This question has deceptively simple constraints.
The pattern seems quite unusual, but it is not difficult to see a recursive definition for G(n) that behaves similarly to the Fibonacci sequence, with a twist. showing that what I have is indeed the recursive formula is probably is sufficient for the proof part of the question
The hard part of the question is in proving that my formula is indeed correct. I believe I know how to, with some help from a combinatorics formula.
This is a great question that I am really enjoying working through. It feels great to work through a problem like this without outside help and without getting stuck.
Wednesday, October 22, 2008
Tuesday, October 21, 2008
Test 1
Test 1 didn't go as well as I expected.
Even though i had the right induction insights, I had lots of mistakes in the write up. With one question completely missing the base cases. I also got marks off for not stating the conclusion... I thought the conclusion was implicitly obvious if we stated P(n) clearly... The course notes are like this too iirc.
The test ended with me not having enough time to finish write ups.
I think I spent too much time thinking of the insight, and had to rush through the write up. I Need more practice.
Had to miss class this Monday to complete a music essay. Apparently I missed the lecture about preconditions, and PS4 is on preconditions. I have no idea what it's about, and lecture notes aren't posted yet. so I must attend the evening lecture this week.
Even though i had the right induction insights, I had lots of mistakes in the write up. With one question completely missing the base cases. I also got marks off for not stating the conclusion... I thought the conclusion was implicitly obvious if we stated P(n) clearly... The course notes are like this too iirc.
The test ended with me not having enough time to finish write ups.
I think I spent too much time thinking of the insight, and had to rush through the write up. I Need more practice.
Had to miss class this Monday to complete a music essay. Apparently I missed the lecture about preconditions, and PS4 is on preconditions. I have no idea what it's about, and lecture notes aren't posted yet. so I must attend the evening lecture this week.
Friday, October 10, 2008
Unwinding
My blog was apparently flagged by a spam filtering system implemented by blogger.com... They say the system is inherently fuzzy... I wonder if it uses fuzzy logic and whether I will learn about it in later CSC theory courses.
I really like the way Danny first discussed and showed how the sum of the Fibonacci sequence up to n is equal to F(n+2) - 1. Then in the next lecture, showed us how to unwind T(n) of zpf(n), where the same sequence of Fibonacci sums showed up. The way he structures the course is really helping me learn more than I would have otherwise.
I am still feeling unclear about how to get from unwinding to a closed form, how and if unwinding helps in proofs. I was feeling the same about PSI, PCI, PWO as well, but now I feel quite comfortable with them. I'm sure with a bit of time and practice I will feel comfortable and clear about it
Written the first term test today. It was not too bad, but I wish I had time to finish the subset question... I believe I was on the right track . If I had 10 more minutes I might have finished a correct proof. I suppose I spent more time than I should have on the other questions, which are pretty straightforward.
In response to Danny's comment on my test structure concern post: I thought the test was structured quite well and fairly. Although personally I felt that I spent more time looking for insight than I'd have been comfortable with, and possibly more time than Danny intended. Not so used to doing the problems with such a short time constraint. All the practice I had in a1 and problem sets have days-long time constraints. I will be keeping that in mind while I do problems from now on, and perhaps not taking such a leisurely pace.
I really like the way Danny first discussed and showed how the sum of the Fibonacci sequence up to n is equal to F(n+2) - 1. Then in the next lecture, showed us how to unwind T(n) of zpf(n), where the same sequence of Fibonacci sums showed up. The way he structures the course is really helping me learn more than I would have otherwise.
I am still feeling unclear about how to get from unwinding to a closed form, how and if unwinding helps in proofs. I was feeling the same about PSI, PCI, PWO as well, but now I feel quite comfortable with them. I'm sure with a bit of time and practice I will feel comfortable and clear about it
Written the first term test today. It was not too bad, but I wish I had time to finish the subset question... I believe I was on the right track . If I had 10 more minutes I might have finished a correct proof. I suppose I spent more time than I should have on the other questions, which are pretty straightforward.
In response to Danny's comment on my test structure concern post: I thought the test was structured quite well and fairly. Although personally I felt that I spent more time looking for insight than I'd have been comfortable with, and possibly more time than Danny intended. Not so used to doing the problems with such a short time constraint. All the practice I had in a1 and problem sets have days-long time constraints. I will be keeping that in mind while I do problems from now on, and perhaps not taking such a leisurely pace.
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