A lecture class taught by Wittgenstein, however, hardly resembled a lecture. He sat on a chair in the middle of the room, with some of the class sitting in chairs, some on the floor. He never used notes. He paused frequently, sometimes for several minutes, while he puzzled out a problem. He often asked his listeners questions and reacted to their replies. Many meetings were largely conversation. These lectures were attended by, among others, D. A. T. Gasking, J. N. Findlay, Stephen Toulmin, Alan Turing, G. H. von Wright, R. G. Bosanquet, Norman Malcolm, Rush Rhees, and Yorick Smythies. Notes taken by these last four are the basis for the thirty-one lectures in this book. The lectures covered such topics as the nature of mathematics, the distinctions between mathematical and everyday languages, the truth of mathematical propositions, consistency and contradiction in formal systems, the logicism of Frege and Russell, Platonism, identity, negation, and necessary truth. The mathematical examples used are nearly always elementary.

    

      Statistics are everywhere, as integral to science as they are to business, and in the popular media hundreds of times a day. In this age of big data, a basic grasp of statistical literacy is more important than ever if we want to separate the fact from the fiction, the ostentatious embellishments from the raw evidence -- and even more so if we hope to participate in the future, rather than being simple bystanders. In The Art of Statistics, world-renowned statistician David Spiegelhalter shows readers how to derive knowledge from raw data by focusing on the concepts and connections behind the math. Drawing on real world examples to introduce complex issues, he shows us how statistics can help us determine the luckiest passenger on the Titanic, whether a notorious serial killer could have been caught earlier, and if screening for ovarian cancer is beneficial. The Art of Statistics not only shows us how mathematicians have used statistical science to solve these problems -- it teaches us how we too can think like statisticians. We learn how to clarify our questions, assumptions, and expectations when approaching a problem, and -- perhaps even more importantly -- we learn how to responsibly interpret the answers we receive. Combining the incomparable insight of an expert with the playful enthusiasm of an aficionado, The Art of Statistics is the definitive guide to stats that every modern person needs.

    Now, in one of the greatest undertakings of the twenty-first century, a savvy group of mathematicians and computer scientists is beginning to sift through this data to dissect us and map out our next steps. Their goal? To manipulate our behavior -- what we buy, how we vote -- without our even realizing it.In this tour de force of original reporting and analysis, journalist Stephen Baker provides us with a fascinating guide to the world we're all entering -- and to the people controlling that world. The Numerati have infiltrated every realm of human affairs, profiling us as workers, shoppers, patients, voters, potential terrorists -- and lovers. The implications are vast. Our privacy evaporates. Our bosses can monitor and measure our every move (then reward or punish us). Politicians can find the swing voters among us, by plunking us all into new political groupings with names like "Hearth Keepers" and "Crossing Guards." It can sound scary. But the Numerati can also work on our behalf, diagnosing an illness before we're aware of the symptoms, or even helping us find our soul mate. Surprising, enlightening, and deeply relevant, The Numerati shows how a powerful new endeavor -- the mathematical modeling of humanity -- will transform every aspect of our lives. STEPHEN BAKER has written for BusinessWeek for over twenty years, covering Mexico and Latin America, the Rust Belt, European technology, and a host of other topics, including blogs, math, and nanotechnology. But he's always considered himself a foreign correspondent. This, he says, was especially useful as he met the Numerati. "While I came from the world of words, they inhabited the symbolic realms of math and computer science. This was foreign to me. My reporting became an anthropological mission." Baker has written for many publications, including the Wall Street Journal, the Los Angeles Times, and the Boston Globe. He won an Overseas Press Club Award for his portrait of the rising Mexican auto industry. He is the coauthor of blogspotting.net, featured by the New York Times as one of fifty blogs to watch.

    Here is an altogether new, refreshing, alternative history of math revealing how simple questions anyone might ask about space -- in the living room or in some other galaxy -- have been the hidden engine of the highest achievements in science and technology. Based on Mlodinow's extensive historical research; his studies alongside colleagues such as Richard Feynman and Kip Thorne; and interviews with leading physicists and mathematicians such as Murray Gell-Mann, Edward Witten, and Brian Greene, Euclid's Window is an extraordinary blend of rigorous, authoritative investigation and accessible, good-humored storytelling that makes a stunningly original argument asserting the primacy of geometry. For those who have looked through Euclid's Window, no space, no thing, and no time will ever be quite the same.

    Rare Book

    . . in which Sydney Padua transforms one of the most compelling scientific collaborations into a hilarious series of adventures. Meet Victorian London’s most dynamic duo: Charles Babbage, the unrealized inventor of the computer, and his accomplice, Ada, Countess of Lovelace, the peculiar protoprogrammer and daughter of Lord Byron. When Lovelace translated a description of Babbage’s plans for an enormous mechanical calculating machine in 1842, she added annotations three times longer than the original work. Her footnotes contained the first appearance of the general computing theory, a hundred years before an actual computer was built. Sadly, Lovelace died of cancer a decade after publishing the paper, and Babbage never built any of his machines. But do not despair! The Thrilling Adventures of Lovelace and Babbage presents a rollicking alternate reality in which Lovelace and Babbage do build the Difference Engine and then use it to build runaway economic models, battle the scourge of spelling errors, explore the wilder realms of mathematics, and, of course, fight crime—for the sake of both London and science. Complete with extensive footnotes that rival those penned by Lovelace herself, historical curiosities, and never-before-seen diagrams of Babbage’s mechanical, steam-powered computer, The Thrilling Adventures of Lovelace and Babbage is wonderfully whimsical, utterly unusual, and, above all, entirely irresistible.(With black-and-white illustrations throughout.)

