I haven't been updating the SLOG at all, which I would blame it on my other school works. Anyhow, I think test 3 was fair enough. But I found the second question to be a bit tricky.
The last chapters (7 and 8) are more challenging to me in a sense that I didn't know much about regular expression and all the language so-called notations. The exercise about regex we did in CSC207 actually helped a lot with my understanding. Structural induction was interesting to use and quite handy when proving the string in a language, which is better than using simple induction or complete induction in some cases. The pumping lemma kind of confused me during the lectures. But after reading the wording in the textbook, I understood it better.
This course has been interesting, which I had handled it better than I thought. I didn't get to the a problem, but since I really don't have time... I will let the marks for that part slipped away. Overall, I enjoyed the course and hopefully the exam won't be too bad!
Friday, December 5, 2008
Sunday, November 16, 2008
Test2
I was quite surprised to see my mark for this test. And I was very glad to see that mark, actually. I found this one to be easier to approach than the first test. (For the first test, I did not complete the third question since I was running out of time and also wasn't quite understand how to do it.)
The mark for A2 was also fair enough. Surprisingly, the question I thought I didn't do well actually got a full mark. And of course, the one I thought well turned out to be not well. But I kind of understand where I went wrong in my explanation. But I really can't believe the answer for question 1 on A2 was that simple.
As far as the course goes, I still need to catch up with some of the materials. I understand the states and how we determined them. But I still kind of confused on the whole idea of language and strings. With many assignments due the coming week, I hope I will have time to spare for this course.
The mark for A2 was also fair enough. Surprisingly, the question I thought I didn't do well actually got a full mark. And of course, the one I thought well turned out to be not well. But I kind of understand where I went wrong in my explanation. But I really can't believe the answer for question 1 on A2 was that simple.
As far as the course goes, I still need to catch up with some of the materials. I understand the states and how we determined them. But I still kind of confused on the whole idea of language and strings. With many assignments due the coming week, I hope I will have time to spare for this course.
Monday, October 27, 2008
A2 Thoughts
For this assignment, I felt that question 1 and 2 were the challenging one. It may also be because I didn't start the assignment early enough, so I didn't grasp many ideas.
Question 1 was more difficult because I was struggled to find such formula. After I went to the office hour, I found my way of thinking is quite inefficient espeacially if n > 4. Danny told me the quicker way, which somehow I didn't catch on it while reading the bulletin board. This way he told me makes sense and less headache. But when I have to translate it to the formula, I was struck once again. It took me awhile to recognize the patterns. So, I think I got the idea (and the formula) but because the time is running out I didn't complete this question.
To add to that, I asked my brother to help me find the formula. And he gave me the formula (3n)!/(n!)(2n+1)! which outputs the correct value! (He got it from this page.) It was useful for checking whether I was getting the right number. It's also short and simple.
Question 2 was not as hard as question 1 in a sense that we just need to prove that closed form we got. Some suggested using the monoticity argument which the length of work is a lot. (But I did it this way since I can't come up with another way.) There is a shorter way which deal with property of integer and stuffs like that but I have no clue of how to do that. I would say that the hard part was to prove that T(n) = clog7n.
Question 3 and 4 weren't as time consuming as the first two questions. Question 3 was straightforward in what it wanted us to do. It was interesting to think that grasshopper can make either 1 step or 3 steps. Question 4 was similar to the example we did in class, so it was not too difficult to do. I didn't do the bonus part which the question itself reminds me of csc165's material.
Overall, the assignment was challenging for the first two questions but it also had the other two questions to make it enjoyable.
Question 1 was more difficult because I was struggled to find such formula. After I went to the office hour, I found my way of thinking is quite inefficient espeacially if n > 4. Danny told me the quicker way, which somehow I didn't catch on it while reading the bulletin board. This way he told me makes sense and less headache. But when I have to translate it to the formula, I was struck once again. It took me awhile to recognize the patterns. So, I think I got the idea (and the formula) but because the time is running out I didn't complete this question.
To add to that, I asked my brother to help me find the formula. And he gave me the formula (3n)!/(n!)(2n+1)! which outputs the correct value! (He got it from this page.) It was useful for checking whether I was getting the right number. It's also short and simple.
Question 2 was not as hard as question 1 in a sense that we just need to prove that closed form we got. Some suggested using the monoticity argument which the length of work is a lot. (But I did it this way since I can't come up with another way.) There is a shorter way which deal with property of integer and stuffs like that but I have no clue of how to do that. I would say that the hard part was to prove that T(n) = clog7n.
