In this lively book of essays, Stephen Wolfram takes the reader along on some of his most surprising and engaging intellectual adventures in science, technology, artificial intelligence and language design.

    Linear Equations; Vector Spaces; Linear Transformations; Polynomials; Determinants; Elementary canonical Forms; Rational and Jordan Forms; Inner Product Spaces; Operators on Inner Product Spaces; Bilinear Forms For all readers interested in linear algebra.

    Would you believe that these five pieces can be reassembled in such a fashion so as to create two apples equal in shape and size to the original? Would you believe that you could make something as large as the sun by breaking a pea into a finite number of pieces and putting it back together again? Neither did Leonard Wapner, author of The Pea and the Sun, when he was first introduced to the Banach-Tarski paradox, which asserts exactly such a notion. Written in an engaging style, The Pea and the Sun catalogues the people, events, and mathematics that contributed to the discovery of Banach and Tarski's magical paradox. Wapner makes one of the most interesting problems of advanced mathematics accessible to the non-mathematician.

    A modern classic by an accomplished mathematician and best-selling author has been updated to encompass and explain the recent headline-making advances in the field in non-technical terms.

    Linear algebra is tightly integrated into the text.

    The convergence of old technology and new has centralized unimaginable power into the hands of a few gigantic corporations that now dictate how we communicate with each other and perceive the outside world. Media analyst Mark Dice details how the rise of social media that tipped the balance of power regarding the production and distribution of information has also resulted in a massive backslash from those conspiring to regain the influence they once held. Now conservatives are experiencing widespread censorship as the tech giants scramble to put the genie back in the bottle. The liberal media has launched an information war against President Trump and his supporters, and are using their monopolies to manipulate public opinion in order to further their aims of a socialist revolution.

    Since then, Sylvia Nasar's celebrated biography A Beautiful Mind, the basis of a new major motion picture, has revealed the man. The Essential John Nash reveals his work--in his own words. This book presents, for the first time, the full range of Nash's diverse contributions not only to game theory, for which he received the Nobel, but to pure mathematics--from Riemannian geometry and partial differential equations--in which he commands even greater acclaim among academics. Included are nine of Nash's most influential papers, most of them written over the decade beginning in 1949.From 1959 until his astonishing remission three decades later, the man behind the concepts "Nash equilibrium" and "Nash bargaining"--concepts that today pervade not only economics but nuclear strategy and contract talks in major league sports--had lived in the shadow of a condition diagnosed as paranoid schizophrenia. In the introduction to this book, Nasar recounts how Nash had, by the age of thirty, gone from being a wunderkind at Princeton and a rising mathematical star at MIT to the depths of mental illness.In his preface, Harold Kuhn offers personal insights on his longtime friend and colleague; and in introductions to several of Nash's papers, he provides scholarly context. In an afterword, Nash describes his current work, and he discusses an error in one of his papers. A photo essay chronicles Nash's career from his student days in Princeton to the present. Also included are Nash's Nobel citation and autobiography.The Essential John Nash makes it plain why one of Nash's colleagues termed his style of intellectual inquiry as "like lightning striking." All those inspired by Nash's dazzling ideas will welcome this unprecedented opportunity to trace these ideas back to the exceptional mind they came from.

    According to theorists, the missing six are curled up in bizarre structures known as Calabi-Yau manifolds. In The Shape of Inner Space, Shing-Tung Yau, the man who mathematically proved that these manifolds exist, argues that not only is geometry fundamental to string theory, it is also fundamental to the very nature of our universe.Time and again, where Yau has gone, physics has followed. Now for the first time, readers will follow Yau’s penetrating thinking on where we’ve been, and where mathematics will take us next. A fascinating exploration of a world we are only just beginning to grasp, The Shape of Inner Space will change the way we consider the universe on both its grandest and smallest scales.

    The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. To help students construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. Previous Edition Hb (1994) 0-521-44116-1 Previous Edition Pb (1994) 0-521-44663-5

    Until, at the tender age of sixteen, he worked out how to use the credit card system to his advantage. Identifying the banks' security weaknesses, utilising his intelligence and charm, Elliot embarked on a massive spending spree. From London to New York, Ibiza to Beverly Hills, he lived the fantasy life, staying in famous hotels, flying first class, blowing a fortune on designer clothes. Time and time again, Elliot managed to wriggle free of the numerous authorities who were on his tail, while his life spiralled out of control. Meanwhile, from a police station at Heathrow, a detective was patiently tracking him down . . . With a likeable hero, filled with humour and as fast-paced as a thriller, Other People's Money is crime writing at its best.'A fascinating and illuminating story' Irvine Welsh'Exhilarating Brit variation on Catch Me if You Can, which never misses an opportunity to up the sweaty-palmed suspense.' "Arena"

