24.1-24.3, due on December 11

Difficult:
    I can't follow any of the given proofs.

Reflective:
    I think its interesting that all of these proofs come down to the fact that a sequence of integers that goes to zero in the limit must always be zero after some point.

22.3-22.4, due on December 9

Difficult:
    The instructions for calculating the Galois group of an arbitrary polynomial are absurd. You might as well crack RSA by factoring.

Reflective:
    I was most interested in the concept of the discriminant. Rather than doing a difficult process to find out exactly what the Galois group is, just rely a simple one to find out if it is in the alternating group or not.

22.1-22.2, due on December 6

Difficult:
    Learning the content wasn't so difficult, but I have no idea what motivated using phi and psi to calculate a Galois group.

Reflective:
    I find it interesting that a result that is supposed to be important and far reaching, namely the fundamental theorem of Galois theory, relies on such a difficult operation, namely finding Galois groups of polynomials, to be applied directly.

21.5-21.7, due on December 4

Difficult:
    The proofs in sections 21.5-21.6 all fit together nicely, but as was mentioned in class, they don't really imply theorem 21.3

Reflective:
    I find the table of cyclotomic polynomials in section 21.7 quite elegant. The fact that they all seem to have coefficients in the set {-1, 0, 1} is stated, but I find it interesting that they all seem to follow a simple pattern as well.

21.3-21.4, due on December 2

Difficult:
    I got lost at the end of the proof of theorem 21.2, most of page 243, specifically.

Reflective:
    It's not exactly clear to me how this result is so close to proving Galois theory; I do remember needing roots of unity, but how it leads to finding the rest is beyond me. Nevertheless, it is interesting that the history of mathematics could have taken a different turn if Vandermonde was more rigorous in his assertion that roots of unity had non-trivial radical expressions.

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.