Hermann Weyl explores the concept of symmetry beginning with the idea that it represents a harmony of proportions, and gradually departs to examine its more abstract varieties and manifestations--as bilateral, translatory, rotational, ornamental, and crystallographic. Weyl investigates the general abstract mathematical idea underlying all these special forms, using a wealth of illustrations as support. Symmetry is a work of seminal relevance that explores the great variety of applications and importance of symmetry.

    It had to be found. But projects as big as CERN’s Large Hadron Collider don’t happen without incredible risks – and occasional skullduggery. In the definitive account of this landmark event, Caltech physicist and acclaimed science writer Sean Carroll reveals the insights, rivalry, and wonder that fuelled the Higgs discovery, and takes us on a riveting and irresistible ride to the very edge of physics today.

    Admittedly, computers now play chess at the grandmaster level, but do they understand the game as we do? Can a computer eventually do everything a human mind can do? In this absorbing and frequently contentious book, Roger Penrose--eminent physicist and winner, with Stephen Hawking, of the prestigious Wolf prize--puts forward his view that there are some facets of human thinking that can never be emulated by a machine. Penrose examines what physics and mathematics can tell us about how the mind works, what they can't, and what we need to know to understand the physical processes of consciousness. He is among a growing number of physicists who think Einstein wasn't being stubborn when he said his little finger told him that quantum mechanics is incomplete, and he concludes that laws even deeper than quantum mechanics are essential for the operation of a mind. To support this contention, Penrose takes the reader on a dazzling tour that covers such topics as complex numbers, Turing machines, complexity theory, quantum mechanics, formal systems, Godel undecidability, phase spaces, Hilbert spaces, black holes, white holes, Hawking radiation, entropy, quasicrystals, the structure of the brain, and scores of other subjects. The Emperor's New Mind will appeal to anyone with a serious interest in modern physics and its relation to philosophical issues, as well as to physicists, mathematicians, philosophers and those on either side of the AI debate.

    Why is it better to buy a lottery ticket on a Friday? Why are showers always too hot or too cold? And what's the connection between a rugby player taking a conversion and a tourist trying to get the best photograph of Nelson's Column?These and many other fascinating questions are answered in this entertaining and highly informative book, which is ideal for anyone wanting to remind themselves – or discover for the first time – that maths is relevant to almost everything we do.Dating, cooking, travelling by car, gambling and even life-saving techniques have links with intriguing mathematical problems, as you will find explained here. Whether you have a PhD in astrophysics or haven't touched a maths problem since your school days, this book will give you a fresh understanding of the world around you.

    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.

    But the dot, though perfect in every way, only had eyes for a wild and unkempt squiggle. All of the line's romantic dreams were in vain, until he discovered...angles! Now, with newfound self-expression, he can be anything he wants to be--a square, a triangle, a parallelogram....And that's just the beginning!First published in 1963 and made into an Academy Award-winning animated short film, here is a supremely witty love story with a twist that reveals profound truths about relationships--both human and mathematical--sure to tickle lovers of all ages.

    We like to imagine that it’s based on evidence and the results of fair tests. In reality, those tests are often profoundly flawed. We like to imagine that doctors are familiar with the research literature surrounding a drug, when in reality much of the research is hidden from them by drug companies. We like to imagine that doctors are impartially educated, when in reality much of their education is funded by industry. We like to imagine that regulators let only effective drugs onto the market, when in reality they approve hopeless drugs, with data on side effects casually withheld from doctors and patients.All these problems have been protected from public scrutiny because they’re too complex to capture in a sound bite. But Dr. Ben Goldacre shows that the true scale of this murderous disaster fully reveals itself only when the details are untangled. He believes we should all be able to understand precisely how data manipulation works and how research misconduct on a global scale affects us. In his own words, “the tricks and distortions documented in these pages are beautiful, intricate, and fascinating in their details.” With Goldacre’s characteristic flair and a forensic attention to detail, Bad Pharma reveals a shockingly broken system and calls for something to be done. This is the pharmaceutical industry as it has never been seen before.