    Such was his faith in the power of the mind that he was able to conclude that what you think, you become.The mind is a powerful thing to have. The thoughts that run through your mind shape and become your reality. You are one huge magnet. You attract into your life the energy that vibrates in the same frequency that your thoughts are vibrating into. If you think negative thoughts, then you will also attract the same level of negative energy. If you allow positive thoughts to flow through your mind, then positive things will also come your way.The life that you are living now is the product of your thoughts. Your mind is so powerful that it can create and destroy things at a blink of an eye. Everything begins and ends in your mind. You can give it the power to enslave you or you can empower yourself to control it.Be mindful of your own thoughts. Learn to select them the way that you would select the clothes that you would wear. You can’t control life from happening but you can control your mind and the thoughts that run through it and once you do, you will begin to gain control over your life. This book will help you understand why you have been losing focus. It was written in a light manner to help you better grasp the reasons for lack of focus in your life. There are no complex theories and concepts to comprehend. This book was written for you to help you find your way back to you. It was written to light your way towards your dreams and aspirations. It was written to give you the courage to regain control of your life.Give yourself the gift of focus by reading this book. Allow yourself to break free from your fears and apprehension. Learn how to take charge of your life.Most of all, this book will show you ten easy and simple ways to control your mind. As you begin to regain control of your life, this book will be your guide, your mentor and your friend. It will walk you through each step as if you were talking to a life coach yourself. It will help you overcome the challenges that will come your way. It will not just tell what to do to stay focused, it will also show you how.Dive into this book with an open mind. Allow it to help you gain control over your life. Let it reveal to you the things that are keeping you from achieving your true potential. Let it show you the way towards success, happiness and fulfillment. Allow this book to speak to you. Let it empower you. You are brought into this world for a reason. Do not let anything or anyone distract you from your true destiny. You are what you think you are. Don’ t ever doubt that. This book will help you see that.

    At the time we were hoping that our approach of writing a book which would be both accessible without mathematical sophistication and portray these exiting new fields in an authentic manner would find an audience. Now we know it did. We know from many reviews and personal letters that the book is used in a wide range of ways: researchers use it to acquaint themselves, teachers use it in college and university courses, students use it for background reading, and there is also a substantial audience of lay people who just want to know what chaos and fractals are about. Every book that is somewhat technical in nature is likely to have a number of misprints and errors in its first edition. Some of these were caught and brought to our attention by our readers. One of them, Hermann Flaschka, deserves to be thanked in particular for his suggestions and improvements. This second edition has several changes. We have taken out the two appendices from the firstedition. At the time of the first edition Yuval Fishers contribution, which we published as an appendix was probably the first complete expository account on fractal image compression. Meanwhile, Yuvals book Fractal Image Compression: Theory and Application appeared and is now the publication to refer to.

    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.

    If it takes a book to get it across, I hope this book will do it. It ought to.”—Thomas Schelling, Distinguished University Professor, School of Public Policy, University of Maryland, and 2005 Nobel Prize Laureate in Economics “With humor, insight, piercing logic and a nod to history, Ziliak and McCloskey show how economists—and other scientists—suffer from a mass delusion about statistical analysis. The quest for statistical significance that pervades science today is a deeply flawed substitute for thoughtful analysis. . . . Yet few participants in the scientific bureaucracy have been willing to admit what Ziliak and McCloskey make clear: the emperor has no clothes.”—Kenneth Rothman, Professor of Epidemiology, Boston University School of Health The Cult of Statistical Significance shows, field by field, how “statistical significance,” a technique that dominates many sciences, has been a huge mistake. The authors find that researchers in a broad spectrum of fields, from agronomy to zoology, employ “testing” that doesn’t test and “estimating” that doesn’t estimate. The facts will startle the outside reader: how could a group of brilliant scientists wander so far from scientific magnitudes? This study will encourage scientists who want to know how to get the statistical sciences back on track and fulfill their quantitative promise. The book shows for the first time how wide the disaster is, and how bad for science, and it traces the problem to its historical, sociological, and philosophical roots. Stephen T. Ziliak is the author or editor of many articles and two books. He currently lives in Chicago, where he is Professor of Economics at Roosevelt University. Deirdre N. McCloskey, Distinguished Professor of Economics, History, English, and Communication at the University of Illinois at Chicago, is the author of twenty books and three hundred scholarly articles. She has held Guggenheim and National Humanities Fellowships. She is best known for How to Be Human* Though an Economist (University of Michigan Press, 2000) and her most recent book, The Bourgeois Virtues: Ethics for an Age of Commerce (2006).

    The Golden Retriever's personality is as golden as his outer coat. He was bred to please, and please he does. He started out as a hunting partner who delivered birds to hand and has evolved into modern times delivering whatever suits his owner's fancy. Because Golden Retrievers were originally bred to work in tandem with humans, they are also highly trainable. Golden Retrievers For Dummies is intended for busy 21st century dog owners who don't have time to sit down and read through 300 pages at a crack. This is a reference you can jump in and out of as dog questions rear their furry heads. This handy guide is also for you ifYou own a Golden Retriever or thinking about getting one. You've just brought home a Golden pup. You want to find the best way to raise and train your Golden. You want to help your Golde n to not just survive but to thrive. Find out what it takes to own this active, intelligent, and friendly dog. Explore the Golden's personality traits and living requirements. Discover which diseases are hereditary. This reference guide covers all the aspects of dog ownership, including:Looking at breeders, rescue groups, and animal shelters Adopting and caring for older dogs Selecting a puppy with help from an established testing process Dog-proofing your house and yard Crate training, housetraining, and obedience training Canine communication and growing pains Feeding, exercising, and playing with your Golden Dealing with illness, problem behavior, and treatment Grooming for health and beauty If you're serious about this Golden business and not just caving in to the kids or some other wild impulse, follow the advice of responsible dog owners and breeders. Look deep into your dog-loving soul and carefully consider the big picture. Love alone is not enough.