due April 11

I think that the most important topics and theorems that we have studied are the different kinds of proofs that we can use (direct, contrapositive, contradiction), the Principle of Mathematical Induction (SPMI as well), Equivalence relations/classes, bijective functions, and the Schroder-Bernstein Theorem.

I think that I need to understand chapters ten and eleven more before the final exam. I don't think I understand very well the different ideas and logic behind the uncountable proofs among most of the other materials in chapter eleven. I thought that I did well on the midterm which covered these chapters as I was going through the problems, I felt like I understood them. However, my score was the lowest out of all three midterms. So I would like to spend most of my time reviewing these principles and ideas.

The problem that I would like to see worked out would be one like 21 on the last exam where we needed to prove that the square of every odd integer is of the form 8k+1, for some integer k.

For this course, I have made some connections with previous theorems and logic that I have been taught in other math classes but never went into the details that made up the proof. However, now I think as I continue to take math classes I will be able to see connections with future theorems that I learn and be able to hopefully understand them better than I would have without having taken this class. Therefore, I hopefully will be able to apply them more effectively to problems I am given.