Worst Case Scenario (Week 8)

I have neglected to post anything for a while because I had been preoccupied with studying for multiple tests and as such simply forgot about this.
All throughout week 8, I really had no idea what I was doing anyways, so I wouldn't have had much to say. Generally speaking, I didn't understand how Big O works and what we were even trying to prove. The counting using tick marks beside each line of a search or sort algorithm seemed really strange and I couldn't see the purpose in counting steps of such algorithms. I knew that we wanted to determine the worse case which would be the scenario in which the program takes the most number of steps to execute. In the linear search algorithm, that would be if the item being searched for isn't actually in the list at all. In which case, the program will have to loop through every item in a list L until it reaches the end to confirm that the item was not found.
One of the things that threw me off was the counting of the while loops. It just looked like a bunch of mismatched i's and j's to me. Another thing was proving that the worst case of insertion sort is within Big O of n^2. The only thing that I got from that is the basic proof structure. The thinking section in the middle did not make sense to me. I was simply copying notes down in class. I guess the most confusing part was the listing of the contributions of each line and then suddenly going to some sort of equations of n. The Omega part was strange too.
I decided to let myself naturally learn this concept over time like I always do for things I don't understand right away. So, I left all of this stuff alone until the following tutorial. As my TA went over the tutorial question sheet, I began to felt that it seemed simpler than what we did in lecture. However, that was only because the tutorial questions didn't actually talk about Big O, since it was only on counting steps which seemed simple enough this time around. I realized that each line within a while loop will iterate once per counting variable outside of it, generating steps equal to the number of lines inside of it times the number of iteration plus one for the last checking of the loop before it stops executing.
Fortunately, things became a little clearer in week 9.