Powerpoint and LaTeX source files and LaTeX macros are available to instructors by request: email Prof. Albert Meyer at meyer at csail dot mit dot edu.
| SES # | TOPICS | SLIDES | IN-CLASS PROBLEMS | IN-CLASS PROBLEM SOLUTIONS |
|---|---|---|---|---|
| Week 1 | ||||
| 1 | Good and Bad Proofs Course Information |
(PDF) | (PDF) | (PDF) |
| 2 | Propositions and Proofs | (PDF) | (PDF) | (PDF) |
| Week 2 | ||||
| 3 | Proofs by Contradiction and Cases | (PDF) | (PDF) | (PDF) |
| 4 | Predicate Logic | (PDF) | (PDF) | (PDF) |
| 5 | Sets and Functions | (PDF) | (PDF) | (PDF) |
| Week 3 | ||||
| 6 | Induction I | (PDF) | (PDF) | (PDF) |
| 7 | Induction II | (PDF) | (PDF) | (PDF) |
| Week 4 | ||||
| 8 | Relations I | (PDF) | (PDF) | (PDF) |
| 9 | Relations II | (PDF) | (PDF) | (PDF) |
| 10 | Graph Theory I | (PDF) | (PDF) | (PDF) |
| Week 5 | ||||
| 11 | Graph Theory II | (PDF) | (PDF) | (PDF) |
| 12 | Graph Theory III | (PDF) | (PDF) | (PDF) |
| 13 | Graph Theory IV | (PDF 1) (PDF 2) |
(PDF) | (PDF) |
| Week 6 | ||||
| 14 | Number Theory I | (PDF) | (PDF) | (PDF) |
| 15 | Number Theory II | (PDF) | (PDF) | |
| Week 7 | ||||
| 16 | Quiz 1 and Solution | |||
| 17 | Number Theory III | (PDF) | (PDF) | (PDF) |
| 18 | State Machines I: Invariants Fallacies with Infinity |
(PDF) | (PDF) | (PDF) |
| Week 8 | ||||
| 19 | State Machines II: Derived Variables, Stable Marriage Problem | (PDF - 1.9 MB) | (PDF) | (PDF) |
| 20 | Sums and Series I | (PDF) | (PDF) | (PDF) |
| 21 | Sums and Series II Mid-course Survey |
(PDF) | (PDF) | (PDF) |
| Week 9 | ||||
| 22 | Asymptotics | (PDF) | (PDF) | (PDF) |
| 23 | Counting I | (PDF) | (PDF) | |
| 24 | Counting II | (PDF) | (PDF) | |
| Week 10 | ||||
| 25 | Counting III (with Magic Trick Solution) | (PDF) | (PDF) | |
| 26 | Counting IV | (PDF) | (PDF) | |
| Week 11 | ||||
| 27 | Quiz 2 and Solution | |||
| 28 | Generating Functions I | (PDF) | (PDF) | |
| 29 | Generating Functions II | (PDF) | (PDF) | |
| Week 12 | ||||
| 30 | Introduction to Probability | (PDF) | (PDF) | |
| 31 | Conditional Probability and Independence | (PDF) | (PDF) | |
| Week 13 | ||||
| 32 | Random Variables | (PDF) | (PDF) | |
| 33 | Distribution and Density, Binomial Distribution | (PDF) | (PDF) | |
| 34 | Expectation | (PDF) | (PDF) | |
| Week 14 | ||||
| 35 | Linearity of Expectation | (PDF) | (PDF) | |
| 36 | Variance | (PDF) | (PDF) | |
| 37 | Sampling and Confidence | (PDF) | (PDF) | |
| Week 15 | ||||
| 38 | Law of Large Numbers | (PDF) | (PDF) | (PDF) |
| 39 | Random Walks | (PDF) | (PDF) | (PDF) |