As well as looking at logic in theoretical terms the book considers its everyday uses and demonstrates how it has genuine practical applications. It will take you step by step through the most difficult concepts and is packed with exercises to help you consolidate your learning at every stage. Covering everything from syllogistic logic to logical paradoxes and even looking at logic in Alice in Wonderland, this is the only guide you will ever need.

    The books also provides a companion web site that provides the toold and materials necessary to build the hardware and software.

    This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes.Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known.Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there.

    Standing on those pillars, humans spent 100,000 years spreading out into the galaxy: warring, exploring, partying — the usual. Then there was the fifth science. And that killed the empire stone dead. The Fifth Science is a collection of 12 stories, beginning at the start of the Galactic Human Empire and following right through to its final days. We’ll see some untypical things along the way, meet some untypical folk: galactic lighthouses from the distant future, alien tombs from the distant past, murderers, emperors, archaeologists and drunks; mad mathematicians attempting to wake the universe itself up. And when humans have fallen back into savagery, when the secrets of space folding and perfect wisdom are forgotten, we’ll attend the empire’s deathbed, hold its hand as it goes. Unfortunately that may well only be the beginning.

    Short-Cut Math is a concise, remarkably clear compendium of about 150 math short-cuts — timesaving tricks that provide faster, easier ways to add, subtract, multiply, and divide.By using the simple foolproof methods in this volume, you can double or triple your calculation speed — even if you always hated math in school. Here's a sampling of the amazingly effective techniques you will learn in minutes: Adding by 10 Groups; No-Carry Addition; Subtraction Without Borrowing; Multiplying by Aliquot Parts; Test for Divisibility by Odd and Even Numbers; Simplifying Dividends and Divisors; Fastest Way to Add or Subtract Any Pair of Fractions; Multiplying and Dividing with Mixed Numbers, and more.The short-cuts in this book require no special math ability. If you can do ordinary arithmetic, you will have no trouble with these methods. There are no complicated formulas or unfamiliar jargon — no long drills or exercises. For each problem, the author provides an explanation of the method and a step-by-step solution. Then the short-cut is applied, with a proof and an explanation of why it works.Students, teachers, businesspeople, accountants, bank tellers, check-out clerks — anyone who uses numbers and wishes to increase his or her speed and arithmetical agility, can benefit from the clear, easy-to-follow techniques given here.

    Taking as territory everything from the Big Bang to the rise of civilization, Bryson seeks to understand how we got from there being nothing at all to there being us. To that end, he has attached himself to a host of the world’s most advanced (and often obsessed) archaeologists, anthropologists, and mathematicians, travelling to their offices, laboratories, and field camps. He has read (or tried to read) their books, pestered them with questions, apprenticed himself to their powerful minds. A Short History of Nearly Everything is the record of this quest, and it is a sometimes profound, sometimes funny, and always supremely clear and entertaining adventure in the realms of human knowledge, as only Bill Bryson can render it. Science has never been more involving or entertaining.

    His profound management sutras are derived from his bestselling books on business and management. They show how individuals can realize their potential, create wealth and achieve lasting success by following uniquely Indian principles (based on Hindu, Jain and Buddhist mythology) of goal setting, strategic thinking and decision-making.

    Taking examples from sources as diverse as Plato and Steven Spielberg, author Julian Baggini presents abstract philosophical issues in concrete terms, suggesting possible solutions while encouraging readers to draw their own conclusions: Lively, clever, and thought-provoking, The Pig That Wants to Be Eaten is a portable feast for the mind that is sure to satisfy any intellectual appetite.

    Over the centuries, cities and governments have risen and fallen beyond the concent's walls. Three times during history's darkest epochs violence born of superstition and ignorance has invaded and devastated the cloistered mathic community. Yet the avout have always managed to adapt in the wake of catastrophe, becoming out of necessity even more austere and less dependent on technology and material things. And Erasmas has no fear of the outside—the Extramuros—for the last of the terrible times was long, long ago.Now, in celebration of the week-long, once-in-a-decade rite of Apert, the fraas and suurs prepare to venture beyond the concent's gates—at the same time opening them wide to welcome the curious "extras" in. During his first Apert as a fraa, Erasmas eagerly anticipates reconnecting with the landmarks and family he hasn't seen since he was "collected." But before the week is out, both the existence he abandoned and the one he embraced will stand poised on the brink of cataclysmic change.Powerful unforeseen forces jeopardize the peaceful stability of mathic life and the established ennui of the Extramuros—a threat that only an unsteady alliance of saecular and avout can oppose—as, one by one, Erasmas and his colleagues, teachers, and friends are summoned forth from the safety of the concent in hopes of warding off global disaster. Suddenly burdened with a staggering responsibility, Erasmas finds himself a major player in a drama that will determine the future of his world—as he sets out on an extraordinary odyssey that will carry him to the most dangerous, inhospitable corners of the planet . . . and beyond.

    What happens to them is beyond your most terrifying nightmares.You’re History: The discovery of a human skull panics a killer into a confession. Perhaps he should have waited for the coroner’s report.Cold-Blooded: Karen was the former wife of an American icon. But celebrity is no shield against a determined psychopath.The Janitor: When a preteen girl goes missing from a school, suspicion falls on the one person all of the female students are wary of – the creepy janitor.A Bullet for Your Broken Heart: Roy Joe had been dealt many tribulations in his life. None of them, though, was as bad as Carolyn.The Other Ripper: For years, Joan was thought to be a victim of Britain’s most notorious slayer. Her killer turned out to be a different psychopath entirely.Young Blood: Two teenagers meet up for a moonlight tryst in an abandoned building. One of them won’t make it out alive.Neighborhood Monster: It was a simple errand, a quick run to the store in a safe neighborhood. It should not have cost a little girl her life.Plus 10 more horrific true murder cases. Scroll up to grab a copy of Cold Cases: Solved Volume 1.

