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.
Here's a sample of other books in this Dover category
On Formally Undecidable Propositions of Principia Mathematica and Related Systems by Kurt Gödel First English translation of revolutionary paper (1931) that established that even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. Introduction by R. B. Braithwaite.
Dynamic Programming by Richard Bellman Introduction to mathematical theory of multistage decision processes takes a "functional equation" approach. Topics include existence and uniqueness theorems, optimal inventory equation, bottleneck problems, multistage games, Markovian decision processes and more. 1957 edition.
Mathematical Theory of Computation by Zohar Manna Attempting to make into a science the art of verifying computer programs (debugging), the author addresses both practical and theoretical aspects. This self-contained treatment includes selected concepts of computability theory and mathematical logic.
The Philosophy of Mathematics: An Introductory Essay by Stephan Körner A distinguished philosopher surveys the mathematical views and influence of Plato, Aristotle, Leibniz, and Kant. He also examines the relationship between mathematical theories, empirical data, and philosophical presuppositions. 1968 edition.
