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Computability Theory
Rebecca Weber
Price
:
₹
900.00
ISBN
:
978-1-4704-2594-4
Pages
:
208
Binding
:
Paperback
Language
:
English
Book Size
:
140 x 216 mm
Year
:
2016
Series
:
American Mathematical Society
Territorial Rights
:
Restricted
Book
Contents
Author
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
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
Bibliography
Index
Contributors (Author(s), Editor(s), Translator(s), Illustrator(s) etc.)
Rebecca Weber
is Associate Professor at the Department of Mathematics, Dartmouth College, Hanover, USA