Nationals 2010

MIT is hosting the United States Rubik’s Cube Championships this summer, August 6-8. All ages welcome! Normally I wouldn’t post about such things, but I happen to be a member of the Rubik’s Cube club here, and Some people use the Rubik’s cube group to motivate group theory. I’m a fan of hands-on mathematics, and [...]

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GILA II: Orbits, stabilizers, and classifying group actions

Now that we’ve discussed group actions a bit, it’s time to characterize them. In this post I’d like to take a leaf from Tim Gowers’ book and try to make each step taken in the post “obvious.” While the content of the proofs is not too difficult, its motivation is rarely discussed. First, it’s important [...]

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Non-canonical isomorphisms

I find non-canonical isomorphisms very interesting, but I wish I knew more examples. To be vague, an isomorphism (perhaps in a category) is said to be non-canonical if it requires making an “arbitrary choice.” One of the reasons I find them interesting is that we often think of objects only up to isomorphism, but in [...]

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