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) |