Student Mathematical Library 2003; 166 pp; softcover Volume: 19 ISBN10: 0821827324 ISBN13: 9780821827321 List Price: US$34 Institutional Members: US$27.20 All Individuals: US$27.20 Order Code: STML/19
 In 1936, before the development of modern computers, Alan Turing proposed the concept of a machine that would embody the interaction of mind, machine, and logical instruction. The idea of a "universal machine" inspired the notion of programs stored in a computer's memory. Nowadays, the study of computable functions is a core topic taught to mathematics and computer science undergraduates. Based on the lectures for undergraduates at Moscow State University, this book presents a lively and concise introduction to the central facts and basic notions of the general theory of computation. It begins with the definition of a computable function and an algorithm and discusses decidability, enumerability, universal functions, numberings and their properties, \(m\)completeness, the fixed point theorem, arithmetical hierarchy, oracle computations, and degrees of unsolvability. The authors complement the main text with over 150 problems. They also cover specific computational models, such as Turing machines and recursive functions. The intended audience includes undergraduate students majoring in mathematics or computer science, and all mathematicians and computer scientists who would like to learn basics of the general theory of computation. The book is also an ideal reference source for designing a course. Readership Undergraduates, graduate students, research mathematicians, and computer scientists and programmers interested in the general theory of computation. Reviews "Material is a presented quite clearly and with a minimum of fuss ... an excellent text for a first course in computability."  Mathematical Reviews Table of Contents  Computable functions, decidable and enumerable sets
 Universal functions and undecidability
 Numberings and operations
 Properties of Gödel numberings
 Fixed point theorem
 \(m\)reducibility and properties of enumerable sets
 Oracle computations
 Arithmetical hierarchy
 Turing machines
 Arithmeticity of computable functions
 Recursive functions
 Bibliography
 Glossary
 Index
