In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space.Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man’s journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century’s leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat’s last theorem, that had seemed intractable before.At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics.

    This text is of interest to the curious, non-scientist who wants to know how modern physics came to be, and figure out what lies behind the stories in the science columns of their newspapers.

    Get ready to amaze your friends—and yourself—with incredible calculations you never thought you could master, as renowned “mathemagician” Arthur Benjamin shares his techniques for lightning-quick calculations and amazing number tricks. This book will teach you to do math in your head faster than you ever thought possible, dramatically improve your memory for numbers, and—maybe for the first time—make mathematics fun.Yes, even you can learn to do seemingly complex equations in your head; all you need to learn are a few tricks. You’ll be able to quickly multiply and divide triple digits, compute with fractions, and determine squares, cubes, and roots without blinking an eye. No matter what your age or current math ability, Secrets of Mental Math will allow you to perform fantastic feats of the mind effortlessly. This is the math they never taught you in school.Also available as an eBook

    Here he explains how our image of the world has changed throughout centuries. Fom Aristotle to Albert Einstein, Michael Faraday to the Higgs boson, he takes us on a wondrous journey to show us that beyond our ever-changing idea of reality is a whole new world that has yet to be discovered.

    Our Big Bang, our distant future, parallel worlds, the sub-atomic and intergalactic - none of them are what they seem. But there is a way to understand this immense strangeness - mathematics. Seeking an answer to the fundamental puzzle of why our universe seems so mathematical, Tegmark proposes a radical idea: that our physical world not only is described by mathematics, but that it is mathematics. This may offer answers to our deepest questions: How large is reality? What is everything made of? Why is our universe the way it is?Table of ContentsPreface 1 What Is Reality? Not What It Seems • What’s the Ultimate Question? • The Journey Begins Part One: Zooming Out 2 Our Place in Space Cosmic Questions • How Big Is Space? • The Size of Earth • Distance to the Moon • Distance to the Sun and the Planets • Distance to the Stars • Distance to the Galaxies • What Is Space? 3 Our Place in TimeWhere Did Our Solar System Come From? • Where Did theGalaxies Come From? • Where Did the Mysterious MicrowavesCome From? • Where Did the Atoms Come From? 4 Our Universe by NumbersWanted: Precision Cosmology • Precision Microwave-Background Fluctuations • Precision Galaxy Clustering • The Ultimate Map of Our Universe • Where Did Our Big Bang Come From? 5 Our Cosmic Origins What’s Wrong with Our Big Bang? • How Inflation Works • The Gift That Keeps on Giving • Eternal Inflation 6 Welcome to the Multiverse The Level I Multiverse • The Level II Multiverse • Multiverse Halftime Roundup Part Two: Zooming In 7 Cosmic Legos Atomic Legos • Nuclear Legos • Particle-Physics Legos • Mathematical Legos • Photon Legos • Above the Law? • Quanta and Rainbows • Making Waves • Quantum Weirdness • The Collapse of Consensus • The Weirdness Can’t Be Confined • Quantum Confusion 8 The Level III Multiverse The Level III Multiverse • The Illusion of Randomness • Quantum Censorship • The Joys of Getting Scooped • Why Your Brain Isn’t a Quantum Computer • Subject, Object and Environment • Quantum Suicide • Quantum Immortality? • Multiverses Unified • Shifting Views: Many Worlds or Many Words? Part Three: Stepping Back 9 Internal Reality, External Reality and Consensus Reality External Reality and Internal Reality • The Truth, the Whole Truth and Nothing but the Truth • Consensus Reality • Physics: Linking External to Consensus Reality 10 Physical Reality and Mathematical Reality Math, Math Everywhere! • The Mathematical Universe Hypothesis • What Is a Mathematical Structure? 11 Is Time an Illusion? How Can Physical Reality Be Mathematical? • What Are You? • Where Are You? (And What Do You Perceive?) • When Are You? 12 The Level IV Multiverse Why I Believe in the Level IV Multiverse • Exploring the Level IV Multiverse: What’s Out There? • Implications of the Level IV Multiverse • Are We Living in a Simulation? • Relation Between the MUH, the Level IV Multiverse and Other Hypotheses •Testing the Level IV Multiverse 13 Life, Our Universe and Everything How Big Is Our Physical Reality? • The Future of Physics • The Future of Our Universe—How Will It End? • The Future of Life •The Future of You—Are You Insignificant? Acknowledgments Suggestions for Further Reading Index

