This hilarious and informative book is designed for anyone who is sci-curious and wants to know more about the world around them, especially the elements of everyday science that other books ignore.

    Now he brings his considerable talents to the history of one of math's most enduring puzzles: the seemingly paradoxical nature of infinity.Is infinity a valid mathematical property or a meaningless abstraction? The nineteenth-century mathematical genius Georg Cantor's answer to this question not only surprised him but also shook the very foundations upon which math had been built. Cantor's counterintuitive discovery of a progression of larger and larger infinities created controversy in his time and may have hastened his mental breakdown, but it also helped lead to the development of set theory, analytic philosophy, and even computer technology.Smart, challenging, and thoroughly rewarding, Wallace's tour de force brings immediate and high-profile recognition to the bizarre and fascinating world of higher mathematics.

    Heller Wilson has found the key. From acclaimed writer Charles Soule (27, Strongman, Swamp Thing) comes a mathematical thriller about Chaos, Probability, and the race to stop a citywide disaster. In 1978, Dr. Spencer Brownfield saved New York City from itself, bringing the city back from the verge of collapse and ruin. And for thirty years, his small, unnoticed adjustments to the city's systems have kept the city afloat. Or so he claims to Heller Wilson, a young graduate student that Dr. Brownfield has chosen as his successor. But are Dr. Brownfield's claims about The Butterfly Effect and how his "complexity math" apply to the city's patterns of life real, or are they the ravings of a man broken by the death of his wife and daughter, desperate to find some kind of control over the world around him? Part sci-fi, part philosophical exploration, part thriller, STRANGE ATTRACTORS examines what you can control in your life and what you can't, and how important it is to recognize the difference.

    Kurt Giidel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th-century mathematics.The present volume reprints the first English translation of Giidel's far-reaching work. Not only does it make the argument more intelligible, but the introduction contributed by Professor R. B. Braithwaite (Cambridge University}, an excellent work of scholarship in its own right, illuminates it by paraphrasing the major part of the argument.This Dover edition thus makes widely available a superb edition of a classic work of original thought, one that will be of profound interest to mathematicians, logicians and anyone interested in the history of attempts to establish axioms that would provide a rigorous basis for all mathematics. Translated by B. Meltzer, University of Edinburgh. Preface. Introduction by R. B. Braithwaite.

    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.

    Ten dimensions? Most of us have barely gotten used to the idea that there are four.Using simple geometry and an easygoing writing style, author Rob Bryanton starts with the lower dimensions that we are all familiar with, then uses those concepts to build one layer upon another, ultimately arriving at a way of imagining the tenth dimension.Part scientific exploration, part philosophy, this unique book touches upon such diverse topics as dark matter, Feynman's "sum over paths", the quantum observer, and the soul. It is aimed at anyone interested in leading-edge theories about cosmology and the nature of reality, but it is not about mainstream physics. Rather, Imagining the Tenth Dimension is a mind-expanding exercise that could change the way you view this incredible universe in which we live.

    These themes include mathematical reasoning, combinatorial analysis, discrete structures, algorithmic thinking, and enhanced problem-solving skills through modeling. Its intent is to demonstrate the relevance and practicality of discrete mathematics to all students. The Fifth Edition includes a more thorough and linear presentation of logic, proof types and proof writing, and mathematical reasoning. This enhanced coverage will provide students with a solid understanding of the material as it relates to their immediate field of study and other relevant subjects. The inclusion of applications and examples to key topics has been significantly addressed to add clarity to every subject. True to the Fourth Edition, the text-specific web site supplements the subject matter in meaningful ways, offering additional material for students and instructors. Discrete math is an active subject with new discoveries made every year. The continual growth and updates to the web site reflect the active nature of the topics being discussed. The book is appropriate for a one- or two-term introductory discrete mathematics course to be taken by students in a wide variety of majors, including computer science, mathematics, and engineering. College Algebra is the only explicit prerequisite.

    Of course, it’s not all cooking; we’ll also run the New York and Chicago marathons, pay visits to Cinderella and Lewis Carroll, and even get to the bottom of a tomato’s identity as a vegetable. This is not the math of our high school classes: mathematics, Cheng shows us, is less about numbers and formulas and more about how we know, believe, and understand anything, including whether our brother took too much cake.At the heart of How to Bake Pi is Cheng’s work on category theory—a cutting-edge “mathematics of mathematics.” Cheng combines her theory work with her enthusiasm for cooking both to shed new light on the fundamentals of mathematics and to give readers a tour of a vast territory no popular book on math has explored before. Lively, funny, and clear, How to Bake Pi will dazzle the initiated while amusing and enlightening even the most hardened math-phobe.

