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.

    

    A basic idea that proved elusive for hundreds of years and bent the minds of the greatest thinkers in the world, the algorithm is what made the modern world possible. Without the algorithm, there would have been no computer, no Internet, no virtual reality, no e-mail, or any other technological advance that we rely on every day.In The Advent of the Algorithm, David Berlinski combines science, history, and math to explain and explore the intriguing story of how the algorithm was finally discovered by a succession of mathematicians and logicians, and how this paved the way for the digital age. Beginning with Leibniz and culminating in the middle of the twentieth century with the groundbreaking work of Gödel and Turing, The Advent of the Algorithm is an epic tale told with clarity and imaginative brilliance.

    An authoritative introduction to "fuzzy logic" brings readers up to speed on the "smart" products and computers that will change all of our lives in the future.

    Kathryn Schulz, editor of Grist magazine, argues that error is the fundamental human condition and should be celebrated as such. Guiding the reader through the history and psychology of error, from Socrates to Alan Greenspan, Being Wrong will change the way you perceive screw-ups, both of the mammoth and daily variety, forever.

    It’ll have you scratching your head wondering why we even bother to go to school.Think Magellan was the first man to circumnavigate the globe, baseball was invented in America, Henry VIII had six wives, Mount Everest is the tallest mountain? Wrong, wrong, wrong, and wrong again. You’ll be surprised at how much you don’t know! Check out THE BOOK OF GENERAL IGNORANCE for more fun entries and complete answers to the following:How long can a chicken live without its head?About two years.What do chameleons do?They don’t change color to match the background. Never have; never will. Complete myth. Utter fabrication. Total Lie. They change color as a result of different emotional states.How many legs does a centipede have?Not a hundred.How many toes has a two-toed sloth?It’s either six or eight.Who was the first American president?Peyton Randolph.What were George Washington’s false teeth made from?Mostly hippopotamus.What was James Bond’s favorite drink?Not the vodka martini.

    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.

    So wrong that a chimpanzee choosing answers at random will consistently outguess teachers, journalists, Nobel laureates, and investment bankers.In Factfulness, Professor of International Health and global TED phenomenon Hans Rosling, together with his two long-time collaborators, Anna and Ola, offers a radical new explanation of why this happens. They reveal the ten instincts that distort our perspective—from our tendency to divide the world into two camps (usually some version of us and them) to the way we consume media (where fear rules) to how we perceive progress (believing that most things are getting worse).Our problem is that we don’t know what we don’t know, and even our guesses are informed by unconscious and predictable biases.It turns out that the world, for all its imperfections, is in a much better state than we might think. That doesn’t mean there aren’t real concerns. But when we worry about everything all the time instead of embracing a worldview based on facts, we can lose our ability to focus on the things that threaten us most.Inspiring and revelatory, filled with lively anecdotes and moving stories, Factfulness is an urgent and essential book that will change the way you see the world and empower you to respond to the crises and opportunities of the future.

    Will our world ever become a ruin for future archaeologists to dig up and explore? The questions themselves are both philosophical and like something out of The Twilight Zone.Combining his trademark mix of storytelling, history and weirdness Dan Carlin connects the past and future in fascinating and colorful ways. At the same time the questions he asks us to consider involve the most important issue imaginable: human survival. From the collapse of the Bronze Age to the challenges of the nuclear era the issue has hung over humanity like a persistent Sword of Damocles.Inspired by his podcast, The End is Always Near challenges the way we look at the past and ourselves. In this absorbing compendium, Carlin embarks on a whole new set of stories and major cliffhangers that will keep readers enthralled. Idiosyncratic and erudite, offbeat yet profound, The End is Always Near examines issues that are rarely presented, and makes the past immediately relevant to our very turbulent present.

