This groundbreaking and powerful theory now forms the basis of computer science. In Turing's Vision, Chris Bernhardt explains the theory, Turing's most important contribution, for the general reader. Bernhardt argues that the strength of Turing's theory is its simplicity, and that, explained in a straightforward manner, it is eminently understandable by the nonspecialist. As Marvin Minsky writes, -The sheer simplicity of the theory's foundation and extraordinary short path from this foundation to its logical and surprising conclusions give the theory a mathematical beauty that alone guarantees it a permanent place in computer theory.- Bernhardt begins with the foundation and systematically builds to the surprising conclusions. He also views Turing's theory in the context of mathematical history, other views of computation (including those of Alonzo Church), Turing's later work, and the birth of the modern computer.In the paper, -On Computable Numbers, with an Application to the Entscheidungsproblem, - Turing thinks carefully about how humans perform computation, breaking it down into a sequence of steps, and then constructs theoretical machines capable of performing each step. Turing wanted to show that there were problems that were beyond any computer's ability to solve; in particular, he wanted to find a decision problem that he could prove was undecidable. To explain Turing's ideas, Bernhardt examines three well-known decision problems to explore the concept of undecidability; investigates theoretical computing machines, including Turing machines; explains universal machines; and proves that certain problems are undecidable, including Turing's problem concerning computable numbers.

    Requiring essentially no background apart from mathematical maturity, the book can be used as a reference for self-study for anyone interested in complexity, including physicists, mathematicians, and other scientists, as well as a textbook for a variety of courses and seminars. More than 300 exercises are included with a selected hint set.

    K. Dewdney's The Turing Omnibus.Updated and expanded, The Turing Omnibus offers 66 concise, brilliantly written articles on the major points of interest in computer science theory, technology, and applications. New for this tour: updated information on algorithms, detecting primes, noncomputable functions, and self-replicating computers--plus completely new sections on the Mandelbrot set, genetic algorithms, the Newton-Raphson Method, neural networks that learn, DOS systems for personal computers, and computer viruses.Contents:1 Algorithms 2 Finite Automata 3 Systems of Logic 4 Simulation 5 Godel's Theorem 6 Game Trees 7 The Chomsky Hierarchy 8 Random Numbers 9 Mathematical Research 10 Program Correctness 11 Search Trees 12 Error-Corecting Codes 13 Boolean Logic 14 Regular Languages 15 Time and Space Complexity 16 Genetic Algorithms 17 The Random Access Machine 18 Spline Curves 19 Computer Vision 20 Karnaugh Maps 21 The Newton-Raphson Method 22 Minimum Spanning Trees 23 Generative Grammars 24 Recursion 25 Fast Multiplication 26 Nondeterminism 27 Perceptrons 28 Encoders and Multiplexers 29 CAT Scanning 30 The Partition Problem 31 Turing Machines 32 The Fast Fourier Transform 33 Analog Computing 34 Satisfiability 35 Sequential Sorting 36 Neural Networks That Learn 37 Public Key Cryptography 38 Sequential Cirucits 39 Noncomputerable Functions 40 Heaps and Merges 41 NP-Completeness 42 Number Systems for Computing 43 Storage by Hashing 44 Cellular Automata 45 Cook's Theorem 46 Self-Replicating Computers 47 Storing Images 48 The SCRAM 49 Shannon's Theory 50 Detecting Primes 51 Universal Turing Machines 52 Text Compression 53 Disk Operating Systems 54 NP-Complete Problems 55 Iteration and Recursion 56 VLSI Computers 57 Linear Programming 58 Predicate Calculus 59 The Halting Problem 60 Computer Viruses 61 Searching Strings 62 Parallel Computing 63 The Word Problem 64 Logic Programming 65 Relational Data Bases 66 Church's Thesis

    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.

    In this lively book of essays, Stephen Wolfram takes the reader along on some of his most surprising and engaging intellectual adventures in science, technology, artificial intelligence and language design.

    Numerous tables and figures.

    David Peat explains the development and meaning of this Superstring Theory in a thoroughly readable, dramatic manner accessible to lay readers with no knowledge of mathematics. The consequences of the Superstring Theory are nothing less than astonishing.

    However, rather than resting on that reputation, the new edition of this text marks a significant advance in the already excellent quality of the book. While preserving concise language, state of the art educational pedagogy, and top-notch worked examples, the Eighth Edition features a unified art design as well as streamlined and carefully reorganized problem sets that enhance the thoughtful instruction for which Raymond A. Serway and John W. Jewett, Jr. earned their reputations. Likewise, PHYSICS FOR SCIENTISTS AND ENGINEERS, will continue to accompany Enhanced WebAssign in the most integrated text-technology offering available today. In an environment where new Physics texts have appeared with challenging and novel means to teach students, this book exceeds all modern standards of education from the most solid foundation in the Physics market today.

