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.

    Amazingly, he completed the task in an intense six weeks, and Eine kurze Weltgeschichte für junge Leser was published in Vienna to immediate success, and is now available in seventeen languages across the world. Toward the end of his long life, Gombrich embarked upon a revision and, at last, an English translation. A Little History of the World presents his lively and involving history to English-language readers for the first time. Superbly designed and freshly illustrated, this is a book to be savored and collected. In forty concise chapters, Gombrich tells the story of man from the stone age to the atomic bomb. In between emerges a colorful picture of wars and conquests, grand works of art, and the spread and limitations of science. This is a text dominated not by dates and facts, but by the sweep of mankind's experience across the centuries, a guide to humanity's achievements and an acute witness to its frailties. The product of a generous and humane sensibility, this timeless account makes intelligible the full span of human history.

    Topics covered include matrix multiplication, row reduction, matrix inverse, orthogonality and computation. The self-teaching book is loaded with examples and graphics and provides a wide array of probing problems, accompanying solutions, and a glossary. Chapter 1: Introduction to Vectors; Chapter 2: Solving Linear Equations; Chapter 3: Vector Spaces and Subspaces; Chapter 4: Orthogonality; Chapter 5: Determinants; Chapter 6: Eigenvalues and Eigenvectors; Chapter 7: Linear Transformations; Chapter 8: Applications; Chapter 9: Numerical Linear Algebra; Chapter 10: Complex Vectors and Matrices; Solutions to Selected Exercises; Final Exam. Matrix Factorizations. Conceptual Questions for Review. Glossary: A Dictionary for Linear Algebra Index Teaching Codes Linear Algebra in a Nutshell.

    In 1996 Joseph LeDoux's "The Emotional Brain" presented a revelatory examination of the biological bases of our emotions and memories. Now, the world-renowned expert on the brain has produced with a groundbreaking work that tells a more profound story: how the little spaces between the neurons-the brain's synapses--are the channels through which we think, act, imagine, feel, and remember. Synapses encode the essence of personality, enabling each of us to function as a distinctive, integrated individual from moment to moment. Exploring the functioning of memory, the synaptic basis of mental illness and drug addiction, and the mechanism of self-awareness, "Synaptic Self" is a provocative and mind-expanding work that is destined to become a classic.

    Len Fisher turns his attention to the science of cooperation in his lively and thought-provoking book. Fisher shows how the modern science of game theory has helped biologists to understand the evolution of cooperation in nature, and investigates how we might apply those lessons to our own society. In a series of experiments that take him from the polite confines of an English dinner party to crowded supermarkets, congested Indian roads, and the wilds of outback Australia, not to mention baseball strategies and the intricacies of quantum mechanics, Fisher sheds light on the problem of global cooperation. The outcomes are sometimes hilarious, sometimes alarming, but always revealing. A witty romp through a serious science, Rock, Paper, Scissors will both teach and delight anyone interested in what it what it takes to get people to work together.

    What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today? In Enlightening Symbols, popular math writer Joseph Mazur explains the fascinating history behind the development of our mathematical notation system. He shows how symbols were used initially, how one symbol replaced another over time, and how written math was conveyed before and after symbols became widely adopted.Traversing mathematical history and the foundations of numerals in different cultures, Mazur looks at how historians have disagreed over the origins of the numerical system for the past two centuries. He follows the transfigurations of algebra from a rhetorical style to a symbolic one, demonstrating that most algebra before the sixteenth century was written in prose or in verse employing the written names of numerals. Mazur also investigates the subconscious and psychological effects that mathematical symbols have had on mathematical thought, moods, meaning, communication, and comprehension. He considers how these symbols influence us (through similarity, association, identity, resemblance, and repeated imagery), how they lead to new ideas by subconscious associations, how they make connections between experience and the unknown, and how they contribute to the communication of basic mathematics.From words to abbreviations to symbols, this book shows how math evolved to the familiar forms we use today.

