This is the amazing story of how the "map problem" was solved.The problem posed in the letter came from a former student: What is the least possible number of colors needed to fill in any map (real or invented) so that neighboring counties are always colored differently? This deceptively simple question was of minimal interest to cartographers, who saw little need to limit how many colors they used. But the problem set off a frenzy among professional mathematicians and amateur problem solvers, among them Lewis Carroll, an astronomer, a botanist, an obsessive golfer, the Bishop of London, a man who set his watch only once a year, a California traffic cop, and a bridegroom who spent his honeymoon coloring maps. In their pursuit of the solution, mathematicians painted maps on doughnuts and horseshoes and played with patterned soccer balls and the great rhombicuboctahedron. It would be more than one hundred years (and countless colored maps) later before the result was finally established. Even then, difficult questions remained, and the intricate solution--which involved no fewer than 1,200 hours of computer time--was greeted with as much dismay as enthusiasm.Providing a clear and elegant explanation of the problem and the proof, Robin Wilson tells how a seemingly innocuous question baffled great minds and stimulated exciting mathematics with far-flung applications. This is the entertaining story of those who failed to prove, and those who ultimately did prove, that four colors do indeed suffice to color any map.

    "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems."

    Features exceptionally clear explanations and descriptions, step-by-step examples, more than 50 practical applications, over 2000 easy-to-challenging practice problems, and comprehensive coverage of essentials. PSpice, OrCAd version 9.2 Lite Edition, Multisims 2001 version of Electronics Workbench, and MathCad software references and examples are used throughout. Computer programs (C++, BASIC and PSpice) are printed in color, as they run, at the point in the book where they are discussed. Current and Voltage. Resistance. Ohm's Law, Power, and Energy. Series Circuits. Parallel Circuits. Series-Parallel Networks. Methods of Analysis & Selected Topics. Network Theorems. Capacitors. Magnetic Circuits. Inductors. Sinusodial Alternating Waveforms. The Basic Elements and Phasors. Series and Parallel ac Circuits. Series-Parallel ac Networks. Methods of Analysis and Related Topics. Network Theorems (ac). Power (ac). Resonance. Transformers. Polyphase Systems. Decibels, Filters, and Bode Points. Pulse Waveforms and the R-C Response. Nonsinusodial Circuits. System Analysis: An Introduction. For those working in electronic technology.

    In the West, many have learned of its pleasures, especially after the game appeared in a number of hit movies, TV series, and books, and was included on major Internet game sites. By eliciting the highest powers of rational thought, the game draws players, not just for the thrills of competition, but because they feel it enhances their mental, artistic, and even spiritual lives.Go! More Than a Game uses the most modern methods of teaching, so that, in a few minutes, anyone can understand the two basic rules that generate the game. The object of Go is surrounding territory, but the problem is that while you are doing this, the opponent may be surrounding you! In a series of exciting teaching games, you will watch as Go's beautiful complexities begin to unfold in intertwining patterns of black and white stones. These games progress from small 9x9 boards to 13x13 and then to the traditional 19x19 size.Go! More Than a Game has been completely revised by the author based on new data about the history of early go and the Confucians who wrote about it. This popular book includes updated information such as the impact of computer versions on the game, the mysterious new developments of Go combininatroics, advances in Combinatorial Game Theory and a look at the current international professional playing scene.

    They'll also find the related analytic geometry much easier. The clear review of algebra and geometry in this edition will make calculus easier for students who wish to strengthen their knowledge in these areas. Updated to meet the emphasis in current courses, this new edition of a popular guide--more than 104,000 copies were bought of the prior edition--includes problems and examples using graphing calculators..

    It provides a transition from elementary calculus to advanced courses in real and complex function theory and introduces the reader to some of the abstract thinking that pervades modern analysis.

    From Mary, Queen of Scots, trapped by her own code, to the Navajo Code Talkers who helped the Allies win World War II, to the incredible (and incredibly simple) logisitical breakthrough that made Internet commerce secure, The Code Book tells the story of the most powerful intellectual weapon ever known: secrecy.Throughout the text are clear technical and mathematical explanations, and portraits of the remarkable personalities who wrote and broke the world’s most difficult codes. Accessible, compelling, and remarkably far-reaching, this book will forever alter your view of history and what drives it. It will also make you wonder how private that e-mail you just sent really is.

