Hofstadter's collection of quirky essays is unified by its primary concern: to examine the way people perceive and think.

    Yet Euler's formula is so simple it can be explained to a child. Euler's Gem tells the illuminating story of this indispensable mathematical idea.From ancient Greek geometry to today's cutting-edge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. In 1750, Euler observed that any polyhedron composed of V vertices, E edges, and F faces satisfies the equation V-E+F=2. David Richeson tells how the Greeks missed the formula entirely; how Descartes almost discovered it but fell short; how nineteenth-century mathematicians widened the formula's scope in ways that Euler never envisioned by adapting it for use with doughnut shapes, smooth surfaces, and higher dimensional shapes; and how twentieth-century mathematicians discovered that every shape has its own Euler's formula. Using wonderful examples and numerous illustrations, Richeson presents the formula's many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map.Filled with a who's who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem's development, Euler's Gem will fascinate every mathematics enthusiast.

    This book, which accompanies the major Channel 4 series, brings to life the hidden history of codes and code breaking. Since the birth of writing, there has also been the need for secrecy. The story of codes is the story of the brilliant men and women who used mathematics, linguistics, machines, computers, gut instinct, logic and detective work to encrypt and break these secrect messages and the effect their work has had on history. In each episode of "The Science of Secrecy" Simon Singh tells us a fascinating story from the history of codes: how the course of Crimean War was changed by the cracking of "unbreakable" Vigenere code; how the well-timed cracking of a single encoded telegram altered the course of World War I or how the mysteries of the Rosetta stone were revealed. The programme, and book, also investigates present day concerns about privacy on the internet and public key cryptography and looks to the future and the possibilities that quantum computing will radically change the science of secrecy in the 21st century.

    In "Musimathics," Loy teaches us the tune, providing a friendly and spirited tour of the mathematics of music -- a commonsense, self-contained introduction for the nonspecialist reader. It is designed for musicians who find their art increasingly mediated by technology, and for anyone who is interested in the intersection of art and science.In Volume 1, Loy presents the materials of music (notes, intervals, and scales); the physical properties of music (frequency, amplitude, duration, and timbre); the perception of music and sound (how we hear); and music composition. Calling himself "a composer seduced into mathematics," Loy provides answers to foundational questions about the mathematics of music accessibly yet rigorously. The examples given are all practical problems in music and audio.Additional material can be found at http: //www.musimathics.com.

    This is a very old science and its gems have lost their charm for us through everyday use. We have tried in this book to refresh them for you. The main part of the book is made up of problems. The best way to deal with them is: Solve the problem by yourself - compare your solution with the solution in the book (if it exists) - go to the next problem. However, if you have difficulties solving a problem (and some of them are quite difficult), you may read the hint or start to read the solution. If there is no solution in the book for some problem, you may skip it (it is not heavily used in the sequel) and return to it later. The book is divided into sections devoted to different topics. Some of them are very short, others are rather long. Of course, you know arithmetic pretty well. However, we shall go through it once more, starting with easy things. 2 Exchange of terms in addition Let's add 3 and 5: 3+5=8. And now change the order: 5+3=8. We get the same result. Adding three apples to five apples is the same as adding five apples to three - apples do not disappear and we get eight of them in both cases. 3 Exchange of terms in multiplication Multiplication has a similar property. But let us first agree on notation.

    Text, illustrations, and suggested activities offer a common-sense approach to mathematic fundamentals for those who are slightly terrified of numbers.

    Why, he wondered, do we inflict a full menu of mathematics—algebra, geometry, trigonometry, even calculus—on all young Americans, regardless of their interests or aptitudes?The Math Myth expands Hacker’s scrutiny of many widely held assumptions, like the notions that mathematics broadens our minds, that mastery of azimuths and asymptotes will be needed for most jobs, that the entire Common Core syllabus should be required of every student. He worries that a frenzied emphasis on STEM is diverting attention from other pursuits and subverting the spirit of the country.In fact, Hacker honors mathematics as a calling (he has been a professor of mathematics) and extols its glories and its goals. Yet he shows how mandating it for everyone prevents other talents from being developed and acts as an irrational barrier to graduation and careers. He proposes alternatives, including teaching facility with figures, quantitative reasoning, and understanding statistics.The Math Myth is sure to spark a heated and needed national conversation not just about mathematics but about the kind of people and society we want to be.

