Section 1.1-1.3, due on September 1

Some of the more difficult parts of the material for me included the proof of the division algorithm. Towards the end of the proof when we are showing that q and r are unique (bottom of pg. 5) I am still a little confused as to why we can just add those two inequalities to further the proof.

The other difficult parts of the material for me were convincing myself that the theorems and lemmas actually worked, and understanding what they were actually saying at the same time. For example, Lemma 1.7 took me awhile to process what was actually going on. I also found it difficult to follow the Euclidean Algorithm and recognize the pattern, keep track of all the subscripts, and retain what it was saying. In general, as equations are written in different forms and we say x divides y and so on, it is difficult for me to keep track of what is the dividend and what is the divisor.

While this material was the most difficult for me, I also found parts of it to be the most interesting. I really think Lemma 1.7 is cool as it basically states that the g.c.d. of a dividend and a divisor is the same as the g.c.d. of the divisor and the remainder. This was a really interesting pattern to me. I also found it interesting how Theorem 1.5 and 1.8 related in that they were both provide specific cases which answer the question: If a divides bc under what conditions is it true that a divides b or a divides c?