Books in the Theory and Applications of Computability series

This book offers a self-contained exposition of the theory of computability in a higher-order context, where 'computable operations' may themselves be passed as arguments to other computable operations.

This book emphasizes three very important concepts: computability, as opposed to recursion or induction; classical computability; and the art of computability, a skill to be practiced but also important in an esthetic sense of beauty and taste in mathematics.

This book questions the relevance of computation to the physical universe.

Computability and complexity theory are two central areas of research in theoretical computer science. This book provides a systematic, technical development of "algorithmic randomness" and complexity for scientists from diverse fields.