I think that the First Isomorphism Theorem for rings is one of the most important things we have learned (because it was stated in class that the proof essentially used all the skills we have learned). I also think that knowing all of the definitions is going to be huge. I would expect (if the test is formatted similarly to exam 1) that there will be five or so definitions probably about kernels, maximal ideals, principal ideals, homomorphism/isomorphism of rings, and quotient rings; five or so questions asking examples of ideals that are non-prime and maximal, some type of polynomial, examples of fields that properly contain the rations and reals, and rings with some special property of their quotient ring; two or three questions that use a lot of the theorems to prove and a the proof of the First Isomorphism Theorem for rings.
In addition to wanting to see numbers 4, 5, 7, and 9 from the practice exam (or all of them if you are so inclined), I would also mainly like to see examples of every variety of thing we have covered. I know this is an unrealistic request but I think the reason why I don't understand what we are learning is because I don't have enough examples to understand the definitions from and I am a learner by following examples.
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