4.5, due on June 1

(difficult)
The two or three proofs after Lagrange's theorem were difficult.

(reflective)
So groups now have the congruence relation. It will be interesting to see what will be the next level of abstraction.

7.3-7.4, due on May 27

(difficult)
Homomorphisms, isomorphisms were the most difficult parts for me. Switching back and forth between additive and multiplicative groups. Those funny groups formed by
(reflective)
It's interesting to see the tie in from rings to groups. There was the discussion in class of the optimal way to approach the course. I wonder if, in other books, rings are treated like special groups. Obviously, rings require additional and more complex axioms. But perhaps group theory is richer, and so deserves to be treated second?

6.1, due on May 18

(difficult)
All very similar theorems and definitions, so maybe the intuition is the hard part. Some examples would probably be helpful. Also, if we have time, more talk on 5.3 would be welcome.

(reflective)
Generalizations are nice. It will be interesting to see where this goes.

5.1-5.3, due on May 16

(difficult)
The author stated several times the grand significance and subtlety of the results of these sections; I struggled to understand the implications. Some help flushing them out would be nice. It seems the example of the equivalence between the complex numbers and R/(x^2 + 1) is instructive.

(reflective)
Again, the author said these results are profound, and I'd like to appreciate more fully what he intends. The definition he gives for the complex numbers is intriguing.

4.3-4.4, due on May 13

(difficult)
The proof of theorem 4.11 seemed difficult (even though it's analogous to a theorem in ch 1). It seems like the difficulty of the proofs increased in this section.

(reflective)
I thought the method of dividing f by (x-a) to find f(a) (in 4.4) was very interesting. I suppose we may use this property again when we talk about more general rings.

Apdx G, 4.1-4.2, due May 11

(difficult)
It would be useful to work through the definition of multiplication in R[x]. I've had a hard time with it before.

(reflective)
The author talks about x like we've been using it incorrectly this whole time. I suppose this viewpoint indicates a way in which algebraists view mathematics differently from other mathematicians. Or perhaps I don't understand how other mathematicians view it.

3.3, due May 9

(Difficult)
It seems like the proofs at the end of the section will be the most difficult, conceptually. These are finding a homomorphism, proving there is an isomorphism, proving two rings are not isomorphic, etc.

(reflective)
I can never seem to remember what an iso- or homomorphism is. I'm happy to see it another time. Also, proving a function is one-to-one and onto is very useful