Section 3.3 Part 3

Difficult: Especially on pages 118-119, when the sums are changing form over and over I get lost. I admit that I have a hard time fully follwing this part of the proofs. When we talk about them in class I can mainly see it, but not always, and that is what was the hardest in the proof.

Reflective: Theorem 3.3.7 seems very interesting to me. I would have never thought that there would be arithmetic progressions of length k. If possible I would love to see the proof some time during the class.

Section 3.3 Part 2

Difficult: I find that I have a hard time following the part of the proof, Lemma 3.3.8, where they go from the Dirichlet L-series to the Euler product representation. I don't get how the multiplication goes to summation. Does this relate back to something we did with Riemann zeta function?

Reflective: I still find it amazing that mathematicians thought up these proofs. They are so layered and complex, that it just blows my mind.

Section 3.6

Difficult: I didn't think there was much that was that hard to understand in this section. The math is all very simple, and for once I think the book actually described it rather well.

Reflective: I think it is interesting that we have these relations between various arithmetic functions. I am interested to see how this all plays out in the next section.

Section 3.3 First Half

Difficult: I didn't know what a root of unity was, so that made it harder to understand the proof. I looked it up and now can follow it, but it doesn't come the most intuitively.

Reflective: I think it is interesting that we have so much knowledge about the characters mod k. What I find the most interesting is how each proof is very straightforward and simple, nothing really that complex.

Section 3.2.5

Difficult: I got lost when they used Lemma 3.2.5.1 in their proof of the infinite primes. I guess that probably comes from the fact that I didn't understand the Lemma that clearly when I read it in the first place.

Reflective: Another proof. I am not sure what this tells us about the primes though, but I am sure that it adds something of value.

Section 3.2.4

Difficult: I find myself a little bit lost around the part of the proof here we show the existence of m'. I think I mostly follow it, but it is the most hazy part.

Reflective: I think it is interesting that we know the fewest number of terms to the k power we need to get every other term. This may not be very applicable, but to me it is a very interesting fact.

Section 3.2.2

Difficult: I got lost during the explanation of Fermat's two-square theorem. I could understand the first part, but when the began to add all the different functions I got lost as to what they were speaking about.

Reflective: I think it is very interesting that we have defined all the numbers that can be the sum of squares. I am also interested to see how the Dirichlet character and function will be used later.