    Many today are well on their way to becoming a sad statistic in the war on obesity, high blood sugar, and the related diseases—including diabetes—that can result from a diet that’s seriously out of whack. In his previous bestselling book, Overcoming Runaway Blood Sugar, Dennis Pollock shared his personal experience with this deadly epidemic—including his success at lowering his runaway blood sugar to acceptable levels. Now Dennis offers readers the next step in the battle: 60 practical ways to manage their blood sugar without resorting to a bland unsatisfying diet of turnips and tuna fish. In this step by step, change by change plan, readers will learn how to: reduce their intake of carbs, exercise more effectively, and shed excess weight. A must-have book for readers serious about regaining their health while also lowering their weight and increasing their energy.

    Thorough in its coverage of basic theory, from the lever and inclined plane to internal combustion engines and power trains, it requires nothing more than an understanding of the most elementary mathematics. Beginning with the simplest of machines — the lever — the text proceeds to discussions of the block and tackle (pulleys and hoists), wheel and axle, the inclined plane and the wedge, the screw, and different types of gears (simple, spur, bevel, herringbone, spiral, worm, etc.). A chapter on the concept of work discusses the measurement of work, friction, and efficiency; this is followed by investigations of power, force, and pressure, with explanations of the uses of scales, balances, gauges, and barometers. The fundamentals of hydrostatic and hydraulic machines (such as the hydraulic braking system and the hydraulic press) are discussed in detail. The remaining chapters cover machine elements (bearings and springs), basic mechanisms (gear differential, couplings, cams, clutches), the internal combustion engine and power trains (including explanations of various transmission systems — synchromesh, auxiliary, etc.). Every concept is clearly defined, and discussions always build easily from elementary theory to specific applications familiar to anyone with the slightest interest in mechanics. Important concepts, machine components, and techniques are clearly illustrated in more than 200 diagrams, drawings, and cross-sections that reveal inner workings — all of these help to clarify even further an already clear and well-organized presentation. Although it was originally designed for use in U.S. Naval Training Schools, this book can be used to great advantage as a basic text in mechanical engineering in standard technical schools, and it will be immensely valuable even to lay readers who desire a basic knowledge of mechanics.

    There are more than seventy games here, 50 of them all new, plus many more recommendations, and they cover the full gambit, from old-fashioned favorites to today’s high-tech games. The book offers a gold mine of creative, constructive fun: intricate clapping games, bike rodeo, Google Earth challenges, croquet golf, capture the flag, and the best ever apps to play with Grandma, to name only a handful. Gaming is a whole culture for kids to explore, and the book will be complete with gaming history and interviews with awesome game designers. The lessons here: all games can be self-customized, or hacked. You can even make up your own games. Some could even change the world.The original UNBORED has taken its place as a much beloved, distinctly contemporary family brand. UNBORED Games extends the franchise—to be followed by UNBORED Adventure—in a new handy flexibound format, illustrated in full color throughout. Soon, there will be a whole shelf of serious fun the whole family can enjoy indoors, outdoors, online and offline.

    Covering number theory, algebra, analysis, Euclidean geometry, and analytic geometry, Solving Mathematical Problems includes numerous exercises and model solutions throughout. Assuming only a basic level of mathematics, the text is ideal for students of 14 years and above in pure mathematics.

