Truth tables, logical connectives (AND, OR, NOT, implication), quantifiers (∀ "for all" and ∃ "there exists"), and the all-important concept of contrapositive. You learn that "If P then Q" is logically equivalent to "If not Q then not P"—a trick that will save your life on exams.
The heart of the course lies in mastering various methods of proof, including: 18.090 introduction to mathematical reasoning mit
Introductory concepts including permutations, fields, and vector spaces. tautologies | | 2 | Quantifiers
Typical syllabus structure (concept progression) logical connectives (AND
Properties of integers, divisibility, and prime numbers.
| Week | Topic | |------|-------| | 1 | Logical connectives, truth tables, tautologies | | 2 | Quantifiers, negations, converse/inverse | | 3 | Proof techniques: direct, contrapositive, contradiction | | 4 | Mathematical induction (ordinary and strong) | | 5 | Sets: union, intersection, power sets, Cartesian products | | 6 | Functions: injective, surjective, bijective, inverses | | 7 | Relations: equivalence relations, partitions | | 8 | Midterm review & exam | | 9 | Number theory: divisibility, primes, GCD, Euclidean algorithm | | 10 | Modular arithmetic and proofs | | 11 | Real numbers: least upper bound property, sequences | | 12 | Countability: finite, countably infinite, uncountable sets | | 13 | Introduction to combinatorial proofs | | 14 | Final review and project presentations |