Last blog! due April 13

Every named theorem I want to be sure that I know really well. Also, there are a lot of theorems that we use pretty regularly in the same general way which I feel are important to know well. I really need to work toward understand 7.10-8.3 better before the final because those were incredibly difficult for me for some reason. Any problems from the review will be helpful for me because I haven't had time to get very far into the review yet and the ones that I have done didn't go especially well. There are definitely algebra concepts that I understand better because of this class and this will definitely help me to be a more effective teacher. I've also learned a little more about self-discipline and even surprised myself by what I have been able to accomplish in this class. Obviously that's going to be helpful to me for the rest of my future.

8.3, due April 11

I feel like these theorems (once i understand/use them more) will help me to  figure out how many subgroups a group has. This would be awesome because right now I have no idea how to tell if I have found them all or not. I'm not really sure how the second sylow theorem is particularly useful (even after reading the examples). Even though I feel pretty unsure about this section, things usually come together by the time I do the homework, so i think it'll be okay.

8.2, due April 8

I've felt a little behind and confused since we started chapter 8. I feel like I understand enough to be able to do the homework but I typically have a hard time reading through the chapter and understand amidst the new notation and the logic of the proofs. Since I already feel behind, each new section is difficult for me to understand as well. It does it significantly better after the lecture, I just feel like I missed something. The Fundamental Theorem of Finite Abelian Groups is pretty cool just because it seems pretty simple/straightforward. The most difficult thing for me right now is probably keeping the notation for groups straight (especially with the direct sum vs direct product) and also applying theorems from previous, recent sections.

8.1, due April 6

What does the internal/external stuff mean? I mostly understand the example, but when we go to the general case and the proof of it, I get pretty lost in there. It's kinda cool that we have this other way of looking at the group, and that we can write out an isomorphism. I'll probably think it's cooler once I understand it more though...

7.10, due April 4

The problem with this section for me is that I didn't completely understand the A groups and what they are. So then in this section when we were proving theorems/lemmas  and extending our knowledge of them I was just a little bit confused/behind still. I'm sure once I finish the homework for the last section I'll be a little more caught up and able to understand better. It sounds like they will be really useful since they will help us to classify finite groups which we could previously only do to some extent.