    At any given time, the brain is collecting, filtering, and analyzing information and, in response, performing countless intricate processes, some of which are automatic, some voluntary, some conscious, and some unconscious.Cognitive neuroscience is one of the ways we have to understand the workings of our minds. It's the study of the brain biology behind our mental functions: a collection of methods--like brain scanning and computational modeling--combined with a way of looking at psychological phenomena and discovering where, why, and how the brain makes them happen.Want to know more? Mind Hacks is a collection of probes into the moment-by-moment works of the brain. Using cognitive neuroscience, these experiments, tricks, and tips related to vision, motor skills, attention, cognition, subliminal perception, and more throw light on how the human brain works. Each hack examines specific operations of the brain. By seeing how the brain responds, we pick up clues about the architecture and design of the brain, learning a little bit more about how the brain is put together.Mind Hacks begins your exploration of the mind with a look inside the brain itself, using hacks such as "Transcranial Magnetic Stimulation: Turn On and Off Bits of the Brain" and "Tour the Cortex and the Four Lobes." Also among the 100 hacks in this book, you'll find:Release Eye Fixations for Faster ReactionsSee Movement When All is StillFeel the Presence and Loss of AttentionDetect Sounds on the Margins of CertaintyMold Your Body SchemaTest Your HandednessSee a Person in Moving LightsMake Events Understandable as Cause-and-EffectBoost Memory by Using ContextUnderstand Detail and the Limits of AttentionSteven Johnson, author of "Mind Wide Open" writes in his foreword to the book, "These hacks amaze because they reveal the brain's hidden logic; they shed light on the cheats and shortcuts and latent assumptions our brains make about the world." If you want to know more about what's going on in your head, then Mind Hacks is the key--let yourself play with the interface between you and the world.

    But it wasn't because she was a "natural" or smarter than everyone else -- in fact, she succeeded as a student in spite of an undiagnosed learning disability. What she gradually realized was that her classmates were making mistakes, and lots of them.The Secrets of Top Students is a conversational, down-to-earth guide for high school and college students on how to maximize their learning and get the grades they want. It is full of innovative tips from Stefanie and 45 other top students -- including Rhodes scholars, Goldwater scholars, Fulbright award winners, college valedictorians, Intel Science Fair finalists, a National Spelling Bee champion, and more -- that not only work but have received little or no attention in other books. The Secrets of Top Students will appeal to students of all levels, providing them with the advice they need from a voice they can trust.The Secrets of Top Students includes tips and techniques that every student should know. For example: What is the first thing you should do when taking a math test? What is an often overlooked place for coming up with a thesis? How can you use mantras to get better grades? What music should you listen to while studying? Should you bring your laptop to class? Why is it bad to be a perfectionist? What motivates top students to achieve academic success? What foods should you eat to boost your brainpower? How can sleep, diet, and exercise affect your GPA? How much do top students really study? What are the Top 50 Tips for acing exams? How can you take killer notes? What are three game-changing learning techniques? And much, much more.

    Now, on YouTube and blogs and Facebook and Twitter, we are media. And while we watch more television than ever before, how we watch it is changing in ways we have barely slowed down to register. No longer content in our traditional role as couch potatoes, we approach television shows, movies, even advertising as invitations to participate—as experiences to immerse ourselves in at will. Wired contributing editor Frank Rose introduces us to the people who are reshaping media for a two-way world—people like Will Wright (The Sims), James Cameron (Avatar), Damon Lindelof (Lost), and dozens of others whose ideas are changing how we play, how we chill, and even how we think. The Art of Immersion is an eye-opening look at the shifting shape of entertainment today.

    It suggests that patience and confusion--rather than rigor and certainty--are the essential precursors of wisdom.With a compelling argument that the mind works best when we trust our unconscious, or "undermind," psychologist Guy Claxton makes an appeal that we be less analytical and let our creativity have free rein. He also encourages reevaluation of society's obsession with results-oriented thinking and problem-solving under pressure. Packed with Interesting anecdotes, a dozen puzzles to test your reasoning, and the latest related research, Hare Brain, Tortoise Mind is an Illuminating, uplifting, stimulating read that focuses on a new kind of well-being and cognition.