- Let's take a look at your homework
assignment, to make sure that you all know what you're supposed to
do! It's supposed to be due Friday, but I'm going to move that to
Monday, because of ....
- Important change: This Friday we will have a visit from members of
the BCC -- Burkhardt Consulting Center -- affiliated with the math
department.
Members of the BCC are local experts in the analysis of statistical information, and they will be talking to us about our upcoming survey.
Your new assignment for midnight tomorrow: take a look at the questions you and your peers asked, and choose your top five. Then send me a one page typed paper with first the questions, in the following form:
Andy.1: (followed by the question) which would mean Andy's first question. So give credit, then paste the question.
Following would be your description of why you chose this question.
You may not choose your own questions.
I need these by midnight, Thursday night, so that I can compile a list for the members of Burkhardt to consider when we get together on Friday morning.
Okay?
Question of the Day:
- Before we go there, however, let's just recall what we talked about
last time: how do we represent graphs in the computer? One answer: "Adjacency matrices"
- Adjacency: those will be our edges
- Matrix: a rectangular array of data (frequently numbers).
- We built a few adjancy matrices:
- $K_{5}$ and $K_{3,3}$
- Konigsberg (weighted)
- Google example (directed)
- $K_{5}$ and $K_{3,3}$
- Now: how might we tie this back to Pascal's Triangle?
- Pascal's triangle can be thought of as a calculator. It calculates the number of ways of doing things. This is why Pascal was interested in it: it proved handy in his work on probability with the great mathematician Fermat.
- "Plinko"
- Triangular numbers, and Triangles in adjacency matrices
- Counting all simple groups on $n$ labelled
vertices:
- Rows of Pascal's triangle (made up of "combinations")
- "All the ways of picking distinct items" -- powers of two!
- A curiousity: Fibonacci numbers in Pascal's triangle