The author has a direct style. His book presents detailed and intensive explanations. Many diagrams and key examples are used to aid understanding, as well as the application of calculus to physics and engineering and economics. The text is well organized, and it covers single variable and multivariable calculus in depth. An instructor's manual and student guide are available online at http: //ocw.mit.edu/ans7870/resources/Strang/....

    This staggering amount of information—unprecedented in history—can tell us a great deal about who we are—the fears, desires, and behaviors that drive us, and the conscious and unconscious decisions we make. From the profound to the mundane, we can gain astonishing knowledge about the human psyche that less than twenty years ago, seemed unfathomable.Everybody Lies offers fascinating, surprising, and sometimes laugh-out-loud insights into everything from economics to ethics to sports to race to sex, gender and more, all drawn from the world of big data. What percentage of white voters didn’t vote for Barack Obama because he’s black? Does where you go to school effect how successful you are in life? Do parents secretly favor boy children over girls? Do violent films affect the crime rate? Can you beat the stock market? How regularly do we lie about our sex lives and who’s more self-conscious about sex, men or women?Investigating these questions and a host of others, Seth Stephens-Davidowitz offers revelations that can help us understand ourselves and our lives better. Drawing on studies and experiments on how we really live and think, he demonstrates in fascinating and often funny ways the extent to which all the world is indeed a lab. With conclusions ranging from strange-but-true to thought-provoking to disturbing, he explores the power of this digital truth serum and its deeper potential—revealing biases deeply embedded within us, information we can use to change our culture, and the questions we’re afraid to ask that might be essential to our health—both emotional and physical. All of us are touched by big data everyday, and its influence is multiplying. Everybody Lies challenges us to think differently about how we see it and the world.

    His uniqueness lies not only in the fact that at the young age of 19 and a half, he travelled to snow clad Himalayas from Kerala, and there he met and lived for several years with a ‘real-time’ yogi, Babaji, but also that he should undertake such an unusual and adventurous exploration, given his non-Hindu birth and antecedents.The metamorphosis of Mumtaz Ali Khan into Sri ‘M’, a yogi with profound knowledge of the Upanishads and deep personal insights, born of first hand experiences with higher levels of consciousness is indeed a fascinating story.The bonus for those interested in the secrets of yoga, meditation and sankhyan metaphysics is that Sri ‘M’ is still living and easily reachable. He leads a normal life, married with two children, wears no special robes and conducts himself without pomp or paraphernalia.Someone who met him recently said, “I expected a flashy godman and instead I saw a jean clad gentleman with a smile of his face, ready to discuss my problems. In five minutes flat, I said to myself, this is no ordinary man. The peace and tranquility that enters your system is tangible”.

    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

    W. R. Dedekind. The first presents Dedekind's theory of the irrational number-the Dedekind cut idea-perhaps the most famous of several such theories created in the 19th century to give a precise meaning to irrational numbers, which had been used on an intuitive basis since Greek times. This paper provided a purely arithmetic and perfectly rigorous foundation for the irrational numbers and thereby a rigorous meaning of continuity in analysis.The second essay is an attempt to give a logical basis for transfinite numbers and properties of the natural numbers. It examines the notion of natural numbers, the distinction between finite and transfinite (infinite) whole numbers, and the logical validity of the type of proof called mathematical or complete induction.The contents of these essays belong to the foundations of mathematics and will be welcomed by those who are prepared to look into the somewhat subtle meanings of the elements of our number system. As a major work of an important mathematician, the book deserves a place in the personal library of every practicing mathematician and every teacher and historian of mathematics. Authorized translations by "Vooster " V. Beman.

    In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn’t confined to abstract incidents that never occur in real life, but rather touches everything we do—the whole world is shot through with it.Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer?How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman—minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God.Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.” With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.

    There are equally many advanced textbooks which delve into the far reaches of statistical theory, while bypassing practical applications. But between these two approaches is an unfilled gap, in which theory and practice merge at an intermediate level. Professor M. G. Bulmer's Principles of Statistics, originally published in 1965, was created to fill that need. The new, corrected Dover edition of Principles of Statistics makes this invaluable mid-level text available once again for the classroom or for self-study.Principles of Statistics was created primarily for the student of natural sciences, the social scientist, the undergraduate mathematics student, or anyone familiar with the basics of mathematical language. It assumes no previous knowledge of statistics or probability; nor is extensive mathematical knowledge necessary beyond a familiarity with the fundamentals of differential and integral calculus. (The calculus is used primarily for ease of notation; skill in the techniques of integration is not necessary in order to understand the text.)Professor Bulmer devotes the first chapters to a concise, admirably clear description of basic terminology and fundamental statistical theory: abstract concepts of probability and their applications in dice games, Mendelian heredity, etc.; definitions and examples of discrete and continuous random variables; multivariate distributions and the descriptive tools used to delineate them; expected values; etc. The book then moves quickly to more advanced levels, as Professor Bulmer describes important distributions (binomial, Poisson, exponential, normal, etc.), tests of significance, statistical inference, point estimation, regression, and correlation. Dozens of exercises and problems appear at the end of various chapters, with answers provided at the back of the book. Also included are a number of statistical tables and selected references.