Question 3 and 4 weren't as time consuming as the first two questions. Question 3 was straightforward in what it wanted us to do. It was interesting to think that grasshopper can make either 1 step or 3 steps. Question 4 was similar to the example we did in class, so it was not too difficult to do. I didn't do the bonus part which the question itself reminds me of csc165's material.
Overall, the assignment was challenging for the first two questions but it also had the other two questions to make it enjoyable.
Sunday, October 5, 2008
Third Week
I'm a bit late in updating my SLOG, but it couldn't be helped since I was quite busy.
It struck me that the Principle of Well-Ordering seems to be "simple." Though when I was trying to use it in the proof, I wasn't sure of how to do so. The problem we did in the lecture ("round-robin") was quite confusing to me, as I cannot exactly remember how it was. Anyhow, I had to re-read the slides for a couple of time to start understanding it. You just need some times to understand it.
The fact that all three priniciples are connected was quite fascinating. I like the idea that if you believe in one principle then you also believe in the other principle (maybe not volunteerily.) By being able to prove that each principle is connected to one another, it really did strengthen the idea. So far, I have more understanding in PSI. Complete induction is useful for some problem that using PSI will be quite painful, especially that postage problem. As I have said, Principle of Well-Ordering is still not very clear to me.
Sometimes you felt like you understand it, but you were actually having no clue about it.
It struck me that the Principle of Well-Ordering seems to be "simple." Though when I was trying to use it in the proof, I wasn't sure of how to do so. The problem we did in the lecture ("round-robin") was quite confusing to me, as I cannot exactly remember how it was. Anyhow, I had to re-read the slides for a couple of time to start understanding it. You just need some times to understand it.
The fact that all three priniciples are connected was quite fascinating. I like the idea that if you believe in one principle then you also believe in the other principle (maybe not volunteerily.) By being able to prove that each principle is connected to one another, it really did strengthen the idea. So far, I have more understanding in PSI. Complete induction is useful for some problem that using PSI will be quite painful, especially that postage problem. As I have said, Principle of Well-Ordering is still not very clear to me.
Sometimes you felt like you understand it, but you were actually having no clue about it.
Monday, September 22, 2008
Second Week
For the second week, we covered the topic of Complete induction.
At first I wasn't really clear about the concept of complete induction. After the examples we did in class, the clouds started to disappear but not completely. I was a bit confused with the chocolar bar example, as I wasn't sure what it meant by "break". It required me to reread the example several times before I came to understand it better. Sometimes, the wording was not so clear.
The postage example was interesting. We did a similar one in 165 last term but with simple induction if I remembered correctly. To be honest, I'm not fond of this problem. When we were asked to do some scratch works, I did it and thought that I had got some clues about it. But as we took it up as a class, I found that my clues was not as well as I thought. And to find that Problem Set #2 is about the postage frightened me a bit; although after reading through the textbook and the class notes, it was not that bad.
The most challenging part right now is to be able to believe that P(n) is true and find the reason to back my belief.
At first I wasn't really clear about the concept of complete induction. After the examples we did in class, the clouds started to disappear but not completely. I was a bit confused with the chocolar bar example, as I wasn't sure what it meant by "break". It required me to reread the example several times before I came to understand it better. Sometimes, the wording was not so clear.
The postage example was interesting. We did a similar one in 165 last term but with simple induction if I remembered correctly. To be honest, I'm not fond of this problem. When we were asked to do some scratch works, I did it and thought that I had got some clues about it. But as we took it up as a class, I found that my clues was not as well as I thought. And to find that Problem Set #2 is about the postage frightened me a bit; although after reading through the textbook and the class notes, it was not that bad.
The most challenging part right now is to be able to believe that P(n) is true and find the reason to back my belief.
Monday, September 15, 2008
First Week
It's been awhile since I have school since I did not take any summer course. Anyhow, I'm slowly getting back to the pace of school.
My first impression for the this week is that this course looked so similar to CSC165. The lecture itself reminds me of many things I learned from last spring. It isn't too bad as I'm still able to recall the materials we refer to. It was good to hear that the structure for our proof doesn't need to be as rigid as 165; not that I dislike the structure of 165.
And since I have nothing else to write, I will end the first post here.
P.S. I'm glad that Danny is teaching this course!
My first impression for the this week is that this course looked so similar to CSC165. The lecture itself reminds me of many things I learned from last spring. It isn't too bad as I'm still able to recall the materials we refer to. It was good to hear that the structure for our proof doesn't need to be as rigid as 165; not that I dislike the structure of 165.
And since I have nothing else to write, I will end the first post here.
P.S. I'm glad that Danny is teaching this course!
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