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.