nLab Computability
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nLab wiki entry on computability, relating Turing machines, partial recursive functions, and realizability to type theory and category theory. Useful for readers who already know basic computability and want to see how it connects to constructive mathematics and topos theory.
More resources on Computability Theory
theoryofcomputing.org
Theoryofcomputing.org is a practical resource hub for theory of computation, featuring lecture notes, tutorials, and problem sets on automata, formal languages, computability, and complexity to help learners build intuition and tackle exercises.
Logic II (MIT 24.242)
Computability theory followed by a detailed study of Gödel's incompleteness theorems and their applications, including Church's undecidability theorem and Tarski's theorem on the undefinability of truth. Lecture notes and problem sets with solutions let learners work through these proofs themselves.
Theory of Computation
Learn computability theory with Kamala Krithivasan's Theory of Computation course. Explore fundamental concepts and problem-solving!
Theory of Computation (MIT 18.404J)
Sipser's course on automata, computability and complexity: regular and context-free languages, decidability, reducibility, the recursion theorem, time and space complexity, NP-completeness, hierarchy theorems, probabilistic computation and interactive proofs. 25 lecture videos, slides, problem sets and exams support rigorous proof-based study.
On Computable Numbers, with an Application to the Entscheidungsproblem (1936)
The founding paper. Turing defines his machines, builds a universal machine, proves by diagonalisation that no machine decides halting, and settles Hilbert's Entscheidungsproblem negatively. Reading it shows where every later definition of computability came from.
brilliant.org
Brilliant.org is an online, interactive learning platform offering problem-based courses in math and computer science, including topics in automata theory, computation, and discrete mathematics, with guided lessons and practice problems.