Computable Functions

American Mathem

ISBN 10: 0821827324 / ISBN 13: 9780821827321

Published by American Mathematical Society, US, 2002

About this Item

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.

Seller Inventory # LU-9780821827321

Bibliographic Details

• Title: Computable Functions
• Publisher: American Mathematical Society, US
• Publication Date: 2002
• Language: English
• ISBN 10: 0821827324
• ISBN 13: 9780821827321
• Binding: Paperback
• Condition: New
• Weight: 215 grams

About this title

Synopsis

Shen and Vereshchagin base this text on lectures presented at the Moscow State U. Mathematics Dept., for which they select central notions and facts from the general theory of algorithms. Coverage includes computable functions, decidable and enumerable sets; universal functions and undecidability; numberings and operations; properties of G÷del numberings; fixed point theorem; m -reducibility and properties of enumerable sets; oracle computations; arithmetical hierarchy; Turing machines; arithmeticity of computable functions; and recursive functions. For undergraduate mathematics or computer science majors, mathematicians and programmers. Translated from Russian by V. N. Dubrovskii. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Language Notes

Text: English (translation)
Original Language: Russian