I spoke at Swarthmore College last week. Here are the abstracts and here are the talks: Mathematical vs. statistical models in social science (for the general audience) and Coalitions, voting power, and political instability (for math and stat majors).
Visiting the Swarthmore math dept was lots of fun. It’s great to be at a place where teaching is taken seriously. The classrooms, student common areas, faculty common areas, and faculty offices were all near each other, and students were always walking by and dropping in to faculty offices. After my talk on the first day, there was a dinner, at which I sat at a table with several students. I was impressed at the level of discussion–it seemed to be a really intellectual place. (It also was fun, in a way, to eat dining hall food–I hadn’t done that for many years!)
Class-participation activities
On the second day, I did a probability demo for the students in the math-stat course, and a statistics demo for the students in the intro stat course. The probability demo involved a jar of coins and culminates in an expected-monetary-value calculation that can be done by differentiating xp(x) (where p is the normal density function with a specified mean and variance); setting the derivative to zero reduces to solving a quadratic equation. The instructor for both classes the was Walter Stromquist, who did mathematics in the “real world” for many years as a consultant before coming to teach. While I was differentiating and solving the equation on the board, he quickly programmed the formula into a spreadsheet and computed the optimal solution before I could finish. For the second class, I did the real- and fake-coin-flips demo: while I was out of the room, each pair of students created either a sequence of 100 coin flips or a sequence of 100 1’s and 0’s that were supposed to be fake. Then I returned and was shown sequences in pairs, with my task being to tell the real and fake sequences apart. I’m embarrassed to say that I only got 4 out of the 5 pairs correct.
Mathtalk
Overheard in the hallway of the math department:
Teacher 1: When a proof has a gap, use L’Hopital’s Rule.
Teacher 2: Everytime my lectures have a gap, I tell a joke.
Teacher 1: What happens if the joke has a gap?
May I know which program you used to build up your slides? They look extremely good.
Beamer. It's a Latex class (google for more information). Jouni told me about it. In case you want a template to work from, the script for the first of my Swarthmore talks is here.
Thanks a thousand, I know a bit of LaTeX and will work on this class. You made my day.
Greetings! I am glad to learn that you enjoyed your visit to Swarthmore, where I graduated 2 years ago — from the math department no less.
I came across your blog while searching on the topic of statistics. I am a math major, but I didn't concentrate on statistics when I was at Swarthmore. Now I am finding that a basic understanding of statistic modeling (of economics, finance, or social sciences in general) is useful for my job. I am wondering if you could recommend some introductory books (even better, websites) on this topic.
At any rate. I like your blog. I learned a few things from reading it. Thanks!
Feng
Regarding the second game (real vs fake coin flips): I heard a story that RA Fisher was the first to do that, having just derived the non-intuitive results on how low the probability of getting back to "zero" (i.e. as many heads as tails) once your net score had deviated by some suprisingly small amount. Is that more or less correct?
MITecon,
I don't know about Fisher, but Feller devotes a chapter in one of his famous probability books to the random walk, including simulations to show the rarity of zero-crossings and then deriving some relevant results mathematically.