    The rise of the Internet and the wide availability of inexpensive computers have made it possible to gather and analyze network data on a large scale, and the development of a variety of new theoretical tools has allowed us to extract new knowledge from many different kinds of networks.The study of networks is broadly interdisciplinary and important developments have occurred in many fields, including mathematics, physics, computer and information sciences, biology, and the social sciences. This book brings together for the first time the most important breakthroughs in each of these fields and presents them in a coherent fashion, highlighting the strong interconnections between work in different areas.Subjects covered include the measurement and structure of networks in many branches of science, methods for analyzing network data, including methods developed in physics, statistics, and sociology, the fundamentals of graph theory, computer algorithms, and spectral methods, mathematical models of networks, including random graph models and generative models, and theories of dynamical processes taking place on networks.

    

    Simply stated, it asks whether every problem whose solution can be quickly checked by computer can also be quickly solved by computer. The Golden Ticket provides a nontechnical introduction to P-NP, its rich history, and its algorithmic implications for everything we do with computers and beyond. Lance Fortnow traces the history and development of P-NP, giving examples from a variety of disciplines, including economics, physics, and biology. He explores problems that capture the full difficulty of the P-NP dilemma, from discovering the shortest route through all the rides at Disney World to finding large groups of friends on Facebook. The Golden Ticket explores what we truly can and cannot achieve computationally, describing the benefits and unexpected challenges of this compelling problem.

    From the movement of flocks of birds to the Internet, environmental sustainability, and market regulation, the study and understanding of complex non-linear systems has become highly influential over the last 30 years.In this Very Short Introduction, one of the leading figures in the field, John Holland, introduces the key elements and conceptual framework of complexity. From complex physical systems such as fluid flow and the difficulties of predicting weather, to complex adaptive systems such as the highly diverse and interdependent ecosystems of rainforests, he combines simple, well-known examples -- Adam Smith's pin factory, Darwin's comet orchid, and Simon's 'watchmaker' -- with an account of the approaches, involving agents and urn models, taken by complexity theory.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

    It is so important that it provides the fundamental underpinning of all modern sciences. Without it, we'd have no nuclear power or nuclear bombs, no lasers, no TV, no computers, no science of molecular biology, no understanding of DNA, no genetic engineering—at all. John Gribbin tells the complete story of quantum mechanics, a truth far stranger than any fiction. He takes us step-by-step into an ever more bizarre and fascinating place—requiring only that we approach it with an open mind. He introduces the scientists who developed quantum theory. He investigates the atom, radiation, time travel, the birth of the universe, superconductors and life itself. And in a world full of its own delights, mysteries and surprises, he searches for Schrödinger's Cat—a search for quantum reality—as he brings every reader to a clear understanding of the most important area of scientific study today—quantum physics.

    It is a ‘ must’ book for those in every branch of science . . . in addition, economists, politicians, statesmen, and businessmen cannot afford to overlook cybernetics and its tremendous, even terrifying implications. "It is a beautifully written book, lucid, direct, and despite its complexity, as readable by the layman as the trained scientist." -- John B. Thurston, "The Saturday Review of Literature" Acclaimed one of the "seminal books . . . comparable in ultimate importance to . . . Galileo or Malthus or Rousseau or Mill," "Cybernetics" was judged by twenty-seven historians, economists, educators, and philosophers to be one of those books published during the "past four decades", which may have a substantial impact on public thought and action in the years ahead." -- Saturday Review

    Its aim is to deduce all the fundamental propositions of logic and mathematics from a small number of logical premises and primitive ideas, establishing that mathematics is a development of logic. This abridged text of Volume I contains the material that is most relevant to an introductory study of logic and the philosophy of mathematics (more advanced students will of course wish to refer to the complete edition). It contains the whole of the preliminary sections (which present the authors' justification of the philosophical standpoint adopted at the outset of their work); the whole of Part I (in which the logical properties of propositions, propositional functions, classes and relations are established); section A of Part II (dealing with unit classes and couples); and Appendices A and C (which give further developments of the argument on the theory of deduction and truth functions).

    Mathematical concepts and computational problems are motivated by applications in computer science. The reader learns by "doing," writing programs to implement the mathematical concepts and using them to carry out tasks and explore the applications. Examples include: error-correcting codes, transformations in graphics, face detection, encryption and secret-sharing, integer factoring, removing perspective from an image, PageRank (Google's ranking algorithm), and cancer detection from cell features. A companion web site, codingthematrix.com provides data and support code. Most of the assignments can be auto-graded online. Over two hundred illustrations, including a selection of relevant "xkcd" comics. Chapters: "The Function," "The Field," "The Vector," "The Vector Space," "The Matrix," "The Basis," "Dimension," "Gaussian Elimination," "The Inner Product," "Special Bases," "The Singular Value Decomposition," "The Eigenvector," "The Linear Program"