As we enter the year 2000, zero is once again making its presence felt. Nothing itself, it makes possible a myriad of calculations. Indeed, without zero mathematicsas we know it would not exist. And without mathematics our understanding of the universe would be vastly impoverished. But where did this nothing, this hollow circle, come from? Who created it? And what, exactly, does it mean? Robert Kaplan's The Nothing That Is: A Natural History of Zero begins as a mystery story, taking us back to Sumerian times, and then to Greece and India, piecing together the way the idea of a symbol for nothing evolved. Kaplan shows us just how handicapped our ancestors were in trying to figurelarge sums without the aid of the zero. (Try multiplying CLXIV by XXIV). Remarkably, even the Greeks, mathematically brilliant as they were, didn't have a zero--or did they? We follow the trail to the East where, a millennium or two ago, Indian mathematicians took another crucial step. By treatingzero for the first time like any other number, instead of a unique symbol, they allowed huge new leaps forward in computation, and also in our understanding of how mathematics itself works. In the Middle Ages, this mathematical knowledge swept across western Europe via Arab traders. At first it was called dangerous Saracen magic and considered the Devil's work, but it wasn't long before merchants and bankers saw how handy this magic was, and used it to develop tools likedouble-entry bookkeeping. Zero quickly became an essential part of increasingly sophisticated equations, and with the invention of calculus, one could say it was a linchpin of the scientific revolution. And now even deeper layers of this thing that is nothing are coming to light: our computers speakonly in zeros and ones, and modern mathematics shows that zero alone can be made to generate everything.Robert Kaplan serves up all this history with immense zest and humor; his writing is full of anecdotes and asides, and quotations from Shakespeare to Wallace Stevens extend the book's context far beyond the scope of scientific specialists. For Kaplan, the history of zero is a lens for looking notonly into the evolution of mathematics but into very nature of human thought. He points out how the history of mathematics is a process of recursive abstraction: how once a symbol is created to represent an idea, that symbol itself gives rise to new operations that in turn lead to new ideas. Thebeauty of mathematics is that even though we invent it, we seem to be discovering something that already exists.The joy of that discovery shines from Kaplan's pages, as he ranges from Archimedes to Einstein, making fascinating connections between mathematical insights from every age and culture. A tour de force of science history, The Nothing That Is takes us through the hollow circle that leads to infinity.

    There is joy and beauty in mathematics, and in more than two dozen essays drawn from his popular “Good Math” blog, you’ll find concepts, proofs, and examples that are often surprising, counterintuitive, or just plain weird.Mark begins his journey with the basics of numbers, with an entertaining trip through the integers and the natural, rational, irrational, and transcendental numbers. The voyage continues with a look at some of the oddest numbers in mathematics, including zero, the golden ratio, imaginary numbers, Roman numerals, and Egyptian and continuing fractions. After a deep dive into modern logic, including an introduction to linear logic and the logic-savvy Prolog language, the trip concludes with a tour of modern set theory and the advances and paradoxes of modern mechanical computing.If your high school or college math courses left you grasping for the inner meaning behind the numbers, Mark’s book will both entertain and enlighten you.

    However, it is one of the basic principles of quantum theory, the most widely accepted explanation of the subatomic world - and one of the fascinating subjects dealt with in Equations of Eternity.

    It had a decisive impact on twentieth century philosophy and is one of few works to have influenced both continental and analytic philosophy.This is the first time both volumes have been available in paperback. They include a new introduction by Dermot Moran, placing the Investigations in historical context and bringing out their contemporary philosophical importance.These editions include a new preface by Sir Michael Dummett.

