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dcernst / IBL-AbstractAlgebra

IBL course materials for an undergraduate first-semester abstract algebra course that emphasizes visualization.
http://dcernst.github.io/IBL-AbstractAlgebra/
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Fix critical error in Cayley diagram in Prob 2.74 #152

Closed mitchkeller closed 2 years ago

mitchkeller commented 2 years ago

The s's and t's were all backward in the labels on the group elements in the first Cayley diagram in Problem 2.74, which I didn't realize until I sent my students off to work on it and then we were comparing things in class and they had some serious befuddlement. (Paradoxically, the "harder" second one worked out better, since it didn't have the issue.)

dcernst commented 2 years ago

Doh! That's a newly added problem that I copied from Matt Macauley. I guess I didn't inspect it. I think Matt does right actions instead of left actions.

dcernst commented 2 years ago

Also, you are now ahead of me!

dcernst commented 2 years ago

I also just noticed that if the last part of the problem, I say, "for each x...". Since one of the elements in the second group is already called x, this is potentially confusing. I think I'll changed this to, "For each g..."

mitchkeller commented 2 years ago

Also, you are now ahead of me!

Yeah, I went to your website right after class to see if you had a note on this and saw that my class is, for the moment, ahead. I am taking your suggestion and not getting bogged down in some of the things that suck up time to do precisely at this stage. I think it will be OK since I had all these students in ring theory in the fall, and there are a couple of theorems in Chapter 2 that are worth having them write up before we hit the more theorem-proof stuff that's coming.

I also just noticed that if the last part of the problem, I say, "for each x...". Since one of the elements in the second group is already called x, this is potentially confusing. I think I'll changed this to, "For each g..."

Good call. I was so focused on submitting the updated Cayley diagram that I didn't think to mention this. I think for one of the students who did the second one (I had two students do the left diagram and three do the right one.), the repetition of x was confusing.