Final Exam, Due April 13

• Which topics and theorems do you think are important out of those we have studied?

Honestly. I have no idea. I'm going to spend the next few days trying to learn (not even re-learn) this entire course, because hardly anything had made sense to me.

• What do you need to work on understanding better before the exam? Come up with a mathematical question you would like to see answered or a problem you would like to see worked out in class on Wednesday.

As I said previously, I'm SO far behind in this class, that I don't think I could make a list of things I need to better understand. I could probably make a list of things I DO understand, but it would be a very short list. However, one thing that comes to mind is I'd really like to know what the heck it means when you have G/H or A/B or K/I or any of those things involving a /. It always seems to mean something different.

• How do you think the things you learned in this course might be useful to you in the future?

 I've had this discussion with quite a few people. I don't know why Math Ed. majors are required to take a course like 371. It's SO much harder than anything we'll have to use in a high school. Perhaps it's there purely for the benefit of those who are considering going on to get their masters in Math Ed? If this course was helpful, it was because it showed me that there are MAJOR flaws in my study habits, and abstract/analytical math is NOT for me.

8.3, due April 11

• Difficult:  The sylow theorems actually seemed to make sense to me. Of course, I won't really know until I try to put them into practice. However, I'll admit that I still don't really understand the x^(-1)Kx. I feel like we've seen that a lot, but I have no idea what it means.
• Reflective: I feel like Cauchy's Theorem in this section is very similar to LeGrange's theorem. I guess the difference is that p must be prime, and then G DEFINITELY contains an element of order p, rather than it could contain an element of order p. Yes?

 

8.2, due April 8th

• Difficult: Woah. This whole chapter made so little sense that I don't even know where to begin! First of all, I didn't know why any of this was important (let alone what it means). But then again, I don't really know why any of this is important (at least in my discipline). But I guess what confused me the most is it seemed like they were pulling letters out of nowhere. They were sure to clarify that a was in g, but then they were saying ak=0 and sa=k_1, etc. But what is k? What is s? Where are all these things coming from?
• Reflective: I think I've reached that point of no return. I wasn't able to grasp the earlier concepts quick enough, and now all of these new concepts don't make ANY sense to me. I'm still trying to figure out what exactly an abelian group IS!

8.1, Due April 6th

• Difficult: I was confused by Theorem 8.1. When it says N_1, N_2 ..., N_k, does it mean that those are ALL of the normal subgroups of G, or can it be any number of normal subgroups of G? Or does that second part of the proof say it doesn't matter how many normal subgroups there are so long as ever element is covered? It wasn't clear. Also, because I didn't understand Theorem 8.1, I don't understand why Lemma 8.2 is important.
• Reflective: A lot of this was pretty straight forward. In fact, i wasn't really sure what we were supposed to find in this section that was NEW. It seemed like it was just showing you how to take cartesian products of groups, and isn't that what we've already been doing?