Entry 9 - Week 12

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!

Entry 8 - Week 9

I actually had quite a bit of fun on assignment 2. Proofs are less stressful when you have plenty of time to do them, and I got really creative with some of my answers; in the same vein, I think some of my answers were a bit excessive, so I hope the person marking them doesn't mind! While the proofs on the tests weren't that hard, and pretty similar to the ones on the assignment, I did have some trouble with the time constraints. I'm not really sure how I can try to improve on this for the next test, since no amount of studying or preparation can really help you solve proofs quickly; I guess I'll just try to offset the marks by working hard on the assignments and tutorials.

I had to miss Friday's lecture because of a cold, which is unfortunate because it seems like some really important material was covered. While I can figure out some of the material from the annotated slides, I certainly don't understand all of it. I can make the Friday office hours, so I'll see if I can get some assistance there, or even at my tutorial.

Entry 7 - Week 8

Assignment 2 is coming along very well. At first, it was a bit difficult to find the right place to start my proofs, but once I got started it turns out that each of the proofs are actually strongly connected to each other. While the proofs are considerably harder than the ones we've gotten in our tutorials, the format is the same, so for once I'm not too worried about proper form when writing up an assignment!

One thing that really stood out for me during Friday's lecture was when Professor Heap told us that proofs can actually contain sentences and writing. While working through assignment 2's more difficult proofs, I found that sticking to a bunch of "Then..." statements was really awkward and limiting; being able to actually write in an argument would have been much more convenient. I'd already finished most of my proofs by Friday, so this discovery came a bit late, but it's good to know for the future.

Looking at the sample test given, I'm feeling confident in my grasp of the material so far. Between the tutorials and the assignment, I'm not having too many difficulties with proofs. I think I could still use some help on complexity and big-O, but it doesn't look like that will be on Wednesday's test, so I'll deal with it after.

Entry 6 - Week 7

Wednesday's lecture on complexity and worst-cases moved pretty quickly, and I didn't have the time to really grasp all of the content. I reviewed the slides on the webpage to catch up, and also checked chapter 4 of the course notes, which were actually really helpful and intuitive. What I still find odd, though, is that the number of steps for an insertion or selection sort increases according to a quadratic. I understand why the number of steps in these sorts increases exponentially, but I have no idea how you would prove that the number of steps can be represented by, specifically, a quadratic. I think that's beyond the material we've covered so far, though. Maybe we'll cover it next week.

The week's tutorial went well, and I'm feeling much more confident going into them now that I've been through a couple. The due date for Assignment 2 is coming really quickly, though, so I think I'll get started on that.

Entry 5 - Week 6

No tutorial or Monday lecture this week because of Thanksgiving, so there isn't all that much to say this week. Most of the stuff in the lecture was pretty intuitive; proving negations is just combining what we learned about negations with the work we've been doing on proofs. I did the problems for next week's tutorial and didn't have too much trouble, so I'm feeling fairly confident for what's ahead.

Entry 4 - Week 5

The test has been this week's big focus, though I was pleasantly surprised to find it fairly simple and straightforward. It was really similar to the test from last year which we were provided for practice; having reviewed the practice test the night before, I was perfectly comfortable sitting down for this one. I'm feeling confident that I performed well this test, and hope that it will continue in the future.

I spent most of this week obsessing over and preparing for the test, so I don't really remember much else of what we did in class. I understood the tutorial on proof structures well enough; we've been doing a lot of proofs in math, which I think helped me to get in the right mindset. I actually found the tutorial material to be fairly interesting; in math, we've gone right into actually doing the proofs, while the tutorial took a more theoretical approach regarding the structure of a proof; breaking a larger proof down into several smaller components which each need to be proven through, then working through these components individually. I think this way of thinking about proofs will help me out in both classes.

Third Entry - Week 4

I found this week's material to be a bit more challenging than before, but not overwhelming. I went into the tutorial confident in most of my answers, although I could not figure out how to prove the equivalency of the statements in Part 1. I wasn't sure how to properly turn implications into conjunctions and disjunctions. Once my TA explained that (P ⇒ Q) ⇔ (¬P ∨ Q), the questions became very clear to me, and I was very prepared for the quiz at the end of the tutorial. While reviewing my notes later, I discovered that we had actually covered this during one of the lectures last week; in the future, I think I'll review the past few weeks' notes if I ever get stuck on a tutorial problem set.

One thing that I found particularly challenging during this week's lectures was the definition of a limit. I understood all the of material about proofs, but I get confused when it comes to the definition of a limit. To use one of the examples in the lecture, I just don't see how ∀e ∈ R⁺ , ∃ d∈ R⁺ , ∀x ∈ R, | x - 0.6| < d ⇒ | x² - 0.6| < e proves that the limit as x approaches 0.6 of x² equals 0.36. We're covering the same thing in math, and I'm having similar difficulties there. Since this seems to be pretty important to both courses, I think I should devote some time to making sure I understand it properly. My math lectures have been focusing heavily on the definition of a limit recently, and I have extensive notes from those, so this weekend I'm going to sit down with both sets of notes and see if, between them, I can figure something out. Failing that, I'll get clarification during my next tutorial for either class (they're actually both on Tuesday, so I'll have plenty of opportunity to make sure I understand everything about the concept).

Assignment 1 was due yesterday, and I'm feeling very confident in my answers. I had to think for a while on some of the questions, but none of them totally perplexed me. Finishing the assignment early also meant I had a lot of time to check over my answers. I'm eager to see the results!