    Just read this till the end You don’t have to buy this book. Just read this till end & you will learn something that will change the way you do math forever. Warning: I am revealing this secret only to the first set of readers who will buy this book & plan to put this secret back inside the book once I have enough sales. So read this until the very end while you still can.School taught you the wrong way to do mathThe way you were taught to do math, uses a lot of working memory. Working memory is the short term memory used to complete a mental task. You struggle because trying to do mental math the way you were taught in school, overloads your working memory. Let me show you what I mean with an example:Try to multiply the 73201 x 3. To do this you multiply the following:1 x 3 =0 x 3 =2 x 3 =3 x 3 =7 x 3 =This wasn’t hard, & it might have taken you just seconds to multiply the individual numbers. However, to get the final answer, you need to remember every single digit you calculated to put them back together. It takes effort to get the answer because you spend time trying to recall the numbers you already calculated. Math would be easier to do in your head if you didn’t have to remember so many numbers. Imagine when you tried to multiply 73201 x 3, if you could have come up with the answer, in the time it took you to multiply the individual numbers. Wouldn’t you have solved the problem faster than the time it would have taken you to punch in the numbers inside a calculator? Do the opposite of what you were taught in schoolThe secret of doing mental math is to calculate from left to right instead of from right to left. This is the opposite of what you were taught in school. This works so well because it frees your working memory almost completely. It is called the LR Method where LR stands for Left to Right.Lets try to do the earlier example where we multiplied 73201 x 3. This time multiply from left to right, so we get:7 x 3 = 213 x 3 = 93 x 2 = 60 x 3 = 03 x 1 = 3Notice that you started to call out the answer before you even finished the whole multiplication problem. You don’t have to remember a thing to recall & use later. So you end up doing math a lot faster. The Smart ChoiceYou could use what you learnt & apply it to solve math in the future. This might not be easy, because we just scratched the surface. I've already done the work for you. Why try to reinvent the wheel, when there is already a proven & tested system you can immediately apply. This book was first available in video format & has helped 10,000+ students from 132 countries. It is available at ofpad.com/mathcourse to enroll. This book was written to reach students who consume the information in text format. You can use the simple techniques in this book to do math faster than a calculator effortlessly in your head, even if you have no aptitude for math to begin with.Imagine waking up tomorrow being able to do lightning fast math in your head. Your family & friends will look at you like you are some kind of a genius. Since calculations are done in your head, you will acquire better mental habits in the process. So you will not just look like a genius. You will actually be one. Limited Time BonusWeekly training delivered through email for $97 is available for free as a bonus at the end of this book for the first set of readers. Once we have enough readers, this bonus will be charged $97. Why Price Is So LowThis book is priced at a ridiculous discount only to get our first set of readers. When we have enough readers the price will go up.

    Tobias Dantzig shows that the development of math—from the invention of counting to the discovery of infinity—is a profoundly human story that progressed by “trying and erring, by groping and stumbling.” He shows how commerce, war, and religion led to advances in math, and he recounts the stories of individuals whose breakthroughs expanded the concept of number and created the mathematics that we know today.

    That is, it is a piece of bad logic. Just as it is a good idea to avoid eating bad food, it is also a rather good idea to avoid bad reasoning. Unfortunately, bad reasoning is all too common—it pours out of the television and infests the web like an army of venomous spiders. Perhaps even worse than the fallacies inflicted from the outside are self-inflicted fallacies. These can lead people to make poor decisions about matters great and small.Fortunately, there is a defense against bad reasoning, namely knowledge. This concise book provides the reader with definitions and examples of seventy-six common fallacies—the knowledge a person needs to defend herself in a world awash in fallacies.In addition to combining the content of my 42 Fallacies and 30 More Fallacies, this book features some revisions as well as a new section on common formal fallacies. The focus is on providing the reader with definitions and examples of these common fallacies rather than being a handbook on winning arguments or a text on general logic.The book presents the following 73 informal fallacies:Accent, Fallacy ofAccident, Fallacy ofAd HominemAd Hominem Tu QuoqueAmphiboly, Fallacy ofAnecdotal Evidence, Fallacy OfAppeal to the Consequences of a BeliefAppeal to Authority, FallaciousAppeal to BeliefAppeal to Common PracticeAppeal to EmotionAppeal to EnvyAppeal to FearAppeal to FlatteryAppeal to Group IdentityAppeal to GuiltAppeal to NoveltyAppeal to PityAppeal to PopularityAppeal to RidiculeAppeal to SpiteAppeal to TraditionAppeal to SilenceAppeal to VanityArgumentum ad HitlerumBegging the QuestionBiased GeneralizationBurden of ProofComplex QuestionComposition, Fallacy ofConfusing Cause and EffectConfusing Explanations and ExcusesCircumstantial Ad HominemCum Hoc, Ergo Propter HocDivision, Fallacy ofEquivocation, Fallacy ofFallacious ExampleFallacy FallacyFalse DilemmaGambler’s FallacyGenetic FallacyGuilt by AssociationHasty GeneralizationHistorian’s FallacyIllicit ConversionIgnoring a Common CauseIncomplete EvidenceMiddle GroundMisleading VividnessMoving the Goal PostsOversimplified CauseOverconfident Inference from Unknown StatisticsPathetic FallacyPeer PressurePersonal AttackPoisoning the WellPositive Ad HominemPost HocProving X, Concluding YPsychologist's fallacyQuestionable CauseRationalizationRed HerringReification, Fallacy ofRelativist FallacySlippery SlopeSpecial PleadingSpotlightStraw ManTexas Sharpshooter FallacyTwo Wrongs Make a RightVictim FallacyWeak AnalogyThe book contains the following three formal (deductive) fallacies:Affirming the ConsequentDenying the AntecedentUndistributed Middle

    Only world band radio delivers this no matter what, and quick-access Passport to World Band Radio is the #1 seller to this market-over a million copies sold to date. Each edition is welcomed by established and emerging readers alike, as Passport delivers in nearly 600 pages what world band listeners seek: * Three-way guide to what's on from stations in dozens of countries: news, entertainment and opinion in English and other languages. All three formats: country-by-country, channel-by-channel, hour-by-hour. * Award-winning reviews of world band radios and accessories, with ratings of dozens of models from Sony, Grundig and others. Radios for emergencies, too. * Wealth of helpful how-to articles, along with a directory of station contacts, webcasts and a glossary. This annual title keeps readers coming back year after year, making it what one chain buyer hails as a quiet bestseller.

