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.

12.4-12.5, due April 9

Difficult: The more difficult part of this reading was section 12.4. I am having difficulty with this section with understanding the different proofs behind the theorems. I can understand a little bit more how to apply these theorems for different types of math problems, however, I have some trouble with the breakdown behind the logic of how these theorems have been proved and how they have been constructed.

Reflective: My favorite part of this reading was section 12.5 about continuity. I liked this best because I remember learning this term and its definition in other math classes such as calculus. I think that it is fairly easy to understand, especially when put in the simple terms as "can you draw the graph without lifting up your pencil?".

12.3, due April 6

Difficult: I did not understand the part about having a deleted neighborhood. I did not understand what this referred to and what exactly it meant. I am assuming that it has to do with finding limits, but other than that I do not know anything about them.

Reflective: The part of this section of reading that I thought was the easiest was the discussion on Limits. I thought that this was relatively easy to understand after having taken calculus and other math classes where I have worked with limits before.

12.1, due April 4

Difficult: I did not really find any specific parts of this reading all that difficult to understand since I have taken calculus before. If I did have to pick though I would probably go with the terms converge and diverge. I remember learning about these and it being very simple, however, I would like to go over them again to be sure that I completely understand them.

Reflective: My favorite part of this section was the discussion of the concept of ceilings. There is nothing really all that special about them per se, however I just remember really liking them when I did calculus. I would however like to know if there is any particular reason that you would want to use a ceiling for a result, or if it is just a preference thing.