2.1

1.What was the most difficult part of the material for you?
I feel like doing Congruence and Modular Arithmatic is like speaking Spanish for me. I understand the rules of Spanish, I can speak it and understand a lot of it (I served a Spanish speaking mission), but it takes me a little longer than speaking and listening to English. I understand this section, but when it comes to doing these types of problems, I feel like I have to take a little extra time to write the congruence whatever into the equation that I can understand a little better. Also, the 'classes' aren't completely clear to me. Again, I kind of understand what they are, but it takes me a little extra time to process the problems. I think it will be helpful to talk about this stuff at the beginning of the semester so hopefully I can see why this concept is useful at all, because I still don't get it.

2. A little more clear this time around....
The last (and first) time I learned about these modulo things I struggled understanding what was going on. Reading though this section, I was able to visualize things a little. For example, for mod3, I imagined a long number line where starting at zero there was a mark for every number that was a multiple of 3. (...,-6,-3,0,3,6,....). Then, if I think of [2] in congruence modulo 3, I imagine those same intervals of 3 shifted to the left 2 numbers (...,-4,-1,2,5,8...) which is why [2]=[-1] in congruence modulo 3. Does that make sense? It makes sense to me.