I think that the most important topics we have studied have been rings and groups. Within rings, we focused on congruence modulo n, congruence classes, polynomial arithmetic, and ideals. These are the main topics that we have covered, and they are the most important. Theorems that are important are the theorems that involve ring properties, subrings, and fields.
On the exam, I expect to see questions that test my knowledge on rings and fields, basic group properties that we have learned, proving that a set is a ring, group, field, or integral domain, isomorphisms, giving examples of different rings and groups, and proving that a subset is actually a subring or a subgroup.
For the exam, I need to study more examples of all different types of rings, fields, and groups. I also need to make sure I know the definitions in the book and that were emphasized in class. Some concepts I have trouble with are how to prove that two rings or groups are isomorphic, what a cyclic group is, and ideals and cyclic groups generated by a finite number of elements.
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