1.1-1.3

1. What was the most difficult part of the material for you?
Well, this reading assignment was probably easier than any future assignment we'll have, since 2/3 of it was already covered in class. Also, it seemed pretty basic because it was the first reading. However, as someone who just managed to not fail Theory of Analysis and is pretty nervous about this class, I will point out what I think will be difficult for me from here on out. I, like a lot of people, really don't like proofs. I imagine that the proofs will be the hardest thing for me in this class, and the reason why I find them difficult is that they are so darn imaginative. As I was reading these sections, and after Wednesdays class, I just kept thinking to myself, "Who would think to do it that way?!?"

 For example, Theorem 1.11 just seems so basic to me. Of course every number is prime or made up of a unique combination of primes. And, as I follow the book it all makes sense, but I don't think I would ever think to write that proof using a contradiction (mostly because I am afraid of contradiction proofs).

The creativity astounds and intimidates me. Sure, when a proof is shown to me I can usually follow it, but I am so bad at thinking of them on my own. Even if I think I might have a good idea to write a proof, I get very intimidated by the wording of it, and usually mess it up in that way. So, I think that is what is going to be hard for me with this material in the future. Being intelligent and creative enough to be able to write reasonable proofs.

2. What can I do to overcome my Creative Proof Shortcoming (CPS)?
My best friend is in a basic algebra class at UVU and was asking me for help with proof by induction. I always try to help when I can, and was nervous when he asked me to help him with proofs. However, I remembered something about proof by induction that I shared with him. I remember sitting down with him and saying, "Okay, write what you know," which was usually your basic n formula. Then I told him to write what he wanted his equation to look like at the end (the n+1 formula). Then, I explained to him that the trick was to get from the n formula to the n+1 formula using only what you know to be true. I told him that the key was that you can't look at that as a 'restriction' but rather as a guideline showing you how to write the proof. Since the n formula was given, I explained that he would definitely be using THAT formula somewhere in the proof, and it would usually be somewhere in the middle. The hypothesis wasn't restricting him, it was pretty much giving him the answer. I realize that this is very similar to how I need to be thinking to be successful at writing proofs. Not that it will always be as easy as induction proofs, but hypotheses (?) are worded very carefully, and if I actually use the information given, getting from point A to point B should be easier, because the tools are usually given, you just have to put them in the right place. So, whenever I get stuck, I will do the same thing and ask, "Where am I? Where do I want to go? And what have they already given to me to get me there?"