Convincing Myself, and some Fundamentals

After finishing Q3 of a1, I had lingering thoughts about a certain part of the proof - I wasn't fully convinced that it works. I kept wondering if I needed induction to justify the implication, or if doing that is unnecessary and what I have is sufficient.

A dose of the very helpful Danny's Office Hour gave me the answer.
So, I believe the lesson today is that if I'm not fully convinced myself, I need to do more work on justifying the part of concern.

Danny also pointed out some problems with "big jumps" and generality issues. I think I had an idea of what he meant, but wasn't entirely sure.

As I worked on adding the induction proof, I encountered very similar generality issues, having to do with fundamental definitions of natural numbers, integers. It was then that I realized what Danny meant, and understood the importance of these fundamental definitions that I never really internalized.

So, the second lesson today is, even if I feel like I'm convinced, it may not be due to correct understanding, and so it's a good idea to visit Danny or a TA to check my works.

a1 and Renewed Concern

Since the beginning of the term, I've gained a deeper understanding of Zen and Zen practice. Now, I should replace the word "unease" with the more accurately representative word "concern".

I really liked the way a1 questions are structured. It was challenging, but not overly so. Q1 and Q2 challenged me in putting ideas in formal language. Q3 is a great question, I love the structure and the way it guides into an elegant proof.

At this point after finishing A1 (minus Q4), I feel a sense of accomplishment, and a new level of acuteness in my logical sense.

The honeymoon feeling is quickly over, such is the norm during the school-year. I'm not even sure I understand the definition of a ternary tree in a1Q4 yet, and recursion wasn't easy for me in 148 when I took it several years ago. But, that was the immature and irresponsible me several years ago, with a terrible work ethic.

I'm also slightly concerned about the structure of tests in 236. Sometimes insights to proofs come in seconds, sometimes several minutes, and sometimes sleeping on it works wonders. It all seems rather arbitrary. Will the test structure be able to accurately represent a student's level of understanding?

thoughts after first 2 weeks

I began the course with some uneasiness: I was never good at theory and proofs, so I believed that I preferred programming, rather than theory. It's also been a few years since I took csc165 and mat137, so I have not been doing rigorous proofs for a while.

We started with simple induction. In mat137 I was never really convinced that induction works. I just followed the general format without digging really deeply. So I didn't really understanding it fully, and naturally I didn't really believe that it works.

Somehow, after the way it was explained in 236, it just clicked. I think the "training" I had before, plus the way it is explained in lecture just made it click. This understanding made me feel really good. The way Danny explained the intuitive method of partitioning in the induction step was also very clear and very helpful.

Surprisingly, I actually enjoyed the process of working through problem set 1. It really solidified my understanding of PSI, and I got a pretty good grade for it :)

I have to say, after working through PS1, PS2, A1 (I've finished them all), I'm really starting to like theory.