I feel like the most important thing that we have covered so far this semester is rings. There are so many different kinds, and I feel like a lot of the stuff we have learned since learning about rings involves rings, or integral domains, or fields. So knowing the definitions and how to use these things is very fundamental. Maybe that is why I think they are so important; because I don't really understand them that well, or how and when to apply them. Something that I think is important and that I will need to study a lot is the theorems about rings, fields, and integral domains. I need to know these theorems really well so that I will know when they will be useful to me on a problem.
I expect that on the exam, there will be questions involving definitions, maybe fill in the blank or something. I also think that there will be a lot of questions asking for examples of different things we have talked about in class. I think there will also be many proofs. The proofs are what make me the most nervous. I have a hard time understanding where to begin with most proofs, but once I can understand what the question is asking, I can usually figure out how to go about proving it. I also expect that there will probably be lots of questions that are similar to homework questions.
Basically, I think I need to work on understanding the past couple of chapters. I did fine with modular arithmetic and integers, but rings, and isomorphism stuff got really confusing for me. I have had a really hard time understanding what it is talking about and how to apply that to a proof or problem. I need to work on homework from these chapters and learning the theorems to be able to use them on the exam.
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