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.

    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.

    In the past, discoveries often had to wait for the rise of the next generation to see questions in a new light and let go of old truisms. Today, in a world that is defined by a rapid rate of change, staying on the cutting edge has as much to do with shedding outdated notions as adopting new ones. In this spirit, John Brockman, publisher of the online salon Edge.org ("the world's smartest website"—The Guardian), asked 175 of the world's most influential scientists, economists, artists, and philosophers: What scientific idea is ready for retirement?Jared Diamond explores the diverse ways that new ideas emerge * Nassim Nicholas Taleb takes down the standard deviation * Richard Thaler and novelist Ian McEwan reveal the usefulness of "bad" ideas * Steven Pinker dismantles the working theory of human behavior * Richard Dawkins renounces essentialism * Sherry Turkle reevaluates our expectations of artificial intelligence * Physicist Andrei Linde suggests that our universe and its laws may not be as unique as we think * Martin Rees explains why scientific understanding is a limitless goal * Alan Guth rethinks the origins of the universe * Sam Harris argues that our definition of science is too narrow * Nobel Prize winner Frank Wilczek disputes the division between mind and matter * Lawrence Krauss challenges the notion that the laws of physics were preordained * plus contributions from Daniel Goleman, Mihaly Csikszentmihalyi, Nicholas Carr, Rebecca Newberger Goldstein, Matt Ridley, Stewart Brand, Sean Carroll, Daniel C. Dennett, Helen Fisher, Douglas Rushkoff, Lee Smolin, Kevin Kelly, Freeman Dyson, and others.

    It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.

    His illuminating explanation is addressed to the person who wants to understand the place of mathematics in modern civilization but who has been intimidated by its supposed difficulty. Mathematics is the language of size, shape, and order—a language Hogben shows one can both master and enjoy.

    Bronowski's exciting, illustrated investigation offers a perspective not just on science, but on civilization itself. Lower than the angelsForewordThe harvest of the seasons The grain in the stoneThe hidden structure The music of the spheresThe starry messanger The majestic clockworkThe drive for power The ladder of creation World within world Knowledge or certainty Generation upon generationThe long childhoodBibliographyIndex

    Astonishing images of Earth from above, the phenomena of our solar system, and the celestial bodies of deep space will captivate readers and photography lovers with an interest in science, astronomy, and the great beyond. Each extraordinary photograph from the legendary space agency is paired with explanatory text that contextualizes its place in the cosmic ballet of planets, stars, dust, and matter—from Earth's limb to solar flares, the Jellyfish Nebula to Pandora's Cluster. Featuring a preface by Bill Nye, this engaging volume offers up-close views of our remarkable cosmos, and sparks wonder at the marvels of Earth and space.

    Your head hurts. You're mildly annoyed as you get the kids ready for school and dress for work yourself. Meanwhile, an epic war is being fought, just below your skin. Millions are fighting and dying for you to be able to complain as you head out the door.So what, exactly, is your immune system?Second only to the human brain in its complexity, it is one of the oldest and most critical facets of life on Earth. Without it, you would die within days. In Immune, Philipp Dettmer, the brains behind the most popular science channel on YouTube, takes readers on a journey through the fortress of the human body and its defenses. There is a constant battle of staggering scale raging within us, full of stories of invasion, strategy, defeat, and noble self-sacrifice. In fact, in the time you've been reading this, your immune system has probably identified and eradicated a cancer cell that started to grow in your body.Each chapter delves into an element of the immune system, including defenses like antibodies and inflammation as well as threats like bacteria, allergies, and cancer, as Dettmer reveals why boosting your immune system is actually nonsense, how parasites sneak their way past your body's defenses, how viruses work, and what goes on in your wounds when you cut yourself.Enlivened by engaging graphics and immersive descriptions, Immune turns one of the most intricate, interconnected, and confusing subjects—immunology—into a gripping adventure through an astonishing alien landscape. Immune is a vital and remarkably fun crash course in what is arguably, and increasingly, the most important system in the body.

    With the authority of a scholar and the sparkle of an old-time storyteller, Dr. Volney Steele takes the reader from rotgut whiskey to modern anesthetics, from castor oil to antibiotics, and from barroom surgery to modern hospital operations. Dr. Steele wrote Bleed, Blister, and Purge "to shed light on and celebrate the dedication and humanitarianism of those many physicians, nurses, shamans, and people of sound practical sense who saw their patients--often friends and family--through the adversities that bedeviled them."

    We are very pleased to be the first U.S. publisher to offer Ediths timeless watercolors.

    Just about everyone has at least heard of Albert Einstein's formulation of 1905, which came into the world as something of an afterthought. But far fewer can explain his insightful linkage of energy to mass. David Bodanis offers an easily grasped gloss on the equation. Mass, he writes, "is simply the ultimate type of condensed or concentrated energy," whereas energy "is what billows out as an alternate form of mass under the right circumstances." Just what those circumstances are occupies much of Bodanis's book, which pays homage to Einstein and, just as important, to predecessors such as Maxwell, Faraday, and Lavoisier, who are not as well known as Einstein today. Balancing writerly energy and scholarly weight, Bodanis offers a primer in modern physics and cosmology, explaining that the universe today is an expression of mass that will, in some vastly distant future, one day slide back to the energy side of the equation, replacing the "dominion of matter" with "a great stillness"--a vision that is at once lovely and profoundly frightening. Without sliding into easy psychobiography, Bodanis explores other circumstances as well; namely, Einstein's background and character, which combined with a sterling intelligence to afford him an idiosyncratic view of the way things work--a view that would change the world. --Gregory McNamee

    The perceived distances between objects in the sky mirrored (and were mirrored by) the spaces between notes forming chords and scales. The smooth operation of the cosmos created a divine harmony that composers sought to capture and express. Jamie James allows readers to see how this scientific philosophy emerged, how it was shattered by changing views of the universe and the rise of Romanticism, and to what extent it survives today - if at all. From Pythagoras to Newton, Bach to Beethoven, and on to the twentieth century of Einstein, Schoenberg, Stravinsky, Cage and Glass. A spellbinding examination of the interwoven fates of science and music throughout history.

    It may hide additional dimensions of space other than the familier three we recognize. There might even be another universe adjacent to ours, invisible and unattainable . . . for now.Warped Passages is a brilliantly readable and altogether exhilarating journey that tracks the arc of discovery from early twentieth-century physics to the razor's edge of modern scientific theory. One of the world's leading theoretical physicists, Lisa Randall provides astonishing scientific possibilities that, until recently, were restricted to the realm of science fiction. Unraveling the twisted threads of the most current debates on relativity, quantum mechanics, and gravity, she explores some of the most fundamental questions posed by Nature—taking us into the warped, hidden dimensions underpinning the universe we live in, demystifying the science of the myriad worlds that may exist just beyond our own.

    “The most entertaining logician and set theorist who ever lived” (Martin Gardner) gives us an encore to The Lady or the Tiger?-a fiendishly clever, utterly captivating new collection of 225 brainteasers, puzzles, and paradoxes.

    Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation.In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge--from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool--the general principle--from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems.Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.