Nov 30th - Dec 3

This is the last week of this term, Danny did some reviewing with us.
First he talks about the possible topics in the exam, which covers all chapters we have learnt including quantifiers, implication,negation, venn diagram,connectives, proofs techniques, proving statements and structures, comments, algorithms, worst-case, big-Oh, big-Omega, big-Theta, limit technique and computability.And then he showed us some examples and tactics. Then, he talked to us about something we need to notice before and during the exam. Today, before the lecture, I was thinking about something I haven't figured out. It is about halting problems, if we say that meaning of life can be reduced to halt, then halt is included in the body of meaning of life, then there must be another function which contain f(i) and a return after it. But when we call meaning of life, it cannot be evaluate until f(i) halts, if f(i) does not halt, function meaning of life will never halt,too. So there is no such function to be called as a parameter inside meaning of life that accomplish the requirement 'if meaning of life halt, halt will also halt.' there is no code can express such function. We can only get its contradiction ' halt does not halt so does meaning of life'

Nov23- 29

This week, we continue on computability and diagonalization. We discussed a lot and I cannot recall all of them. However, I remember there was a very interesting topic about infinity and functions, that is , f(n) = 2n, is one-to-on and onto, so that there are same number of even number and nature number! That is amazing. I had never thought of this thing before, and it just like open a door for me. Mathematics is so interesting! And then, we talked about the rational number. Are there same number of rational numbers as natural numbers? The answer is no. The level of infinity of rational number and natural number is different. Rational number seems more than natural number and its infinity is larger than the infinity of natural number! Then we talked about python functions. At what level is the python functions' infinity? And here is the tricky part. We can write each function as a series of numbers and if we treat it as natural number(because it is a integer and bigger than 0) than we can get the conclusion that there are same number of python functions as natural numbers! Finally, we talked about simple induction, I learnt this before in my high school Mathematics courses. It says if we can prove P(n) => P(n+1) and P(0), then we can prove it is  true for all natural numbers. But there is a tricky part. True antecedent and False consequence is false. So FFFT...is true but TTTTFTT is false. And we need to find the beginning  n that makes our statement true

Nov16 - 22

This weekend! We lost CDF website! I just want to say what's going on!? I cannot read slides after class and we learnt something really tough this week! It seems like we began learning algorithms and halting problems. I am still confused what is really halting problems talking about. I just don't understand those principals talked in the slides. I think I may need to read the course materials carefully during this weekend. And there are only 5 classes to the final. lol!! I am dying....

Nov 9 -15

This week, we learnt more about big-O and big-Omega.We talked about using limit to solve problems of big-Omega and to prove that f is not in omega. And more, we learnt L'Hopital's Rule and apply it to CSC165 prblems. Finally, we learnt big-theta. Big-theta is interesting, for which it is the combination of big-o and big-Omega, so that there exist a C1 and a C2 that C1g<f<C2g. And then, we learn f is in Big-O of g can imply g is in big-O of f,and f is in big-O of g can imply that f^2 is in big-O of g^2, and f is in big-o of h and g is in big-o of h implies f+g is in big-o of h... They are interesting if you really interested in this kind of proving or disproving. But I guess I just want to understand what is going on and follow the prof's teaching. And finish this term as soon as possible!

Nov 2nd - Nov 8th

This week we learnt sum_up function which counts the steps that the function runs. I am a little bit confused. To tell the truth, I did not really fully understand what is this function about. And I did quite badly in this week's Tutorial and quiz. I even misunderstood the question in quiz. I feel terrible about this week. And we began to learn big-O and big-Omega. That is quite hard and needs me to understand a lot. I feel bad.

Oct 26th - Nov 1st

This week we learnt Big-O and Big-Omega. Initially, I totally did not understand what was the prof  talking about. And I went to his office during his office hours. I asked him a lot of question and began feeling better. Personally, I think Big-O is some kind of worse than worse case because I need to overestimate the step whenever I need to choose. And therefore Big-Omega is some kind of better than worse cases, but it is still worse case because it goes as many steps as possible and just underestimate the steps. In Danny' words, 'no more than these steps' and ' takes at least so many steps'. This week's learning is interesting!

Oct 19th -25th

Another week has been passed.This week, we summarized inference that could be used when dealing with proofs. And more, we learnt some sorting methods. It to some extend makes me more comfortable because the example is written in Python language and that makes it easier for me to read(compare with the multiple quantifiers of proving we learnt last week). But it makes me difficult to understand why is there a lower boundary and upper boundary. It just so weird that I think the worst case should be a certain number of steps. I talked to professor and he explained, but I did not quite get what he said. He said 'In those worst cases, there are some cases that would take some more steps than others, and we can find a case that all worst cases takes no more than this steps. This is upper boundary.' I just want to ask why(TAT).

And on Friday, we did problem-solving handout. It is interesting. But I had a question about problem-solving. Is it some kind of skills that we need to understand? Will same kind of questions on the Test paper? Or is it just to help us develop a scientific thinking?