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Student Mathematical Library
2012; 203 pp; softcover
List Price: US$37
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All Individuals: US$29.60
Order Code: STML/62
Computable Functions - A Shen and N K Vereshchagin
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.
"This is only a 200 page book, but it covers a wealth of material...[A] clear, concise introduction that would be ideal for a one-term undergraduate course...Recommended."
"This short text does an excellent job of covering those topics that should be included in an undergraduate introduction to computability theory... There are both appropriate exercises and enticing doorways to open topics and current research. The exposition is precise, but still conversational. I believe my students will enjoy reading this text."
-- Jeffry L. Hirst, Zentralblatt MATH
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