Following closely behind is y, or gamma, a constant that arises in many mathematical areas yet maintains a profound sense of mystery. In a tantalizing blend of history and mathematics, Julian Havil takes the reader on a journey through logarithms and the harmonic series, the two defining elements of gamma, toward the first account of gamma's place in mathematics. Introduced by the Swiss mathematician Leonhard Euler (1707-1783), who figures prominently in this book, gamma is defined as the limit of the sum of 1 + 1/2 + 1/3 + . . . Up to 1/n, minus the natural logarithm of n--the numerical value being 0.5772156. . . . But unlike its more celebrated colleagues π and e, the exact nature of gamma remains a mystery--we don't even know if gamma can be expressed as a fraction. Among the numerous topics that arise during this historical odyssey into fundamental mathematical ideas are the Prime Number Theorem and the most important open problem in mathematics today--the Riemann Hypothesis (though no proof of either is offered!). Sure to be popular with not only students and instructors but all math aficionados, Gamma takes us through countries, centuries, lives, and works, unfolding along the way the stories of some remarkable mathematics from some remarkable mathematicians.-- "Notices of the American Mathematical Society"

    Today, scientists are attempting to measure the entire universe and to determine its origin. Although the methods have changed, the quest to chart the horizons of space and time continues to be one of the great adventures of science.Measuring the Universe is an eloquent chronicle of the men and women– from Aristarchus to Cassini, Sir Isaac Newton to Henrietta Leavitt and Stephen Hawking–who have gradually unlocked the mysteries of "how far" and in so doing have changed our ideas about the size and nature of the universe and our place in it. Kitty Ferguson reveals their methods to have been as inventive as their results were–and are–eye-opening. Advances such as Copernicus's revolutionary insights about the arrangement of the solar system, William Herschel's meticulous creation of the first three-dimensional map of the universe, and Edwin Hubble's astonishing discovery that the universe is expanding have by turns revolutionized our concept of the universe. Connecting centuries of breakthroughs with the political and cultural events surrounding them, Ferguson makes astronomy part of the sweep of history.To measure the seemingly immeasurable, scientists have always pushed the boundaries of the imagination–today, for example, facing the paradox of an ever-expanding universe that doesn't appear to expand into anything. In Kitty Fergeson's skillfill hands, the unimaginable becomes accessible and the splendid quest something we all can share.

    Shankar, a well-known physicist and contagiously enthusiastic educator, was among the first to offer a course through the innovative Open Yale Course program. His popular online video lectures on introductory physics have been viewed over a million times. In this concise and self-contained book based on his online Yale course, Shankar explains the fundamental concepts of physics from Galileo’s and Newton’s discoveries to the twentieth-century’s revolutionary ideas on relativity and quantum mechanics.   The book begins at the simplest level, develops the basics, and reinforces fundamentals, ensuring a solid foundation in the principles and methods of physics. It provides an ideal introduction for college-level students of physics, chemistry, and engineering, for motivated AP Physics students, and for general readers interested in advances in the sciences. Instructor resources--including problem sets and sample examinations--and more information about Professor Shankar's course are available at http://oyc.yale.edu/physics/phys-200.

    How To is a guide to the third kind of approach. It's full of highly impractical advice for everything from landing a plane to digging a hole.Bestselling author and cartoonist Randall Munroe explains how to predict the weather by analyzing the pixels of your Facebook photos. He teaches you how to tell if you're a baby boomer or a 90's kid by measuring the radioactivity of your teeth. He offers tips for taking a selfie with a telescope, crossing a river by boiling it, and powering your house by destroying the fabric of space-time. And if you want to get rid of the book once you're done with it, he walks you through your options for proper disposal, including dissolving it in the ocean, converting it to a vapor, using tectonic plates to subduct it into the Earth's mantle, or launching it into the Sun.By exploring the most complicated ways to do simple tasks, Munroe doesn't just make things difficult for himself and his readers. As he did so brilliantly in What If?, Munroe invites us to explore the most absurd reaches of the possible. Full of clever infographics and amusing illustrations, How To is a delightfully mind-bending way to better understand the science and technology underlying the things we do every day.

    Stimulating, illuminating, and always surprising, The Big Questions challenges readers to re-evaluate their most fundamental beliefs and reveals the relationship between the loftiest philosophical quests and our everyday lives.

