Theoretical / proof-based
Mathematical logic & set theory · Undergraduate · Math
Topics
Propositional and predicate logic
- Syntax and semantics of propositional logic
- Truth tables, tautologies, and logical equivalence
- Normal forms: CNF and DNF
- Predicate logic: quantifiers, scope, and interpretation
- Validity, satisfiability, and logical consequence
Proof systems and completeness
- Natural deduction or Hilbert-style proof systems (introduction)
- Soundness and completeness theorems (statements)
- Compactness theorem and its consequences (introduction)
- Löwenheim–Skolem theorems (overview)
- Undecidability and Gödel's incompleteness theorems (introduction)
Axiomatic set theory
- Zermelo–Fraenkel axioms (ZFC) and the cumulative hierarchy
- Ordinals and cardinals; cardinality and Cantor's theorem
- Axiom of choice and well-ordering (equivalents overview)
- Construction of number systems from set theory
- Russell's paradox and limitations of naive set theory
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$1,162 · Mathematical logic & set theory · 18 tutoring hrs
Study guides, worksheets, reviews, practice tests, and answer keys for 1 class. 18 tutoring hours (1 hr / week · semester). Bundle discount applied vs buying separately. Pay in full via Zelle or Venmo.