December 7, 2016

Difficult: So do alternating groups A_n have order 3n?
Reflective: Corollary 8.28 could have been helpful on the last homework.  And 8.31.

I think any named theorem is important out of what we've studied.  I also think general knowledge of rings, groups and quotient rings/groups are fundamental to whatever will show up on the test.

I need work on polynomial rings in general.  Like the proof of Theorem 5.11 would be great.  I don't see any sample problems including polynomials (which I like), but if you're planning on sneaking one in, I'd like to see a similar example :).

In this course I learned how to do mathematical proofs.  To be honest, I probably won't use this much after I graduate next week, but it has helped me stop feeling like I was a complete failure as a math major.  I thought I would go my entire college career and not figure out what every math major is expected to be good at, and I felt so defeated.  But I finally became able to do it this semester, and this class helped immensely.  I can now proudly say I graduated in Math instead of feeling like I just scraped by the entire time.  So that's pretty huge.

November 16, 2016

Difficult: I'm not quite sure what the difference is between what a normal subgroup is (Na=aN) and what it is not (na=an for all n in N).
Reflective: You're right.  That theorem 7.34 is super helpful!  That's a lot easier than going through and showing kind of commutativity every single time.

November 11, 2016

Reflective: It's interesting that we pretty much are doing the same things over and over again.
Difficult: Which makes it more interesting that it gets weirder and harder every time we do it. I'm going to need general explaining of this one.

November 9, 2016

Difficult: Can we go over coming up with factoring permutations?
Reflective: Theorem 7.47 is kind of like how numbers/polynomials can be written as products of primes/irreducibles, except for uniqueness.

November 7, 2016

Difficult: What do they mean by a symmetric group S_n?
Reflective: I think theorem 7.18 is really neat. Like that just works out way too nicely.

November 4, 2016

Difficult: I need help with cyclic groups/subgroups in general.  More examples, more explanation.
Reflective: I love this whole "you only need to check two things to see if a ring/group is a sub-ring/group" thing.

November 2, 2016

Difficult: I don't really get Corollary 7.9.
Reflective: The order of element rules are quite like idempotency.  Is that significant?  Related?