CSC165 has been a great experience for me. at first, everything seems to be very hard and complicated. all the symbols and proof and stuff. I am so scared that I could not pass this course because of the logic stuff, However, if you understand the material, even the basic of it, everything seems to be a lot easier. I do not know about anyone else, but for me, I enjoy taking this course very much. I love this course, although, I do not know what my mark would be. It's great to be Dr. Heap student. I think he is very nice, he explain very clear and he made it sounds very interesting.
For me the most useful thing in 165 is the tutorial and the assignment, I did not mean that the class is not useful. It is very useful too, but after class, sometimes, I still feel quite confuse. After tutoril and assignment, I actually understand the material a lot better. I don't really like tutorial for other courses, but for 165 the tutorial is extremely useful because I get the notes, a very useful notes from TA and I can ask question when I get confuse with the material from the lecture.
At first, honestly, I thought Slog was the least useful task in csc165, but after I did it for the whole semester, I feel that it is actually very useful to keep me on track of the material, sometimes, i can even ask question and answer by TAs.
The most interesting part and I find it very enjoyable is the proof part, it comes very difficult and complicated at the beginning, but once I understand, it becomes very fun when you can actually solve the proof, it fells very satisfying if I can solve it, but sometimes, it can get very complicated too.
The challenge that I find the most in this course is from the halting material, the last chapter from the course notes, the reduction of halting problem. I don't understand at all how to do it, at least not yet I hope. i know the step how to do it, but the most difficult is to write the program. usually after tutorial and assignment, I will be able to understand the material better, but even after tutorial and assignment, I still don't understand how to write the program using the reduction. I do not know how to come up with the program.
Well, aside from the challenge, I like this course and I hope the test will not be so difficult.
Thank you especially for Prof. Heap for the really fun, useful, interesting, and enjoyable lecture. I am looking forward to attend your other class next year. Also, special thanks to my TA, Maria Tsimpoukelli for the very useful notes you gave us in tutorial, it helps a lot, and also for answering many of my questions...:)
Thursday 4 April 2013
Tiling Problem
1. understand my problem.
in my understanding, I am suppose to come up with general procedure of this tiling problem. I am supposed to match the 1 x 2 tiles to 2 x n units.
2. Plan
My plan is i am going to draw the units with the actual size (my plan is to draw 2x1, 2x2, 2x3, 2x4, 2x5, 2x6, 2x7, and 2x8) and also draw several 1 x 2 tiles with different color to differentiate, also, some of them is horizontal, and some of them is vertical. Then i will try to match up the tiles to the unit in different ways to determine how many ways are there to tile each unit. then, I am going to record every different way and compare different size. After I have my data, I am going to try to determine the general formula to be able to know how many different way possible to tile 2 x n unit.
3. first, I am going to draw the unit and the tiles, here is the example on how i do it.
After I tried different way to tile the unit, I record it and here is the data I have got, I am using the 'v and h' code, v is vertical tile and h as horizontal tiles.
now, I compare the date in order to come up with the general formula.
It took me quite sometimes to figure out the formula, there is no much similarity between each other, I can see the pattern, it is quite obvious, for example, for 2 x n unit, there will be at least n number of way. But after that there is no obvious similarity. Until I see the total number of each different unit.
unit 2 x 3 where the total is 3 is the sum of the previous 2 units which are 2 + 1. Another example, unit 2 x 5, with the total of 8 is the sum of the total for unit 2 x 3 and 2 x 4 which -> 5 = 3 + 5. And this pattern works for all the units I have drawn. Therefore, I conclude, the general pattern for 2 x n unit is
Un = U(n-1) + U(n-2).
4. The challenge I find doing this problem are, first, it is not quite easy to record the data as n grows larger, I had to repeat for more that 4 times in order to get right result because as the unit grows bigger, more and more tiles can fit into the unit, and this means more possibilities of patterns.
second, coming up with the formula is not easy, because as I mentioned before, there is no obvious pattern that I can see from the data, I even make the color difference in order to see the difference.
Saturday 30 March 2013
week 11
This week we still learn a little bit about bid-Oh, Big-Omega, and big-Theta. This material is very new for me, I have never seen this kind of thing in any of my previous math courses. I think it looks a lot more complicated, but if we understand the concept, it gets easier. The challenge that I find when doing these type of question is determining whether to prove or disprove. I always confuse on how to check if we have to prove of disprove the question. Also, proving using the limit technique sometimes confuse me. I am always wondering, the limit is the proof or just the way to check whether to prove or disprove the question.
Tutorial this week is also still about proving big-Oh, and big-Theta. at first, I don't know what is big-Theta, I just knew that big-Theta is both big-Oh and big-Omega and I have no idea about the structure and how to solve big-Theta. Luckily, I was guided and helped by TAs, now, I understand how to prove big-Theta.
