Computability Theory

Rebecca Weber

ISBN: 9781470425944 | Year: 2016 | Paperback | Pages: 208 | Language : English

Book Size: 140 X 216 mm | Territorial Rights: Restricted| Series American Mathematical Society

Price: 900.00

About the Book

What can we compute—even with unlimited resources? Is everything within reach? Or are computations necessarily drastically limited, not just in practice, but theoretically? These questions are at the heart of computability theory. The goal of this book is to give the reader a firm grounding in the fundamentals of computability theory and an overview of currently active areas of research, such as reverse mathematics and algorithmic randomness. Turing machines and partial recursive functions are explored in detail, and vital tools and concepts including coding, uniformity, and diagonalization are described explicitly. From there the material continues with universal machines, the halting problem, parametrization and the recursion theorem, and thence to computability for sets, enumerability, and Turing reduction and degrees. A few more advanced topics round out the book before the chapter on areas of research. The text is designed to be self-contained, with an entire chapter of preliminary material including relations, recursion, induction, and logical and set notation and operators. That background, along with ample explanation, examples, exercises, and suggestions for further reading, make this book ideal for independent study or courses with few prerequisites

Contributors (Author(s), Editor(s), Translator(s), Illustrator(s) etc.)

Rebecca Weber is Associate Professor at the Department of Mathematics, Dartmouth College, Hanover, USA

Table of Contents

Chapter 1. Introduction 
Chapter 2. Background 
Chapter 3. Defining Computability 
Chapter 4. Working with Computable Functions 
Chapter 5. Computing and Enumerating Sets 
Chapter 6. Turing Reduction and Post’s Problem 
Chapter 7. Two Hierarchies of Sets 
Chapter 8. Further Tools and Results 
Chapter 9. Areas of Research 
Appendix A. Mathematical Asides