backward movement of the planets and the rise and fall of the tides, the modern discipline of science eventually emerged. Along the way, Weinberg examines historic clashes and collaborations between science and the competing spheres of religion, technology, poetry, mathematics, and philosophy.An illuminating exploration of the way we consider and analyze the world around us, To Explain the World is a sweeping, ambitious account of how difficult it was to discover the goals and methods of modern science, and the impact of this discovery on human knowledge and development.

    From the first time mankind had an inkling of the vast space that surrounds us, those who study the universe have had to struggle against political and religious preconceptions. They have included some of the most charismatic, courageous, and idiosyncratic thinkers of all time. In Coming of Age in the Milky Way, Timothy Ferris uses his unique blend of rigorous research and captivating narrative skill to draw us into the lives and minds of these extraordinary figures, creating a landmark work of scientific history.

    In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi, or 1.6180339887...This curious mathematical relationship, widely known as "The Golden Ratio," was discovered by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. Since then it has shown a propensity to appear in the most astonishing variety of places, from mollusk shells, sunflower florets, and rose petals to the shape of the galaxy. Psychological studies have investigated whether the Golden Ratio is the most aesthetically pleasing proportion extant, and it has been asserted that the creators of the Pyramids and the Parthenon employed it. It is believed to feature in works of art from Leonardo da Vinci's Mona Lisa to Salvador Dali's The Sacrament of the Last Supper, and poets and composers have used it in their works. It has even been found to be connected to the behavior of the stock market!The Golden Ratio is a captivating journey through art and architecture, botany and biology, physics and mathematics. It tells the human story of numerous phi-fixated individuals, including the followers of Pythagoras who believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as the greatest treasure of geometry; such Renaissance thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Goethe, Cezanne, Bartok, and physicist Roger Penrose. Wherever his quest for the meaning of phi takes him, Mario Livio reveals the world as a place where order, beauty, and eternal mystery will always coexist.From the Hardcover edition.

    His previous collection, N-Space, was lauded by the Houston Post as "outstanding . . . hours of entertainment," while Publishers Weekly called it "a must for science fiction fans." A follow-up volume, Playgrounds of the Mind, was similarly praised by Kirkus Reviews: "An abundance of Niven's curious yet disciplined inventiveness and his fun-filled knack for turning seemingly absurd notions into credible, absorbing fiction. Grand entertainment."Now, ten years later, Scatterbrain collects an equally engaging assortment of Niven's latest work, all in one captivating volume. Here are choice excerpts from several of his most recent novels, including his upcoming Ringworld's Child and Rainbow Mars, as well as numerous short stories, nonfiction articles, interviews, editorials, collaborations, and correspondence. True to its title, Scatterbrain roams all over a wide variety of fascinating topics, featuring Niven's singular insights into everything from space stations to convention etiquette.So give yourself a treat, and feel free to pick the brain-or Scatterbrain-of one of modern science fiction's most fascinating thinkers.

    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.

    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.

    Beginning at Stonehenge and ending with the current crisis in String Theory, the story of this eternal question to uncover the mysteries of the universe describes a narrative that includes some of the greatest discoveries of all time and leading personalities, including Aristotle, Copernicus, and Isaac Newton, and the rise to the modern era of Einstein, Eddington, and Hawking.

    This book offers the opportunity to truly comprehend the workings of one of humanity's greatest minds. Acclaimed by Einstein himself, it is among the clearest, most readable expositions of relativity theory. It explains the problems Einstein faced, the experiments that led to his theories, and what his findings reveal about the forces that govern the universe. The concepts of relativity and the fourth dimension unfold with all the vivid excitement of research into the unknown, in language anyone can readily understand.

