Preparation for Final Exam, Due on April 15

For the final exam, there is so much to choose from as far as topics and theorems go.  It is comprehensive, so we could really see anything that we've studied all semester.  I think that the most important topics are the following, in no particular order:

1. Sets and subsets
2. Set operations
3. Proofs: direct, contrapositive, and contradiction
4. Equivalence classes
5. Relations: reflexive, symmetric, and transitive
6. Functions: injective, surjective, bijective
7. Sets: denumerable, countable, uncountable
8. Linear combinations and the division algorithm

I feel like the class was well-organized, with principles learned at the end of the semester having been effectively built on a foundation of what was learned earlier.  When I look back at the semester, I think that I need to work on many things to better understand the material.  I have read all of the readings and am familiar with the material, but I just don't know it enough to perform well on tests.  I think that I really need to practice, no matter how time-consuming that may be, many sample problems.  Especially the proofs.  I need a variety of sample problems and I need to be able to work them out on my own without study aids.

I know there are study guides for the first three exams, but they don't include the last chapter we studied.  Perhaps I'd like to see a sample problem of a typical calculus proof that might appear on a final exam, if possible.

In this course, I have learned a lot.  The material was interesting, for the most part, and the professor was really great.  Rather than list specific mathematical topics that I learned, I can say that, overall, I learned that I am not as strong at mathematics as I thought or I hoped I would be.  For some strange reason, the material never made a permanent dwelling place in my mind.  It would visit, stay awhile, and then leave.  There are many bright mathematical minds and I really look up to the teacher and some of my classmates for how they just "get it" so well.  So, I guess what I'm trying to say is that I learned that I didn't easily "get it" in this class and I've come to be okay with it.  This will help me as I modify my future academic and career paths.

Sincere thanks for the good class!