Editors:
- Computability and complexity theory are two central areas of research in mathematical logic and theoretical computer science
- Researchers and graduate students will appreciate the book's systematic introductions into many branches of computable analysis
- Dedicated to Klaus Weihrauch, the leading pioneer and teacher in this domain
- Further domain information available at http://cca-net.de/
Part of the book series: Theory and Applications of Computability (THEOAPPLCOM)
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Table of contents (11 chapters)
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Front Matter
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Computability in Analysis
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Front Matter
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Complexity, Dynamics, and Randomness
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Front Matter
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Constructivity, Logic, and Descriptive Complexity
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Front Matter
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Back Matter
About this book
Computable analysis is the modern theory of computability and complexity in analysis that arose out of Turing's seminal work in the 1930s. This was motivated by questions such as: which real numbers and real number functions are computable, and which mathematical tasks in analysis can be solved by algorithmic means?
Nowadays this theory has many different facets that embrace topics from computability theory, algorithmic randomness, computational complexity, dynamical systems, fractals, and analog computers, up to logic, descriptive set theory, constructivism, and reverse mathematics. In recent decades computable analysis has invaded many branches of analysis, and researchers have studied computability and complexity questions arising from real and complex analysis, functional analysis, and the theory of differential equations, up to (geometric) measure theory and topology.
This handbook represents the first coherent cross-section through most active research topics on the more theoretical side of the field. It contains 11 chapters grouped into parts on computability in analysis; complexity, dynamics, and randomness; and constructivity, logic, and descriptive complexity. All chapters are written by leading experts working at the cutting edge of the respective topic. Researchers and graduate students in the areas of theoretical computer science and mathematical logic will find systematic introductions into many branches of computable analysis, and a wealth of information and references that will help them to navigate the modern research literature in this field.
Editors and Affiliations
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Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, South Africa
Vasco Brattka
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Fakultät für Informatik, Universität der Bundeswehr München, Neubiberg, Germany
Peter Hertling
About the editors
Peter Hertling is a professor in the Institut für Theoretische Informatik, Mathematik und Operations Research at the Universität der Bundeswehr München. He is an Associate Editor of the Journal of Complexity, published by Elsevier. His research interests include computable analysis, descriptive complexity and algorithmic randomness, complexity theory over the real numbers, and information-based complexity.
Bibliographic Information
Book Title: Handbook of Computability and Complexity in Analysis
Editors: Vasco Brattka, Peter Hertling
Series Title: Theory and Applications of Computability
DOI: https://doi.org/10.1007/978-3-030-59234-9
Publisher: Springer Cham
eBook Packages: Computer Science, Computer Science (R0)
Copyright Information: Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-59233-2Published: 05 June 2021
Softcover ISBN: 978-3-030-59236-3Published: 06 June 2022
eBook ISBN: 978-3-030-59234-9Published: 04 June 2021
Series ISSN: 2190-619X
Series E-ISSN: 2190-6203
Edition Number: 1
Number of Pages: XXV, 427
Topics: Theory of Computation, Mathematics of Computing, Mathematical Logic and Foundations