Some quick thoughts on Test #1: 3 questions, 8 marks each. The first one was a binomial expression which I attempted to solve via simple induction. I'm fairly sure this is the right flavour to use for this question; except I got stuck on the induction step and couldn't figure out how to show P(n) --> P(n+1). I probably spent a little too much time on this question.
Question 2, with the Fibonacci sequence. I used complete induction. I don't totally remember the question. In my head I think i'm getting it confused with #1 and mixing the problems. I think it was F(n)^2 > 2n? Or something of that nature. Using complete induction, my proof went something like this; I showed the F(n) is the sum of F(n-1) and F(n-2) [by definition], which are both greater than 2(n-1) and 2(n-2) respectively [by IH]. Since F(n)'s predecors were both greater than 2n it should follow F(n) also.
Question 3, I'm drawing a blank on what the question was. I do remember running out of time since I spent a little much time thinking about #1's induction step. I think I started out using simple induction and then realized I should've used complete induction. I ran out of time to fix this and to finish the proof, but I had a structure of a proof and I put down some ideas of how to solve it.
Overall I felt prepared for the test, I just ran into a the problem of not being able to see the induction step for #1 which cost me some time. I always feel a little rushed when writting a 50min test. But I can't complain, everyone else is in the same boat and a few people seemed to have finished and left the room with some time to spare.
Saturday, October 11, 2008
Wednesday, October 8, 2008
Assignment 1 Marks and Test Prep
Just got back the marks and feedback for A1. I was fairly pleased with my marks. Only question I really lost a lot of marks was 3b, since I wasn't too sure which part from 3a to use. But all in all I'm pleased with how things went.
Seems like A1 was due yesterday and now midterms are coming for all my courses. I'm not too worried for Friday. I've been keeping up with all the readings and lecture material so I should be fine. Just going to go over some exercises and through the slides. Time for some reading!
Seems like A1 was due yesterday and now midterms are coming for all my courses. I'm not too worried for Friday. I've been keeping up with all the readings and lecture material so I should be fine. Just going to go over some exercises and through the slides. Time for some reading!
Monday, September 29, 2008
PSet 2 and Assignment 1
Just finished a really busy weekend, had to finish writing up the problem set for Friday. The problem set wasn't bad. Took a little bit of scratch work to come up with k for the postage stamps. Followed by a proof using complete induction.
For part b) to prove that k is an impossible postage to create with 5-cent and 11-cent stamps was fairly simple too. The question gave a little hint that induction wasn't the way to go so I used a proof by contradiction. It seems the sample solution was a lot less formal in proving this but none the less arrives at the same conclusion.
Assignment 1 was definitely more challenging than the problem sets. I found myself thinking about the problems a lot more than for the problem sets. Number 3; the golden ratio definitely had me scratching my head for a big. Even after reading up on it a bit, I was still pretty stumped. I came up with a solution that associated the principle of well ordering but I'm not sure if I was 'hitting the nail on the head'. As for part 3b, I was just as baffled but of course took a shot as trying to prove it while using part a. I guess I will just have to wait until the sample solution comes out or when I get some feedback on my submission.
Oh and I mistakenly hand-wrote my assignment instead of typing it. I felt a bit dumb not knowing that it had to be typed; while everyone else in the lecture seemed to have typed theirs. In my defense no where on the assignment does it say that it must be typed. Only by looking at a specific post on the bulletin board by Prof. Heap does it say it must typed. Luckily the assignment wasn't due for another 11 hours and I had plenty of time to go type up my answers since all the hard work was already done.
For part b) to prove that k is an impossible postage to create with 5-cent and 11-cent stamps was fairly simple too. The question gave a little hint that induction wasn't the way to go so I used a proof by contradiction. It seems the sample solution was a lot less formal in proving this but none the less arrives at the same conclusion.
Assignment 1 was definitely more challenging than the problem sets. I found myself thinking about the problems a lot more than for the problem sets. Number 3; the golden ratio definitely had me scratching my head for a big. Even after reading up on it a bit, I was still pretty stumped. I came up with a solution that associated the principle of well ordering but I'm not sure if I was 'hitting the nail on the head'. As for part 3b, I was just as baffled but of course took a shot as trying to prove it while using part a. I guess I will just have to wait until the sample solution comes out or when I get some feedback on my submission.
Oh and I mistakenly hand-wrote my assignment instead of typing it. I felt a bit dumb not knowing that it had to be typed; while everyone else in the lecture seemed to have typed theirs. In my defense no where on the assignment does it say that it must be typed. Only by looking at a specific post on the bulletin board by Prof. Heap does it say it must typed. Luckily the assignment wasn't due for another 11 hours and I had plenty of time to go type up my answers since all the hard work was already done.
Sunday, September 21, 2008
2nd Week
Just finished up the 2nd week of classes and the first problem set. The problem set wasn't bad at all. It was very similar to the lecture which was good. It let's you know if you're really understanding the lecture material. It's easy to come to class and watch proof be written up and follow along; but it's a bit different when you have to do all the thinking and writing.
I'm sure glad the problem sets aren't like the problem sets in MAT137!
I've started up on problem set 2 but have yet to do much work on assignment 1. I'm kind of on the fence of how to manage my time between these two assignments as well as my other courses. Either way it all needs to get done. Hopefully I can finish up the problem set by tomorrow and get moving on assignment 1.
I'm sure glad the problem sets aren't like the problem sets in MAT137!
I've started up on problem set 2 but have yet to do much work on assignment 1. I'm kind of on the fence of how to manage my time between these two assignments as well as my other courses. Either way it all needs to get done. Hopefully I can finish up the problem set by tomorrow and get moving on assignment 1.
Monday, September 15, 2008
First Post
Just starting the second week of the course. Things are already starting to pick up in terms of course work.
The first week covered induction proofs. Not too bad, similar to CSC165 so far. I don't feel too bad about the material to this point; but am afraid of what the rest of the course holds.
The first assignment and first problem sets have both been posted. I've downloaded both but haven't had a chance to look at them yet. I'm going to get on it tonight. Hopefully they won't be too bad and similar to lecture material.
Not much else to say at this point. Will be updating soon.
The first week covered induction proofs. Not too bad, similar to CSC165 so far. I don't feel too bad about the material to this point; but am afraid of what the rest of the course holds.
The first assignment and first problem sets have both been posted. I've downloaded both but haven't had a chance to look at them yet. I'm going to get on it tonight. Hopefully they won't be too bad and similar to lecture material.
Not much else to say at this point. Will be updating soon.
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