    Abbott published a brilliant novel about mathematics and philosophy that charmed and fascinated all of England. As both a witty satire of Victorian society and a means by which to explore the fourth dimension, Flatland remains a tour de force. Now, British mathematician and accomplished science writer Ian Stewart has written a fascinating, modern sequel to Abbott's book. Through larger-than-life characters and an inspired story line, Flatterland explores our present understanding of the shape and origins of the universe, the nature of space, time, and matter, as well as modern geometries and their applications. The journey begins when our heroine, Victoria Line, comes upon her great-great-grandfather A. Square's diary, hidden in the attic. The writings help her to contact the Space Hopper, who becomes her guide and mentor through eleven dimensions. Along the way, we meet Schröger's Cat, The Charming Construction Entity, The Mandelblot (who lives in Fractalia), and Moobius the one-sided cow. In the tradition of Alice in Wonder-land and The Phantom Toll Booth, this magnificent investigation into the nature of reality is destined to become a modern classic.

    George's parents, who have always been wary of technology, warn him about their new neighbors: Eric is a scientist and his daughter, Annie, seems to be following in his footsteps. But when George befriends them and Cosmos, their super-computer, he finds himself on a wildly fun adventure, while learning about physics, time, and the universe. With Cosmos's help, he can travel to other planets and a black hole. But what would happen if the wrong people got their hands on Cosmos? George, Annie, and Eric aren't about to find out, and what ensues is a funny adventure that clearly explains the mysteries of science. Garry Parsons' energetic illustrations add humor and interest, and his scientific drawings add clarity; there are also eight 4-page full-color inserts of scientific photos.

    The Universe, of course, is our own. And Roundworld is Earth. As the wizards watch their accidental creation grow, we follow the story of our universe from the primal singularity of the Big Bang to the Internet and beyond. Through this original Terry Pratchett story (with intervening chapters from Cohen and Stewart) we discover how puny and insignificant individual lives are against a cosmic backdrop of creation and disaster. Yet, paradoxically, we see how the richness of a universe based on rules, has led to a complex world and at least one species that tried to get a grip of what was going on.

    Jim Carter, the Einstein of outsiders, has developed his own complete theory of matter and energy and gravity that he demonstrates with experiments in his backyard,-with garbage cans and a disco fog machine he makes smoke rings to test his ideas about atoms. Captivated by the imaginative power of his theories and his resolutely DIY attitude, Wertheim has been following Carter's progress for the past decade.Centuries ago, natural philosophers puzzled out the laws of nature using the tools of observation and experimentation. Today, theoretical physics has become mathematically inscrutable, accessible only to an elite few. In rejecting this abstraction, outsider theorists insist that nature speaks a language we can all understand. Through a profoundly human profile of Jim Carter, Wertheim's exploration of the bizarre world of fringe physics challenges our conception of what science is, how it works, and who it is for.

    Using illustrations and examples from science fiction pulp magazines and comic books, The Amazing Story of Quantum Mechanics explains the fundamental principles of quantum mechanics that underlie the world we live in.Watch a Video

     This top-selling, theorem-proof text presents a careful treatment of the principal topics of linear algebra, and illustrates the power of the subject through a variety of applications. It emphasizes the symbiotic relationship between linear transformations and matrices, but states theorems in the more general infinite-dimensional case where appropriate.

    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.

    Richard Gott leads time travel out of the world of H. G. Wells and into the realm of scientific possibility. Building on theories posited by Einstein and advanced by scientists such as Stephen Hawking and Kip Thorne, Gott explains how time travel can actually occur. He describes, with boundless enthusiasm and humor, how travel to the future is not only possible but has already happened, and he contemplates whether travel to the past is also conceivable. Notable not only for its extraordinary subject matter and scientific brilliance, Time Travel in Einstein’s Universe is a delightful and captivating exploration of the surprising facts behind the science fiction of time travel.

    Rare Book

    Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the street to the chemist, but that's just peanuts to space.' Douglas Adams, Hitch-hiker's Guide to the GalaxyWe human beings have trouble with infinity - yet infinity is a surprisingly human subject. Philosophers and mathematicians have gone mad contemplating its nature and complexity - yet it is a concept routinely used by schoolchildren. Exploring the infinite is a journey into paradox. Here is a quantity that turns arithmetic on its head, making it feasible that 1 = 0. Here is a concept that enables us to cram as many extra guests as we like into an already full hotel. Most bizarrely of all, it is quite easy to show that there must be something bigger than infinity - when it surely should be the biggest thing that could possibly be. Brian Clegg takes us on a fascinating tour of that borderland between the extremely large and the ultimate that takes us from Archimedes, counting the grains of sand that would fill the universe, to the latest theories on the physical reality of the infinite. Full of unexpected delights, whether St Augustine contemplating the nature of creation, Newton and Leibniz battling over ownership of calculus, or Cantor struggling to publicise his vision of the transfinite, infinity's fascination is in the way it brings together the everyday and the extraordinary, prosaic daily life and the esoteric.Whether your interest in infinity is mathematical, philosophical, spiritual or just plain curious, this accessible book offers a stimulating and entertaining read.