    Theory has been provided in points between each chapter for clarifying relevant basic concepts. The book consist four parts algebra and trigonometry, fundamentals of analysis, geometry and vector algebra and the problems and questions set during oral examinations. Each chapter consist topic wise problems. Sample examples are provided after each text for understanding the topic well. The fourth part "oral examination problems and question" includes samples suggested by the higher schools for the help of students. Answers and hints are given at the end of the book for understanding the concept well. About the Book: Problems in Mathematics with Hints and Solutions Contents: Preface Part 1. Algebra, Trigonometry and Elementary Functions Problems on Integers. Criteria for Divisibility Real Number, Transformation of Algebraic Expressions Mathematical Induction. Elements of Combinatorics. BinomialTheorem Equations and Inequalities of the First and the SecondDegree Equations of Higher Degrees, Rational Inequalities Irrational Equations and Inequalities Systems of Equations and Inequalities The Domain of Definition and the Range of a Function Exponential and Logarithmic Equations and Inequalities Transformations of Trigonometric Expressions. InverseTrigonometric Functions Solutions of Trigonometric Equations, Inequalities and Systemsof Equations Progressions Solutions of Problems on Derivation of Equations Complex Numbers Part 2. Fundamentals of Mathematical Analysis Sequences and Their Limits. An Infinitely Decreasing GeometricProgression. Limits of Functions The Derivative. Investigating the Behaviors of Functions withthe Aid of the Derivative Graphs of Functions The Antiderivative. The Integral. The Area of a CurvilinearTrapezoid Part 3. Geometry and Vector Algebra Vector Algebra Plane Geometry. Problems on Proof Plane Geometry. Construction Problems Plane Geometry. C

    We don't do a chemical analysis on food we eat.Trust and cooperation are the first problems we had to solve before we could become a social species. In the 21st century, they have become the most important problems we need to solve — again. Our global society has become so large and complex that our traditional trust mechanisms no longer work.Bruce Schneier, world-renowned for his level-headed thinking on security and technology, tackles this complex subject head-on. Society can't function without trust, and yet must function even when people are untrustworthy.Liars and Outliers reaches across academic disciplines to develop an understanding of trust, cooperation, and social stability. From the subtle social cues we use to recognize trustworthy people to the laws that punish the noncompliant, from the way our brains reward our honesty to the bank vaults that keep out the dishonest, keeping people cooperative is a delicate balance of rewards and punishments. It's a series of evolutionary tricks, social pressures, legal mechanisms, and physical barriers.In the absence of personal relationships, we have no choice but to substitute security for trust, compliance for trustworthiness. This progression has enabled society to scale to unprecedented complexity, but has also permitted massive global failures.At the same time, too much cooperation is bad. Without some level of rule-breaking, innovation and social progress become impossible. Society stagnates.Today's problems require new thinking, and Liars and Outliers provides that. It is essential that we learn to think clearly about trust. Our future depends on it.

    With exceptional clarity, Franz n gives careful, non-technical explanations both of what those theorems say and, more importantly, what they do not. No other book aims, as his does, to address in detail the misunderstandings and abuses of the incompleteness theorems that are so rife in popular discussions of their significance. As an antidote to the many spurious appeals to incompleteness in theological, anti-mechanist and post-modernist debates, it is a valuable addition to the literature." --- John W. Dawson, author of "Logical Dilemmas: The Life and Work of Kurt G del

    The Clay Mathematics Institute is offering a prize of $1 million to anyone who can discover a general solution to the problem. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem.The key to the conjecture lies in elliptic curves, which are cubic equations in two variables. These equations may appear simple, yet they arise from some very deep--and often very mystifying--mathematical ideas. Using only basic algebra and calculus while presenting numerous eye-opening examples, Ash and Gross make these ideas accessible to general readers, and in the process venture to the very frontiers of modern mathematics. Along the way, they give an informative and entertaining introduction to some of the most profound discoveries of the last three centuries in algebraic geometry, abstract algebra, and number theory. They demonstrate how mathematics grows more abstract to tackle ever more challenging problems, and how each new generation of mathematicians builds on the accomplishments of those who preceded them. Ash and Gross fully explain how the Birch and Swinnerton-Dyer Conjecture sheds light on the number theory of elliptic curves, and how it provides a beautiful and startling connection between two very different objects arising from an elliptic curve, one based on calculus, the other on algebra.

    What they don't realize—and what Daniel Hillis's short book brilliantly demonstrates—is that computers' seemingly complex operations can be broken down into a few simple parts that perform the same simple procedures over and over again.Computer wizard Hillis offers an easy-to-follow explanation of how data is processed that makes the operations of a computer seem as straightforward as those of a bicycle. Avoiding technobabble or discussions of advanced hardware, the lucid explanations and colorful anecdotes in The Pattern on the Stone go straight to the heart of what computers really do.Hillis proceeds from an outline of basic logic to clear descriptions of programming languages, algorithms, and memory. He then takes readers in simple steps up to the most exciting developments in computing today—quantum computing, parallel computing, neural networks, and self-organizing systems.Written clearly and succinctly by one of the world's leading computer scientists, The Pattern on the Stone is an indispensable guide to understanding the workings of that most ubiquitous and important of machines: the computer.