9th Week - Nov 7th

By looking backward, the school year has been past so quickly. On this week, the term2 test was given and three proofs were included on this test. Comparing to the first term test, I regarded this one was easier and I was pretty sure that I was able to do it better – I was quite comfortable with the proofs chapter and the questions given on the test were basically like those materials went over during tutorial. Therefore, personally I think there was nothing much to worry about for this test.

Besides the one-hour test, the topics about “Big-Oh of polynomials, non-polynomials, and limits” were taught through the rest of the lecture. Among them, the cases of “Big-Oh” were emphasized. What we normally do to solve “Big-Oh” problems is to pick C (some certain wisely chosen constant multiplier) and B (breakpoint). For example, if we want to prove 3n^2 + 2n ϵ O (n^2), we should always consider the picks of C and B first. In this case, the picks that C > 3 make sense because the coefficient number of the highest-term is 3. Besides, let’s assume n=1, then 3n² + 2n = 3 + 2 = 5 = 5n². Therefore, pick c = 5, with B = 1 is good after you double check with n equals other natural numbers. Since you are on the right track to start with, the rest part was nothing hard but just regular proofs.
 
 Another thing I want to talk about is this week’s tutorial. On this week, algorithm of a while loop functions is asked to consider about. The method talking about during tutorial was to examine form smallest part respectively, and finally we can count the number of steps. However, as far as I am concerned, it would be much easier if we only look at the analysis of the numbers, which just like a pattern observation.

As a brief summary, understanding is the most priority. But based on that, careful observation and considerate thinking are the key points.