1st question
Trying to choose which topics/theorems are important? I would assume all of them, but mostly rings, groups, ideals, quotient rings, quotient groups. Also, Lagrange's Theorem, Cauchy's Theorem, Division algorithm, polynomials, congruence classes.
2nd question
I need to understand the finite abelian groups and sylow theorems as well as direct products...basically chapter 8 is scary to me. A mathematical question: how do you compose k-cycles? I'm sure I did those wrong.
3rd question
The things I learned will most likely not be used directly after this semester. However, like any math course, this class has helped me become better at proving and thinking. Also, it has been interesting. So I will take from this course a greater appreciation for algebra and a sharpened intellect and ability to prove things--which I value very highly. It's been a good course, though tough at times.
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