    Pinker is the high priest of rationalism' Sunday Times'If you've ever considered taking drugs to make yourself smarter, read Rationality instead. It's cheaper, more entertaining, and more effective' Jonathan Haidt, author of The Righteous MindIn the twenty-first century, humanity is reaching new heights of scientific understanding - and at the same time appears to be losing its mind. How can a species that discovered vaccines for Covid-19 in less than a year produce so much fake news, quack cures and conspiracy theorizing?In Rationality, Pinker rejects the cynical cliché that humans are simply an irrational species - cavemen out of time fatally cursed with biases, fallacies and illusions. After all, we discovered the laws of nature, lengthened and enriched our lives and set the benchmarks for rationality itself. Instead, he explains, we think in ways that suit the low-tech contexts in which we spend most of our lives, but fail to take advantage of the powerful tools of reasoning we have built up over millennia: logic, critical thinking, probability, causal inference, and decision-making under uncertainty. These tools are not a standard part of our educational curricula, and have never been presented clearly and entertainingly in a single book - until now.Rationality matters. It leads to better choices in our lives and in the public sphere, and is the ultimate driver of social justice and moral progress. Brimming with insight and humour, Rationality will enlighten, inspire and empower.'A terrific book, much-needed for our time' Peter Singer

    When Dr Ben Goldacre saw someone on daytime TV dipping her feet in an 'Aqua Detox' footbath, releasing her toxins into the water, turning it brown, he thought he'd try the same at home. 'Like some kind of Johnny Ball cum Witchfinder General', using his girlfriend's Barbie doll, he gently passed an electrical current through the warm salt water. It turned brown. In his words: 'before my very eyes, the world's first Detox Barbie was sat, with her feet in a pool of brown sludge, purged of a weekend's immorality.' Dr Ben Goldacre is the author of the Bad Science column in the Guardian. His book is about all the 'bad science' we are constantly bombarded with in the media and in advertising. At a time when science is used to prove everything and nothing, everyone has their own 'bad science' moments from the useless pie-chart on the back of cereal packets to the use of the word 'visibly' in cosmetics ads.

    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.

    How do we reconcile common sense and science? John Searle argues vigorously that the truths of common sense and the truths of science are both right and that the only question is how to fit them together.Searle explains how we can reconcile an intuitive view of ourselves as conscious, free, rational agents with a universe that science tells us consists of mindless physical particles. He briskly and lucidly sets out his arguments against the familiar positions in the philosophy of mind, and details the consequences of his ideas for the mind-body problem, artificial intelligence, cognitive science, questions of action and free will, and the philosophy of the social sciences.

    The long-anticipated revision of this best-selling text offers the most comprehensive, up-to-date introduction to the theory and practice of artificial intelligence. *NEW-Nontechnical learning material-Accompanies each part of the book. *NEW-The Internet as a sample application for intelligent systems-Added in several places including logical agents, planning, and natural language. *NEW-Increased coverage of material - Includes expanded coverage of: default reasoning and truth maintenance systems, including multi-agent/distributed AI and game theory; probabilistic approaches to learning including EM; more detailed descriptions of probabilistic inference algorithms. *NEW-Updated and expanded exercises-75% of the exercises are revised, with 100 new exercises. *NEW-On-line Java software. *Makes it easy for students to do projects on the web using intelligent agents. *A unified, agent-based approach to AI-Organizes the material around the task of building intelligent agents. *Comprehensive, up-to-date coverage-Includes a unified view of the field organized around the rational decision making pa

    That they exist, Simon Singh reveals, underscores the brilliance of the shows' writers, many of whom have advanced degrees in mathematics in addition to their unparalleled sense of humor. While recounting memorable episodes such as “Bart the Genius” and “Homer3,” Singh weaves in mathematical stories that explore everything from p to Mersenne primes, Euler's equation to the unsolved riddle of P v. NP; from perfect numbers to narcissistic numbers, infinity to even bigger infinities, and much more. Along the way, Singh meets members of The Simpsons' brilliant writing team-among them David X. Cohen, Al Jean, Jeff Westbrook, and Mike Reiss-whose love of arcane mathematics becomes clear as they reveal the stories behind the episodes. With wit and clarity, displaying a true fan's zeal, and replete with images from the shows, photographs of the writers, and diagrams and proofs, The Simpsons and Their Mathematical Secrets offers an entirely new insight into the most successful show in television history.