    . . a book that enriches our understanding of how the struggle to think new thoughts is shared across time and space and people.”—The Sunday Telegraph (London)Christmas, 1859. Just one month after the publication of On the Origin of Species, Charles Darwin received an unsettling letter. He had expected criticism; in fact, letters were arriving daily, most expressing outrage and accusations of heresy. But this letter was different. It accused him of failing to acknowledge his predecessors, of taking credit for a theory that had already been discovered by others. Darwin realized that he had made an error in omitting from Origin of Species any mention of his intellectual forebears. Yet when he tried to trace all of the natural philosophers who had laid the groundwork for his theory, he found that history had already forgotten many of them.Darwin’s Ghosts tells the story of the collective discovery of evolution, from Aristotle, walking the shores of Lesbos with his pupils, to Al-Jahiz, an Arab writer in the first century, from Leonardo da Vinci, searching for fossils in the mine shafts of the Tuscan hills, to Denis Diderot in Paris, exploring the origins of species while under the surveillance of the secret police, and the brilliant naturalists of the Jardin de Plantes, finding evidence for evolutionary change in the natural history collections stolen during the Napoleonic wars. Evolution was not discovered single-handedly, Rebecca Stott argues, contrary to what has become standard lore, but is an idea that emerged over many centuries, advanced by daring individuals across the globe who had the imagination to speculate on nature’s extraordinary ways, and who had the courage to articulate such speculations at a time when to do so was often considered heresy.With each chapter focusing on an early evolutionary thinker, Darwin’s Ghosts is a fascinating account of a diverse group of individuals who, despite the very real dangers of challenging a system in which everything was presumed to have been created perfectly by God, felt compelled to understand where we came from. Ultimately, Stott demonstrates, ideas—including evolution itself—evolve just as animals and plants do, by intermingling, toppling weaker notions, and developing over stretches of time. Darwin’s Ghosts presents a groundbreaking new theory of an idea that has changed our very understanding of who we are.

    Even when dealing with standard material, Stillwell manages to dramatize it and to make it worth rethinking. In short, his book is a splendid addition to the genre of works that build royal roads to mathematical culture for the many." (Mathematical Intelligencer)This second edition includes new chapters on Chinese and Indian number theory, on hypercomplex numbers, and on algebraic number theory. Many more exercises have been added, as well as commentary to the exercises explaining how they relate to the preceding section, and how they foreshadow later topics.

    From the epic poets of antiquity to contemporary writers of science fiction, from the authors of the Holy Scriptures to modern raconteurs of fairy tales, writers and storytellers through the ages have invented imaginary and mythical lands, projecting onto them all of our human dreams, ideals, and fears. In the tradition of his acclaimed History of Beauty, On Ugliness, and The Infinity of Lists, renowned writer and cultural critic Umberto Eco leads us on a beautifully illustrated journey through these lands of myth and invention, showing us their inhabitants, the passions that rule them, their heroes and antagonists, and, above all, the importance they hold for us. He explores this human urge to create such places, the utopias and dystopias where our imagination can confront things that are too incredible or challenging for our limited real world. Illuminated with more than 300 color images, The Book of Legendary Lands is both erudite and thoroughly enjoyable, bringing together disparate elements of our shared literary legacy in a way only Umberto Eco can. Homer’s poems and other ancient and medieval texts are presented side by side with Gulliver’s Travels and Alice in Wonderland; Tolkien shares space with Marco Polo’s Books of the Marvels of the World; films complement poems, and comics inform novels. Together, these stories have influenced the sensibilities and worldview of all of us.

    Pi-or ? as it is symbolically known-is infinite and, in The Joy of pi, it proves to be infinitely intriguing. With incisive historical insight and a refreshing sense of humor, David Blatner explores the many facets of pi and humankind's fascination with it-from the ancient Egyptians and Archimedes to Leonardo da Vinci and the modern-day Chudnovsky brothers, who have calculated pi to eight billion digits with a homemade supercomputer.The Joy of Pi is a book of many parts. Breezy narratives recount the history of pi and the quirky stories of those obsessed with it. Sidebars document fascinating pi trivia (including a segment from the 0. J. Simpson trial). Dozens of snippets and factoids reveal pi's remarkable impact over the centuries. Mnemonic devices teach how to memorize pi to many hundreds of digits (or more, if you're so inclined). Pi-inspired cartoons, poems, limericks, and jokes offer delightfully "square" pi humor. And, to satisfy even the most exacting of number jocks, the first one million digits of pi appear throughout the book.A tribute to all things pi, The Joy of pi is sure to foster a newfound affection and respect for the big number with the funny little symbol.