21.1-21.2, due on November 26

Difficult:
    Ironically, I understood everything that was going on until they starting including Galois groups, at which point I became entirely lost.

Reflective:
    I did not expect it to be so easy (relatively speaking) to find a meaningful radical expression for non-real n-th roots of unity.

20.1.-20.2, due on November 25

Difficult:
    The corollaries in section 20.2 were straight forward, but I couldn't follow the group exponent stuff before it. I also had trouble following theorem 20.2. What did they mean let p=p^n? how can you just say that?

Reflective:
    I find it interesting that the classification of finite fields is so simple. Perhaps there is more interesting structure in the non-commutative case, but it's surprising how few conditions you need to severely limit the structure of what remains.

18.4-18.5, due on November 22

Difficult:
    I was lost for all of 18.4

Reflective:
    It was interesting that every formula for finding roots is based on symmetries of the said roots.

Exam 2 Prep, due on November 18

Important:
    I think the most important bit is the Fundamental Theorem of Galois Theory, and how it is different in the complex numbers than in general fields, although we didn't quite finish the general case.

Expected:
   I expect a lot of finding Galois groups and proving solvability and finding normal subgroups.

Needed:
    I need a better grip on the content of FToGT, as well as the important lemmas that surround it.

17.5-17.6, due on November 15

Difficult:
    The Frobenius map made sense. Everything afterwards that relied on it did not.

Reflective:
    I am glad that the Frobenius map is the only way to mess up separability for fields. I bet it's a lot worse with non-commutative rings.

17.1-17.4, due on November 13

Difficult:
    I read the sections, but I couldn't get anything from 17.2 or 17.3 to stick.

Reflective:
    I at first found it strange that learning math from a book would be so much harder than from a teacher, until I realized that there are at least three qualities that teachers have that makes them superior to books. Teachers can respond to a lack of knowledge if you ask, they can perceive missing knowledge when you do not, and they force you to slow down enough to comprehend all of the material.

16.3-16.5, due on November 11

Difficult:
    The notation used for theorem 16.9 threw me a bit, making it hard to follow. Also, the proof for lemma 16.11 seems less than adequate.

Reflective:
    It almost feels more natural to be in general rings and fields than to be in C or Q, now that I'm a little further into it. I suppose the rigor of 371 made it so for me.

16.1-16.2, due on November 8

Difficult:
    This was all basically review from 371, so nothing too hard here. I was momentary confused by axiom M1, until I saw the note that greater generality was not necessary in this context. I didn't remember ideals from 371, but they were adequately defined here.

Reflective:
    I am worried about generalizing Galois theory to more general fields, as I have not fully internalized the theorems from chapter 12, and the added complexity of a need for separability will not help my case.

15.2-15.3, due on November 6

Difficult:
    There wasn't really anything difficult in these sections. All the hard work was in the lead up to this. I suppose if I must put something, I don't understand the point of writing all this down, as I learn so readily in the classroom, and so slowly on my own.

Reflective:
    I would be more impressed by Klein's unification achievement if I hadn't already heard of it in a previous book I read on group theory.

15.1, due on November 4

Difficult:
    I didn't quite follow the logic of the proof for lemma 15.4, where they say that the auto-morphism tau implies that beta-ij is radical. Also, I got lost in the proof of lemma 15.7, and the proof of theorem 15.3 wasn't terribly easy either

Reflective:
    I found the definition of a radical extension very pleasant for some reason. I guess I just enjoy seeing a intuitive concept reduced to a concise symbolic expression.