Full of insights, arguments and philosophical perspectives, the book covers an amazing array of topics. Beginning in antiquity with Democritus, it progresses through logic and set theory, computability and complexity theory, quantum computing, cryptography, the information content of quantum states and the interpretation of quantum mechanics. There are also extended discussions about time travel, Newcomb's Paradox, the anthropic principle and the views of Roger Penrose. Aaronson's informal style makes this fascinating book accessible to readers with scientific backgrounds, as well as students and researchers working in physics, computer science, mathematics and philosophy.

    

    Along the tidal rivers of Malaysia, thousands of fireflies congregate and flash in unison; the moon spins in perfect resonance with its orbit around the earth; our hearts depend on the synchronous firing of ten thousand pacemaker cells. While the forces that synchronize the flashing of fireflies may seem to have nothing to do with our heart cells, there is in fact a deep connection. Synchrony is a science in its infancy, and Strogatz is a pioneer in this new frontier in which mathematicians and physicists attempt to pinpoint just how spontaneous order emerges from chaos. From underground caves in Texas where a French scientist spent six months alone tracking his sleep-wake cycle, to the home of a Dutch physicist who in 1665 discovered two of his pendulum clocks swinging in perfect time, this fascinating book spans disciplines, continents, and centuries. Engagingly written for readers of books such as Chaos and The Elegant Universe, Sync is a tour-de-force of nonfiction writing.

    Hand argues that extraordinarily rare events are anything but. In fact, they’re commonplace. Not only that, we should all expect to experience a miracle roughly once every month.     But Hand is no believer in superstitions, prophecies, or the paranormal. His definition of “miracle” is thoroughly rational. No mystical or supernatural explanation is necessary to understand why someone is lucky enough to win the lottery twice, or is destined to be hit by lightning three times and still survive. All we need, Hand argues, is a firm grounding in a powerful set of laws: the laws of inevitability, of truly large numbers, of selection, of the probability lever, and of near enough.     Together, these constitute Hand’s groundbreaking Improbability Principle. And together, they explain why we should not be so surprised to bump into a friend in a foreign country, or to come across the same unfamiliar word four times in one day. Hand wrestles with seemingly less explicable questions as well: what the Bible and Shakespeare have in common, why financial crashes are par for the course, and why lightning does strike the same place (and the same person) twice. Along the way, he teaches us how to use the Improbability Principle in our own lives—including how to cash in at a casino and how to recognize when a medicine is truly effective.     An irresistible adventure into the laws behind “chance” moments and a trusty guide for understanding the world and universe we live in, The Improbability Principle will transform how you think about serendipity and luck, whether it’s in the world of business and finance or you’re merely sitting in your backyard, tossing a ball into the air and wondering where it will land.

    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.

    It comprises non-technical essays on every aspect of the vast subject, including articles by scores of eminent mathematicians and other thinkers.

    First published in 1986, this mind-boggling and entertaining dictionary, arranged in order of magnitude, exposes the fascinating facts about certain numbers and number sequences - very large primes, amicable numbers and golden squares to give but a few examples.

    Aiming to tell the dark secrets of computer arithmetic, this title is suitable for library developers, compiler writers, and lovers of elegant hacks.

    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.

    In The Master Algorithm, Pedro Domingos lifts the veil to give us a peek inside the learning machines that power Google, Amazon, and your smartphone. He assembles a blueprint for the future universal learner--the Master Algorithm--and discusses what it will mean for business, science, and society. If data-ism is today's philosophy, this book is its bible.

    Shows how any proof can be understood as a sequence of techniques. Covers the full range of techniques used in proofs, such as the contrapositive, induction, and proof by contradiction. Explains how to identify which techniques are used and how they are applied in the specific problem. Illustrates how to read written proofs with many step-by-step examples. Includes new, expanded appendices related to discrete mathematics, linear algebra, modern algebra and real analysis.

    Through the book’s many examples, you’ll quickly learn how OCaml stands out as a tool for writing fast, succinct, and readable systems code.Real World OCaml takes you through the concepts of the language at a brisk pace, and then helps you explore the tools and techniques that make OCaml an effective and practical tool. In the book’s third section, you’ll delve deep into the details of the compiler toolchain and OCaml’s simple and efficient runtime system.Learn the foundations of the language, such as higher-order functions, algebraic data types, and modulesExplore advanced features such as functors, first-class modules, and objectsLeverage Core, a comprehensive general-purpose standard library for OCamlDesign effective and reusable libraries, making the most of OCaml’s approach to abstraction and modularityTackle practical programming problems from command-line parsing to asynchronous network programmingExamine profiling and interactive debugging techniques with tools such as GNU gdb

    Army and Navy. While their brothers and boyfriends took up arms, these women moved to the nation's capital to learn the top secret art of code breaking. Through their work, the "code girls" helped save countless lives and were vital in ending the war. But due to the top secret nature of their accomplishments, these women have never been able to talk about their story--until now. Through research and countless interviews with the surviving code girls, Liza Mundy brings their story to life. Abridged and adapted for a middle grade audience, Code Girls brings this story to young readers for the first time, showcasing this vital story of American courage, service, and scientific accomplishment.

    Pure Mathematics 1 corresponds to unit P1. It covers quadratics, functions, coordinate geometry, circular measure, trigonometry, vectors, series, differentiation and integration.

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