    . . 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

    Now he brings his considerable talents to the history of one of math's most enduring puzzles: the seemingly paradoxical nature of infinity.Is infinity a valid mathematical property or a meaningless abstraction? The nineteenth-century mathematical genius Georg Cantor's answer to this question not only surprised him but also shook the very foundations upon which math had been built. Cantor's counterintuitive discovery of a progression of larger and larger infinities created controversy in his time and may have hastened his mental breakdown, but it also helped lead to the development of set theory, analytic philosophy, and even computer technology.Smart, challenging, and thoroughly rewarding, Wallace's tour de force brings immediate and high-profile recognition to the bizarre and fascinating world of higher mathematics.

    This Penguin Classics edition is edited with an introduction by James Moore and Adrian Desmond.In The Origin of Species, Charles Darwin refused to discuss human evolution, believing the subject too 'surrounded with prejudices'. He had been reworking his notes since the 1830s, but only with trepidation did he finally publish The Descent of Man in 1871. The book notoriously put apes in our family tree and made the races one family, diversified by 'sexual selection' - Darwin's provocative theory that female choice among competing males leads to diverging racial characteristics. Named by Sigmund Freud as 'one of the ten most significant books' ever written, Darwin's Descent of Man continues to shape the way we think about what it is that makes us uniquely human.In their introduction, James Moore and Adrian Desmond, acclaimed biographers of Charles Darwin, call for a radical re-assessment of the book, arguing that its core ideas on race were fired by Darwin's hatred of slavery. The text is the second and definitive edition and this volume also contains suggestions for further reading, a chronology and biographical sketches of prominent individuals mentioned.Charles Darwin (1809-82), a Victorian scientist and naturalist, has become one of the most famous figures of science to date. The advent of On the Origin of Species by Means of Natural Selection in 1859 challenged and contradicted all contemporary biological and religious beliefs.If you enjoyed The Descent of Man, you might like Darwin's On the Origin of Species, also available in Penguin Classics.

    One of the most influential figures of the twentieth century, he transformed philosophy and can lay claim to being one of the greatest philosophers of all time. He was a Nobel Prize winner for Literature and was imprisoned several times as a result of his pacifism. His views on religion, education, sex, politics and many other topics, made him one of the most read and revered writers of the age. This, his autobiography, is one of the most compelling and vivid ever written. This one-volume, compact paperback edition contains an introduction by the politician and scholar, Michael Foot, which explores the status of this classic nearly 30 years after the publication of the final volume.

    Czerski provides the tools to alter the way we see everything around us by linking ordinary objects and occurrences, like popcorn popping, coffee stains, and fridge magnets, to big ideas like climate change, the energy crisis, or innovative medical testing. She provides answers to vexing questions: How do ducks keep their feet warm when walking on ice? Why does it take so long for ketchup to come out of a bottle? Why does milk, when added to tea, look like billowing storm clouds? In an engaging voice at once warm and witty, Czerski shares her stunning breadth of knowledge to lift the veil of familiarity from the ordinary.

    Topics include the development of counting and numbers systems, the emergence of zero, cultures that don’t have numbers, algebra, solid geometry, symmetry and beauty, perspective, riddles and problems, calculus, mathematical logic, friction force and displacement, subatomic particles, and the expansion of the universe. Great mathematical thinkers covered include Napier, Liu Hui, Aryabhata, Galileo, Newton, Russell, Einstein, Riemann, Euclid, Carl Friedrich Gauss, Charles Babbage, Montmort, Wittgenstein, and many more. The book is beautifully illustrated throughout in full color.

    This time physicist Robert Gilmore takes us on a journey with Dorothy, following the yellow building block road through the land of the Wizard of Quarks. Using characters and situations based on the Wizard of Oz story, we learn along the way about the fascinating world of particle physics. Classes of particles, from quarks to leptons are shown in an atomic garden, where atoms and molecules are produced. See how Dorothy, The Tin Geek, and the Cowardly Lion experience the bizarre world of subatomic particles.