1.1-1.3, due January 7

1. Difficult: The hardest thing for me in this entire class is going to be proofs. I already know that. I often have a hard time knowing where to start, what theorems to use, etc. The hardest part for me in this specific section was a) the uniqueness part of the division algorithm proof, and b) The proof of theorem 1.8. The concepts themselves make sense to me, but the way the proof is worded is hard. I have a hard time following the logic. The division algorithm proof is a beast, and it doesn't help that I've seen it proved many different ways. After a minute my eyes just glaze over. And I had to read theorem 1.8 a few times before I had some idea what it was saying. It seems like a simple enough concept, but the way the book has worked through the proof is making it really hard for me to grasp it. I don't know how crucial either of these theorem proofs are to future exercises, but I hope they're not too heavily used.
2. Reflective: I LOVE THE EUCLIDIAN ALGORITHM! I remember that when we were introduced to this in math 290 I got so excited! Finally! Something that was computational! I also love the way it's kind of like a puzzle, with all the numbers shifting around, and how you can solve it backwards to find the linear combination. That's just plain cool! However, the EA can get a little messy when you get up to huge numbers without a calculator. WITH a calculator it makes finding the GCD of big numbers infinitely times easier than the grade-school way of listing out all the factors of both numbers.