Well the midterm went very well... lots of concepts which were familiar from the past midterm and the course as a whole. So I must have listened well in class.
We're moving into more detailed proofs now, which is fun (for now). I'm a problem-solver, so I like looking at the problem and the solution and trying to mash them together. The technique of "work-from-the-end" is one I've often used in the past, and I'm glad to see that going backwards is still useful when confronted with two seemingly different functions to be reconciled.
I enjoy the notion of using contrapositives and negation to work through a problem. In class today we worked towards proving a statement was a contradiction in order to prove its negation. Useful stuff - Euclid apparently thought so at any rate.
I'm curious about how else we can play around with that sort of thing. The converse doesn't seem to have much value at first in my head, aside from the possibility that, if the converse and the statement are true, then the statement is an "iff statement." But that doesn't seem all that helpful in most scenarios. More musing will be necessary.
I'm impressed with the course, overall. I did some logic in high school and found it a bit annoyingly anal after a while, but I guess I'm more comfortable with dealing with incredibly anal systems. Probably thanks to computer science.
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