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.

Section 3.2-3.2.1

Difficult: The infinite descent proof confused me. Someone the transitions seem hand wavy to me. I can mostly follow the in between steps, but it doesn't come together as I was expecting.

Reflective: I don't really know what to say. I am interested to see where this is going, but I don't yet see why this is going to apply to the infinitude of primes.

Section 3.1.5

Difficult: I got lost on the proof of Lemma 3.1.5.5. It just keeps going and I don't think I get the very first part quite well enough to follow it through. I also don't understand why in Lemma 3.1.5.1 we need primes that are congruent to 1 mod 4 in the first part.

Reflective: It is interesting to see some proofs of specific cases, but I would rather just get straight into seeing the main proof.

Rest of Section 1.3.4

Difficult: Some of the proofs of the Fibonacci numbers leave me confused. They treat some of the inductive steps of the Fibonacci numbers as obvious, but I am not seeing them.

Reflective: It was interesting to see all the various properties of the Fibonacci numbers. Some seem pretty obvious, but others were pretty crazy. I am surprised that there is so much interesting about them.

Section 3.1.4 through Page 72

Difficult: The most difficult part was just remembering all the various geometric rules. I havn't dealt with many of them in a long time, so I was rather hazy on some of them. Other than that it was pretty interesting.

Reflective: I found it rather cool to see how easy it was to draw a line with length equal to the golden number, even though it is irrational.

Section 3.1.3

Difficult: I got lost on the proof of Euler's theorem on the relation of perfect numbers to Mersenne primes. I don't understand how we can directly state the value of the sum of the factors of u.

Reflective: I didn't know that perfect numbers had any way to directly calculate them. I guess they still don't since Mersenne primes don't either, but it is still interesting to see this relationship. I wonder what this means in a larger picture sense.

Section 3.1.2

Difficult: All of it was pretty hard to follow, but the worst was the Riemann zeta function. I just had a hard time on the second page of its description.

Reflective: Analytic proofs are an interesting difference to most of the proofs we have been doing, but I have to admit they are much more confusing for me.