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

I would say that the isomorphism theorems were used quite a lot and seemed to impact a lot of other topics and theorems. I also think I've used Lagrange's theorem a lot, so it must be important.

What do you need to work on understanding better before the exam?

I still struggle with cyclic groups and the order of elements. When I work on filling out the study guide, I also usually have the hardest time finding enough examples of all the different things.

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

I'll be honest. I don't really think it will be. And perhaps that is because I barely understand most of what we talked about in class, which makes it hard to apply it to things outside of the course. Additionally, I'm almost done with my Math Education degree and realistically I won't be getting a job after I graduate because I have 2 kids. I'm just trying to make it through and pass so I can graduate! I found that it was hard to find applications to teacher education for some of the advanced math courses that are required for the MthEd degree.

8.3, Due April 11

Difficult:

I was confused about the statement that if K is a Sylow p-subgroup of G, then so is x^-1Kx. Perhaps this is related to confusion about 'the image' of something. Were they just trying to say that a subgroup and it's image are isomorphic?

Reflective:

I noticed that Cauchy's thm was in this section - so we must have done it early in class and not with section 8.3. Why is that?

8.2, Due April 8

Difficult:

Oh boy. I really struggle with the "order" idea. I think it's very confusing that they have orders of groups relating to the number of elements, but then there are orders of elements and sometimes groups ARE elements of another group and it just all blends together. I have a hard time separating them and remembering which one we are talking about.

Reflective:

I thought it was helpful to have the little dictionary for translating from multiplicative to additive notation. I think we have seen some of it before, but I thought it was good that they reprinted it when it would be more usable for us.

8.1, Due April 6

Difficult:

For Lemma 8.2, I think I am confused. What is ? The cyclic subgroup generated by e? How is this different from the whole group? I think I've had this question before...

Reflective:

I thought it was cool that we looked at the cartesian product of more than two groups. I think it would be a little hard to keep track of what the elements actually look like, but it was cool anyways :)

7.10, Due April 4

Difficult:

Maybe it was because it was at the end of 7.9, and because we didn't cover it in class, but I don't feel like I understand what an alternating group is. Because of that, it's really hard to understand the theorems from 7.10.

Reflective:

I just find it interesting that we have a single-sentence theorem, and it takes 2 lemmas and 2 pages of textbook just to prove it. I really really hope we aren't expected to state & prove that :O

7.9, Due April 1

Difficult:

I don't understand why we would factor permutations down. Why would we care to write the identity permutation as (12)(12)? Why is every transposition it's own inverse? Does that mean every element has order 2?

Reflective:

I think it's cool that we are cutting down on the notation for symmetric groups, I'm just worried that I will get confused when I try to follow the composition through.

7.8, Due March 30

Difficult:

I think I am still confused on cyclic groups and generators of groups. When they say does that mean the set of elements generated by e? Wouldn't that be the whole group? Or is it just e because when you add(mult) e, you just keep getting e over and over?

Reflective:

I thought it was interesting that instead of the kernel being the set of things that are mapped to zero, it's the set of things that are mapped to the identity. In an additive group like Z, it would be the same thing, but in say the multiplicative group of units of Z8 it would be 1.