    New co-authors--Irl Bivens and Stephen Davis--from Davidson College; both distinguished educators and writers.* More emphasis on graphing calculators in exercises and examples, including CAS capabilities of graphing calculators.* More problems using tabular data and more emphasis on mathematical modeling.

    But in the practical experience of erotic love—and perhaps especially in marriage—we find that love and lies often work hand in hand, and that it may be difficult to sustain long-term romantic love without deception, both of oneself and of others. Drawing on contemporary philosophy, psychoanalysis and cognitive neuroscience, his own personal experience, and such famed and diverse writers on love as Shakespeare, Stendhal, Proust, Adrienne Rich, and Raymond Carver, Clancy Martin—himself divorced twice and married three times—explores how love, truthfulness, and deception work together in contemporary life and society. He concludes that learning how to love and loving well inevitably requires lying, but also argues that the best love relationships draw us slowly and with difficulty toward honesty and trust.Love and Lies is a relentlessly honest book about the difficulty of love, which is certain to both provoke and entertain.

    Author Manuel Velasquez combines clear prose and primary source readings to take you on a meaningful exploration of a range of philosophical topics, such as human nature, feminist theory, diversity, and aesthetics. Plus, the text's carefully crafted built-in learning aids will help you succeed in your course.

    Economists Ivan and Tuvana Pastine explain why, in these situations, we sometimes cooperate, sometimes clash, and sometimes act in a way that seems completely random.Stylishly brought to life by award-winning cartoonist Tom Humberstone, Game Theory will help readers understand behaviour in everything from our social lives to business, global politics to evolutionary biology. It provides a thrilling new perspective on the world we live in.

    In this entertaining and ingenious book, Blastland reveals how in our quest to make the world more understandable, we lose sight of how unexplainable it often is. The result - from GDP figures to medicine - is that experts know a lot less than they think. Filled with compelling stories from economics, genetics, business, and science, The Hidden Half is a warning that an explanation which works in one arena may not work in another. Entertaining and provocative, it will change how you view the world.

    Infinite games are more mysterious -- and ultimately more rewarding. They are unscripted and unpredictable; they are the source of true freedom.In this elegant and compelling work, James Carse explores what these games mean, and what they can mean to you. He offers stunning new insights into the nature of property and power, of culture and community, of sexuality and self-discovery, opening the door to a world of infinite delight and possibility."An extraordinary little book . . . a wise and intimate companion, an elegant reminder of the real."-- Brain/Mind Bulletin

    Real rationality, of the sort studied by psychologists, social scientists, and mathematicians. The kind of rationality where you make good decisions, even when it's hard; where you reason well, even in the face of massive uncertainty; where you recognize and make full use of your fuzzy intuitions and emotions, rather than trying to discard them. In "Rationality: From AI to Zombies," Eliezer Yudkowsky explains the science underlying human irrationality with a mix of fables, argumentative essays, and personal vignettes. These eye-opening accounts of how the mind works (and how, all too often, it doesn't!) are then put to the test through some genuinely difficult puzzles: computer scientists' debates about the future of artificial intelligence (AI), physicists' debates about the relationship between the quantum and classical worlds, philosophers' debates about the metaphysics of zombies and the nature of morality, and many more. In the process, "Rationality: From AI to Zombies" delves into the human significance of correct reasoning more deeply than you'll find in any conventional textbook on cognitive science or philosophy of mind. A decision theorist and researcher at the Machine Intelligence Research Institute, Yudkowsky published earlier drafts of his writings to the websites Overcoming Bias and Less Wrong. "Rationality: From AI to Zombies" compiles six volumes of Yudkowsky's essays into a single electronic tome. Collectively, these sequences of linked essays serve as a rich and lively introduction to the science—and the art—of human rationality.

