Synopses & Reviews
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.
Frequent historical information presented throughout More extensive motivation for each of the topics than other texts currently available Connects with topics not included in other textbooks, such as complexity theory
Review
"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
Synopsis
This textbook is designed to introduce undergraduate mathematics and computer science students to computability theory (recursion theory). It is based on teaching experience, and is designed to be accessible to junior and senior students without a previous background in the subject. The book will prepare the students for further study in computational complexity, logic, theoretical computer science, as well as other topics. It focuses on computability theory, and excludes computer-science topics such as automata theory, and context-free languages.
Undergraduates can read and understand the material
Pointers to more advanced topics, and provides a base for further study of such topics
Covers a strong introductory set of material from a modern mathematical viewpoint
Table of Contents
1. The Computability Concept; 2. General Recursive Functions; 3. Programs and Machines; 4. Recursive Enumerability; 5. Connections to Logic; 6. Degrees of Unsolvability; 7. Polynomial-Time Computability; Appendix: Mathspeak; Appendix: Countability; Appendix: Decadic Notation;