3.1 Part 1

1. What was the most difficult part of the material for you?
Oh man, I can tell that we're about to venture into something pretty darn complicated. You can tell just by the set up that this is headed somewhere scary. The thing that is the most difficult is being able to remember the different axioms and which part of the definitions they belong to. I feel worried that I won't be able to just look at something and know that it is a "ring," a "commutative ring" or a "ring with identity". I know that I'll probably have to write down the different axioms, similar to what's in the book, and just work off of that until I get the hang of things, but I guess I'll just wait until that homework assignment to know for sure.

2. How are you going to keep it straight?
Because I'm nervous about venturing into this unknown world or 'rings' and whatever, I've really been trying to read things carefully, and, on my own, think of examples/counter examples to what they are talking about. For example, as I was reading and they were talking about the set E (even numbers) and how it was a commutative ring, I stopped a moment and asked, "would the set of odd numbers also be a ring?" and doing this helped me kind of run through the axioms and stuff. I also asked, "would this be a ring with identity" before the book even talked about it! (yea me!) and knew it couldn't be, because 1 is odd. Similarly, before the book even mentioned matrices, I asked myself about what would be a ring but not a commutative ring, and instantly I thought about how most matrices are not commutative. So, I felt excited when the book later talked about it. So, the moral of the story is: the best way to keep things straight is to ask yourself a lot of questions, and not move on until you know the answer. You know?