Course Overview

I really like how there are course notes designed specifically for this course but one downfall is the lack of practice questions. I don't expect them to be in course notes or else it would become a full blown textbook. Luckily, there's even a book mentioned in the course notes on page 5.2.

I think what was learned during the course was interesting but I can't contextualize most of the concepts it into my limited understanding of computer science. I came into this class with very little knowledge of computer science. As I come out of this class, I sort of understand the basics of logical notation and the basics of the fundamentals of proof problem solving and format. From what I understand from calculus, this will allow me to read more complex math to understand more math and computer science. The algorithmic analysis has let me peek into the complicated world of the process of writing a solution to a problem before any code is written. As for computability theory, I have no clue how the smart people like Cantor would have thought of using diagonalization to determine there are countable and uncountable infinities and I don't understand it enough to put this info in a context.

This slog ends with a boring bang!

Goodbye!

Although the course notes don't seem that long compared to other classes, the content is more dense.

While I'm reading back, I'm starting to realize just how much can be learned in 12 weeks.


Side note: The course isn't even over yet it's already been useful!

I've noticed this one video that has math logic on a Youtube channel that I watch regularly while procrastinating. The math is at 2:47
https://www.youtube.com/watch?v=Ao0dqJvH4a0#t=167

It's almost over

There's just studying for the exam left and looking back.
The relative shortness of the course notes  doesn't look like a lot in the course notes, I know it took a lot of understanding to get here and I know there's still more to come both in the upcoming week and in the next course.

Lazy caterer's sequence

I searched the problem below online and I found out that it's called the lazy caterer's sequence.

The answer online is  

So I assumed my solution was wrong until I expanded my solution of 1 + (n*(n+1)) / 2

= 1 + (n^2 + n) / 2             #algebra

= (n^2 + n + 2) / 2             #put the one in the fraction

So, YAY!

Unscholarly Sources:

http://en.wikipedia.org/wiki/Lazy_caterer's_sequence

Space Slicing Problem

Problem: If n is some positive whole number, what is the maximum number of regions I can divide a sheet of paper into with n straight lines?

Input: Number of divisions
Output: Max number of regions resulted from divisions.

Plan 1: Draw and find patterns. (I don't know how to show that on this slog)
What I noticed immediately is that each line had to interact with all the other lines.
Also, since the divisions were all lines with different slopes, they could only intersect with all the other lines once.
When the new line went from the boundary of the paper to the first division, it split a region in 2 (or "created" a new area).
However, this thinking didn't really go with the empirical findings. I could only find 10 regions when I drew 4 lines. Then I tried it on the computer and it worked.

Divisions - Regions
1 - 2
2 - 4 (2 + 2)
3 - 7 (2 lines + line going through page -1st line, 1st - 2nd, 2nd and page)
4 - 11 (3 lines: page-1st, 1st-2nd, 2nd-3rd, 3rd-page) or 7 + 4
5 - 11 + 5 = 16

I'm going to quickly guess the answer based on this pattern.
If the number of divisions is n, then the number of regions increases by n every time.
Mathematically, this looks something like: 2 + 2 + 3 + 4 + 5 + ... + n
This looks really similar to 1 + 2 + 3 + 4 + ... + n
and is the same as 1 + (1 + 2 + ... + n)
which is 1 + (n* (n+1)) / 2
and that's my answer for now.

Week 9:

In high school, the week after after a test was usually really chill because there would be very little new material. I guess that's never going to happen until finals. Right after each test, I'm still scrambling to try to catch up all the time. Although I'm learning the stuff in this course, I don't think I'm learning it fast enough.

It's Past Week 8 Mate!

Wow! It's been more than 3/4 of the course already!

I'm getting really nervous about this course with so much new stuff I've never seen before and the future three weeks of even more new stuff that I still have to get trampled by before the exam.

At the end of last week, we got the penny pile problem which I still have no idea how to approach. I am also currently failing to understand the floor function and how to use the definition to prove a modified version of the definition of a limit in Assignment 2.