Hoping to make like an alternating series that converges...

CSC165 for me, seemed to contain a lot of flailing about and stabbing in the dark.

I feel less like I am randomly messing around with numbers and logic symbols, and more like I have an organized attack, and I find I am actually enjoying the material now.
Which honestly, is something I never thought I would think.
I was... prepared to hide in a fortress and battle the course down when I began this semester.

But, I started on a totally different mindset this time around (I think I gave up before I even tried in CSC165), and I enjoyed doing the assignment 1, well mostly, I still have part 3b left.

I wrote out proofs for questions 1 and 2 from A1 on Wednesday as the actual intuitive reasoning behind them wasn't that hard to see, and went to the TA hours on Thursday morning, to make sure someone besides me could understand it, and that I was indeed actually proving something.
(And with some advice to clear some fog in my writing, it seemed that I was.)

I also didn't understand what I actually had to prove for 3a, so I went to ask about that as well, but another student asked about it before me, so it's nice to know I was not the only one who couldn't figure out the question.
I wrote the proof up yesterday morning, and I have some confidence in it...

Yesterday, after seeing the second invalid proof in the lecture, I started to get really scared that I would write proofs like that. I think I may be forever haunted by the hexagon proof. The seemingly glaringly obvious truth that hides lies?
AH!!

--------------------

And something that has been bugging me is using n = 0 as a base case.
Because the conventions used like n^0 = 1 and 0! = 1 can sometimes make a base case valid when it shouldn't be, or invalid when the statement works for other numbers. And sometimes it seems that n^0 = 0 makes more sense.

And also, the fact that the set of all real numbers can be defined as open or closed, with the empty set then defined as the opposite, makes me confused as well.
Why this flexibility here?
In my MAT237 lecture, we were given a counter example to a statement that included the fact that the reals was a open set. But if the reals can be defined as open or closed, is that really a good enough counter example?
My first reaction was that it was very weak and I was rather disappointed with the example since it didn't lead to a very concrete reason why the statement failed, but instead left me more confused.

3^n

I went in for help this morning because I didn't understand the 3^n proof, but now I do, clearly. I didn't see how we were assuming the pattern 1, 3, 7, 9 and I wanted to know why and how we were.
But now I see that you write the case for one, to imply three, and the case for three to imply seven... etc.
I didn't realize that was what we were doing.
Seeing more formal math of the steps helped cleared my confusion.
Poof.

And I also wanted to check about how I did for question two on the problem set, so I got the math down, that was the easy part. Explaining how I got there was a problem.
I wrote out the proof in words and got the TA to look at it.
He didn't get it. It made sense to me, no one else.
Definitely not good when the whole point of the course is quite the opposite.
Want to make the point clear and not obscure it.
But he helped me make it more concise and clear, though, I still have a bit of trouble deciding just what needs to be said in the proof, and what doesn't.
I don't think I'd want to read my own proof.
That I'm sure, signifies something bad...

So I feel a bit less like I don't know what I am doing now.
I think I will be in for help every week that I can though...
(Did I learn anything in CSC165? It's really feeling like I didn't.. -_-)

Convention Confusion and Problem Set One

So I was trying to read the textbook.
Chapter 0. Done.
Then Chapter 1 came along, seemingly, innocently, skipping along.
And it brought back some of my confusion (like a mudslide over my brain) about proving such simple things.

Did we not create the number system?
Is it not the way natural numbers work just the way the system was made?
Why do we have to prove it?
In what way could it possibly happen that adding one suddenly doesn't not make the next number exactly one larger?
No matter how large the number, is it not just the way of numbers to be that way?
Why, why, WHY, must it be proved?
And yet I know, without proving those simple things, we could say that everything we know in math could be wrong, because we haven't justified the most basic parts of the system.
And yet...
...

And I started working on problem set one.
I didn't understand quite why the proof worked the way it did for 3^n in class, it seems so simple and yet I don't see why it can imply that for all the numbers, why it can imply there is a pattern.
But the second question I think I actually managed to somehow workout.
Of course I have no idea what I am doing, like blindly waving about my hands, in some feeble way hoping to reach for the sun like a wilting tree.
-_-
So I am planning to go in for TA hours on Thursday to resolve my confusion and sort out the fuzziness of my head.
(And ask a lot of questions I probably should have asked in CSC165.)

First post of random rambling - nothing to do with anything

CSC263H... An extension of CSC165H? Oh no!
My gut reaction is sickness. But I am trying to change that.
I will try to like to this course! I will! I will!
I am surprised I survived CSC165. Most people didn't seem to find CSC165 as evil as I did.
I find nitpicking English to get precision gives me headache.
But I do like math, so I'm no stranger to rigor...
I don't quite know what it was about CSC165.
But I have a goal for myself to do much better in this course!
*punches the air*

And I feel rather strange that I already have a blog on this site...
And blogger forces me to make my account with my gmail account.
(I don't feel it worth the bother to create a different one for just this purpose)
The other blog has little in it - only two posts, but it's not something I ever planned to share with people. Look how I waste my time! o_o;

I'm used to keeping a journal. I have one (in Word, on the computer) that I write around 4 pages a day in, just to get stuff out of my head. I enjoy writing. It helps me make sense of the vagueness and swirling confusion of what's up there in my head. It helps coalesce it into something concrete.

Now that I unloaded that from my mind I will make posts solely related to CSC236 as much as I can.
And the first week already scared the crap out of me (because somehow I passed CSC165 with an okay mark [even good enough for a specialist program...] but I can't seem to do a proof in this course to save my life).
I'm in four courses based a lot on math proofs this semester and I suck at them.
I like math but... I am no good at it.
(I have no belief in myself either. Yay!)
Many proofs kill me.

>>>This semester == doom
>>>True