I got caught up with a lot of work the past two weeks and missed my entries, but I'm back to make one more before the end of the semester! I found big O, Omega, and Theta to be pretty intuitive, and once you understand the concept it's really just another proof. I find that a lot of things in the course come back to the basic proof techniques we learned in the first few weeks. Of course, doing big O, Omega, and Theta with exponentials is something quite different from what I'm used to, and I'm having a bit of trouble with that. I think I managed to do the problems on assignment 3 well enough, but I just find proofs involving limits to be awkward, and far less straightforward than doing big O, Omega, and Theta with polynomials. Looking through the other SLOG's, I was relieved to find that many of my classmates feel the same way, though perhaps as a result there weren't very many people sharing new insights on the topic.
I found computability theory to be both interesting and extremely challenging to wrap my mind around. I really like the intuitiveness of the Cantor's set example, but I find it odd that one can compare the sizes of two infinitely large sets. It kind of contradicts what I've learned in math; that the sizes of two infinities cannot be compared because infinity is not an actual number.
All in all, I'm feeling pretty confident going into the final exam. I've done well on all the assignments and tutorials so far, and there's nothing in the material that totally perplexes me. With a bit more review on exponential big O/Omega/Theta and computability theory, I think I'll do fine.
I'm also hoping to get in one more problem solving episode before the end of the semester, besides the one I did for week 3. I found the diagonals problem from last Friday to be really interesting, and I have some ideas on how to go about solving it, but I need to actually get the answer first!
