Computability Theory: An Introduction to Recursion Theory 1st Edition by Herbert B. Enderton (PDF)

Description

Computability Theory: An Introduction to Recursion Theory provides a concise, comprehensive, and authoritative introduction to contemporary computability theory, techniques, and results. The basic concepts and techniques of computability theory are placed in their historical, philosophical and logical context. This presentation is characterized by an unusual breadth of coverage and the inclusion of advanced topics not to be found elsewhere in the literature at this level. The text includes both the standard material for a first course in computability and more advanced looks at degree structures, forcing, priority methods, and determinacy. The final chapter explores a variety of computability applications to mathematics and science. Computability Theory is an invaluable text, reference, and guide to the direction of current research in the field. Nowhere else will you find the techniques and results of this beautiful and basic subject brought alive in such an approachable way.

User’s Reviews

Editorial Reviews: Review “…would benefit its target audience, especially now that a lot of mathematics courses eschew proofs…As with Enderton’s well-known text in mathematical logic,…this is a thoughtfully written account of the basic facts, and I for one will likely use it in the future.” –Mathematical Reviews, Computability Theory”This textbook on basic computability theory is at the upper-undergraduate level.” –Zentralblatt MATH, 2012″Enderton (U. of California, Los Angeles) has written a clear, focused, and surprisingly literate textbook ― it is a rare mathematician who is this adept with words ― describing the history and theory of recursion theory that will be ideal for one-semester advanced courses in mathematics and computer science. After the concepts and theories are introduced, the equivalence of computable partial function and recursive partial function are demonstrated, in part through proofs of the unsolvability of the halting problem and of the enumeration theorem. Other chapters describe the properties of recursively enumerable sets, the link between computability theory and Gödel’s incompleteness theorem, relative computability and degrees of unsolvability, and polynomial time computability. Appendices are included on Mathspeak, countability, and decadic notation.” –SciTechBookNews”Computability is concerned with the question of what computers can do in principle. Since Enderton directly contributed to the very areas that this book covers (computability and computational complexity), he is able to provide a concise and comprehensive firsthand view on the subject. As a scholar in the field, as well as in the history of logic, he frequently includes historical passages when presenting new concepts in the book…. This is a beautifully written and beautifully printed book…. The book fits perfectly as a textbook, covering standard material for one- or two-semester courses in computability or recursion theory. It is also an excellent study guide and reference for students and researchers in related areas. It is a lovely, short book that contains great ideas.” –Computing Reviews Review Accessible undergraduate textbook for a one-term course on computability theory (i.e., recursion theory)

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I like Enderton’s style, which is why I purchased his Computability text, but as it is a first edition, there are MANY mistakes in the text that I have seen so far and I am only on the second chapter. A lot of them are in examples and make the math more difficult to understand. Other than that, computability is an awesome subject, so there isn’t much bad that can be said.

⭐Très bonne introduction sur la théorie de la calculabilité.L’ouvrage est très passionnant avec des exercices pour vérifier la compréhension.

⭐

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