| Date | Description |
|---|---|
| March 31 |
Propositions; ¬, ∧, ∨, → truth tables Reading: 1.1-1.3 (7th), 1.1-1.2 (6th) |
| April 2 |
↔, logical equivalences Reading: 1.4-1.5 (7th), 1.3-1.4 (6th) |
| April 4 |
Complexity of proving tautologies; predicates, quantifiers Reading: 2.1-2.2 |
| April 7 | Sets: ∈, ⊆; first proofs |
| April 9 | Set equality, power set, Cartesian product |
| April 11 |
Set union, intersection, difference Reading: 2.3 |
| April 14 |
Functions: injective, surjective, bijective Reading: 4.1&4.3 (7th), 3.4-3.5 (6th) |
| April 16 | Functions: inverse, composition; divisibility, primes |
| April 18 | Prime factorization, division theorem, equivalence (mod m) |
| April 21 |
Modular arithmetic and exponentiation Reading: Modular exponentiation from the end of 4.2 (7th), 3.6 (6th) |
| April 23 | GCD, Euclid's algorithm |
| April 25 | Proof by contradiction |
| April 28 |
Public key cryptography Reading: Slides |
| April 30 | Coin flipping on the phone, induction |
| May 2 |
Induction, correctness of Euclid's algorithm Reading: 5.1-5.2 (7th), 4.1-4.2 (6th) |
| May 5 |
Course-of-values induction Reading: 5.3 (7th), 4.3 (6th) |
| May 9 |
Recursive definitions Reading: 9.1 (7th), 8.1 (6th) |
| May 12 |
Relations Reading: 9.5 (7th), 8.5 (6th) |
| May 14 |
Equivalence relations and partitions Reading: 10.1, 12.1 (7th), 9.1, 11.1 (6th) |
| May 16 |
Directed graphs, Boolean functions, gates Reading: 12.2-12.3 (7th), 11.2-11.3 (6th) |
| May 19 |
Combinational circuits, adders Reading: 13.2-13.3 (7th), 12.2-12.3 (6th) |
| May 21 |
Finite-state machines Reading: 13.4 (7th), 12.4 (6th) |
| May 23 | Finite-state automata |
| May 28 | Regular expressions |
| May 30 |
Kleene's Theorem example |
| June 2 |
Nonregular languages Reading: end of 3.1 |
| June 4 |
Halting problem Reading: 13.5 (7th), 12.5 (6th) |
| June 6 | More undecidable problems |