18.090 Introduction To Mathematical Reasoning Mit -

| 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 |

Divisibility, modular arithmetic, greatest common divisors (GCD), the Euclidean algorithm, and Bézout's identity. This is where you get your hands dirty with actual math. 18.090 introduction to mathematical reasoning mit

MIT 18.090: Introduction to Mathematical Reasoning For many students arriving at MIT, mathematics has been a journey of calculation—solving for | Week | Topic | |------|-------| | 1