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?

7.9, due April 1

• Difficult: I was a little confused by the example in the middle of page 231. It says (2 4 3)(1 2 4 3) = (1 4 2 3). No... to me this says 1 goes to 2, and 2 goes to 4 so one goes to 4. Then 2 goes to 4 and 4 goes to 3 so 2 goes to 3. Then 3 goes to 1, and 1 goes to 1, so 3 goes to 1. Then 4 goes to 3, and 3 goes to 2 so 4 goes to 2. Thus I get (4  3 1 2) which is NOT the same answer they got. What am I doing wrong?
• Reflexive: I think I really like this new notation. It totally makes sense to have (2465) mean 2 -> 4 -> 6 ->5. However, I haven't been able to make it work. So... maybe it isn't that great.

Make Up Post-- ME Social

I attended MEA's activity where we got together and met with other majors who's initials were ME (Math Education, Music Education, and Mechanical Engineering). The reflective part of this post is easy: I enjoyed discussing with the mechanical engineers the similar classes we have taken, and the different classes. Their major is MUCH more computational than mine (as made evident by this class). I'm not sure if I can find a "difficult" part, though. It was just... fun.

Make Up Post-- MEA Core Curriculum

• I attended a lecture by Dr. Peterson on the current math core curriculum in schools and how it is changing.
• Difficult: I had a really hard time understanding if Dr. Peterson thought that the core curriculum was good or if it needed improvement, or both. He seemed... certainly not abivalent, but abiguous and disjointed. He frequently gave his opinion on the core, but sometimes his opinions would contradict themselves. Very confusing.
• Reflective: I've noticed that the BYU math education program seems to be full of a lot of ideals, but I have a feeling most of them are vain. Yes, there are so many wonderful ways to incorporate math into the classroom so that it becomes more than just memorizing formulas. But with the way the core is currently set up, I don't know if it's possible. And I don't think the system is ready for a complete overhaul of the core. I wish he had talked about that. How will we incorporate these ideals, not just the ideals themselves.