- Announcements:
- This week our quiz will cover section 6.2: trees.
- I'll linger after class, in case anyone would like to get access to the wiki.
- Last time:
- We wrapped up 6.2 trees, and had a quiz.
- Let's talk about the quiz:
- Key
- Observations about Problem 1 (a homework problem): symmetry, and duality, and graphs!
- About Problem 2: duality!
- Today:
- Let's start with a story in Nature: New
maths formula answers long-standing party problem: How many
invitees guarantee at least a certain number all know each
other? Formula is first major improvement since 1935.
- "The problem can be mapped onto the mathematical
theory of networks, the abstract objects made of nodes
and links connecting them. Each node will represent a
person at the party, and any two people are connected
by a link, which is colour-coded -- red if two people
know each other, and blue if they do not. The question
then becomes, how large does a network need to be to
guarantee that it contains at least one all-blue or one
all-red subset of a certain size?"
- Upper-bounds
- Tighter upper-bounds!
- Application: Using trees (and symmetry) to solve
the last problem on your exam: see the key for your
midterm -- I forgot to say something about
bounds....
- Today we'll cover Decision
Trees.
- Links:
Website maintained by Andy Long.
Comments appreciated.
