Assignment 3: Section 2.1

Difficult: I read this section carefully, trying to capture each idea. I have learned these concepts before, but they were extremely difficult for me the first time. It is refreshing to learn them again! I think the hardest part of the material for me to understand is the meaning of modular arithmetic. After taking a few classes that have used it, I have become much more comfortable with it. However, I want to understand why we do modular arithmetic--what is advantageous about modular arithmetic? If I understand modular arithmetic, how will this help me be a better math teacher? How will it allow me to access further mathematical knowledge? Is this a key element in the foundation of abstract algebra?

Reflective: For me, the most interesting parts of this chapter were the theorems about congruence classes and their relationship to the set Z(n) and congruence mod n. It is interesting to me that there are n congruence classes from [0] to [n - 1]. When we start to experiment and use modular arithmetic, the fact that there are n congruence classes starts to make a lot of sense. I want to better understand the congruence classes because I think it will help me to better understand numbers and their relationship to each other. I want to be able to recognize the relationships between numbers more quickly. Understanding modular arithmetic and congruence classes will help me to do so.