This post is 2 days late, but then again, I have been very busy. Week 3 was nice. I really liked the problem with the round-robin tournament, especially its solution. Seeing it put a smile on my face. It was so simple, and yet I could not think of it on my own. That also upset me a bit.
I am ashamed to say that I did not pay any attention to the proof of the equivalence of the three principles. It was about 7:30 and I was very tired. However I did read the proofs in the notes.
I also liked the wrong proofs that we had to analyze. I am a big fan of bug hunting in general, be it in proofs or programs. It's like vaccination. In fact, I would like to do more of this here and there, especially in circumstances when we are not expecting them. It will make us less susceptible to blindly believing things we are told. Also, it will keep us on our toes.
I finally finished the first 3 questions of the assignment. In retrospect, my proofs in the third question could have been better. That's what happens when you leave things for the last minute.
Tuesday, September 30, 2008
Saturday, September 20, 2008
Problem set 2.
And I am finished with problem set 2. I was a little disappointed when I saw "5 cent, and 11 cent stamp". I thought it would be identical to what we did in class, but question (b) makes it a good problem set. It's that kind of problem that can be solved by brute force, but that approach is annoying and long enough to make you look for better ways.
Friday, September 19, 2008
Week 2, continued.
I am sorry for the two quick posts, but this is a bit too long to just stick in the previous one as an edit.
A few days ago we proved that any chocolate bar of n squares can be broken up into 1x1 squares by n-1 breaks. We didn't consider the case n=0. I claimed that P(n) was vacuously true for n=0 because there are no chocolate bars with 0 squares. Prof. Heap countered this claim, but I am not fully convinced and this matter has been bothering me since then.
How can there be a chocolate bar with 0 squares? If we reduce the size of a chocolate bar to 0 rows and 0 column, we're left with nothing. So there's nothing there, so there is no chocolate bar at all.
Right?
A few days ago we proved that any chocolate bar of n squares can be broken up into 1x1 squares by n-1 breaks. We didn't consider the case n=0. I claimed that P(n) was vacuously true for n=0 because there are no chocolate bars with 0 squares. Prof. Heap countered this claim, but I am not fully convinced and this matter has been bothering me since then.
How can there be a chocolate bar with 0 squares? If we reduce the size of a chocolate bar to 0 rows and 0 column, we're left with nothing. So there's nothing there, so there is no chocolate bar at all.
Right?
Week 2.
I must say that this has been a very rough start to the year. My bad time-management skills and laziness meant that I did not do as much work as I should have in the first week. So, unfortunately, this week I have focused on math to the exclusion of all else, including csc236 and this blog. This means that the assignment (still not started) is in the bottom of a very long priority queue, but at least I have two weekends to complete it. All of this is making me suspect that maybe summer school burned me out.
I finally could not endure any more of the (how long before the sled stops)/(what's the speed at position x)/(what's the terminal velocity) questions in MAT267, so I dropped it and took CSC438. I am excited and terrified at the same time. It should be very theoretical and fun, and I am looking forward to Professor Cook's lectures. On the other hand, it's a fourth year course (graduate course too), and I have missed the first four lectures, and still have not done all the reading. This relates to CSC236 in the following way: 438 conflicts with 236 on all 3 days, so I will have to start attending the evening section. I am not happy about this. I took an evening course last year (ECO100), and the third hour was a battle just to stay awake. On the other hand economics is a lot more boring than computer science so it may not be as bad as I am expecting.
One more thing. I was very upset to discover that CSC448 has been canceled. It almost seems like a sequel to 438, it has all the prerequisites of 438 with the addition of CSC236, and my next semester isn't very busy so it would have been perfect for me to take. But it is canceled, and 438 seems like it is offered in alternating years, which makes me think that 448 is offered in alternating years. So if it was supposed to be offered this year, it might not be offered the next year, which means I cannot take it before 4th year.
It is a pity - many great courses were canceled this year.
I finally could not endure any more of the (how long before the sled stops)/(what's the speed at position x)/(what's the terminal velocity) questions in MAT267, so I dropped it and took CSC438. I am excited and terrified at the same time. It should be very theoretical and fun, and I am looking forward to Professor Cook's lectures. On the other hand, it's a fourth year course (graduate course too), and I have missed the first four lectures, and still have not done all the reading. This relates to CSC236 in the following way: 438 conflicts with 236 on all 3 days, so I will have to start attending the evening section. I am not happy about this. I took an evening course last year (ECO100), and the third hour was a battle just to stay awake. On the other hand economics is a lot more boring than computer science so it may not be as bad as I am expecting.
One more thing. I was very upset to discover that CSC448 has been canceled. It almost seems like a sequel to 438, it has all the prerequisites of 438 with the addition of CSC236, and my next semester isn't very busy so it would have been perfect for me to take. But it is canceled, and 438 seems like it is offered in alternating years, which makes me think that 448 is offered in alternating years. So if it was supposed to be offered this year, it might not be offered the next year, which means I cannot take it before 4th year.
