Section 7.9 due April 1

What was most difficult?
Theorems 7.50 and 7.51 just seem a little vague, but I'm confident it will clear once I've done some exercises with them.

Reflection
I have been swamped with computer science lately, and it's made it way hard to attend class. When you have projects that are time intensive, or exams to study for (both of which have been constant the last week and a half, including 5 exams in one week(!), it comes down to, "study for this thing, or go to lecture?" and I feel bad about missing lecture. It also makes the homework much harder. I should be able to go tomorrow though, as things have let up in my other classes...CS is still busy though. *sigh*

Section 7.8, due march 30

What was most difficult?
It's hard to know...I read this too fast. I am so swamped with 17 credits and tests and assignments, and my job, that I keep putting these readings off until the last minute (or last five minutes). I can usually find something interesting, but not tonight...I need to be a bit more organized this last stretch, but it's hard with so much going on.

Reflection
Where is the Second Isomorphism Theorem for Groups?

Section 7.7, due March 28

What was most difficult?
The most difficult part of this is just trying to grasp it without having worked with it or seen it in lecture yet. I mean, what I'm really saying is, it's hard to know what will be difficult until I start playing around with it. You can tell by the time of writing that I don't have time to play around with it right now. I thought quotient rings were a bit annoying or difficult to understand--the hw problems were certainly harder--and I hope quotient groups aren't quite as bad.

Reflection
This doesn't seem too bad. We'll see how things go these next couple of days.

The rest of 7.6, due March 25

What was most difficult?
The bold print at the top of page 212 seemed a bit confusing at first, I didn't know what it meant by saying Na=aN does not imply an=na For all n in N. But the example right below cleared it up.

ReflectionJust glad the exam is over and that we are moving forward to the end of the semester!

Section 7.6, first part, due March 23

What was most difficult?
The most difficult part of this section was focusing! I'm finishing my preparations for the exam, so it's hard to be thinking of new material. I thought it would be difficult to deal with right and left cosets for these subgroups, but once I read the examples after the definition of normal subgroups, it seems pretty straightforward and manageable.

Reflection
The best thing about this section, was that it cleared up cosets for me. For some reason, I was struggling in the last section with the assignment. Using the definition as exactly as I thought it was written, I kept getting the wrong idea for cosets. This section made it totally clear.

Pre-exam writing, due March 21

What topics/theorems are most important?
I think quotient rings, ideals, and groups, especially congruence in those areas, are the most important concepts learned in class since the last exam.

What kind of questions do I expect to see?
Based on the last exam, I expect to see some conjectures that are either true or false, and require our justification. I also expect to see some proofs of some of the named theorems from class.

What do I need to work on understanding?
I really need to review things like cosets and cyclic subgroups.
A question: List all the cyclic subgroups of D_{4}
I had a hard time seeing how this definition fit in with this idea, because it seemed as though all the rotations in D_{4} can be done several times...there is something I'm not understanding about this definition.

Section 7.5 part 2, due March 18

What was most difficult?
Nothing was difficult in this section, at least I don't think so. I feel like it's really hard to judge this until I've done the problems, which doesn't happen yet because it's not due for two more class periods, as I'm working on 7.5 1st part right now. I'm having some difficulties in the previous section, namely with right cosets.

Reflection
I'm starting to feel more dumb, and less good at algebra as this class continues. It's probably a combination of being very busy, this material being totally new, feeling tired, and a little bit of senioritis.

Section 7.4, due March 14

What was most difficult?
The most difficult thing for me is cyclic
Groups, covered in 7.3, but referenced here in the context of
Isomorphism

Reflections
Not much to reflect on.I guess i usually
Find it fun to show somethng is an isomorphism, so i'm looking forward to the
homework assignmwent.

Section 7.3, due March 11

What was most difficult?
Theorem 7.15 has a confusing hypothesis....multiplicative group of nonzero elements of a field? Wolfram helped a bit, but it was just kind of wordy.

Reflection
I always enjoy it when we do the subspace, subring, subroup, etc. There are less axioms to prove!

Section 7.2, due March 9

What was most difficult?
The most difficult thing is just keeping things straight between rings and groups. Nothing too major, just gotta get the definitions down pat.

Reflection
I like dealing with groups much better than dealing with quotient rings!

Section 7.1, due March 4

What was most difficult?
Nothing was too difficult about this. It is pretty straightforward they way they are laying out the function as an array and composing it. Hopefully this gets easier to understand than the last bit about quotient rings and what not.

Reflection
Excited for a new section!

Section 6.3, due March 2

What was most difficult?
The most difficult thing right now is...everything. The text is getting less and less clear, or I'm getting more and more stupid. I think really though, it's just understanding why we are abstracting these things that is a bit unclear and makes it hard to grasp this. It was pretty clear in the earlier sections why were doing this abstraction...but things like maximal ideals? What is it for? I don't care if it's used in the "real world" how is it used in algebra?

Most Interesting
I think it's interesting that every maximal ideal in a commutative ring with identity is prime.