Math Circles


The University of Waterloo’s CEMC holds Math Circles in which they invite local grade 6-12 kids to come to the university one evening a week for math enrichment activities. In the past years I have participated for 2-3 weeks per year, running sessions on the topics of Game Theory and Conics (ellipses, parabolas, etc). This year my topic is Graphs! Here are six small graphs (you can ignore the numbers on the edges):

The first session, yesterday, was very enjoyable (at least to me, but it also seemed to get positive feedback from the other participants as well).

In my experience, it can be tricky to guess the appropriate level of discourse when preparing the lessons, mostly since I have no prior experience with most of the kids in the session. This caused me to “lose” about a 1/3 of my first session to covering background material: proof by induction. (It’s not really a “loss” because I would say that the time spent was still fun for me and beneficial for the students.)

In the course of developing the online notes to accompany the presentation, I wanted to see if there was a good resource online with an appropriate explanation of “proof by induction.” There are certainly hundreds of books including the subject, and given the size of the internet, one might conclude that there are thousands of articles online about induction? Well, it doesn’t quite seem to be that many. I found that Wikipedia had the best all-purpose description (with an example, and without getting too abstract) and there is another online at Carnegie Mellon University. I was hoping to find something good at the Art of Problem Solving website but their description was a little too terse. It looks like there is still some room on the internet for well-written mathematical enrichment material, I am glad the Math Circles content is available to help fill that hole.

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