Questions, Due April 11, 2012

Honestly, I feel that all the theorems that we need to know for the final are the most important. :) But written below is a theorem that I feel is important, but I am not exactly sure why. I can tell that if I understand this theorem better than a lot of other things will make much more sense to me, like quotient rings and groups for example. Anything dealing with those I feel is just very difficult for me for some reason, I do not know why.

• Theorem: If R is a commutative ring with identity and I is an ideal of R, then R/I is an integral domain if and only if I is a prime ideal. 

The general topics of the different kinds of rings and groups I think would be good topics to know. 

Any past homework question relating to A(n) is something that I need to understand how to do because I am not even sure what A(n) is. How do I even go about finding it? 

If there is one thing that this course has taught me I think it would be the importance of being exact, precise, and disciplined. There is great power that comes from exactness, and I think I am just starting to understand it, because it is a hard thing to learn how to always do. Also I have learned better how to problem solve and look at problem from the inside out, step by step, instead of the whole mountain at once. And of course this class has taught me patience. Patience in myself, my work and in those around me.