As for the assignment this week, I don't know if it is more difficult than other assignment or not, but I think I can handle the first 4 question, although I don't know if it is right or wrong. The fifth question on the other hand, I do not understand it at all. I have not read it carefully, I've just read through it, and it looks different than other question. I still have to figure out what the question and asking. If I am still do not understand it, I think I am going to ask TA or Prof. Heap in his office hour. Hopefully, I can figure out how to do it.
Tutorial this week is also still about proving big-Oh, and big-Theta. at first, I don't know what is big-Theta, I just knew that big-Theta is both big-Oh and big-Omega and I have no idea about the structure and how to solve big-Theta. Luckily, I was guided and helped by TAs, now, I understand how to prove big-Theta.
As for the assignment this week, I don't know if it is more difficult than other assignment or not, but I think I can handle the first 4 question, although I don't know if it is right or wrong. The fifth question on the other hand, I do not understand it at all. I have not read it carefully, I've just read through it, and it looks different than other question. I still have to figure out what the question and asking. If I am still do not understand it, I think I am going to ask TA or Prof. Heap in his office hour. Hopefully, I can figure out how to do it.
Saturday 23 March 2013
week 10
This week we got our test and assignment result back. For me, its not so bad, get quite good for test 2 result actually. I am quite happy. As for the assignment 2 result, it was actually not so bad, but I got my marks cut because of the style, I mean because of the indentation. The overall proof is right, its just that the indentation is not correct. And this got me thinking about final exam, do I have to worried about indentation during final exam?or it does not matter.
This week also, Dr. Heap uploaded assignment 3. Learning from last week assignment, I am going to start early, so that I have time to ask questions if I got stuck. I think this assignment its a bit more complicated than the last 2. So far, I know that I should prove or disprove, however, I am still confuse on how to construct the proof and disproof itself. Sometimes while doing this assignment, I do not understand some points from the slide or the course notes. And I think it is a good thing, because then I get to learn and understand the part that I am weak at. My strategy for this assignment is, first, I am going to try to understand the question, what are they asking me to do, or what should I do with the question. And the other thing and the most important thing is to ask question to TAs or Professor if I dont understand something. That way, I can do my assignment well and also learning for final exam.
Tutorial this week, as usual, we get to do the weekly problems, and as usual, I always learn something more in tutorial. I do not really understand Big-Oh before, but after doing the tutorial exercise and after explanation in tutorial, I understand a little bit more. Although I am still confuse about Big-Omega.
There is something that I am really confuse about from the course slide show from march 20th.
Based on that slide, it show the notation when the limit evaluates to infinity, but how if the limit evaluate to 0? I get really confuse about big Omega. And I think I have to figure this out first in order to do the assignment.
This week also, Dr. Heap uploaded assignment 3. Learning from last week assignment, I am going to start early, so that I have time to ask questions if I got stuck. I think this assignment its a bit more complicated than the last 2. So far, I know that I should prove or disprove, however, I am still confuse on how to construct the proof and disproof itself. Sometimes while doing this assignment, I do not understand some points from the slide or the course notes. And I think it is a good thing, because then I get to learn and understand the part that I am weak at. My strategy for this assignment is, first, I am going to try to understand the question, what are they asking me to do, or what should I do with the question. And the other thing and the most important thing is to ask question to TAs or Professor if I dont understand something. That way, I can do my assignment well and also learning for final exam.
Tutorial this week, as usual, we get to do the weekly problems, and as usual, I always learn something more in tutorial. I do not really understand Big-Oh before, but after doing the tutorial exercise and after explanation in tutorial, I understand a little bit more. Although I am still confuse about Big-Omega.
There is something that I am really confuse about from the course slide show from march 20th.
Sunday 17 March 2013
week 9
Last week we had test 2, which about proofs. I think it was not really difficult, that is why I am quite worried, because people said that in UofT, if something seems pretty easy, that means its a trick. But I hope that is not a trick, and I hope that I will do well, because I did not do very well on the first one.
As for the material, honestly, I am not really familiar yet with this week material. It is all very new to me, I never learn it before. I do not know what is it about, but I think it is still around proof. I thik the material this week is not as interesting as the first 3 chapter. I saw the tutorial handout for this week tutorial, and I still don't know how to do it. I need more information in order to do it. I will read the course notes for chapter 4 this week, and hopefully, TA will give us a useful notes in this week tutorial, because usually, that notes helps me a lot.
for the slog, I am still looking for the difficult math question that we are supposed to post and discuss it in our blog. I am still trying to figure out what kind of question I needed.
