Offers a concise introduction, treating the origins of the subject, the basic notion of set, the axioms of set theory and immediate consequences, the set-theoretic reconstruction of mathematics, and the theory of the infinite, touching also on selected topics from higher set theory, controversial axioms and undecided questions, and philosophical issues raised by technical developments.

Explains, organizes, and compares various algorithmic techniques used in computability theory (which was formerly called "classical recursion theory")..

An accessible yet rigorous crash course on recursive programming using Python and JavaScript examples. Teaches the basics of recursion, exposes the ways it's often poorly taught, and clarifies the fundamental principles behind all recursive algorithms. It is project-based, containing complete, runnable programs in both Python and JavaScript, and covers several common recursive algorithms for tasks like calculating factorials, producing numbers in the Fibonacci sequence, tree traversal, maze solving, binary search, quicksort and merge sort, Karatsuba multiplication, permutations and combinations, and solving the eight queens problem.

An introduction to computability theory (or recursion theory as it is traditionally known to mathematicians). This text begins with a mathematical characterization of computable functions using a simple idealized computer (a register machine); after some comparison with other characterizations, he develops the mathematical theory, including a full discussion of non-computability and undecidability, and the theory of recursive and recursively enumerable sets.

Examines how recursion applies at different levels within a full description of natural language. Specifically, he identifies and evaluates recursion as: a) a central property of the computational system underlying the faculty of language; b) a possible feature of the derivations yielded by this computational system; c) a global characteristic of the structures generated by the language faculty; and d) a probable factor in the parsing operations employed during the processing of recursive structures.

Survey of computability theory offers the techniques and tools that computer scientists (as well as mathematicians and philosophers studying the mathematical foundations of computing) need to mathematically analyze computational processes and investigate the theoretical limitations of computing.

Demonstrates how these algorithms are more appropriate as mathematical models for modern computers and how they present a better framework for computing methods * Develops a new practically-oriented perspective on the theory of algorithms, computation, and automata, as a whole