    Originally marked out by eye and later by use of a stretched cord, in time these forms came to be made with the simple tools of ruler and compass.This small book introduces the origins and basic principles of geometric constructions using these ancient tools, before going on to cover dozens of geometric forms, from practical fundamentals to more challenging constructions.

    Without a doubt, the development of the computer was a massive leap forward in humankind's progress and will stand as one of the twentieth century's greatest achievements. But how many of us know how it really works? "Turing And The Computer" offers a brilliant encapsulation of the groundwork that led to the invention of the computer as we know it, and an absorbing account of the man who helped develop it, only to be largely forgotten after his death. Eccentric and principled, Turing would lay aside a brilliant career in mathematics to serve his country by breaking German codes during the Second World War. Openly homosexual, he would later be put on trial on indecency charges and forced to undergo hormone treatments that wrecked his body and his spirit. But the modern machine he helped create lives on.Concise and thoroughly compelling, "Turing And The Computer" is for all those curious about the philosophy and mechanics behind the now indispensable computer, and for anyone awed by the spark of invention that inspires its birth.

    What if everything in life could be reduced to a simple formula? What if numbers were able to tell us which partners we were best matched with – not just in terms of attractiveness, but for a long-term committed marriage? Or if they could say which films would be the biggest hits at the box office, and what changes could be made to those films to make them even more successful? Or even who out of us is likely to commit certain crimes, and when? This may sound like the world of science-fiction, but in fact it is just the tip of the iceberg in a world that is increasingly ruled by complex algorithms and neural networks.In The Formula, Luke Dormehl takes you inside the world of numbers, asking how we came to believe in the all-conquering power of algorithms; introducing the mathematicians, artificial intelligence experts and Silicon Valley entrepreneurs who are shaping this brave new world, and ultimately asking how we survive in an era where numbers can sometimes seem to create as many problems as they solve.

    The language concepts are aptly explained in simple and easy-to-understand style, supported with examples, illustrations and programming and debugging exercises.

    The story of information begins in a time profoundly unlike our own, when every thought and utterance vanishes as soon as it is born. From the invention of scripts and alphabets to the long-misunderstood talking drums of Africa, Gleick tells the story of information technologies that changed the very nature of human consciousness. He provides portraits of the key figures contributing to the inexorable development of our modern understanding of information: Charles Babbage, the idiosyncratic inventor of the first great mechanical computer; Ada Byron, the brilliant and doomed daughter of the poet, who became the first true programmer; pivotal figures like Samuel Morse and Alan Turing; and Claude Shannon, the creator of information theory itself. And then the information age arrives. Citizens of this world become experts willy-nilly: aficionados of bits and bytes. And we sometimes feel we are drowning, swept by a deluge of signs and signals, news and images, blogs and tweets. The Information is the story of how we got here and where we are heading.

    The Art of Problem Solving, Volume 2, is the classic problem solving textbook used by many successful high school math teams and enrichment programs and have been an important building block for students who, like the authors, performed well enough on the American Mathematics Contest series to qualify for the Math Olympiad Summer Program which trains students for the United States International Math Olympiad team.Volume 2 is appropriate for students who have mastered the problem solving fundamentals presented in Volume 1 and are ready for a greater challenge. Although the Art of Problem Solving is widely used by students preparing for mathematics competitions, the book is not just a collection of tricks. The emphasis on learning and understanding methods rather than memorizing formulas enables students to solve large classes of problems beyond those presented in the book.Speaking of problems, the Art of Problem Solving, Volume 2, contains over 500 examples and exercises culled from such contests as the Mandelbrot Competition, the AMC tests, and ARML. Full solutions (not just answers!) are available for all the problems in the solution manual.

    A simple web search picks out a handful of relevant needles from the world's biggest haystack: the billions of pages on the World Wide Web. Uploading a photo to Facebook transmits millions of pieces of information over numerous error-prone network links, yet somehow a perfect copy of the photo arrives intact. Without even knowing it, we use public-key cryptography to transmit secret information like credit card numbers; and we use digital signatures to verify the identity of the websites we visit. How do our computers perform these tasks with such ease? This is the first book to answer that question in language anyone can understand, revealing the extraordinary ideas that power our PCs, laptops, and smartphones. Using vivid examples, John MacCormick explains the fundamental "tricks" behind nine types of computer algorithms, including artificial intelligence (where we learn about the "nearest neighbor trick" and "twenty questions trick"), Google's famous PageRank algorithm (which uses the "random surfer trick"), data compression, error correction, and much more. These revolutionary algorithms have changed our world: this book unlocks their secrets, and lays bare the incredible ideas that our computers use every day.

    If the idea of a computer science book without computers upsets you, please close your eyes until you’ve finished reading the rest of this page.The truth is that computer science is not really about the computer. It is just a tool to help you see ideas more clearly. You can see the moon and stars without a telescope, smell the flowers without a fluoroscope, have fun without a funoscope, and be silly sans oscilloscope.You can also play with computer science without... you-know-what. Ideas are the real stuff of computer science. This book is about those ideas, and how to find them.