Week 6: More on proofs.

So the week after Thanksgiving we learned more about how to write proofs. For example given a definition and something you have to prove, assume/define and pick as much as you can before you start writing the proof. Mostly to help with the format and leading our proof to where we want to go. I prefer the way that we're learning about proofs in this course more than MAT137 where we're only really given an example of a proof and we're just expected to reproduce that format without much explanation on each individual part of it. So we learned about Proof by cases and Epsilon Delta proofs (Which I don't think are called that in the slides when we learned about it but it was essentially this.)

So as I previously mentioned the way that we learn to write proofs in this course is different and much more structured (Which I think is much more helpful to students learning about this for the first time). So for the proof of a limit that was shown in class, the proof was done more differently than how I learned it; Rough work wasn't separated and for example:

For all ϵ...0 < |x-3| <𝛿 => |x²-3²| < ϵ

It was written as 𝛿|x-3+3+3| instead to manipulate |x+3| into |x-3|. I found this method in a way more straightforward than making |x-3| < 1 and making intervals but I feel like the way we learned it here won't work for functions where there might be say, square root symbols. Now I've only briefly thought about this fact and have not tried a more complicated limit proof with this method so I could be wrong. But overall I did find the way we learned it in this course more intuitive in a sense so that's pretty good!

Week 5

So this week I don't really feel like I learned that much in class, mostly just the introduction to proofs and almost starting to write our own proofs. I've already done some proofs (note the keyword some) in MAT137 so I'm just trying to get used to the proof structure that we're given in this class. Besides that, for this course this week, I've been mostly concentrated on studying for the first of the 2 term tests for this course.

So for the test we were allowed to have an aid sheet, back and forth, but as I starting writing some of the standard properties, negation of implication, the standard stuff really, I realized that I already knew and understood most (Obviously not all since I probably spent about 30 minutes, after finishing the first 2 questions rather quickly, trying to figure out a good pair of sets for the last question on the test which I probably answered incorrectly) of the material that was on the test. As a result my aid sheet was probably shorter than half a page and I could complete the previous year's term test so I felt rather prepared for the test.

I hope that I did well on it even though I'm no good at coming up with sets on the spot. Now this post will probably be shorter since the 'content' in this course was not particularly difficult and we learned less this week because of the test. That's probably all for this week and I have 2 more midterms to study for and some miscellaneous to do!

To anyone reading this (Probably almost no one though :p) and it's actually still Thanksgiving weekend (Even lower chance), Happy thanksgiving!

Week 4: Formal definition of a limit in this course too? :(

So this week we started off with transitivity which wasn't a too hard concept to grasp followed by two other important concepts/subjects that I have learned to hate. First off it was, while not exactly Epsilon Delta proofs, but still learning about that formal definition of a limit. Now this is something that I have learned during week 3 of class (I think) in MAT137 and while I would love to say that since I have already learned about it, this was a piece of cake, it was not. I mean I must have spent hours reading through textbooks, looking for general explanations online and such I feel like I only have a passable understanding of Epsilon Delta in general (Concepts as well as proofs).

But Prof. Heap mentioned that given what we learned solely in CSC165 we should have the tools to write an Epsilon Delta proof and that's where I feel like I still haven't completely grasped the concept of the formal definition of a limit. If I hadn't learned it previously I am almost certain that I would not be able to do a proof of it. In the end I'm still sitting here reading over my notes and the slides for this course, not for this subject specifically but reviewing for the upcoming test on October 8th.

And I can't hit tab to indent right now, I'll look into that later but I digress.

Afterwards we learned the format expected of us in order to write a proof which was rather straight forward as of now. But some things to note are:
- Make sure to comment accordingly to your audience
- Indent to show a new 'world' where your assumptions are true.
That's more or less the jist of it. Doesn't seem too hard now but I am almost positive that it will get more complicated.

Assignment 1
The first assignment of the course was also to be completed this week and handed it on the Friday. Some of the questions were confusing at first but when you take the time to think about it, nothing there was really outside of what we had learned in class. What definitely helped were my partners with whom I could talk and compare answers that we had and then explain to each other why the answer was X and not Y. Also
*It really helps to write the original question out in symbols if you want to negate it and not try and do it just from the words.

But I feel that we did a decent job on the assignment overall, helping each other out and formulating decent reasoning and what we believe were the correct answers. However question 4 on the assignment was rather confusing to me, even in the end. Examples were rather difficult to think of, we weren't all 100% sure what a good way it was to explain it. I mean the quantifier at the beginning of each a) and b) changed up the question, but the Venn diagrams for the two were just...ugh...and I am almost certain that is the question where we did the worse.


Well that's it for this week, I also noticed that I guess I didn't save the problem solving part which was supposed to be a part of last week's post and I'll probably get around to re-writing it again soon. After all I had written up some quick code in python allowing me to 'solve' the problem so I might as well not let that go to waste.

Anyway I have some more work to do and tests to study for so bye! And good luck to everyone on their upcoming midterms!