Proof of Worst Case (Week 8 sLOG)

We have been doing proofs for around 3 weeks, and it was mostly mathematical proof. And this week, we have been introduced proofing the maximum steps of a method, and mostly contains loops in it. When I programming in the past, I never thought of the maximum steps, or time load that would takes to run through a code, maybe because of the processing power and the amount of random access memory our computers have nowadays, most of our program can be run through very quickly and with lots of storage space. Though, if the input is related to the code quadratically, maybe even more, then the larger size of the input is, the more time will be required to run through the code and that will be noticeable. 

However, after proofing the upper bound and the lower bound of the worst case performance, I am still not quite understand the method and the structure of these proofs. I am hoping this will be explain clearly in next week’s tutorial.