6.042J | Fall 2005 | Undergraduate

Mathematics for Computer Science

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 n/a (PDF) (PDF)
Week 7
16 Quiz 1 and Solution n/a n/a n/a
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 n/a (PDF) (PDF)
24 Counting II n/a (PDF) (PDF)
Week 10
25 Counting III (with Magic Trick Solution) n/a (PDF) (PDF)
26 Counting IV n/a (PDF) (PDF)
Week 11
27 Quiz 2 and Solution n/a n/a n/a
28 Generating Functions I n/a (PDF) (PDF)
29 Generating Functions II n/a (PDF) (PDF)
Week 12
30 Introduction to Probability n/a (PDF) (PDF)
31 Conditional Probability and Independence n/a (PDF) (PDF)
Week 13
32 Random Variables n/a (PDF) (PDF)
33 Distribution and Density, Binomial Distribution n/a (PDF) (PDF)
34 Expectation n/a (PDF) (PDF)
Week 14
35 Linearity of Expectation n/a (PDF) (PDF)
36 Variance n/a (PDF) (PDF)
37 Sampling and Confidence n/a (PDF) (PDF)
Week 15
38 Law of Large Numbers (PDF) (PDF) (PDF)
39 Random Walks (PDF) (PDF) (PDF)

Learning Resource Types
Problem Sets with Solutions
Exams with Solutions
Lecture Notes