    However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it. If life can grow out of the formal chemical substrate of the cell, if consciousness can emerge out of a formal system of firing neurons, then so too will computers attain human intelligence. Gödel, Escher, Bach is a wonderful exploration of fascinating ideas at the heart of cognitive science: meaning, reduction, recursion, and much more.

    Collected from the series of blog posts starting at: https://bartoszmilewski.com/2014/10/2...Hardcover available at: http://www.blurb.com/b/9008339-catego...

    Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. Intended for undergraduate courses in abstract algebra, it is suitable for junior- and senior-level math majors and future math teachers. This second edition features additional exercises to improve student familiarity with applications. An introductory chapter traces concepts of abstract algebra from their historical roots. Succeeding chapters avoid the conventional format of definition-theorem-proof-corollary-example; instead, they take the form of a discussion with students, focusing on explanations and offering motivation. Each chapter rests upon a central theme, usually a specific application or use. The author provides elementary background as needed and discusses standard topics in their usual order. He introduces many advanced and peripheral subjects in the plentiful exercises, which are accompanied by ample instruction and commentary and offer a wide range of experiences to students at different levels of ability.

    Several things make this one stand out. Here's the most important: Linux Administration Handbook is designed for administrators working in industrial-strength production environments. It never glosses over the "subtleties" that can get you in big trouble. It doesn't stint on technical detail. It's never satisfied with restating the man pages. And it's full of war stories from folks who've been there. Evi Nemeth and her coauthors: Boy, have they ever been there. (Just ask any gray-bearded Unix sysadmin about their earlier, legendary Unix System Administration Handbook.) There's only been one downside to Linux Administration Handbook: It's been nearly five years since it was written. Well, that flaw's just been remedied. The new Second Edition has been systematically revised for the latest administration tools (think Nagios and LVM). It's carefully targeted at today's five most widely used distributions: Red Hat Enterprise Linux 4.3, Fedora Core 5, SUSE Linux 10.2, Debian 3.2 "Etch," and Ubuntu 6.06. The result: a book you can rely on for the next five years. Rely on to do what? Just about everything. You'll find chapters on booting and shutting down; "rootly" powers; controlling processes; the Linux filesystem; on adding new users. You'll learn the most efficient ways to perform backups. How to make sense of syslogs and log files. Everything you need to know about drivers, the kernel, networking, NFS -- and Internet services, from web hosting to email. Nemeth & Company bring their experience to bear on troubleshooting, performance optimization, print management, security, Windows interoperability, even "policies and politics." Whatever Linux books you already own, if you depend on Linux to run efficiently and reliably, you need this one, too. Bill Camarda, from the December 2006 href="http://www.barnesandnoble.com/newslet... Only

    This concept is at the root of the computational worldview, which basically says that very complex systems — the world we live in — have their beginnings in simple mathematical equations. We've lately come to understand that such an algorithm is only the start of a never-ending story — the real action occurs in the unfolding consequences of the rules. The chip-in-a-box computers so popular in our time have acted as a kind of microscope, letting us see into the secret machinery of the world. In Lifebox, Rucker uses whimsical drawings, fables, and humor to demonstrate that everything is a computation — that thoughts, computations, and physical processes are all the same. Rucker discusses the linguistic and computational advances that make this kind of "digital philosophy" possible, and explains how, like every great new principle, the computational world view contains the seeds of a next step.

    The approach taken here uses elementary versions of modern methods found in sophisticated mathematics. The formal prerequisites include only a term of linear algebra, a nodding acquaintance with the notation of set theory, and a respectable first-year calculus course (one which at least mentions the least upper bound (sup) and greatest lower bound (inf) of a set of real numbers). Beyond this a certain (perhaps latent) rapport with abstract mathematics will be found almost essential.

    “The result is a veritable pi

    His breaking of the German U-boat Enigma cipher in World War II ensured Allied-American control of the Atlantic. But Turing's vision went far beyond the desperate wartime struggle. Already in the 1930s he had defined the concept of the universal machine, which underpins the computer revolution. In 1945 he was a pioneer of electronic computer design. But Turing's true goal was the scientific understanding of the mind, brought out in the drama and wit of the famous "Turing test" for machine intelligence and in his prophecy for the twenty-first century.Drawn in to the cockpit of world events and the forefront of technological innovation, Alan Turing was also an innocent and unpretentious gay man trying to live in a society that criminalized him. In 1952 he revealed his homosexuality and was forced to participate in a humiliating treatment program, and was ever after regarded as a security risk. His suicide in 1954 remains one of the many enigmas in an astonishing life story.