Oct. 24-08
The class has moved on to the new topic, Program Correctness. It was not as hard as the last topic so I was little relieved.
The due date for problem set #4 was extended to next Monday. The second assignment was posted this week. I haven't given any thoughts to the assignment yet. It is also due next Monday, so I have to rush through it during the weekend. It seems things have been really tight recently for every body. We just have to survive through this crisis.
Friday, October 24, 2008
Friday, October 17, 2008
Thanksgiving Is Over
Oct. 17-08
There was no lecture on Monday since it was Thanksgiving. I was stunned when the class discussed the master theorem because I didn't have any clue of what we were talking about. To keep up with the lecture, I read about the master theorem in the textbook but was not really convinced how it works. I thought it would be helpful if I could see more examples applying the theorem. For this purpose, I went to library but didn't find any book useful. I will go to the help centre next week.
Problem set #3 was due today and we also got our tests back. I did very poor on the first term test and I am losing my confidence. At least I can try to work harder next time.
There was no lecture on Monday since it was Thanksgiving. I was stunned when the class discussed the master theorem because I didn't have any clue of what we were talking about. To keep up with the lecture, I read about the master theorem in the textbook but was not really convinced how it works. I thought it would be helpful if I could see more examples applying the theorem. For this purpose, I went to library but didn't find any book useful. I will go to the help centre next week.
Problem set #3 was due today and we also got our tests back. I did very poor on the first term test and I am losing my confidence. At least I can try to work harder next time.
Monday, October 6, 2008
Ice Age I
Oct. 6-08
This is the time, where I would go around and ask people: "What would you do if this is your last day on the earth?" Whenever you hear me talking about things such as "the end of world" or "the coming of the ice age," then there is probably a term test approaching. I am starting to get tense. Just to relax myself, I will watch a horror movie tonight and begin my test study tomorrow.
Today, we have examined some questions on Fibonacci sequence and binary trees. I have come across the Fibonacci sequence several times in my life, but I never liked it. To make things worse, I didn't get the proof of F(n) = (phi^n - phi_hat^n)/sqrt(5). After the lecture, I stared at the slide trying to find out why phi = (1 + sqrt(5))/2. Two hours later, I finally noticed that I could just go ahead to solve r^2 = r + 1 to obtain the root (this was written on the next page of the slides.) Obviously, I was losing my focus and needed to pull my mind away from CSC236 for a while.
This is the time, where I would go around and ask people: "What would you do if this is your last day on the earth?" Whenever you hear me talking about things such as "the end of world" or "the coming of the ice age," then there is probably a term test approaching. I am starting to get tense. Just to relax myself, I will watch a horror movie tonight and begin my test study tomorrow.
Today, we have examined some questions on Fibonacci sequence and binary trees. I have come across the Fibonacci sequence several times in my life, but I never liked it. To make things worse, I didn't get the proof of F(n) = (phi^n - phi_hat^n)/sqrt(5). After the lecture, I stared at the slide trying to find out why phi = (1 + sqrt(5))/2. Two hours later, I finally noticed that I could just go ahead to solve r^2 = r + 1 to obtain the root (this was written on the next page of the slides.) Obviously, I was losing my focus and needed to pull my mind away from CSC236 for a while.
Friday, October 3, 2008
The End of the Starter
Oct. 3-08
Last week of September we moved to chapter 3, Recursive Definitions. The focus of the course has shifted away from induction, but it doesn't change the fact that we are still dealing with inductive proofs. I guess we can never get away from induction in this course.
The concept of recursion is by no mean a new topic to most of the students including me. I believe most people in the class already had plenty of experiences with recursive program before. However when I looked into the logic behind recursion, I could see a whole new aspect of the topic. One thing that I really liked about this topic is "unwinding." I have never heard a problem-solving method with such a fascinating name. "Unwinding" is a very complicated process to look for the pattern of a function. I didn't understand it at all when Danny explained it in the lecture. I revisited lecture slides afterwards and tried to recall what Danny said. Eventually, I got it after staring at the slides for one and half hours.
Last week of September we moved to chapter 3, Recursive Definitions. The focus of the course has shifted away from induction, but it doesn't change the fact that we are still dealing with inductive proofs. I guess we can never get away from induction in this course.
The concept of recursion is by no mean a new topic to most of the students including me. I believe most people in the class already had plenty of experiences with recursive program before. However when I looked into the logic behind recursion, I could see a whole new aspect of the topic. One thing that I really liked about this topic is "unwinding." I have never heard a problem-solving method with such a fascinating name. "Unwinding" is a very complicated process to look for the pattern of a function. I didn't understand it at all when Danny explained it in the lecture. I revisited lecture slides afterwards and tried to recall what Danny said. Eventually, I got it after staring at the slides for one and half hours.
