Post due on October 3rd

I think understanding strict mathematical definitions of basic operations has been very useful and helpful. Modular division has been a new and very useful concept (particularly in our programming). Also the definition of divisors has been a great in thinking about integer relationships. One funny thing is I remember learning about remainders in 3rd grade and then never using that ever again. I just thought it was some kind of unsophisticated way to think about division before introducing decimal expansions and fractions, but now to use remainders as a way to categorize integers has finally made that little piece of math so useful!

On the exam I'm expecting true or false questions that test our understanding of basic definitions and operations, some free response questions that are similar to the homework problems, and then maybe one or two questions that are supposed to stretch our understanding.

I think seeing some examples of proofs of existence (dealing with irrational and rational integers) would be useful. Also, set congruence proofs would be useful. I understand how to outline them, but filling in the gaps of a subset proof seems a little vague to me.