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Look Inside Algorithmic Randomness

Algorithmic Randomness
Progress and Prospects

£95.00

Part of Lecture Notes in Logic

Johanna N. Y. Franklin, Christopher P. Porter, Henry Towsner, Jason Rute, Mathieu Hoyrup, George Barmpalias, Benoit Monin, Donald M. Stull
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  • Publication planned for: May 2020
  • availability: Not yet published - available from May 2020
  • format: Hardback
  • isbn: 9781108478984

£ 95.00
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About the Authors
  • The last two decades have seen a wave of exciting new developments in the theory of algorithmic randomness and its applications to other areas of mathematics. This volume surveys much of the recent work that has not been included in published volumes until now. It contains a range of articles on algorithmic randomness and its interactions with closely related topics such as computability theory and computational complexity, as well as wider applications in areas of mathematics including analysis, probability, and ergodic theory. In addition to being an indispensable reference for researchers in algorithmic randomness, the unified view of the theory presented here makes this an excellent entry point for graduate students and other newcomers to the field.

    • Synthesizes a range of results previously scattered across various journal articles
    • Includes an introductory survey targeted at newcomers to the field
    • Details the interaction between algorithmic randomness and various areas of classical mathematics as well as computable analysis and areas of theoretical computer science
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    Product details

    • Publication planned for: May 2020
    • format: Hardback
    • isbn: 9781108478984
    • dimensions: 228 x 152 mm
    • contains: 5 b/w illus. 3 tables
    • availability: Not yet published - available from May 2020
  • Table of Contents

    1. Key developments in algorithmic randomness Johanna N. Y. Franklin and Christopher P. Porter
    2. Algorithmic randomness in ergodic theory Henry Towsner
    3. Algorithmic randomness and constructive/computable measure theory Jason Rute
    4. Algorithmic randomness and layerwise computability Mathieu Hoyrup
    5. Relativization in randomness Johanna N. Y. Franklin
    6. Aspects of Chaitin's Omega George Barmpalias
    7. Biased algorithmic randomness Christopher P. Porter
    8. Higher randomness Benoit Monin
    9. Resource bounded randomness and its applications Donald M. Stull
    Index.

  • Editors

    Johanna N. Y. Franklin, Hofstra University, New York
    Johanna N. Y. Franklin is an Associate Professor at Hofstra University in Hempstead, NY. She earned her Ph.D. from the Group in Logic and the Methodology of Science at the University of California, Berkeley and has held postdoctoral positions in Singapore, Canada, and the United States.

    Christopher P. Porter, Drake University, Iowa
    Christopher P. Porter is an Assistant Professor of Mathematics at Drake University in Des Moines, IA. After receiving his Ph.D. in the joint program in mathematics and philosophy at the University of Notre Dame, Porter completed postdoctoral positions at the University of Paris 7 and the University of Florida.

    Contributors

    Johanna N. Y. Franklin, Christopher P. Porter, Henry Towsner, Jason Rute, Mathieu Hoyrup, George Barmpalias, Benoit Monin, Donald M. Stull

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