This week, I believe we've finished going through all the different types of proof structures, and boy are they hard to remember. Most recently, we finished proofs by cases which I found interesting, since it felt very un-intuitive to use, however still very useful once I understood that the cases must cover all possible scenarios. Imaging proving a integer relationship, you'd be making an infinite amount of cases!
Anyhow, this course has just gotten very interesting, now we're on algorithm analysis and asymptotic notation. With algorithm analysis, its very interesting as we count the number of steps that an algorithm uses, and its also very surprising that we don't care about the amount of steps it takes, but the difference in steps when input is changed. The course has suddenly become very computer science based and I'm starting to like it even more! My only issue is I have trouble remembering structures or what symbols to use in proofs, and whenever I forget, I get stuck on continuing the proof. More memorization is required I suppose, and I'll get to the problem solving sLOG... eventually, my midterms aren't over yet but it seems like they just keep coming and coming and coming... Until next time!
some programs are so complicated with loops in loops in loops, I'm not sure how to count them when we get to $\forall x\in\mathbb{R}$ loops, maybe the steps are infinity and it's in big O of $\infty$? is infinity in big O of infinity? wow
ReplyDeleteYou can actually count the steps when you are doing a problem like this, but when the figures get complicated, trying to observe the math pattern.
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