The Good, the Bad, and the Hungry Sale
 
 

Recently Viewed clear list


The Powell's Playlist | June 18, 2014

Daniel H. Wilson: IMG The Powell’s Playlist: Daniel H. Wilson



Like many writers, I'm constantly haunting coffee shops with a laptop out and my headphones on. I listen to a lot of music while I write, and songs... Continue »

spacer
Qualifying orders ship free.
$16.95
New Trade Paper
Ships in 1 to 3 days
Add to Wishlist
available for shipping or prepaid pickup only
Available for In-store Pickup
in 7 to 12 days
Qty Store Section
25 Remote Warehouse Mathematics- Logic and Philosophy

Computability and Unsolvability (Mathematics Series)

by

Computability and Unsolvability (Mathematics Series) Cover

 

Synopses & Reviews

Publisher Comments:

"A clearly written, well-presented survey of an intriguing subject." — Scientific American. Classic text considers general theory of computability, computable functions, operations on computable functions, Turing machines self-applied, unsolvable decision problems, applications of general theory, mathematical logic, Kleene hierarchy, computable functionals, classification of unsolvable decision problems and more.

Synopsis:

Classic graduate-level introduction to theory of computability. Discusses general theory of computability, computable functions, operations on computable functions, Turing machines self-applied, unsolvable decision problems, applications of general theory, mathematical logic, Kleene hierarchy, more.

About the Author

Martin Davis: Computer Science Pioneer

Dover's publishing relationship with Martin Davis, now retired from NYU and living in Berkeley, goes back to 1985 when we reprinted his classic 1958 book Computability and Unsolvability, widely regarded as a classic of theoretical computer science. A graduate of New York's City College, Davis received his PhD from Princeton in the late 1940s and became one of the first computer programmers in the early 1950s, working on the ORDVAC computer at The University of Illinois. He later settled at NYU where he helped found the Computer Science Department.

Not many books from the infancy of computer science are still alive after several decades, but Computability and Unsolvability is the exception. And The Undecidable is an anthology of fundamental papers on undecidability and unsolvability by major figures in the field including Godel, Church, Turing, Kleene, and Post.

Critical Acclaim for Computability and Unsolvability:

"This book gives an expository account of the theory of recursive functions and some of its applications to logic and mathematics. It is well written and can be recommended to anyone interested in this field. No specific knowledge of other parts of mathematics is presupposed. Though there are no exercises, the book is suitable for use as a textbook." — J. C. E. Dekker, Bulletin of the American Mathematical Society, 1959

Critical Acclaim for The Undecidable:

"A valuable collection both for original source material as well as historical formulations of current problems." — The Review of Metaphysics

"Much more than a mere collection of papers . . . a valuable addition to the literature." — Mathematics of Computation

Table of Contents

Preface to the Dover Edition; Preface to the First Edition; Glossary of special symbols

