Algorithmic Randomness - Progress and Prospects

Surveys on recent developments in the theory of algorithmic randomness and its interactions with other areas of mathematics.

List 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.

About the author

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 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.

Summary

This volume surveys many exciting recent developments in the field of algorithmic randomness and its interactions with other areas of mathematics, presenting a unified view of the theory. It will be a valuable reference for specialists and an excellent entry point for graduate students and other newcomers to the field.

Product details

• Authors: EDITED BY JOHANNA N., Johanna N. Y. (Hofstra University Franklin
• Assisted by: Johanna N Y Franklin (Editor), Johanna N. Y. Franklin (Editor), Johanna N. Y. (Hofstra University Franklin (Editor), Christopher P Porter (Editor), Christopher P. Porter (Editor), Christopher P. (Drake University Porter (Editor)
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 30.06.2020
• EAN: 9781108478984
• ISBN: 978-1-108-47898-4
• No. of pages: 368
• Series: Lecture Notes in Logic; Lecture Notes in Logic, Series
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; MATHEMATICS / Logic, algorithms and data structures, Probability & statistics, Algorithms & data structures, Mathematical logic, Databases, Probability and statistics