Week #11

This week is the last second week before the class ends, plus there is a fall break with two days off on Monday and Tuesday, which makes me excited. Although this week doesn't cover too many things, what we learnt, again, makes me confused. I heard that this is the last chapter for this course, which i think is also the most difficult part. Basically, what we need to do is to prove non_computable function and computable function using reduction, which is something related to halting function. I still have no idea about it until I see the course note from course website. I can understand the example that was given and structure is clear to me. But that it, I don't think I can solve the same type of question by myself. I really hope that there will be more examples with solutions on this type so that I could have a deep understanding. The following question is the one appears on the course note, which I think is pretty typical. At least, I think we can figure out the structure of same type of questions after understanding this example.
I also check other students' slog like http://davidhanslog.blogspot.ca/to see if we have the same problem on halting problem.And yes! Many people are confused by this kind of problem.

The following is an example using induction:

Week #10

This week, the second term test result has come out, which frustrated me. I remember that when I first saw the test paper, there were only three prove questions and it seemed like i had done them before because it looked familiar. But actually, like the last test, I spent too much time on the first two questions and when I moved on to the last question, I realized that I didn't have enough time to finish. After the test, I heard that the second question is the most difficult and the last one is pretty easy. But what I did is just opposite because I get a full mark of proof on questions two but get 0 on question three.That looks ridiculous. The most regretful thing is that the question that I get 0 is the one that appears on assignment2 which is just due before the test. Although I use a more complicated way to solve it in assignment , I should have done it on the test.I felt like I could have enough time to finish it, then I was so careful to do first two that I forgot the time, which is the main problem. Also, I always think that what if I get more familiar for the stuff that is tested, this result may not happen to me.

It has already been two tests, and only one final left. I can't loose chance to get high mark next time, so I really need to look everything carefully and get familiar with the whole bunches of knowledge that I have learnt in this course.

problem solving:

 if we want to prove something equal, we have to show as following:

Week #9

This week, we began to learn Big O and Big Omega and how to prove or disprove it. This part is pretty interesting, which, I think, is my favorite part in this course. The way we did the prove of Big O and Big Omega is quite different from that we did for other questions. Maybe that's why I like it:)
Although what we learnt this week is kind of easy to me, we have the second assignment that is due on Monday. Some them are pretty easy and we practice lots of time. But others seem not easy to solve like the following question.
∀ x ∈ ℝ, ∀ e ∈ ℝ!, ∃ d ∈ ℝ!, ∀ w ∈ ℝ, |x−w| < d ⇒ | x − w | < e
Here is the way I did:

    

Every time I see there are too many variables in a question, I feel confused and don't know which way should I do it first. However, there is something interesting hidden in this question, which is that this statement is actually a definition of continuous function. Since the graph of floor is obviously not a continuous function, we can say that this statement is False and we need to disprove it, which eventually gives me some ideas to solve the next question that looks similar to this one.
∃ x ∈ ℝ, ∀ e ∈ ℝ!, ∃ d ∈ ℝ!, ∀ w ∈ ℝ, |x−w| < d ⇒ | x − w | < e

Here is the way I did:

Week #8

This is the 8th week and we learn about counting steps using worst case.Basically, what it asks us to do is just counting how many times a line should run in python, which eventually has something related to the course csc108. Overall, this part is not so hard though as long as we understand the meaning of the code which is necessary to know in csc108. What's more, professor also talks a little bit about Big O. At first, I was really confused because there are too many variables in the definition. But later, after we did the prove stuff, I gradually figure out what does it mean and the definition seems pretty clear to me.

There will be a second term test next week, which mainly tests us how to prove based on what we learnt these weeks. I personally have more confidence on this test than on the previous one partly because I did very well on tutorials and the example test that was given to us is pretty easy. But still, I need to do much work to review just in case that there was any knowledge that I didn't cover before.I hope I can get a higher mark on it.

Problem solving:(counting steps)