Lecture Notes

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.

Week 1
1 Good and Bad Proofs
Course Information
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)
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
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
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)