Week 6

I did not attend lecture this week due to the damned A1 for CSC207 so my comments will be solely based on Prof Heap's evening lecture notes. 

Time complexity: We did this a bit last year in 165 (i think) and 148 so this is not new. However, applying the unwrapping principle to time complexities is a nice summation of some of the things we learned so far. I found it interesting how we were allowed to essentially ignore a majority of cases and do the proof for the cases we can, then come back to the other ones later. This strategy seems like it will become quite useful over time. (Since I am writing this retrospectively I know how handy it comes in for A2). The proof however, was very standard, maybe even obvious, after that. 

Week 5

I was hoping on seeing my test before posting this entry but it's pretty late as it is so I will reply to this with my comments about the test when I see it.

The lectures: Well the problem set brings another lost mark from a stupid mistake, but not a bad result anyway. We discussed finding closed forms for recursively defined functions and I found this quite interesting. I have myself wondered if there was an easier way to find those Fibonacci numbers, had I known the closed form those Grade 12 Data tests would have been so much easier. At least I have a new tool in my toolbox. Finding closed forms (using the exponential method) is pretty intuitive once I saw it but I do not believe I would have ever figured out something like that.

Obviously this technique can be applied to almost any recursively defined function in some way yet the Fibonacci one in my opinion is the most interesting. The rest of the proofs were essentially things ive seen before and did have educational value but didn't catch my interest.

Week 4

So my blog has been blocked. Apparently I have created a spam blog where I am spamming very offending links/comments? Now a "human" must review my blog to make sure I'm not spamming. Oh well, I can't fall behind my sLog.

So heres my thoughts on week 4. More induction! Except this time, we use induction on recursively defined functions. Recursion is pretty straight forward (unless you need to figure out how to code it at times) but when I'm doing computer science my brain does not want to think in terms of math, therefore I don't like "unwrapping". But I must admit, I have always found the Fibonacci patterns, despite their recursive nature, quite interest. Next we looked at binary trees and I rather enjoyed this proof. I'm not sure I would have easily seen the idea of "unwrapping" in order to keep both values in the equation relatively similar and I am glad to have seen this now, rather than on the test for the first time.

Yet there is one thing about this week's lecture, and I am asuming from hereon out, that I am beginning to think will frustrate me slightly. We are done with python, and all these problems with python sure aren't helping me remember my java syntax from highschool. I'm sure there's people who were are not required to begin learning java and appreciate the problems being in python but I am wondering if test questions can be written in our programming language of choice. Speaking off the test, it's tommorow! ahh!

Week 3

So week 3 and the assignment are done.

The lectures this week were interesting. I enjoyed the circular proofs of the three induction principles. However, I find a problem with the way we chose to prove them. We said that we would need to take any one of the as an axiom and can prove the other two that way. I have no problems with any of the principles being axioms as they just seem obvious, but if they are axioms then none of them should require a proof. It seems very arbitrary to say "pick one, the other two need proofs". In short, they should all either be axioms or require proofs using something other than a different principle of induction.

The assignment was pretty easy (we will see if this statement holds true when I receive my marks). The first question was structured in such a way that the answer was obvious, although I'm sure that was intended as it was the first question. The second question, about the rotating lunch orders, I found very interesting. The proposition of creating lunch menus that do not differ by more than 1 choice is very easy, yet I find that I wasn't thinking of the algorithm. I somehow naturally knew what the structure should be and only after writing a few different sized lunch combinations did I notice the algorithm. The proof was straightforward. The final question with the golden ratio had me fooled for a little as I tried to equate the hint to the formula, rather than plugging in n1, and n2, into the formula to transform it into the form that the hint was. However, after I reached the n2/(n1-n2) form it was smooth sailing from there.