For a few months now, the NYT Opinionator Blog has been hosting a series of pieces that do a phenomenally good job of explaining mathematics in layman’s terms.

The latest article is about Calculus (with a promise of more to come): Change We Can Believe In is written by Steven Strogatz, an Applied Mathematician at Cornell University.

There are several other articles in this series, and if you haven’t been reading them, you really should go check them out.  Assign them.  Discuss them in your classes.

• From Fish to Infinity (Jan. 31, 2010)
• Rock Groups (Feb. 7, 2010)
• The Enemy of My Enemy (Feb. 14, 2010)
• Division and Its Discontents (Feb. 21, 2010)
• The Joy of X (Feb. 28, 2010)
• Finding Your Roots (March 7, 2010)
• Square Dancing (March 14, 2010)
• Think Globally (March 21, 2010)
• Power Tools (March 28, 2010)
• Take It to the Limit (April 4, 2010)

Given the discussions we’ve been having about teaching Series and Series approximations lately on Facebook, Twitter, and LinkedIn, I wonder if he’d consider writing an article explaining “Why Series?” to students.

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For the last week, in between hours of dissertation work, I’ve been trying to figure out best strategies for the game Chain Factor.

I’m still trying to figure this one out, but there’s got to be a way to turn the analysis of this game into an assignment for a math class.  In particular, I’m thinking about doing some mathematical analysis of games in my Honors Calculus class this winter semester.

For the first six days, I just played in Basic Mode to try to figure out some general strategies.  It seems like it would be a very simple game, but it’s much more complex than it looks.  After a week of play, I still can’t come up with hard and fast strategies that work consistently.

Tonight I started playing in Power Mode and this adds a whole new set of logic and mathematical strategies to the game.  When is the optimum time or situation in which to use each power?  Which are the best powers to choose so that you have a way “out” of any threatening situation?

I’m thinking that, at the very least, it would be an interesting assignment to have students do an analysis of each of the powers, when they are useful, and when using them will actually hurt you.

Another interesting assignment would be to determine a strategy for stacking columns so that you get the best “chains” when they are set off.

The nice thing about the game is that it’s addicting, but just frustrating enough that you can’t just keep playing all day.

Please let me know if you come up with any interesting ideas for assigning this game!

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Is anyone in the mood for a good math puzzle?  The Math Factor is a well-established resource of just that.  University of Arkansas professor, Chaim Goodman-Strauss and radio journalist, Kyle Kellams, have been broadcasting weekly math-puzzle  segments since 2004 on Kellams’ show Ozarks at Large.  The Math Factor website is a steadily-growing archive of their work.  Goodman-Strauss, together with Edmund Harriss , Stephen Morris, and Jeff Yoak, provide the content (which contains works from Lewis Carroll, among others).  Several older puzzle posts include podcasts of Goodman-Strauss, and other contributors, explaining the answers on Kellams’ show.  There are also links for comments if you would like to post a response to a puzzle.

Also available:

• a poster in case you’d like to help advertise!
• The Math Factor on Twitter  (username: @Mathfactor or hashtag #mathfactor)
• Goodman-Strass’ graphics page

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Bruce Bueno de Mesquita, a consultant to the CIA and DOD, uses mathematical analysis to predict the outcome of “messy” human events in this 2009 TED Talk: Three predictions on the future of Iran, and the math to back it up.  He claims that we can use mathematics to predict the outcomes of complex negotiations or situations involving coercion (everything that has to do with politics and business).

His modeling is based in Game Theory, which (he says) is based on three assumptions that (1) people are rationally self-interested, (2) that people have values and beliefs, and (3) people face limitations.  The CIA verifies the predictive ability of the model, claiming it is correct 90% of the time even when the experts are wrong.

To build a model of the outcomes, he says he need to know (1) Who has a stake in the decision? (2) What do they say they want? (3) How focused are they on one issue compared to other issues? (4) How much persuasive influence could they exert?  Using this, we can predict behavior by assuming that everybody cares about two things: the outcome (effect on their career) and the credit (ego).  In the model, you must be able to estimate people’s choices, chances they are willing to take, values, and beliefs about other people.  Believe it or not, history is not necessary for the model.

Other than the mention of mathematics and a really general look at game theory, there was not a lot of mathematics in this talk.  There was one concrete mathematical example that you might be able to utilize in one of your classes (especially if you teach a little combinatorics as part of Probability and Statistics or Liberal Arts Mathematics):

To build a model that predicts the outcome of complicated social events, we need to look at the interactions between all of the people who have input in the decision-making (the influencers).  The number of interactions between n influencers is n!  If we double the number of influencers in the interaction, does that double the number of interactions?  (to use this example, play from 4:24 to about 7:15)

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NOVA Online has put up a nice set of videos (totaling an hour in length) about fractals. The series is broken into five chapters so you can easily browse (or assign) different parts separately.

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