Good idea, but I'm not optimistic about the outcome. There's a good reason that some of the best mathematical minds of the last several centuries have been involved in the analysis of games -- they can be arbitrarily difficult to analyze. Probably the best you can hope for is to instill a respect for the complexity and subtlety required for their analysis, so that these students don't naively think that the answers are obvious. A similarly difficult task is instilling respect for the scientific method. (I'm not trolling here...) The response of the scientific community to "intelligent design" has been anything but intelligent -- instead of utilizing this as an opportunity to explain what science is and how it works, scientists have simply tried to replace one "faith" with another (believe me because I have a Nobel prize -- NOT because a number of experiments have verified my theory). I think that Lewis Carroll found the same problem trying to teach Logic ("What the Tortoise said to Achilles"): "Then Logic would take you by the throat, and force you to do it!" http://www.lewiscarroll.org/achilles.html I think that science fiction writers have discussed this problem at length -- how long will it take human DNA to evolve to the point where rational thinking is the norm? At 08:33 PM 1/19/2006, James Propp wrote:
I'm teaching a course on quantitative reasoning for an audience of nearly two hundred math-averse students, and one of the ways I'm hoping to "sell the product" to them is to pitch the course as a kind of self-defense art that helps you not get ripped off by used car dealers, cell-phone companies, credit-card companies, banks, etc.
For instance, I'll talk about the scam wherein the scammer sends free investment advice to 1024 people (half of whom get one piece of advice and half of whom get a conflicting piece of advice), then sends free advice to the 512 who got good advice on the first round (again splitting his advice half-and-half), then sends free advice to 256 people, and so on, and finally starts to ask a small number of people to pay a lot of money, hoping that they'll reason that someone who's been right so often must be onto something.
I'll also show the class the grifting scene in "Paper Moon".
Can any of you think of other good mathematical cons, or good resources for finding out about them?
("Ricky Jay's Big Book of Math Hustles" would be perfect if such a book existed!)
Jim