    Wilczek’s groundbreaking work in quantum physics was inspired by his intuition to look for a deeper order of beauty in nature. In fact, every major advance in his career came from this intuition: to assume that the universe embodies beautiful forms, forms whose hallmarks are symmetry—harmony, balance, proportion—and economy. There are other meanings of “beauty,” but this is the deep logic of the universe—and it is no accident that it is also at the heart of what we find aesthetically pleasing and inspiring.Wilczek is hardly alone among great scientists in charting his course using beauty as his compass. As he reveals in A Beautiful Question, this has been the heart of scientific pursuit from Pythagoras, the ancient Greek who was the first to argue that “all things are number,” to Galileo, Newton, Maxwell, Einstein, and into the deep waters of twentiethcentury physics. Though the ancients weren’t right about everything, their ardent belief in the music of the spheres has proved true down to the quantum level. Indeed, Wilczek explores just how intertwined our ideas about beauty and art are with our scientific understanding of the cosmos.Wilczek brings us right to the edge of knowledge today, where the core insights of even the craziest quantum ideas apply principles we all understand. The equations for atoms and light are almost literally the same equations that govern musical instruments and sound; the subatomic particles that are responsible for most of our mass are determined by simple geometric symmetries. The universe itself, suggests Wilczek, seems to want to embody beautiful and elegant forms. Perhaps this force is the pure elegance of numbers, perhaps the work of a higher being, or somewhere between. Either way, we don’t depart from the infinite and infinitesimal after all; we’re profoundly connected to them, and we connect them. When we find that our sense of beauty is realized in the physical world, we are discovering something about the world, but also something about ourselves.Gorgeously illustrated, A Beautiful Question is a mind-shifting book that braids the age-old quest for beauty and the age-old quest for truth into a thrilling synthesis. It is a dazzling and important work from one of our best thinkers, whose humor and infectious sense of wonder animate every page. Yes: The world is a work of art, and its deepest truths are ones we already feel, as if they were somehow written in our souls.

    She draws on conversations with hundreds of the world's top scientists and on her own work as a Pulitzer Prize-winning writer for the New York Times to create a thoroughly entertaining guide to scientific literacy. Angier's gifts are on full display in The Canon, an ebullient celebration of science that stands to become a classic. The Canon is vital reading for anyone who wants to understand the great issues of our time -- from stem cells and bird flu to evolution and global warming. And it's for every parent who has ever panicked when a child asked how the earth was formed or what electricity is. Angier's sparkling prose and memorable metaphors bring the science to life, reigniting our own childhood delight in discovering how the world works. "Of course you should know about science," writes Angier, "for the same reason Dr. Seuss counsels his readers to sing with a Ying or play Ring the Gack: These things are fun and fun is good." The Canon is a joyride through the major scientific disciplines: physics, chemistry, biology, geology, and astronomy. Along the way, we learn what is actually happening when our ice cream melts or our coffee gets cold, what our liver cells do when we eat a caramel, why the horse is an example of evolution at work, and how we're all really made of stardust. It's Lewis Carroll meets Lewis Thomas -- a book that will enrapture, inspire, and enlighten.

    Increasingly, the decisions that affect our lives--where we go to school, whether we can get a job or a loan, how much we pay for health insurance--are being made not by humans, but by machines. In theory, this should lead to greater fairness: Everyone is judged according to the same rules.But as mathematician and data scientist Cathy O'Neil reveals, the mathematical models being used today are unregulated and uncontestable, even when they're wrong. Most troubling, they reinforce discrimination--propping up the lucky, punishing the downtrodden, and undermining our democracy in the process.