It is a pity - many great courses were canceled this year.
Saturday, September 13, 2008
CSC236, First Impressions
I must admit, coming into this course I was skeptical. This was fueled by the disappointment of not being able to take CSC240 (since it's only offered in the second semester) and by my suspicions that this course would have a lot of the bad things of CSC165.
I had mixed feelings about CSC165. One one hand, I liked the small amount of material that we learned. On the other hand, I did not appreciate the enormous attention that was paid to the needless formality.
The excessive formality seems to be gone, which is very good, but it has been replaced some other annoying things.
One of those things is the emphasis there seems to be on the problem solving thought process. This is apparent when we do all those exploratory cases in the proofs in class. I don't think that is a good way to approach induction. I find that going immediately to the general induction step is usually more enlightening. It forces you to think in an abstract manner and thus, you gain a deeper understanding of the problem. Moreover, in non-trivial induction proofs (unlike the ones we have been doing) it is usually impossible (or not any easier than the general case) to explore the first few cases. If anyone wants to know what I mean, go to the mathematics section of bookstore and open Friedberg's "Linear algebra" (4th ed.) to page 261 or 490 and read the proofs there.
That is also apparent in the "as well as give some insight into how you found the solution" part of the assignment. Everyone thinks differently and I don't think much can be gained by learning some other person's way of approaching a problem.
Another annoying thing is that we have to submit the assignment solutions as .txt documents.
This seems counterproductive, since typing math is a slow process and because we are doing it in notepad (or some other similar editor), the end result will be very ugly and hard to read. Every small change that we want to make will mean that we have to review and make changes to the whole document after that point (the characters per line limit makes this worse).
One of the good things is that prof. Heap is good at explaining things. I like the use of the tablet PC, and I definitely appreciate the black backgrounds, with yellow and green writing. White backgrounds are harder on the eyes, white writing on black backgrounds provides too much contrast, but yellow and green on black is perfect. It also probably uses less energy compared to white backgrounds, making it more efficient. Efficiency is good.
Even thought this post might seem a bit negative, I am optimistic in thinking that some of the "bad" things that I pointed out will go away, and the rest will not be as big of a problem as they seem. Also, I am very much looking forward to the last 6 weeks (which is when we learn about automata and context-free grammars). However, I wish we did not have to spend so much time on program correctness. We have done a lot of it in CSC165, and it seems like we will do a lot more in CSC263, so I am afraid that what we do in this course might be made redundant by what we do in those two courses.
I had mixed feelings about CSC165. One one hand, I liked the small amount of material that we learned. On the other hand, I did not appreciate the enormous attention that was paid to the needless formality.
The excessive formality seems to be gone, which is very good, but it has been replaced some other annoying things.
One of those things is the emphasis there seems to be on the problem solving thought process. This is apparent when we do all those exploratory cases in the proofs in class. I don't think that is a good way to approach induction. I find that going immediately to the general induction step is usually more enlightening. It forces you to think in an abstract manner and thus, you gain a deeper understanding of the problem. Moreover, in non-trivial induction proofs (unlike the ones we have been doing) it is usually impossible (or not any easier than the general case) to explore the first few cases. If anyone wants to know what I mean, go to the mathematics section of bookstore and open Friedberg's "Linear algebra" (4th ed.) to page 261 or 490 and read the proofs there.
That is also apparent in the "as well as give some insight into how you found the solution" part of the assignment. Everyone thinks differently and I don't think much can be gained by learning some other person's way of approaching a problem.
Another annoying thing is that we have to submit the assignment solutions as .txt documents.
This seems counterproductive, since typing math is a slow process and because we are doing it in notepad (or some other similar editor), the end result will be very ugly and hard to read. Every small change that we want to make will mean that we have to review and make changes to the whole document after that point (the characters per line limit makes this worse).
One of the good things is that prof. Heap is good at explaining things. I like the use of the tablet PC, and I definitely appreciate the black backgrounds, with yellow and green writing. White backgrounds are harder on the eyes, white writing on black backgrounds provides too much contrast, but yellow and green on black is perfect. It also probably uses less energy compared to white backgrounds, making it more efficient. Efficiency is good.
Even thought this post might seem a bit negative, I am optimistic in thinking that some of the "bad" things that I pointed out will go away, and the rest will not be as big of a problem as they seem. Also, I am very much looking forward to the last 6 weeks (which is when we learn about automata and context-free grammars). However, I wish we did not have to spend so much time on program correctness. We have done a lot of it in CSC165, and it seems like we will do a lot more in CSC263, so I am afraid that what we do in this course might be made redundant by what we do in those two courses.
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