    It now has 600,000 to a million page hits daily. Every now and then, Munroe would get emails asking him to arbitrate a science debate. 'My friend and I were arguing about what would happen if a bullet got struck by lightning, and we agreed that you should resolve it . . . ' He liked these questions so much that he started up What If. If your cells suddenly lost the power to divide, how long would you survive? How dangerous is it, really, to be in a swimming pool in a thunderstorm? If we hooked turbines to people exercising in gyms, how much power could we produce? What if everyone only had one soulmate?When (if ever) did the sun go down on the British empire? How fast can you hit a speed bump while driving and live?What would happen if the moon went away?In pursuit of answers, Munroe runs computer simulations, pores over stacks of declassified military research memos, solves differential equations, and consults with nuclear reactor operators. His responses are masterpieces of clarity and hilarity, studded with memorable cartoons and infographics. They often predict the complete annihilation of humankind, or at least a really big explosion. Far more than a book for geeks, WHAT IF: Serious Scientific Answers to Absurd Hypothetical Questions explains the laws of science in operation in a way that every intelligent reader will enjoy and feel much the smarter for having read.

    Since its publication in 1908, it has been a classic work to which successive generations of budding mathematicians have turned at the beginning of their undergraduate courses. In its pages, Hardy combines the enthusiasm of a missionary with the rigor of a purist in his exposition of the fundamental ideas of the differential and integral calculus, of the properties of infinite series and of other topics involving the notion of limit.

    Indeed, if God knows everything, why do we need to learn through pain and suffering? If God is omnipotent, why are we needed to do good? If the universe is fundamentally good, why are wars, crime, and injustice all around us? In modern society, orthodox science takes the rational high-ground and tackles these contradictions by denying the very need for, and the existence of, meaning. Indeed, many of us implicitly accept the notion that rationality somehow contradicts spirituality. That is a modern human tragedy, not only for its insidiousness, but for the fact that it is simply not true. In this book, the author constructs a coherent and logical argument for the meaning of existence, informed by science itself. A framework is laid out wherein all aspects of human existence have a logical, coherent reason and role, including the ones often perceived as negative. The powerful logic of this framework inescapably leads to insightful and inspiring guidelines for living a purposeful and meaningful life.

    For centuries, the power of zero savored of the demonic; once harnessed, it became the most important tool in mathematics. Zero follows this number from its birth as an Eastern philosophical concept to its struggle for acceptance in Europe and its apotheosis as the mystery of the black hole. Today, zero lies at the heart of one of the biggest scientific controversies of all time, the quest for the theory of everything. Elegant, witty, and enlightening, Zero is a compelling look at the strangest number in the universe and one of the greatest paradoxes of human thought.

    He proposes his solution.

    The practice of meditation—which includes living in the moment and being in touch with your emotions—can change your body and brain, keeping them fit, flexible and resilient as you age. TIME’s special edition offers: Mindfulness tips for everyone, from the novice to the lifetime meditator The latest research on mindfulness, heart health and sleep How to bring mindfulness into your day without having to sit still on a cushion

    We currently see no evidence of any kind indicating that extraterrestrials exist outside of our solar system. But at this moment, millions of engineers, scientists, corporations, universities and entrepreneurs are racing to create the second intelligent species right here on planet earth. And we can see the second intelligent species coming from all directions in the form of self-driving cars, automated call centers, chess-playing and Jeopardy-playing computers that beat all human players, airport kiosks, restaurant tablet systems, etc. The frightening thing is that these robots will soon be eliminating human jobs in startling numbers. The first wave of unemployed workers is likely to be a million truck drivers who are replaced by self-driving trucks. Pilots will be eliminated soon as well. Then, as new computer vision systems come online, we will see tens of millions of workers in retail stores, fast food restaurants and construction sites replaced by robots. Unless we take steps now to change the economy, we will soon have tens of millions of workers who are unemployed and seeking welfare because they will have no other choice. Marshall Brain's new book "The Second Intelligent Species: How Humans Will Become as Irrelevant as Cockroaches" explores how the future will unfold as the second intelligent species emerges. The book answers questions like: - How will new computer vision systems affect the job market? - How many people will become unemployed by the second intelligent species? - What will happen to millions of newly unemployed workers? - How can modern society and modern economies cope with run-away unemployment caused by robots? - What will happen when the first sentient, conscious computer appears? - What moral and ethical principles will guide the second intelligent species? - Why do we see no extraterrestrials in our universe? "The Second Intelligent Species" offers a unique and fascinating look at the future of the human race, and the choices we will need to make to avoid massive unemployment and poverty worldwide as intelligent machines start eliminating millions of jobs.