Computable analysis | Constructivism (mathematics) | Computability theory

Computable analysis

In mathematics and computer science, computable analysis is the study of mathematical analysis from the perspective of computability theory. It is concerned with the parts of real analysis and functional analysis that can be carried out in a computable manner. The field is closely related to constructive analysis and numerical analysis. A notable result is that integration (in the sense of the Riemann integral) is computable. This might be considered surprising as an integral is (loosely speaking) an infinite sum. While this result could be explained by the fact that every computable function from to is uniformly continuous, the notable thing is that the modulus of continuity can always be computed without being explicitly given. A similarly surprising fact is that differentiation of complex functions is also computable, while the same result is false for real functions. The above motivating results have no counterpart in Bishop's constructive analysis. Instead, it is the stronger form of constructive analysis developed by Brouwer that provides a counterpart in constructive logic. (Wikipedia).

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This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.

From playlist Introduction to Algorithms

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From playlist Simplify Expressions Using Order of Operations

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From playlist Advanced Calculus / Multivariable Calculus

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From playlist Performing Linear Regression and Correlation

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From playlist Parametric Equations

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From playlist 🔥Data Science | Data Science Full Course | Data Science For Beginners | Data Science Projects | Updated Data Science Playlist 2023 | Simplilearn

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Related pages

Real closed field | Constructive analysis | Equality (mathematics) | Complex analysis | Functional analysis | Heine–Borel theorem | Cauchy's integral formula | Differential calculus | Continuous function | Mathematical analysis | Numerical differentiation | Topos | Computable function | L. E. J. Brouwer | Extreme value theorem | Hausdorff space | Specker sequence | Errett Bishop | Decidability (logic) | Computability in Analysis and Physics | Real analysis | General topology | Discontinuous linear map | Mathematics | Stephen Cole Kleene | Computability theory | Turing machine | Riemann integral | Integral | Uniform norm | Numerical analysis | Partial function | Modulus of continuity | Discrete space | Computability