In a comment to my previous post on the Street-Fighting Math course, Alex wrote:
Have you thought about incorporating this material into more conventional classes? I can see this being very good material for a “principles” section of a linear modeling or other applied statistics course. It could give students a sense for how to justify their model choices by insight into a problem rather than, say, an algorithmic search over possible specifications.
Good point. I’d still like to do the full course—for one thing, that would involve going through Sanjoy Mahajan’s two books, which would have a lot of value in itself—but if we want to be able to incorporate some of these concepts in existing probability and statistics courses, it would make sense to construct a couple of one-week modules.
I’m thinking one on probability and one on statistics.
We can discuss content in a moment but first let me consider structure. I’m thinking that a module would consist of an article (equivalent to a textbook chapter, something for students to read ahead of time that would give them some background, include general principles and worked examples, and point them forward), homework assignments, and a collection of in-class activities.
It’s funny—I’ve been thinking a lot about how to create a full intro stat class with all these components, but I’ve been hung up on the all-important question of what methods to teach. Maybe it would make sense for me to get started by putting together stand-alone one-week modules.
OK, now on to the content. I think that “street-fighting math” would fit into just about any topic in probability and statistics. Some of the material in my book with Deb Nolan
Probability: Law of large numbers, central limit theorem, random walk, birthday problem (some or all of these are included in Mahajan’s books, which is fine, I’m happy to repurpose his material), lots more, I think.
Statistics: Log and log-log, approximation of unknown quantities using what Mahajan calls this the “divide and conquer” method, propagation of uncertainty, sampling, regression to the mean, predictive modeling, evaluating predictive error (for example see section 1.2 of this paper), the replication crisis, and, again, lots more.
Social science: I guess we’d want a separate social science module too. Lots of ideas including coalitions, voting, opinion, negotiation, networks, really a zillion possible topics here. I’d start with things I’ve directly worked on but would be happy to include examples from others. But we can’t call it Street-Fighting Political Science. That would give the wrong impression!