Yesterday I listened to the new episode of the Mathematical Objects podcast:

I love listening to the discussions that Katie Steckles and Peter Rowlett have on this podcast. This episode made for an especially great project for kids, I thought. So, I had the boys listen to it after breakfast and then we talked about some of the ideas that they thought were interesting:

Now we dove into a tiny bit more detail about groups and modular arithmetic. Here I wanted to show the boys that the idea of an identity element was pretty important even though it seems like a pretty simple requirement when you see it for the first time:

Finally, we moved on to talking about some of the group theory ideas that relate to Rubik’s cubes. The specific idea we talked about from the podcast episode was “commutators”. We tried out three examples that – honestly by accident – turned out to be nice illustrations of the idea:

I really enjoyed the podcast and also learning about what the boys found interesting listening to it. It definitely is fun illustrating some basic ideas from group theory with Rubik’s cubes!