But from the perspective of mathematics, groupings of ten are arbitrary, and can have serious shortcomings. Twelve would be better for divisibility, and eight is smaller and well suited to repeated halving. Grouping by two, as in binary code, has turned out to have its own remarkable advantages.Paul Lockhart reveals arithmetic not as the rote manipulation of numbers--a practical if mundane branch of knowledge best suited for balancing a checkbook or filling out tax forms--but as a set of ideas that exhibit the fascinating and sometimes surprising behaviors usually reserved for higher branches of mathematics. The essence of arithmetic is the skillful arrangement of numerical information for ease of communication and comparison, an elegant intellectual craft that arises from our desire to count, add to, take away from, divide up, and multiply quantities of important things. Over centuries, humans devised a variety of strategies for representing and using numerical information, from beads and tally marks to adding machines and computers. Lockhart explores the philosophical and aesthetic nature of counting and of different number systems, both Western and non-Western, weighing the pluses and minuses of each.A passionate, entertaining survey of foundational ideas and methods, Arithmetic invites readers to experience the profound and simple beauty of its subject through the eyes of a modern research mathematician.

    Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. Some of the proofs are classics, but many are new and brilliant proofs of classical results. ...Aigner and Ziegler... write: ..". all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999..". the style is clear and entertaining, the level is close to elementary ... and the proofs are brilliant. ..." LMS Newsletter, January 1999This third edition offers two new chapters, on partition identities, and on card shuffling. Three proofs of Euler's most famous infinite series appear in a separate chapter. There is also a number of other improvements, such as an exciting new way to "enumerate the rationals."

    She puts the English national character under her anthropological microscope, and finds a strange and fascinating culture, governed by complex sets of unspoken rules and byzantine codes of behaviour. The rules of weather-speak. The ironic-gnome rule. The reflex apology rule. The paranoid-pantomime rule. Class indicators and class anxiety tests. The money-talk taboo and many more ...Through a mixture of anthropological analysis and her own unorthodox experiments (using herself as a reluctant guinea-pig), Kate Fox discovers what these unwritten behaviour codes tell us about Englishness.

    Meet a man who can pull two railroad passenger cars with his teeth and a real-life human cannon ball. Come face to face with a dead rattlesnake that still bites. And unlock the secrets of a magician's bodiless head. Welcome to this updated edition of The Flying Circus of Physics, where death-defying stunts, high-flying acrobatics, strange curiosities, and mind-bending illusions bring to life the fascinating feats of physics in the world around us. In 1977, Wiley published the first edition of Jearl Walker's The Flying Circus of Physics, which has sold over 100,000 copies and become a cult classic in the physics community. The Flying Circus is a compendium of interesting real world phenomena that can be explained using basic laws of physics. This new edition represents a thorough updating and modernization of the book. The new edition gives us the opportunity to highlight Jearl's creativity, his communication skills, and his ability to make physics interesting.Jearl Walker, Ph.D., professor of physics at Cleveland State University and the man who frequently walked on hot coals and lay on beds of nails all in the name of science, is the first recipient of the Outstanding Teaching Award from Cleveland State's College of Science. The College's Faculty Affairs Committee selected Dr. Walker as the first honoree based on his impressive contributions to science teaching over the last 30 years. In fact, the award in future years will be named the Jearl Walker Outstanding Teaching Award in recognition of his many achievements.Jearl Walker received his B.S. in physics from MIT in 1967 and his Ph.D. in physics from the University of Maryland in 1973. His popular book, The Flying Circus of Physics, has been translated into at least 10 languages and is still being sold worldwide. For 16 years he toured his fun-filled Flying Circus lecture throughout the U.S. and Canada, introducing countless teachers to such physics phenomena as molecular adhesion by hanging spoons from his face and Leidenfrost's phenomenon by dipping his wet hand in molten lead without getting hurt.These lectures led to his national PBS television show, Kinetic Karnival, which ran for several years and won him a local Emmy Award. During his 13 years as a columnist with Scientific American magazine, Dr. Walker wrote 152 articles for The Amateur Scientist section, which were translated into at least 9 languages worldwide. His topics ranged from the physics of judo to the physics of bearnaise sauce and lemon meringue pie. In 1990, he took over the textbook Fundamentals of Physics from David Halliday and Robert Resnick and has now published the seventh edition of the book. He has appeared countless times on television and radio and in newspapers and magazines.

     The more tools you have at your disposal, the more likely you'll use the right tool for the job — and get it done right. The same is true when it comes to your thinking. The quality of your outcomes depends on the mental models in your head. And most people are going through life with little more than a hammer. Until now. The Great Mental Models: General Thinking Concepts is the first book in The Great Mental Models series designed to upgrade your thinking with the best, most useful and powerful tools so you always have the right one on hand. This volume details nine of the most versatile, all-purpose mental models you can use right away to improve your decision making, productivity, and how clearly you see the world. You will discover what forces govern the universe and how to focus your efforts so you can harness them to your advantage, rather than fight with them or worse yet— ignore them. Upgrade your mental toolbox and get the first volume today!

