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Computable Analysis

An Introduction

  • Textbook
  • © 2000

Overview

Authors:
  1. Klaus Weihrauch

    1. Fachbereich Informatik Theoretische Informatik I, Fern Universität Hagen, Hagen, Germany

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  • First textbook of this kind: a broad systematic introduction to computable analysis connecting analysis with computability and complexity theory
  • With many examples and figures and numerous exercises
  • Includes supplementary material: sn.pub/extras

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Table of contents (9 chapters)

  1. Front Matter

    Pages I-X
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  2. Introduction

    • Klaus Weihrauch
    Pages 1-12

  3. 2. Computability on the Cantor Space

    • Klaus Weihrauch
    Pages 13-49

  4. 3. Naming Systems

    • Klaus Weihrauch
    Pages 51-84

  5. 4. Computability on the Real Numbers

    • Klaus Weihrauch
    Pages 85-122

  6. 5. Computability on Closed, Open and Compact Sets

    • Klaus Weihrauch
    Pages 123-152

  7. 6. Spaces of Continuous Functions

    • Klaus Weihrauch
    Pages 153-194

  8. 7. Computational Complexity

    • Klaus Weihrauch
    Pages 195-235

  9. 8. Some Extensions

    • Klaus Weihrauch
    Pages 237-248

  10. 9. Other Approaches to Computable Analysis

    • Klaus Weihrauch
    Pages 249-268

  11. Back Matter

    Pages 269-285
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Keywords

About this book

Is the exponential function computable? Are union and intersection of closed subsets of the real plane computable? Are differentiation and integration computable operators? Is zero finding for complex polynomials computable? Is the Mandelbrot set decidable? And in case of computability, what is the computational complexity? Computable analysis supplies exact definitions for these and many other similar questions and tries to solve them. - Merging fundamental concepts of analysis and recursion theory to a new exciting theory, this book provides a solid basis for studying various aspects of computability and complexity in analysis. It is the result of an introductory course given for several years and is written in a style suitable for graduate-level and senior students in computer science and mathematics. Many examples illustrate the new concepts while numerous exercises of varying difficulty extend the material and stimulate readers to work actively on the text.

Authors and Affiliations

  • Fachbereich Informatik Theoretische Informatik I, Fern Universität Hagen, Hagen, Germany

    Klaus Weihrauch

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