Math Logic·Course
Math Logic & Algorithms
Mathematical logic: predicate calculus, Gödel's theorems, computability theory, Turing machines, and complexity
Part of the Mathematics track — finish it for a verifiable diploma →
§ 01 — Orientation
New here?
What you'll be able to do, who this is for, how long it takes, and where to begin.
By the end, you will be able to
- 01Work inside formal logical calculi.
- 02Understand Gödel's incompleteness theorems.
- 03Grasp computability and its limits.
- 04Reason about algorithmic complexity (P vs NP).
- 05See the foundations of computer science.
Who this is for
How long it takes
- Quick orientationSkim the opening module and the cheatsheet to get the shape of it.~2 h
- Full read-throughRead every article once, in order.~2 h
- Mastery pathRead, take the quizzes, and space out your reviews.~2 weeks
- APA
Stoa. (2026). Math Logic & Algorithms [Online course]. Stoa. https://stoa.school/course/math-logic
- MLA
Stoa. “Math Logic & Algorithms.” Stoa, 2026, https://stoa.school/course/math-logic.
- Chicago
Stoa. “Math Logic & Algorithms.” Stoa. Accessed September 1, 2026. https://stoa.school/course/math-logic.
§ 02 — Curriculum
5 modules.
Each module is a small unit. Most read in sequence — but a determined reader can begin anywhere.
- M IPropositional LogicSyntax, semantics, normal forms, and the DPLL algorithm3 articles
18 minBegin → - M IIFirst-Order Predicate LogicPredicates, quantifiers, structures, and Gödel’s completeness theorem3 articles
18 minBegin → - M IIIComputability TheoryTuring machines, decidability, and the Church–Turing thesis3 articles
18 minBegin → - M IVProof TheoryNatural deduction, sequent calculus, and the cut-elimination theorem3 articles
18 minBegin → - M VModel TheoryModels, elementary equivalence, types, and the Löwenheim–Skolem theorem3 articles
18 minBegin →
§ 03 — Learning outcomes
4 outcomes.
Work with propositional and predicate calculi and construct formal proofs
Understand the incompleteness theorems and their implications for mathematics
Analyze Turing machines, decidability, and undecidability
Classify problems by computational complexity and understand the classes P and NP
§ 04 — Practices