    But as anyone who has ever opened up a spreadsheet packed with seemingly infinite lines of data knows, numbers aren't enough: we need to know how to make those numbers talk. In The Model Thinker, social scientist Scott E. Page shows us the mathematical, statistical, and computational models—from linear regression to random walks and far beyond—that can turn anyone into a genius. At the core of the book is Page's "many-model paradigm," which shows the reader how to apply multiple models to organize the data, leading to wiser choices, more accurate predictions, and more robust designs. The Model Thinker provides a toolkit for business people, students, scientists, pollsters, and bloggers to make them better, clearer thinkers, able to leverage data and information to their advantage.

    do it? How should you flip your mattress to get the maximum wear out of it? How does Google search the Internet? How many people should you date before settling down? Believe it or not, math plays a crucial role in answering all of these questions and more.Math underpins everything in the cosmos, including us, yet too few of us understand this universal language well enough to revel in its wisdom, its beauty — and its joy. This deeply enlightening, vastly entertaining volume translates math in a way that is at once intelligible and thrilling. Each trenchant chapter of The Joy of x offers an “aha!” moment, starting with why numbers are so helpful, and progressing through the wondrous truths implicit in π, the Pythagorean theorem, irrational numbers, fat tails, even the rigors and surprising charms of calculus. Showing why he has won awards as a professor at Cornell and garnered extensive praise for his articles about math for the New York Times, Strogatz presumes of his readers only curiosity and common sense. And he rewards them with clear, ingenious, and often funny explanations of the most vital and exciting principles of his discipline.Whether you aced integral calculus or aren’t sure what an integer is, you’ll find profound wisdom and persistent delight in The Joy of x.

    But how can you be the person who comes up with those ideas? In this revised and expanded edition of his groundbreaking Thinkertoys, creativity expert Michael Michalko reveals life-changing tools that will help you think like a genius. From the linear to the intuitive, this comprehensive handbook details ingenious creative-thinking techniques for approaching problems in unconventional ways. Through fun and thought-provoking exercises, you’ll learn how to create original ideas that will improve your personal life and your business life. Michalko’s techniques show you how to look at the same information as everyone else and see something different.  With hundreds of hints, tricks, tips, tales, and puzzles, Thinkertoys will open your mind to a world of innovative solutions to everyday and not-so-everyday problems.

    Dennett on decoding the architecture of the "normal" human mindSarah-Jayne Blakemore on mental disorders and the crucial developmental phase of adolescenceJonathan Haidt, Sam Harris, and Roy Baumeister on the science of morality, ethics, and the emerging synthesis of evolutionary and biological thinkingGerd Gigerenzer on rationality and what informs our choices

    

    Describes a technique designed to develop creative thinking and provide a mechanism for organizing projects, breaking writer's block, and brainstorming.

    L. Dodgson) have now been reprinted in their entirety for the pleasure of modern enthusiasts of mathematical puzzles. Written by the 19th-century mathematician who gave us Alice in Wonderland and Through the Looking Glass, they contain an unusual combination of wit and mathematical intricacy that will test your mathematical ingenuity and provide hours of stimulating entertainment.Pillow-Problems is one of the rarest of all Lewis Carroll's works. It contains 72 mathematical posers ranging from those that can be solved by arithmetic, simple algebra, or plane geometry, to those that require more advanced algebra, trigonometry, algebraical geometry, differential calculus, and transcendental probabilities. Both numerical answers and fully worked out solutions are given, each in a separate section so that you can test your methods of problem-solving even after you have looked up the answer to a problem.In A Tangled Tale, Carroll embodies some of his most perplexing mathematical puzzles in the ten knots or chapters of a delightful story that has all the charm and wit of his better-known works. The Tale was originally printed as a monthly magazine serial, and many readers sent in solutions to the problems that were posed in it. In the long Appendix to The Tale, which contains the answers and solutions to the problems, Carroll uses the answers sent in by readers as the basis for illuminating and entertaining discussions of the many wrong ways in which the problems can be attacked, as well as the right ways.

    To understand algebra is to possess the power to grow your skills and knowledge so you can ace your courses and possibly pursue further study in math. Algebra II For Dummies is the fun and easy way to get a handle on this subject and solve even the trickiest algebra problems. This friendly guide shows you how to get up to speed on exponential functions, laws of logarithms, conic sections, matrices, and other advanced algebra concepts. In no time you'll have the tools you need to:Interpret quadratic functions Find the roots of a polynomial Reason with rational functions Expose exponential and logarithmic functions Cut up conic sections Solve linear and non linear systems of equations Equate inequalities Simplifyy complex numbers Make moves with matrices Sort out sequences and sets This straightforward guide offers plenty of multiplication tricks that only math teachers know. It also profiles special types of numbers, making it easy for you to categorize them and solve any problems without breaking a sweat. When it comes to understanding and working out algebraic equations, Algebra II For Dummies is all you need to succeed!

    This brilliantly clear and gratifyingly concise treatment of the ancient Greek discipline identifies the illogical in everything from street signs to tax forms. Complete with puzzles you can try yourself, Logic Made Easy invites readers to identify and ultimately remedy logical slips in everyday life. Designed with dozens of visual examples, the book guides you through those hair-raising times when logic is at odds with our language and common sense. Logic Made Easy is indeed one of those rare books that will actually make you a more logical human being.

    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