This concise introduction shows you how to perform statistical analysis computationally, rather than mathematically, with programs written in Python.You'll work with a case study throughout the book to help you learn the entire data analysis process—from collecting data and generating statistics to identifying patterns and testing hypotheses. Along the way, you'll become familiar with distributions, the rules of probability, visualization, and many other tools and concepts.Develop your understanding of probability and statistics by writing and testing codeRun experiments to test statistical behavior, such as generating samples from several distributionsUse simulations to understand concepts that are hard to grasp mathematicallyLearn topics not usually covered in an introductory course, such as Bayesian estimationImport data from almost any source using Python, rather than be limited to data that has been cleaned and formatted for statistics toolsUse statistical inference to answer questions about real-world data

    Assuming a minimum of mathematical preparation, Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Four case studies illustrate applications of category theory to programming language design, semantics, and the solution of recursive domain equations. A brief literature survey offers suggestions for further study in more advanced texts.

    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 most fundamental differences are philosophical, and readers of this book will emerge with a clearer understandingof paradoxical-sounding concepts such as infinity, curved space, and imaginary numbers. The first few chapters are about general aspects of mathematical thought. These are followed by discussions of more specific topics, and the book closes with a chapter answering common sociological questionsabout the mathematical community (such as Is it true that mathematicians burn out at the age of 25?) It is the ideal introduction for anyone who wishes to deepen their understanding of mathematics.About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundredsof key topics, from philosophy to Freud, quantum theory to Islam.

    Each chapter is relatively self-contained and can be used as a unit of study. The algorithms are described in English and in a pseudocode designed to be readable by anyone who has done a little programming. The explanations have been kept elementary without sacrificing depth of coverage or mathematical rigor.

    Now, in The Unimaginable Mathematics of Borges' Library of Babel, William Goldbloom Bloch takes readers on a fascinating tour of the mathematical ideas hiddenwithin one of the classic works of modern literature.Written in the vein of Douglas R. Hofstadter's Pulitzer Prize-winning G�del, Escher, Bach, this original and imaginative book sheds light on one of Borges' most complex, richly layered works. Bloch begins each chapter with a mathematical idea--combinatorics, topology, geometry, informationtheory--followed by examples and illustrations that put flesh on the theoretical bones. In this way, he provides many fascinating insights into Borges' Library. He explains, for instance, a straightforward way to calculate how many books are in the Library--an easily notated but literallyunimaginable number--and also shows that, if each book were the size of a grain of sand, the entire universe could only hold a fraction of the books in the Library. Indeed, if each book were the size of a proton, our universe would still not be big enough to hold anywhere near all the books.Given Borges' well-known affection for mathematics, this exploration of the story through the eyes of a humanistic mathematician makes a unique and important contribution to the body of Borgesian criticism. Bloch not only illuminates one of the great short stories of modern literature but alsoexposes the reader--including those more inclined to the literary world--to many intriguing and entrancing mathematical ideas.

    This change is being driven by powerful new cognitive tools, enabled by the internet, which are greatly accelerating scientific discovery. There are many books about how the internet is changing business or the workplace or government. But this is the first book about something much more fundamental: how the internet is transforming the nature of our collective intelligence and how we understand the world.Reinventing Discovery tells the exciting story of an unprecedented new era of networked science. We learn, for example, how mathematicians in the Polymath Project are spontaneously coming together to collaborate online, tackling and rapidly demolishing previously unsolved problems. We learn how 250,000 amateur astronomers are working together in a project called Galaxy Zoo to understand the large-scale structure of the Universe, and how they are making astonishing discoveries, including an entirely new kind of galaxy. These efforts are just a small part of the larger story told in this book--the story of how scientists are using the internet to dramatically expand our problem-solving ability and increase our combined brainpower.This is a book for anyone who wants to understand how the online world is revolutionizing scientific discovery today--and why the revolution is just beginning.

    Understanding Computation explains theoretical computer science in a context you’ll recognize, helping you appreciate why these ideas matter and how they can inform your day-to-day programming.Rather than use mathematical notation or an unfamiliar academic programming language like Haskell or Lisp, this book uses Ruby in a reductionist manner to present formal semantics, automata theory, and functional programming with the lambda calculus. It’s ideal for programmers versed in modern languages, with little or no formal training in computer science.* Understand fundamental computing concepts, such as Turing completeness in languages* Discover how programs use dynamic semantics to communicate ideas to machines* Explore what a computer can do when reduced to its bare essentials* Learn how universal Turing machines led to today’s general-purpose computers* Perform complex calculations, using simple languages and cellular automata* Determine which programming language features are essential for computation* Examine how halting and self-referencing make some computing problems unsolvable* Analyze programs by using abstract interpretation and type systems

    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.

    Hardcover published by Quadragle/The New York Times Book Co., third printing, August 1977, copyright 1975.

    The long-anticipated revision of this best-selling text offers the most comprehensive, up-to-date introduction to the theory and practice of artificial intelligence. *NEW-Nontechnical learning material-Accompanies each part of the book. *NEW-The Internet as a sample application for intelligent systems-Added in several places including logical agents, planning, and natural language. *NEW-Increased coverage of material - Includes expanded coverage of: default reasoning and truth maintenance systems, including multi-agent/distributed AI and game theory; probabilistic approaches to learning including EM; more detailed descriptions of probabilistic inference algorithms. *NEW-Updated and expanded exercises-75% of the exercises are revised, with 100 new exercises. *NEW-On-line Java software. *Makes it easy for students to do projects on the web using intelligent agents. *A unified, agent-based approach to AI-Organizes the material around the task of building intelligent agents. *Comprehensive, up-to-date coverage-Includes a unified view of the field organized around the rational decision making pa

    Topics include the limits of knowledge, paradox of complexity, Maxwell's demon, Big Bang theory, much more. 1985 edition.

    

    In this entertaining and ingenious book, Blastland reveals how in our quest to make the world more understandable, we lose sight of how unexplainable it often is. The result - from GDP figures to medicine - is that experts know a lot less than they think. Filled with compelling stories from economics, genetics, business, and science, The Hidden Half is a warning that an explanation which works in one arena may not work in another. Entertaining and provocative, it will change how you view the world.

    Professor Marcus du Sautoy shows how these masters of abstraction find a role in the real world and proves that mathematics is the driving force behind modern science. He explores the relationship between Newton and Leibniz, the men behind the calculus; looks at how the mathematics that Euler invented 200 years ago paved the way for the internet and discovers how Fourier transformed our understanding of heat, light and sound. In addition, he finds out how Galois’ mathematics describes the particles that make up our universe, how Gaussian distribution underpins modern medicine, and how Riemann’s maths helped Einstein with his theory of relativity. Finally, he introduces Cantor, who discovered infinite numbers; Poincaré, whose work gave rise to chaos theory; G.H. Hardy, whose work inspired the millions of codes that help to keep the internet safe, and Nicolas Bourbaki, the mathematician who never was. The BBC Radio 4 series looking at the people who shaped modern mathematics, written and presented by Marcus du Sautoy. 1 CDs, 150 minutes