Final Exam Questions, due on Wednesday, April 13

1. Which topics and theorems do you think are important out of those we have studied?
I think the following items are important: the Cauchy theorem, cyclic groups, normal subgroups, quotient groups, other types of groups: symmetric, alternating, simple, abelian, finite abelian, etc.

2. What do you need to work on understanding better before the exam? Come up with a mathematical question you would like to see answered or a problem you would like to see worked out in class on Wednesday.
I am still confused about things that deal with quotient groups, cyclic groups, and direct products. These are the three things that have not sunk in yet. I still do not know how to create cyclic groups, and I do not know how to apply quotient groups, and I do not know how to figure out direct products. Any problem that deals with one of these three questions would be nice to see on Wednesday. Like an example of writing a direct sum/product of certain groups would be nice to see on Wednesday.

3. How do you think the things you learned in this course might be useful to you in the future?
I do not think I am going to take any of the theorems or properties we have learned in this class in my future for teaching mathematics to middle school students. However, I do think I can take a more non-literal approach with what I have learned in this class and apply it in my future. I have learned how to work really hard, and I have developed my ability to analyze and think about problems and create my own proof. This class has taught me to really think about mathematics and construct mathematical ideas on my own. And I will be able to use these things that I have learned in my future with harder classes that might come my way and for when I am trying to get my future math students to construct their own proofs and properties for mathematics.