12.2, due April 4

1. (difficult) While trying to understand the proofs for convergence of an infinite series, I am having a hard time grasping the concept of epsilon ad it's necessity in the proof. I am also very confused by the notation in the book. It is possible that it is a misprint, but on page 275 directly above the second Lemma 12.8 It has an almost bracket looking symbol around 1/epsilon. I don't have a clue what that means.
2. (reflective) I am realizing as I am trying to understand these proofs how integral an understanding of epsilon is, and I don't know what it means, nor can I glean any sort of understanding from the text. All I know about it is that it is crucial to these proofs.

12.1, due April 2

1. (difficult) The proofs for divergence or convergence are difficult to follow, with many cases and new assumptions.
2. (reflective) Most of the work on these proofs is done in the proof strategy -  the proofs are relatively short. It seems like if you have a good strategy, you won't need to have a long proof.

Questions, due March 31

1. Schroder-Bernstein theorem, continuum hypothesis, division algorithm, euclidean algorithm
2. Gcd questions, comparing cardinality, Denumerability, and infinite sets.
3. Questions like 10.19.

11.5-11.6, due March 28

1. (difficult) It is hard for me to think abstractly about the relatively prime numbers that are introduced here I needed to come up with real examples on my own in order to make sense of the proofs.
2. (reflective) I used to always wonder why the greatest mathematicians loved prime numbers so much, and with the work we keep doing, I can see how these prime numbers are really the building blocks of factorization and many other theorems we are studying.

11.1-11.2, due March 24

1. (difficult) The only difficult part I had was in following the proof of the division Algorithm. I first struggled when the book introduced the value t=r-a, but after some careful looking and reading I understood that. The one spot that I still do not understand is the introduction of, characteristics of , and manipulation of the variables r' and q'.
2. (reflective) I thought it was nice to finally come back and expand on the understandings that we have gained about the integers being able to be described as 2x, or 2x+1, or further as one of the following: 3x, 3x+1, 3x+2. It only makes sense that we come to understand all numbers as being written as aq+r where r<q.

10.4, due March 17

1. (difficult) The gravity of the continuum hypothesis has not hit me yet, and it seems like a statement that says "well, duh."
2. (reflective) It is really interesting that the cardinality of a denumerable set is defined as a letter of the Hebrew alphabet. With mathematics begin mainly written in Greek symbols, I wonder how aleph has survived as being a standard symbol. I'm sure at some point the mathematicians would run out of Greek letters and symbols to use, but Hebrew is a surprising alternative.

10.2, due March 12

1. (difficult) A lot of this section was difficult to understand, beginning with the ideas of Countably infinite, uncountable, and denumerable. The book never explicitly says that these are the same thing, but from what I can tell from the reading, they are. Also, the proof of the theorem "Every infinite subset of a denumerable set is denumerable" is two pages long and very hard to follow.
2. (reflective) I am not quite sure of what use it is to know that a set is denumerable or uncountable. No purpose was given in the text, and I have a hard time finding one on my own. Since I am very tied to practical applications, this may be a difficult concept for me to grasp.