    . . full of intellectual treats and tricks, of whimsy and deep scientific philosophy. It is highbrow entertainment at its best, a teasing challenge to all who aspire to think about the universe." — New York Herald TribuneOne of the world's foremost nuclear physicists (celebrated for his theory of radioactive decay, among other accomplishments), George Gamow possessed the unique ability of making the world of science accessible to the general reader.He brings that ability to bear in this delightful expedition through the problems, pleasures, and puzzles of modern science. Among the topics scrutinized with the author's celebrated good humor and pedagogical prowess are the macrocosm and the microcosm, theory of numbers, relativity of space and time, entropy, genes, atomic structure, nuclear fission, and the origin of the solar system.In the pages of this book readers grapple with such crucial matters as whether it is possible to bend space, why a rocket shrinks, the "end of the world problem," excursions into the fourth dimension, and a host of other tantalizing topics for the scientifically curious. Brimming with amusing anecdotes and provocative problems, One Two Three . . . Infinity also includes over 120 delightful pen-and-ink illustrations by the author, adding another dimension of good-natured charm to these wide-ranging explorations.Whatever your level of scientific expertise, chances are you'll derive a great deal of pleasure, stimulation, and information from this unusual and imaginative book. It belongs in the library of anyone curious about the wonders of the scientific universe. "In One Two Three . . . Infinity, as in his other books, George Gamow succeeds where others fail because of his remarkable ability to combine technical accuracy, choice of material, dignity of expression, and readability." — Saturday Review of Literature

    From the very first attempts by the Greeks to grapple with the complexities of our known world to the latest application of infinity in physics, The Road to Reality carefully explores the movement of the smallest atomic particles and reaches into the vastness of intergalactic space. Here, Penrose examines the mathematical foundations of the physical universe, exposing the underlying beauty of physics and giving us one the most important works in modern science writing.

    Non-fiction.

    The inner platform rises, revealing this exclusive edition of The Jedi Path.This ancient training manual, crafted by early Jedi Masters, has educated and enlightened generations of Jedi. It explains the history and hierarchy of the Jedi Order, and what Jedi must know to take their place as defenders of the peace in the galaxy — from mastery of the Force to the nuances of lightsaber combat.Passed down from Master to Padawan, the pages of this venerable text have been annotated by those who have held it, studied it, and lived its secrets. From Yoda and Luke Skywalker to Count Dooku and Darth Sidious, they have shaped the content of the book by leaving mementos tucked within the pages, tearing out pages, and adding their personal experiences as tangible reminders of the lessons they’ve learned.Through wars and rebellion, only a single copy of this manual has survived. It is now passed on to you.The ancient Masters who wrote the text: Fae Coven, Grand Master and head of the Jedi Council; Crix Sunburris, Jedi Ace starfighter pilot; Restelly Quist, Jedi Chief Librarian; Skarch Vaunk, Jedi Battlemaster and lightsaber expert; Bowspritz, Jedi Biologist and expert on the Living Force; Sabla-Mandibu, Jedi Seer and Holocron expert; Morrit Ch’gally, Jedi Recruiter; Gal-Stod Slagistrough, Jedi leader of the Agricultural Corps.Jedi who added personal commentary: Yoda, Thame Cerulian, Count Dooku, Qui-Gon Jinn, Obi-Wan Kenobi, Anakin Skywalker, Ahsoka Tano, Darth Sidious, and Luke Skywalker.Removable features: A letter tracing the book’s history, a severed Padawan braid, a metal Jedi Credit medallion, a Jedi starfighter patch, a burned poster of the Jedi Code, a map of the Jedi Temple, a lightsaber diagram sketched on the back of a napkin from Dex’s Diner, and a note on the missing pages torn from the book by a Sith.Created in collaboration with Lucasfilm — along with an acclaimed Star Wars author and revered Star Wars illustrators — this volume provides new insights into the history and lore of the Jedi Order while introducing never-before-seen ships, creatures, characters, and details about how one trains to become a Jedi.

    Now The Road to Dune is a companion work comparable to The Silmarillion, shedding light on and following the remarkable development of the bestselling science fiction novel of all time.In this fascinating volume, the world's millions of Dune fans can read--at long last--the unpublished chapters and scenes from Dune and Dune Messiah. The Road to Dune also includes some of the original correspondence between Frank Herbert and famed editor John W. Campbell, Jr., along with other correspondence during Herbert's years-long struggle to get his innovative work published, and the article "They Stopped the Moving Sands," Herbert's original inspiration for Dune.The Road to Dune also features newly discovered papers and manuscripts of Frank Herbert, and Spice Planet, an original novel by Brian Herbert and Kevin J. Anderson, based on a detailed outline left by Frank Herbert.The Road to Dune is a treasure trove of essays, articles, and fiction that every reader of Dune will want to add to their shelf.