I feel like the most important things we have covered in this semester are the big topics. We have focused a lot on rings, ideal, and groups. I feel that these will be the main topics covered on the final, but the final will probably have more specific questions associated with them. I feel like through out the semester, most of the things we covered revolved around these topics.
The most difficult thing for me this semester has been quotient groups, rings, fields, and anything basically involving cosets. I just feel like I panic when I see R/I or G/N. I also feel like I never completely understood normal groups. But mostly its quotient stuff that I am really uncertain about. I would really like to see a problem involving quotient rings or groups. Something involving a ring modulo an ideal would be helpful. I just don't know what to do with these things when I see them in a problem.
In the future, I think this class will help me form more logical arguments. I have learned to not freak out when I see the word proof. Honestly it has given me more confidence in proving things, (especially since theory of analysis shot down any confidence I had from 290). For the most part, I think this class has helped me understand modular arithmetic really well. I didn't have much exposure to this before, so its is nice to feel confident in my ability to do modular arithmetic and actually understand what is going on.
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