Math Logic·Course
Math Logic & Algorithms
Mathematical logic: predicate calculus, Gödel's theorems, computability theory, Turing machines, and complexity
5
Modules
15
Articles
~2 h
Reading
IV
CLOs
§ 01 — 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 →
§ 02 — Learning outcomes
4 outcomes.
CLO I
Logical Calculi
Work with propositional and predicate calculi and construct formal proofs
CLO II
Gödel’s Theorems
Understand the incompleteness theorems and their implications for mathematics
CLO III
Computability Theory
Analyze Turing machines, decidability, and undecidability
CLO IV
Algorithmic Complexity
Classify problems by computational complexity and understand the classes P and NP
§ 03 — Practices