Introduction

1. Heuristic Remarks on Decision Problems

2. Suggestions to the Reader

3. Notational Conventions

Part 1. The general theory of computability

  Chapter 1. Computable Functions

    1. Turing Machines

    2. Computable Functions and Partially Computable functions

    3. Some Examples

    4. Relatively Computable functions

  Chapter 2. Operations on Computable Functions

    1. Preliminary Lemmas

    2. Composition and Minimalization

  Chapter 3. Recursive functions

    1. Some Classes of Functions

    2. Finite Sequences of Natural Numbers

    3. Primitive Recursion

    4. Primitive Recursive functions

    5. Recursive Sets and Predicates

  Chapter 4. Turing Machines Self-applied

    1. Arithmetization of the Theory of Turing Machines

    2. Computability and Recursiveness

    3. A Universal Turing Machine

  Chapter 5. Unsolvable Decision Problems

    1. Semicomputable Predicates

    2. Decision Problems

    3. Properties of Semicomputable Predicates

    4. Recursively enumerable Sets

    5. Two Recursively enumerable Sets

    6. A Set Which Is Not Recursively Enumerable

Part 2. Applications of the General Theory

  Chapter 6. Combinatorial Problems

    1. Combinatorial systems

    2. Turing machines and Semi-Thue Systems

    3. Thue Systems

    4. The Word Problem for Semigroups

    5. Normal Systems and Post Systems

  Chapter 7. Diophantine Equations

    1. Hilbert's Tenth Problem

    2. Arithmetical and Diophantine Predicates

    3. Arithmetical Representation of Semicomputable Predicates

  Chapter 8. Mathematical Logic

    1. Logics

    2. Incompleteness and Unsolvability Theorems for Logics

    3. Arithmetical Logics

    4. First-order Logics

    5. Partial Propositional Calculi

Part 3. Further Development of the General Theory

  Chapter 9. The Kleene Hierarchy

    1. The Interation Theorem

    2. Some First Applications of the Iteration Theorem

    3. Predicates, Sets, and Functions

    4. Strong Reducibility

    5. Some Classes of Predicates

    6. A Representation Theorem for P subscript 2 superscript A

    7. Post's Representation Theorem

  Chapter 10. Computable Functionals

    1. Functionals

    2. Complete Computable functionals

    3. Normal Form Theorems

    4. Partially Computable and Computable Functionals

    5. Functionals and Relative Recursiveness

    6. Decision Problems

    7. The Recursion Theorems

  Chapter 11. The Classification of Unsolvable Decision Problems

    1. Reducibility and the Kleene Hierarchy

    2. Incomparability

    3. Creative Sets and Simple Sets

    4. Constructive Ordinals

    5. Extensions of the Kleene Hierarchy

Appendix 1. Some Results from the Elementary Theory of Numbers

Appendix 2. Hilbert's Tenth Problem is Unsolvable

References; Index

Product Details

ISBN:
9780486614717
Author:
Davis, Martin
Publisher:
Dover Publications
Author:
Davis, Langdon
Author:
Davis, Barbee
Author:
Davis, Harold
Location:
New York :
Subject:
Mathematics
Subject:
Logic
Subject:
Modern mathematics
Subject:
Computable functions
Subject:
Recursive functions
Subject:
Unsolvability (Mathematical logic)
Subject:
Unsolvability
Subject:
General Mathematics
Subject:
Mathematics-Logic and Philosophy
Edition Number:
Dover ed.
Edition Description:
Trade Paper
Series:
Dover Books on Computer Science
Series Volume:
no. 1411
Publication Date:
19851231
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
288
Dimensions:
8.5 x 5.38 in 0.64 lb

Other books you might like

  1. Galois Theory 2ND Edition Used Trade Paper $5.95
  2. Rediscovered Lewis Carroll Puzzles New Trade Paper $6.95
  3. Calculus of Variations Used Trade Paper $7.50
  4. Computer Simulation Techniques Used Hardcover $2.50
  5. Counterexamples in Topology 2ND Edition Used Trade Paper $10.50
  6. How to Solve Problems: Elements of a... Used Trade Paper $2.95

Related Subjects


Science and Mathematics » Mathematics » Advanced
Science and Mathematics » Mathematics » Computer
Science and Mathematics » Mathematics » Foundations and Logic
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Logic and Philosophy
Science and Mathematics » Physics » Acoustics

Computability and Unsolvability (Mathematics Series) New Trade Paper
0 stars - 0 reviews
$16.95 In Stock
Product details 288 pages Dover Publications - English 9780486614717 Reviews:
"Synopsis" by ,
Classic graduate-level introduction to theory of computability. Discusses general theory of computability, computable functions, operations on computable functions, Turing machines self-applied, unsolvable decision problems, applications of general theory, mathematical logic, Kleene hierarchy, more.
spacer
spacer
  • back to top
Follow us on...




Powell's City of Books is an independent bookstore in Portland, Oregon, that fills a whole city block with more than a million new, used, and out of print books. Shop those shelves — plus literally millions more books, DVDs, and gifts — here at Powells.com.