Week 9

This week we had our term test 2, it consisted of three proofs. They weren't that hard. In this weeks lecture we started off with the definition of Big-Oh, we did the notation O(n^2) being a set of functions. We went over some proofs and learned about how to choose c and B. Starting from easy proofs went on to doing harder and harder proofs. Then we learned how to disprove, which is done by first negating the statement and then proving the negation. We did a few proofs about that. We talked about picking c and B by showing the bounding relation. Up till now we had only talked/learned about polynomial functions. With polynomials its comparatively easy to figure out the Big-Oh just by looking at the highest degree term.

After polynomials we started proving non-polynomials, which are proven by the concept of limits. I am actually sick of limits now, we have been doing them since the start of MAT137 and I find them quite hard. The definition of limit is used to prove the Big-Oh of the non-polynomials. So when proving Big-Oh of non-polynomials, the first step is to compute the limit by some calculus, the L'Hopital's rule is used, then we translate the limit into its definition. We then relate the definition of Big-Oh and the definition of limit and then we write the proof according the proof structure. This is all what we learned in this week's lecture. Next week we will be doing some more proofs.