Vasco Brattka, Peter Hertling (eds.)
Series Theory and Applications of Computability
Springer, Cham, 2021
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. |

*Computability of Real Numbers*by Robert Rettinger and Xizhong Zheng*Computability of Subsets of Metric Spaces*by Zvonko Iljazović and Takayuki Kihara*Computability of Differential Equations*by Daniel S. Graça and Ning Zhong*Computable Complex Analysis*by Valentin V. Andreev and Timothy H. McNicholl

*Computable Geometric Complex Analysis and Complex Dynamics*by Cristóbal Rojas and Michael Yampolsky*A Survey on Analog Models of Computation*by Olivier Bournez and Amaury Pouly*Computable Measure Theory and Algorithmic Randomness*by Mathieu Hoyrup and Jason Rute*Algorithmic Fractal Dimensions in Geometric Measure Theory*by Jack Lutz and Elvira Mayordomo

*Admissibly Represented Spaces and Qcb-Spaces*by Matthias Schröder*Bishop-Style Constructive Reverse Mathematics*by Hannes Diener and Hajime Ishihara*Weihrauch Complexity in Computable Analysis*by Vasco Brattka, Guido Gherardi and Arno Pauly