| Unit 1: Proofs |
| 1 |
1.1 Intro to Proofs |
Chapter 1.1–1.6 (PDF) |
| 2 |
1.2 Proof Methods |
Chapter 1.7–1.9 (PDF) |
| 3 |
1.3 Well Ordering Principle |
Chapter 2.1–2.3 (PDF) |
| 4 |
1.4 Logic & Propositions |
Chapter 3.1–3.5 (PDF) |
| 5 |
1.5 Quantifiers & Predicate Logic |
Chapter 3.6 (PDF) |
| 6 |
1.6 Sets |
Chapter 4.1–4.2 (PDF) |
| 7 |
1.7 Binary Relations |
Chapter 4.3–4.5 (PDF) |
| 8 |
1.8 Induction |
Chapter 5.1–5.3 (PDF) |
| 9 |
1.9 State Machines - Invariants |
Chapter 5.4 (PDF) |
| 10 |
1.10 Recursive Definition |
Chapter 6 (PDF) |
| 11 |
1.11 Infinite Sets |
Chapter 7 (PDF) |
| Unit 2: Structures |
| 12 |
2.1 GCDs |
Chapter 8.1–8.5 (PDF) |
| 13 |
2.2 Congruences |
Chapter 8.6–8.9 (PDF) |
| 14 |
2.3 Euler's Theorem |
Chapter 8.10 (PDF) |
| 15 |
2.4 RSA Encryption |
Chapter 8.11–8.12 (PDF) |
| 16 |
2.5 Digraphs: Walks & Paths |
Chapter 9.1–9.4 (PDF) |
| 17 |
2.6 Directed Acyclic Graphs |
Chapter 9.5 (PDF) |
| 18 |
2.7 Partial Orders and Equivalence |
Chapter 9.5–9.11 (PDF) |
| 19 |
2.8 Degrees & Isomorphism |
Chapter 11.1–11.4 (PDF) |
| 20 |
2.9 Coloring & Connectivity |
Chapter 11.7–11.9 (PDF) |
| 21 |
2.10 Trees |
Chapter 11.9–11.10 (PDF) |
| 22 |
2.11 Stable Matching |
Chapter 11.6 (PDF) |
|
Unit 3: Counting |
| 23 |
3.1 Sums & Products |
Chapter 13.1–13.5 (PDF) |
| 24 |
3.2 Asymptotics |
Chapter 13.7 (PDF) |
| 25 |
3.3 Counting with Bijections |
Chapter 14.1–14.2 (PDF) |
| 26 |
3.4 Repetitions & Binomial Theorem |
Chapter 14.4–14.7 (PDF) |
| 27 |
3.5 Pigeonhole Principle, Inclusion-Exclusion |
Chapter 14.8 (PDF) |
|
Unit 4: Probability |
| 28 |
4.1 Intro to Discrete Probability |
Chapter 16.1–16.5 (PDF) |
| 29 |
4.2 Conditional Probability |
Chapter 17.1–17.5 (PDF) |
| 30 |
4.3 Independence & Causality |
Chapter 17.7–17.8 (PDF) |
| 31 |
4.4 Random Variables, Density Functions |
Chapter 18.1–18.3 (PDF) |
| 32 |
4.5 Expectation |
Chapter 18.4–18.5 (PDF) |
| 33 |
4.6 Deviation: Markov & Chebyshev Bounds |
Chapter 19.1–19.3 (PDF) |
| 34 |
4.7 Sampling & Confidence |
Chapter 19.4–19.5 (PDF) |
| 35 |
4.8 Random Walks & Pagerank |
Chapter 20.2 (PDF) |
