| Week 1 |
| 1 |
Good and bad proofs |
|
| 2 |
Proof by contradiction |
|
| Week 2 |
| 3 |
Well ordering principle |
|
| 4 |
Propositional logic |
|
| 5 |
Sets and relations |
Problem set 1 due |
| Week 3 |
| 6 |
Size of sets, mapping lemma |
|
| 7 |
Predicates and quantifiers |
Mini-quiz 1 |
| 8 |
Set theory, Russell paradox |
Problem set 2 due |
| Week 4 |
| 9 |
Induction and strong induction |
|
| 10 |
Partial orders |
|
| 11 |
Partial orders and scheduling |
Problem set 3 due |
| Week 5 |
| 12 |
Digraphs |
|
| 13 |
State machines, preserved invariants |
Mini-quiz 2 |
| 14 |
Derived variables, termination |
Problem set 4 due |
| Week 6 |
| 15 |
Stable matching |
|
| 16 |
Simple graphs, degrees, isomorphism |
|
| 17 |
Graph connectedness, trees |
Problem set 5 due |
| Week 7 |
| 18 |
Graph coloring, bipartite matching |
|
| 19 |
Recursive data |
Mini-quiz 3 |
| 20 |
Planar graphs |
Problem set 6 due |
| Week 8 |
| 21 |
GCD and integer linear combinations |
|
| 22 |
Modular arithmetic |
|
| 23 |
Inverses (mod n), RSA encryption |
Problem set 7 due |
| Week 9 |
| 24 |
Harmonic sums, Stirling's approximation |
|
| 25 |
Asymptotics |
Mini-quiz 4 |
| 26 |
Counting with bijections |
Problem set 8 due |
| Week 10 |
| 27 |
Pigeonhole and division rules |
|
| 28 |
Counting repetitions, card magic |
|
| 29 |
Inclusion-exclusion, counting practice |
Problem set 9 due |
| Week 11 |
| 30 |
Binomial theorem, combinatorial identities |
Mini-quiz 5 |
| 31 |
Generating functions: for counting |
Problem set 10 due |
| Week 12 |
| 32 |
Generating functions: for recurrences |
|
| 33 |
Introduction to probability |
|
| 34 |
Conditional probability, independence |
Problem set 11 due |
| Week 13 |
| 35 |
Random variables |
|
| 36 |
Expectation |
Mini-quiz 6 |
| 37 |
Variance |
Problem set 12 due |
| Week 14 |
| 38 |
Sampling and confidence |
|
| 39 |
Random processes |
|
