1. A lot of this reading was not difficult because it was just applying congruence stuff and cosets to groups now. So the hardest part was just the new terminology and symbols for the index of H in G is denoted [G:H]. This is kind of confusing for me just because it is something that is actually new in this section. So then using that and putting it into Lagrange's theorem is kind of confusing because I am having a hard time wrapping my mind around what it means and how to use it properly.
2. The most interesting part of this reading is that that theorem 7.26 is named Lagrange's theorem. I am curious to know how this relates to like Lagrange multipliers that I have studied before (in, I think, linear algebra but I'm not sure). Is it just the same guy who discovered both of these? Or are they connected principles to each other? I don't know because I don't actually remember Lagrange multipliers other than the name is something I have studied before. So I would be interested in learning the connection between that and the Lagrange's theorem in the reading.
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