Petr Beckmann holds up this mirror, giving the background of the times when pi made progress -- and also when it did not, because science was being stifled by militarism or religious fanaticism.

    This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes.Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known.Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there.

    Topics covered in the book include the properties of arithmetic, exponents, primes and divisors, fractions, equations and inequalities, decimals, ratios and proportions, unit conversions and rates, percents, square roots, basic geometry (angles, perimeter, area, triangles, and quadrilaterals), statistics, counting and probability, and more! The text is structured to inspire the reader to explore and develop new ideas. Each section starts with problems, giving the student a chance to solve them without help before proceeding. The text then includes solutions to these problems, through which algebraic techniques are taught. Important facts and powerful problem solving approaches are highlighted throughout the text. In addition to the instructional material, the book contains well over 1000 problems. The solutions manual (sold separately) contains full solutions to all of the problems, not just answers. This book can serve as a complete Prealgebra course. This text is supplemented by free videos and a free learning system at the publisher's website.

    For reasons of space, the Weekly must often slightly truncate the pieces and also sees fit to change the name of the piece. So, what you read there isn’t always what I sent them. This is one of the reasons I wanted to put this book out. Also, knowing there are a lot of people out there without the time to go to some website and read something every week, I thought it would be a good idea to have the articles all in one place. I hope you enjoy the book and thank you. - Henry

    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.

    Book by Waring, Chris

    Now featuring more than 250 color illustrations throughout, this perennially popular guide is a must for novices who want to work with HTML or XHTML, which continue to be the foundation for any Web site The new edition features nearly 50 percent new and updated content, including expanded coverage of CSS and scripting, new coverage of syndication and podcasting, and new sample HTML projects, including a personal Web page, an eBay auction page, a company Web site, and an online product catalog The companion Web site features an eight-page expanded Cheat Sheet with ready-reference information on commands, syntax, colors, CSS elements, and more Covers planning a Web site, formatting Web pages, using CSS, getting creative with colors and fonts, managing layouts, and integrating scripts

    This book covers relevant geometric principles and how to represent objects algebraically so they can be computed and applied. Recent major developments in the theory and practice of scene reconstruction are described in detail in a unified framework. Richard Hartley and Andrew Zisserman provide comprehensive background material and explain how to apply the methods and implement the algorithms. First Edition HB (2000): 0-521-62304-9

    Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences--perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times."However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject.New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.

    Politicians and marketers present shoddy evidence for dubious claims all the time. But smart people make mistakes too, and when it comes to statistics, plenty of otherwise great scientists--yes, even those published in peer-reviewed journals--are doing statistics wrong."Statistics Done Wrong" comes to the rescue with cautionary tales of all-too-common statistical fallacies. It'll help you see where and why researchers often go wrong and teach you the best practices for avoiding their mistakes.In this book, you'll learn: - Why "statistically significant" doesn't necessarily imply practical significance- Ideas behind hypothesis testing and regression analysis, and common misinterpretations of those ideas- How and how not to ask questions, design experiments, and work with data- Why many studies have too little data to detect what they're looking for-and, surprisingly, why this means published results are often overestimates- Why false positives are much more common than "significant at the 5% level" would suggestBy walking through colorful examples of statistics gone awry, the book offers approachable lessons on proper methodology, and each chapter ends with pro tips for practicing scientists and statisticians. No matter what your level of experience, "Statistics Done Wrong" will teach you how to be a better analyst, data scientist, or researcher.

    He constructed a fleet of customized unicycles and a flamethrowing trumpet, outfoxed Vegas casinos, and built juggling robots. He also wrote the seminal text of the digital revolution, which has been called “the Magna Carta of the Information Age.” His discoveries would lead contemporaries to compare him to Albert Einstein and Isaac Newton. His work anticipated by decades the world we’d be living in today—and gave mathematicians and engineers the tools to bring that world to pass.In this elegantly written, exhaustively researched biography, Jimmy Soni and Rob Goodman reveal Claude Shannon’s full story for the first time. It’s the story of a small-town Michigan boy whose career stretched from the era of room-sized computers powered by gears and string to the age of Apple. It’s the story of the origins of our digital world in the tunnels of MIT and the “idea factory” of Bell Labs, in the “scientists’ war” with Nazi Germany, and in the work of Shannon’s collaborators and rivals, thinkers like Alan Turing, John von Neumann, Vannevar Bush, and Norbert Wiener.And it’s the story of Shannon’s life as an often reclusive, always playful genius. With access to Shannon’s family and friends, A Mind at Play brings this singular innovator and creative genius to life.

    We’ve comea long way since then. With this book, Drs. Romero and Balch liftthe veil from many of these once-opaque concepts in high-techfinance. We can all benefit from learning how the cooperationbetween wetware and software creates fitter models. This bookdoes a fantastic job describing how the latest advances in financialmodeling and data science help today’s portfolio managerssolve these greater riddles. —Michael Himmel, ManagingPartner, Essex Asset ManagementI applaud Phil Romero’s willingness to write about the hedgefund world, an industry that is very private, often flamboyant,and easily misunderstood. As with every sector of the investmentlandscape, the hedge fund industry varies dramaticallyfrom quantitative “black box” technology, to fundamental researchand old-fashioned stock picking. This book helps investorsdistinguish between these diverse opposites and understandtheir place in the new evolving world of finance. —Mick Elfers,Founder and Chief Investment Strategist, Irvington Capital

    He was especially careful to present new and unfamiliar puzzles that had not been included in such classic collections as those by Sam Loyd and Henry Dudeney. Later, these puzzles were published in book collections, incorporating reader feedback on alternate solutions or interesting generalizations.The present volume contains a rich selection of 70 of the best of these brain teasers, in some cases including references to new developments related to the puzzle. Now enthusiasts can challenge their solving skills and rattle their egos with such stimulating mind-benders as The Returning Explorer, The Mutilated Chessboard, Scrambled Box Tops, The Fork in the Road, Bronx vs. Brooklyn, Touching Cigarettes, and 64 other problems involving logic and basic math. Solutions are included.

    The book's conceptual presentation focuses on ADTs and the analysis of algorithms for efficiency, with a particular concentration on performance and running time. The second edition contains a new chapter that examines advanced data structures such as red black trees, top down splay trees, treaps, k-d trees, and pairing heaps among others. All code examples now conform to ANSI C and coverage of the formal proofs underpinning several key data structures has been strengthened.