    We have Mindstorms to thank for that. In this book, pioneering computer scientist Seymour Papert uses the invention of LOGO, the first child-friendly programming language, to make the case for the value of teaching children with computers. Papert argues that children are more than capable of mastering computers, and that teaching computational processes like de-bugging in the classroom can change the way we learn everything else. He also shows that schools saturated with technology can actually improve socialization and interaction among students and between students and teachers.

    The unique on-line grading services instantly grades solutions to hundred of computer exercises. It is specially devised to be used by philosophy instructors in a way that is useful to undergraduates of philosophy, computer science, mathematics, and linguistics.The book is a completely rewritten and much improved version of The Language of First-order Logic. Introductory material is presented in a more systematic and accessible fashion. Advanced chapters include proofs of soundness and completeness for propositional and predicate logic, as well as an accessible sketch of Godel's first incompleteness theorem. The book is appropriate for a wide range of courses, from first logic courses for undergraduates (philosophy, mathematics, and computer science) to a first graduate logic course.The package includes four pieces of software:Tarski's World 5.0, a new version of the popular program that teaches the basic first-order language and its semantics; Fitch, a natural deduction proof environment for giving and checking first-order proofs;Boole, a program that facilitates the construction and checking of truth tables and related notions (tautology, tautological consequence, etc.);Submit, a program that allows students to submit exercises done with the above programs to the Grade Grinder, the automatic grading service.Grade reports are returned to the student and, if requested, to the student's instructor, eliminating the need for tedious checking of homework. All programs are available for Windows, Macintosh and Linux systems.Instructors do not need to use the programs themselves in order to be able to take advantage of their pedagogical value. More about the software can be found at lpl.stanford.edu.The price of a new text/software package includes one Registration ID, which must be used each time work is submitted to the grading service. Once activated, the Registration ID is not transferable.

    Quality assurance was conducted on each of these books in an attempt to remove books with imperfections introduced by the digitization process. Though we have made best efforts - the books may have occasional errors that do not impede the reading experience. We believe this work is culturally important and have elected to bring the book back into print as part of our continuing commitment to the preservation of printed works worldwide.

    On their tender shoulders rests a great nation, a baffling world and a beautiful planet. It is, therefore, my dharma to share what I know so a parent's hand is raised only to protect their child." Penning his thoughts on the art of spiritual and mindful parenting, Om Swami sheds light on many a scenario where parents and children don't always see eye-to-eye. Believing that the right guidance at the right time can make any child recognize their true potential, the author shares some extraordinary insights based on his own knowledge gleaned from experience and various psychological studies that can help steer your child in the right direction. Touching upon parenting challenges, building the right pillars of guidance and nurturing core values, this book has all you need to raise happy, healthy children.

    Heath's translation of the thirteen books of Euclid's Elements. In keeping with Green Lion's design commitment, diagrams have been placed on every spread for convenient reference while working through the proofs; running heads on every page indicate both Euclid's book number and proposition numbers for that page; and adequate space for notes is allowed between propositions and around diagrams. The all-new index has built into it a glossary of Euclid's Greek terms.Heath's translation has stood the test of time, and, as one done by a renowned scholar of ancient mathematics, it can be relied upon not to have inadvertantly introduced modern concepts or nomenclature. We have excised the voluminous historical and scholarly commentary that swells the Dover edition to three volumes and impedes classroom use of the original text. The single volume is not only more convenient, but less expensive as well.

    In this little book Welsh writer and artist David Wade paints a picture of one of the most elusive and pervasive concepts known to man.

    Albert-László Barabási, the nation’s foremost expert in the new science of networks and author of Bursts, takes us on an intellectual adventure to prove that social networks, corporations, and living organisms are more similar than previously thought. Grasping a full understanding of network science will someday allow us to design blue-chip businesses, stop the outbreak of deadly diseases, and influence the exchange of ideas and information. Just as James Gleick and the Erdos–Rényi model brought the discovery of chaos theory to the general public, Linked tells the story of the true science of the future and of experiments in statistical mechanics on the internet, all vital parts of what would eventually be called the Barabási–Albert model.