Week 9

• This week we focused mainly on proving Big-Oh and Big-Omega bounds of polynomials. I have personally been working through a lot of proof statements these past few days, I see that we should use the definition when proving big-oh/big-omega statements in other words, relate your given expression to that of the Big-Oh or Big-Omega definitions.. Also, the constant c can be adjusted to meet our purposes. Also we learned to use limits in check if some functions are larger or smaller when the constants don’t affect .That is, divide one function by the other. If the graph 'approaches infinity', is a good indication that one function is growing extremely faster than the other. This is what the "breakpoint" B is used for. Usually, we pick the point B, and it narrows our proof down into worrying only about the part of the function the expression is completely true for.
• Although some proofs involving proving that functions are in  Big-Oh are challenging, they are nonetheless more simple than proofs showing that a function does not belong to the Big-Oh of another function. Because then we have to negate the definition of Big-Oh then find a counter-example "n" that breaks the expressions.
• we used L'Hopital's rule to show that the limit of 2^n/n^2 is infinity, which is of course greater than c. However, I was still a bit unclear about whether the function on the top is the bigger one or the function on the bottom is the bigger one? I like the Limits introduction Nonetheless, I think a little bit of calculus in the course would do some good. 
• Test Two this week. Probably didn't do too well, the practice questions made me underestimate the range of questions that they could give us causing me to just study simple proofs. Anyways I'm hoping I can make up for it in the Final Exam. "Fingers Crossed"