Friday, September 26, 2008
Endless Realm of Induction
Sept. 26-08
This was our third week on the topic of induction. It is amazing how well inductive reasoning coexists with other mathematical principals such as Principle of Well-Ordering. We have spent all the past weeks studying induction, now I don't have any hesitation using complete induction anymore. It was not as if I went through every practice question in the textbook to get myself familiar with strong induction. It was rather due to the effective lecture style which was newly adopted this year. Thanks to the tablet, I was able to fully concentrate on the lecture instead of putting all my efforts copying the notes [since I was such a slow writer.]
I promised myself to work on the assignment during last weekend, but I couldn't. Whatever I do, it has to be done till next Monday. I have done some scratch works for the assignment, now I need to phrase them into solid proofs. Problem set #2 was due today. Because my mind was taken over by the concerns regarding the first assignment, I completely forgot about the problem set. It was not until the last night when I suddenly remembered to finish it. I need to check the course website more frequently to remind myself what is coming up next.
This was our third week on the topic of induction. It is amazing how well inductive reasoning coexists with other mathematical principals such as Principle of Well-Ordering. We have spent all the past weeks studying induction, now I don't have any hesitation using complete induction anymore. It was not as if I went through every practice question in the textbook to get myself familiar with strong induction. It was rather due to the effective lecture style which was newly adopted this year. Thanks to the tablet, I was able to fully concentrate on the lecture instead of putting all my efforts copying the notes [since I was such a slow writer.]
I promised myself to work on the assignment during last weekend, but I couldn't. Whatever I do, it has to be done till next Monday. I have done some scratch works for the assignment, now I need to phrase them into solid proofs. Problem set #2 was due today. Because my mind was taken over by the concerns regarding the first assignment, I completely forgot about the problem set. It was not until the last night when I suddenly remembered to finish it. I need to check the course website more frequently to remind myself what is coming up next.
Friday, September 19, 2008
Tasting Various Induction Flavours
Sept. 19-08
Complete induction was introduced in the first lecture of week two. We have gone through practice questions of complete induction. It is a very convenient technique to prove complicated statements. Depending on the question, complete induction may require more writings than simple induction does, but a strongly inductive proof can be used to solve a wide variety of problems. Somehow, I felt uncomfortable using complete induction simply because assuming the truth of all the previous cases just sounds a little too good. I think this sense of oddness will naturally disappear once I have enough experience with the applications of complete induction.
The first problem set was due today, and it was a good review of lecture materials. In the other hand, assignment #1 which was posted this week appeared very challenging. I better start working on it right away.
Complete induction was introduced in the first lecture of week two. We have gone through practice questions of complete induction. It is a very convenient technique to prove complicated statements. Depending on the question, complete induction may require more writings than simple induction does, but a strongly inductive proof can be used to solve a wide variety of problems. Somehow, I felt uncomfortable using complete induction simply because assuming the truth of all the previous cases just sounds a little too good. I think this sense of oddness will naturally disappear once I have enough experience with the applications of complete induction.
The first problem set was due today, and it was a good review of lecture materials. In the other hand, assignment #1 which was posted this week appeared very challenging. I better start working on it right away.
Friday, September 12, 2008
First Week of CSC236H1 Fall 2008
Sept. 12-08
CSC236, a theory course of computer science, started this week with three lectures in a row. All lectures focused on the Principle of Simple Induction this week. I have learned the basics of both simple and complete induction in CSC165, so I had a good idea of the material we were doing. Otherwise, it would be very problematic if I cannot even keep up with week-one material although I did have difficulties understanding chapter zero of the textbook.
Chapter zero was supposed to be a review for those who had certain degrees of background for CSC236. When I skimmed through this chapter, I was stunned at some unfamiliar words such as "proper subset", "partial order," and "contiguous sub sequence." I had to reread the chapter several times to have a good grip of its content.
Regarding the lecture style, I am glad that Danny discarded the idea of using blackboards this year. I absolutely love his new medium, the tablet. Writings tend to be more packed in a blackboard since it does not save what was written ten minutes ago. It is easier to read off from a tablet.
CSC236, a theory course of computer science, started this week with three lectures in a row. All lectures focused on the Principle of Simple Induction this week. I have learned the basics of both simple and complete induction in CSC165, so I had a good idea of the material we were doing. Otherwise, it would be very problematic if I cannot even keep up with week-one material although I did have difficulties understanding chapter zero of the textbook.
Chapter zero was supposed to be a review for those who had certain degrees of background for CSC236. When I skimmed through this chapter, I was stunned at some unfamiliar words such as "proper subset", "partial order," and "contiguous sub sequence." I had to reread the chapter several times to have a good grip of its content.
Regarding the lecture style, I am glad that Danny discarded the idea of using blackboards this year. I absolutely love his new medium, the tablet. Writings tend to be more packed in a blackboard since it does not save what was written ten minutes ago. It is easier to read off from a tablet.
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