As for the material, honestly, I am not really familiar yet with this week material. It is all very new to me, I never learn it before. I do not know what is it about, but I think it is still around proof. I thik the material this week is not as interesting as the first 3 chapter. I saw the tutorial handout for this week tutorial, and I still don't know how to do it. I need more information in order to do it. I will read the course notes for chapter 4 this week, and hopefully, TA will give us a useful notes in this week tutorial, because usually, that notes helps me a lot.
for the slog, I am still looking for the difficult math question that we are supposed to post and discuss it in our blog. I am still trying to figure out what kind of question I needed.
Tuesday 12 March 2013
week 8
Last week was all about proof assignment. For me, at first, I have no idea how to do it. I was not really familiar with proof. I've tried to read course notes, however, this time was different than the first assignment. In the first assignment, It helps me to understand the material by reading the course notes and tutorial. But, the course notes about proof was not really helpful for me, because there are more theory than the proof example that I can look at. Tutorial exercise on the other hand, quite helpful, because I have an extra notes from TA. But still, it was not really easy to solve the proof question, because its not that we can find any hints or anything in tutorial or course notes. We have to actually think and do it our selves. Me and my partner spent a lot of time doing it. I did a lot of scratch note to find the proof. But at the end we finished it. It was not really easy, but not so complicated as well.
Our strategy to do the assignment were not different from others I think. First, we look at the questions, try to do scratch notes and determine to disproof or proof. As we were taught, negate if we want to disprove and not if we want to proof. From there, if we find the answer, we just construct the proof structure and type it. The typing process took quite a lot of time as well. It is really difficult to find the symbols, let along the fractions for question 5 or 1.
My lesson from this assignment that I will take to do better in the next assignment are, first, do it early. We did not do it early enough for this assignment. We did it last minutes. That is why maybe we did not as well as if we did it early. Time is very important for this assignment, because there are many scratch work to do to find the proof. Also, I should have go to office hours early when I am stuck. three days before we suppose to submit, I did not have time to go to office hours, the only opportunity I had was with the TA in the tutorial and with Prof. Heap after the class end, and I think that was really helpful. If only I ask many more times, I would have had better result for this assignment. All in all, at least 3 questions is right, hopefully I got part marks for the others.
And one more thing about proof, how do we know when we should use proof by cases?or when we suppose to use proof by other method?
Enough for the assignment 2, move on to this week material. This week material was about the running time for the code. I have not really familiar yet. I do not quite understand yet. Tutorial this week unlike the others tutorial was different. I do not understand a lot of things in the tutorial last Tuesday. I was hoping to understand it more in the tutorial, but maybe I was to distracted with the assignment. The quiz was the hardest too, I think I did not do well on quiz last week. I will just read the course notes to understand it better. And I hope next chapter is going to be easier.
Our strategy to do the assignment were not different from others I think. First, we look at the questions, try to do scratch notes and determine to disproof or proof. As we were taught, negate if we want to disprove and not if we want to proof. From there, if we find the answer, we just construct the proof structure and type it. The typing process took quite a lot of time as well. It is really difficult to find the symbols, let along the fractions for question 5 or 1.
My lesson from this assignment that I will take to do better in the next assignment are, first, do it early. We did not do it early enough for this assignment. We did it last minutes. That is why maybe we did not as well as if we did it early. Time is very important for this assignment, because there are many scratch work to do to find the proof. Also, I should have go to office hours early when I am stuck. three days before we suppose to submit, I did not have time to go to office hours, the only opportunity I had was with the TA in the tutorial and with Prof. Heap after the class end, and I think that was really helpful. If only I ask many more times, I would have had better result for this assignment. All in all, at least 3 questions is right, hopefully I got part marks for the others.
And one more thing about proof, how do we know when we should use proof by cases?or when we suppose to use proof by other method?
Enough for the assignment 2, move on to this week material. This week material was about the running time for the code. I have not really familiar yet. I do not quite understand yet. Tutorial this week unlike the others tutorial was different. I do not understand a lot of things in the tutorial last Tuesday. I was hoping to understand it more in the tutorial, but maybe I was to distracted with the assignment. The quiz was the hardest too, I think I did not do well on quiz last week. I will just read the course notes to understand it better. And I hope next chapter is going to be easier.
Friday 1 March 2013
proof
Last week was all about structure, and this week we learn about proof. It is pretty complicated, the structure was not that difficult, but when it come to the proof itself, I get really confuse. I tried to read the course notes, but sometimes, u do not understand. Maybe, I should do practice, but, where to get more practice about the proof? I need suggestion on where I can find practice question about the proof.
As for tutorial this week, as usual, it is very helpful, I get to understand the material more in tutorial.
Also, I know we are supposed to post one difficult math question in blog, but I do not understand, what kind of question are we suppose to post, and do we have to solve the problems. I do not know how to find those questions.
As for tutorial this week, as usual, it is very helpful, I get to understand the material more in tutorial.
Also, I know we are supposed to post one difficult math question in blog, but I do not understand, what kind of question are we suppose to post, and do we have to solve the problems. I do not know how to find those questions.
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