Section 2.2, due on September 8

One of the most difficult parts of the material for me was trying to understand their definition of addition and multiplication in the set of integers modulo n. Theorem 2.6 makes sense to me until I start thinking more about the discussion preceding it. If 1 is in B and 7 is in C, then B+C=8, so the equivalence class containing 8. Yet if -3 is in B and 15 is in C, then B+C=12, so the equivalence class containing 12. So I don't understand why 8 and 12 aren't in the same congruence class? I also find it difficult to remember which modulo we are in and adjust my arithmetic accordingly.

The most interesting part of the material for me was Theorem 2.7. These properties that are valid for the set of integers modulo n are very similar (probably the exact same) as the axioms that must be proved in Linear Algebra to show that something is a vector space. It is interesting to me to try and think how the set of integers modulo n and the concept of congruence classes will be used in future sections.