October 11th 2014 (Week 5)

    In this week, we did some work on proofs. In my calculus class (MAT137), we have been doing proofs for around two weeks, so the concept of proofs was not new to me. In fact, the proofs in this class are considerably easier than the ones we have been doing in calculus, so I may or may not have been paying attention for a majority of the last couple lectures...
    That being said, I noticed that there is a special format for proofs that we use in this course, which may be my biggest problem, as I tend to just scribble down a bunch of messy rough work and call that "proof." When I realize how to prove something, I get carried away and once I complete the algebra or whatever chain of implications I need, and by the time I complete that, I lose interest in the problem since I have already "solved" it in my mind. Figuring out problems can be fun, but putting it into a format that others can understand? That's just cruel.
    For example, in trying to prove "for all natural numbers n, if n^2 is even, then n is even," I do the algebra and call it a day. Did I realize that it would be easier to prove the contrapositive? Nope, I just see some numbers and start doing things to those numbers until I get what I want. Perhaps I need to reconsider my problem solving strategies.