To start off, obviously today's date isn't the 19th, but this is an update on the previous week. I had put off writing this post for a bit since I didn't feel I had learned anything different or felt that I personally didn't understand any more than I did the week before Thanksgiving week. To recap this past week, we continued running through proofs and learned a different way to structure them, which I found quite useful to trim away a good amount of time while writing proofs, which will come in handy come test/exam days. Using the tinier starting bits of proof to conclude will really help me in these situations. Also, throughout the week, we looked at several different ways to write proofs, one being by case. This one stood out to me, simply because I found the step unnecessary to prove for separate cases, but I digress. I mean, this type of proof will be useful, but to me at the moment, it seems like a bit of unnecessary work. I am still having difficulties with proofs, but I know I'll be able to understand them with time and practice.
Such as today in tutorial, I had a breakthrough (or at least I hope I did) in writing a full proof. The question, although simple, was still conceptually difficult to me, so I tried my hardest to understand it, following the necessary steps: proving the "for all" quantifiers with a statement that all variables under this quantifier are generic in the set they are meant to belong to, setting up the necessary bookends, but then it came to choosing a number to represent a variable, and I froze for a while. I looked at the question more carefully and I read it out in plain english and the lightbulb went off almost immediately for what I had needed to do. I felt pretty good about it, but I'm still not 100% confident that I got the answer right, even though I feel my proof still holds well. As for now, I'll continue practicing and taking whatever results I get as a learning experience.
It's actually not the end of the world if you don't get the answer quite right! We want you to learn how to think through a problem and try to come up with a solution, and as long as your steps are clear and organised, you're better off than just spitting out a solution that may happen to be right.
ReplyDeleteI recommend that you try to find problems, like those presented by Prof. Heap on his website, and work through the solutions—informally, at your own pace and in your own way. You don't need to get the answer, just think about how you'd find it. That's the key to success in this course.
You're doing great! Keep up the Slog :)