Computability theory
Material type:
TextLanguage: English Series: Student mathematical library ; volume 62Publication details: Hyderabad : Universities Press, 2012. Description: vii, 203p. : ill. ; 22 cmISBN: 9781470425944Subject(s): Recursion theory | Computable functionsDDC classification: 510.5 Online resources: Table of Contents | Index | Reviews Summary: 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.
| Item type | Current library | Call number | Status | Date due | Barcode |
|---|---|---|---|---|---|
NBHM Books
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NISER LIBRARY | 510.5 WEB-C (Browse shelf(Opens below)) | Available | N215 | |
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SMS Library | 510.5 WEB-C (Browse shelf(Opens below)) | Available | N414 |
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| 510.223 TAK-A Axiomatic set theory | 510.5 BOR-E Elementary convexity with optimization | 510.5 COR-I Introduction to algorithms | 510.5 WEB-C Computability theory | 510:530.145 ARA-M Mathematical theory of quantum fields | 510.6 BAR-A Algebraic introduction to mathematical logic (an) | 510.6 EBB-M Mathematical logic |
Includes bibliographical references (p. 193-197) and index.
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.
Undergraduate students interested in computability theory and recursion theory.
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