    C. R. Licklider, Doug Engelbart, Bob Taylor, and Alan Kay.The digital revolution did not begin with the teenage millionaires of Silicon Valley, claims Howard Rheingold, but with such early intellectual giants as Charles Babbage, George Boole, and John von Neumann. In a highly engaging style, Rheingold tells the story of what he calls the patriarchs, pioneers, and infonauts of the computer, focusing in particular on such pioneers as J. C. R. Licklider, Doug Engelbart, Bob Taylor, and Alan Kay. Taking the reader step by step from nineteenth-century mathematics to contemporary computing, he introduces a fascinating collection of eccentrics, mavericks, geniuses, and visionaries.The book was originally published in 1985, and Rheingold's attempt to envision computing in the 1990s turns out to have been remarkably prescient. This edition contains an afterword, in which Rheingold interviews some of the pioneers discussed in the book. As an exercise in what he calls retrospective futurism, Rheingold also looks back at how he looked forward.

    Using illustrations and examples from science fiction pulp magazines and comic books, The Amazing Story of Quantum Mechanics explains the fundamental principles of quantum mechanics that underlie the world we live in.Watch a Video

    It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.

    Cosmic Universe and Human History, microcosm and macrocosm, inorganic and living matter coexist and form a unique unity manifested in multiple forms. The Physical and the Mental constitute the form and the content of the World. The world does not consist of subjects and objects, the “subject” and the “object” are metaphysical abstractions of the single and indivisible Wholeness. Man’s finite knowledge separates the Whole into parts and studies fragmentarily the beings. The Wholeness is manifested in multiple forms and each form encapsulates the Wholeness. The rational explanation of the excerpts and the intuitive apprehension of the Wholeness are required to combine and create the open thought and the holistic knowledge. This means that the measurement should be defined by the ''measure'', but the responsibility for determining the ''measure'' depends on the man. This requires that man overcomes the anthropocentric arrogance and the narcissistic selfishness and he joins the Cosmic World in a friendly and creative manner.

     Free BONUS Inside! James Clerk Maxwell was a brilliant mathematician and scientist, but his impact on this world goes even deeper than that. Maxwell singlehandedly overturned what was believed to be fact with a whole new outlook on fundamental aspects of the universe. Maxwell is often credited as one of the first pioneers of quantum physics and rightly so because it was Maxwell who envisioned particles such as electrons spinning inside an electric current before anyone else had so much as guessed that such a thing might be possible. The rarefied scientific mind of James Clerk Maxwell has left us with a lasting legacy of incredible innovations in thought that still affect us to this very day. Read this book in order to get a full grasp of just what kind of enlightening fire this nineteenth-century Prometheus has gifted all of humanity with. Discover a plethora of topics such as Early Life and Loss The World’s First Color Photograph Maxwell’s Equations The Cavendish Laboratory Illness and Death And much more! So if you want a straightforward book on James Clerk Maxwell, simply scroll up and click the "Buy now" button for instant access!

    Admittedly, computers now play chess at the grandmaster level, but do they understand the game as we do? Can a computer eventually do everything a human mind can do? In this absorbing and frequently contentious book, Roger Penrose--eminent physicist and winner, with Stephen Hawking, of the prestigious Wolf prize--puts forward his view that there are some facets of human thinking that can never be emulated by a machine. Penrose examines what physics and mathematics can tell us about how the mind works, what they can't, and what we need to know to understand the physical processes of consciousness. He is among a growing number of physicists who think Einstein wasn't being stubborn when he said his little finger told him that quantum mechanics is incomplete, and he concludes that laws even deeper than quantum mechanics are essential for the operation of a mind. To support this contention, Penrose takes the reader on a dazzling tour that covers such topics as complex numbers, Turing machines, complexity theory, quantum mechanics, formal systems, Godel undecidability, phase spaces, Hilbert spaces, black holes, white holes, Hawking radiation, entropy, quasicrystals, the structure of the brain, and scores of other subjects. The Emperor's New Mind will appeal to anyone with a serious interest in modern physics and its relation to philosophical issues, as well as to physicists, mathematicians, philosophers and those on either side of the AI debate.

    The latter half of our century has seen its own Renaissance - informations technology has changed irrevocable the way we live, work, and think about the world. We are fortunate, therefore, that the authors of Out of Their Minds have been able to talk so candidly with the founders of computer science. In Out of their Minds, readers will hear the Newtons and Euclids of the computer age as they talk about their discoveries in information technology that have changed forever the way we live, work, and think about the world. Based on interviews by freelance writer Cathy Lazere and the expertise of computer scientist Dennis Shasha, Out of their Minds introduces readers to fifteen of the planet's foremost computer scientists, including eight winners of the Turing Award, computing's Nobel Prize. The scientists reveal themselves in fascinating anecdotes about their early inspirations and influences, their contributions to computer science, and their thoughts on its explosive future. These are the programmers whose work