1. The most difficult part of the material was the material itself. I have seen these theorems numerous times in the past, but I have not been asked to rigorously prove them before. I am finding that it took me like 20min just to try to understand the Division Algorithm. However, I know understanding the material will just take time and practice. I don't think I fully understand any of the theorems... yet. But I will work on it! One thing that I did not understand about the division algorithm, for example, is why a-b(q+1)=r-b....
2. I am actually very excited to learn to prove such theorems rigorously! As I said above, I have seen these theorems (division and euclidean algorithms, and greatest common divisors) in many of my math courses, but I never quite understood the rigorous mathematics behind them. I have always wanted to learn how. Having a solid understanding of the proofs will greatly help me in my future math courses, and additionally as I end up teaching some day. The most interesting part of the material was in the section about greatest common divisors where it talks about the gcd being a linear combination of (a,b). I have never thought about it that way before.
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