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.
Friday, September 26, 2008
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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