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!