Aimed at mathematicians and computer scientists who will only be exposed to one course in this area, Computability: A Mathematical Sketchbook provides a brief but rigorous introduction to the abstract theory of computation, sometimes also referred to as recursion theory. It develops major themes in computability theory, such as Rice's theorem and the recursion theorem, and provides a systematic account of Blum's complexity theory as well as an introduction to the theory of computable real numbers and functions. The book is intended as a university text, but it may also be used for self-study; appropriate exercises and solutions are included.

Autorentext

Prof. Douglas S. Bridges is a professor of pure mathematics at the University of Canterbury. His research interests include the constructive foundations of analysis and topology; mathematical economics; computability and abstract complexity theory; and quantum logic. He has published many related articles and papers, among his 8 authored books are "Computability: A Mathematical Sketchbook", "Foundations of Real and Abstract Analysis", and "Techniques of Constructive Analysis". He is a Fellow of the Royal Society of New Zealand, and a Corresponding Fellow of the Royal Society of Edinburgh. Dr. Lumini a Simona Vî is an Adjunct Fellow of the Department of Mathematics and Statistics, University of Canterbury, and a Senior Business Analyst with the New Zealand Customs Service. Her research interests include constructive foundations of analysis and topology, and recursive function theory, computability and complexity. She has published many related articles and papers, and coauthored "Techniques of Constructive Analysis".

Inhalt
Preliminaries.- 1 What Is a Turing Machine?.- 2 Computable Partial Functions.- 3 Effective Enumerations.- 4 Computable Numbers and Functions.- 5 Rice's Theorem and the Recursion Theorem.- 6 Abstract Complexity Theory.- Solutions to Exercises.- Solutions for Chapter 1.- Solutions for Chapter 2.- Solutions for Chapter 3.- Solutions for Chapter 4.- Solutions for Chapter 5.- Solutions for Chapter 6.- References.