1.1-1.3, due on January 6

Part I : What was the most difficult part of the material for you?


     The end of 1.2 was the most difficult part of the material for me. I was definitely getting lost in all the equations and the implications and theories, but at the end of 1.2 I was confused about Theroem 1.6 The Euclidean Algorithm. I am still a bit confused on it. I understood it well in class but reading the actual statement of the theorem doesn't make sense to me with how the book writes it out. I am mostly confused with the second sentence which states, "If b|a, then (a,b)=b." I am confused because I can think of an example such as 3|27 but (3,27)=9 not 3. This also satisfies the first statement which is that a and b are positive integers with a>b or a=b, and in my example 27 > 3. So I just don't understand that statement.


Part II: Write something reflective about the reading.

     I think the most interesting part is the proof for Theorem 1.11 The Fundamental Theorem of Arithmetic. I liked it because it looks long and complicated but it makes complete sense. I also feel like it will lead into a lot of important proofs in the future so it seems like this is an important theorem and proof to remember and memorize. This whole section of reading goes into the idea of number theory which really fascinates me, but I guess the ending just had a good punch to it.