The most difficult thing in these two sections, for me, was Einstein's Criterion (Theorem 4.23) and its proof.
I was very interested to learn the proof of the Rational Root Theorem. I have used it a lot in various math classes and while tutoring in the math lab. It is nice to learn where it comes from.
Questions about Reviewing for the test:
Which topics and theorems do you think are most important out of those we have studied? The Division Algorithm, Rings and their properties, isomorphisms and homomorphisms
What kinds of questions do you expect to see on the exam? I expect to see problems asking if sets are rings, if two rings are isomorphic or homomorphic to eachother, proofs about divisiblity, factoring and dividing polynomials, functions induced by polynomials, etc.
What do you need to work on understanding better before the exam? I need to read through my notes and study the proofs listed on the review sheet. I also should go over the properties of rings, fields, and integral domains.
I would like to see this problem worked out: If there exists a ring isomorphism A
B we write A = B. Prove that = is an equivalence relation
on the class of all rings. .
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