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.
Lecture notes files.
| 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) |