I'm having difficulty when there are discussions about equivalence classes. I think I need to spend more time or attention to them. I did not really understand the addition and multiplication table for Z sub 6. It seems to have something to do with remainders when you add or multiply. That is all I can gather for now and I'm thinking about what the point must be. Then, it went on to talk about the sums or products of two equivalence classes as being well-defined. This also wasn't entirely clear, although the proof of Theorem 8.9 generally made sense from a technical standpoint
I found the following interesting: "If you have more mathematics in your future, it is likely that you will see the equivalence relation we are about to describe again – indeed often." Honestly, before this class I hadn't even heard about Congruence Modulo n. It sounds like it is a noteworthy topic in mathematics and I've appreciated learning about it and all of its properties; however, I am surprised that I hadn't learned really anything about it before now, despite taking math every year in all my years of schooling. Kind of funny, really.
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