| 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) |
available for download (PDF 5.8MB).