Competencies: Mathematics > Logic & Proof Techniques
Logic & Proof Techniques
Body of Knowledge
| Topic | Description | Relevance | Career Tracks |
|---|---|---|---|
Mathematical Logic |
Formal reasoning techniques including direct proof, proof by contradiction, contrapositive, and mathematical induction. Foundation for algorithm correctness and formal verification. |
Medium |
Software Engineer, Formal Methods Engineer, Security Researcher |
Propositional Logic |
Logical connectives, truth tables, logical equivalence, normal forms |
High |
Software Engineer, Security Engineer, AI Engineer |
Predicate Logic |
Quantifiers, predicates, inference rules, first-order logic |
Medium |
Software Engineer, AI Engineer, Formal Methods Engineer |
Mathematical Induction |
Strong induction, structural induction, proofs about algorithms |
Medium |
Software Engineer, Algorithm Designer |
Proof Techniques |
Direct proof, contradiction, contrapositive, cases, counterexamples |
Medium |
Software Engineer, Mathematician |
Formal Verification |
Model checking, theorem provers, correctness proofs, invariants |
Low |
Formal Methods Engineer, Security Researcher |
Personal Status
| Topic | Level | Evidence | Active Projects | Gaps |
|---|---|---|---|---|
Mathematical Logic |
Beginner |
Understand direct proof, contradiction, contrapositive from reading; applied informally in RCA methodology (5 Whys as logical chain) |
No formal proof writing, no mathematical induction, no predicate logic |