Lecture 9 Notes: Graph Theory Part II
1
Coloring Graphs
Each term, the MIT Schedules Ofce must assign a time slot for each nal exam.
This is not easy, because some students are taking several classes with nals, and a
student can take only one test during
Lecture 6 Notes: Number
Theory Part I
Number theory is the study of the
integers. Number theory is right at the core
of math-ematics; even Ug the Caveman
surely had some grasp of the integers at
least the posi-tive ones. In fact, the integers
are so eleme
Lecture 7 Notes: Number
Theory Part II
The man pictured above is Alan
Turing, the most important gure in the
history of computer science. For decades,
his fascinating life story was shrouded by
government secrecy, societal taboo, and
even his own deceptio
Lecture 10 Notes: Sums and Approximations
When you analyze the running time of an algorithm, the probability some
procedure succeeds, or the behavior of a load-balancing or communications scheme,
youll rarely get a simple answer. The world is not so kind.
Lecture 8 Notes: Graph Theory
Part 1
1
Introduction
Informally, a graph is a bunch of dots connected
by lines. Here is an example of a graph:
B
H
A
F
D
G
I
C
E
Sadly, this denition is not precise
enough for mathematical discussion.
Formally, a graph is a
Lecture 2 Notes: Proofs
Why do you believe that 3 + 3 = 6?
Is it because your second-grade teacher, Miss Dalrymple, told you so? She might
have been lying, you know. Or are you trusting life experience? If you have three
coconuts and someone gives you thr
Lecture 1 Notes: Logic
Its really sort of amazing that people
manage to communicate in the English
language. Here are some typical sentences:
1. You may have cake or you may have ice
cream.
2. If pigs can y, then you can understand
the Chernoff bound.
3.
Lecture 5 Notes:
Induction Part III
1
Two Puzzles
Here are two challenging puzzles.
1.1
The 9-Number Puzzle
The numbers 1, 2, . . . , 9 are arranged in a 3 3
grid as shown below:
1 2 3
4 5 6
7 8 9
You can rearrange the numbers by rotating
rows and columns
called induction:
Lecture 3 Notes:
Induction Part I
1
Induction
A professor brings to class a bottomless
bag of assorted miniature candy bars. She
offers to share in accordance with two
rules. First, she numbers the students 0, 1,
2, 3, and so forth for c
Lecture 4 Notes: Induction Part II
1
Unstacking
Here is another wildly fun 6.042 game thats surely about to sweep the nation!
You begin with a stack of n boxes. Then you make a sequence of moves. In each
move, you divide one stack of boxes into two nonemp