week 7

Thankfully, q4 in the assignment does not deal with complexity, and is on correctness, which I find much easier.  I'm finding q1 to be difficult, everytime that I think I'm close to coming up with a formula, I end up stuck (and frustrated).  I'm also finding it difficult to express q3 in the assignment without using the stats combination formula, but I think that its fine that I use it, even if it isn't the model solution.  For q2, I think I have an answer, but it seems almost too easy.  We'll just have to wait and see...

As I mentioned, program correctness looks to be much easier (at least for now).  Rather than having to find induction formulas, or manoeuvre through some tricky proof in complexity, its more like providing an analysis of an already complete algorithm.

week 6

Right now I'm currently busy with assignment #2.  In general, I'm finding divide and conquer recurrences kind of tricky.  Proving a conjecture based upon a more simply defined function such as Fibonacci sequence looked to be much more straightforward.  Trying to deal with complexity, as well as the ceilings and floors looks to add a new degree of difficulty.  But I suppose its a matter of working through it.  The last question on the assignment looks tough, and deals with a divide and conquer recurrence.  I imagine it will be a lot of work to tackle proving a tight asymptotic bound.  I'll write up another post later in the week, after I really get into the assignment.  

after test 1

Well, I found out that the reason q3 was so troubling for me was because of an error in my math.  It was a simple arithmetical error that gave me -phi for n3/n4.  And as a result, I thought that n4 was negative.  I now see (and it makes perfect sense) that the cycle of natural numbers will proceed indefinitely, and that a contradiction can be found by trying to find a smallest number.  I guess the only thing that can be learned from this is to be more careful, and double check all my results.  Also, more time (and help sought) for the next assignment would be advisable.

I had just went through test 1 last week, and found it to be fair, yet challenging.  My last question, was where, if I remember correctly, I had to show that a set of natural numbers {1, ..., n}, which was missing either 1 or 2, or both, had 3*2^(n-2) subsets.  I initially took the wrong approach, where, for some reason, I tried to directly prove this.  I realized, with 5 minutes left, that this question was exactly like the ones seen in the PS and assignment.  I didn't need to show that it works for P(n), but only show that P(n)=>P(n+1).  I will probably get part marks for this, but again, lesson learned.  Hopefully, or eventually, I'll get quicker at seeing what kind of problem is in front of me, and then taking the right approach :).

A1 over with, next up -- test 1

Well, after trying to work through A1, and understanding it better, it proved to be much tougher than I initially thought.  I think I answered the first two questions correctly, but had trouble with the third, and ended up giving a partial solution.

Next time I'm going to start working at the assignment much sooner, so that I can visit office hours and get help, if I need it.  I now have just over a week until the first test and am going to start preparing for it right away.  I'll go through all the exercises in the textbook and maybe go through previous terms questions/tests as well.  Maybe also do some csc165 proofs, just to rehash everything.

First post; difficulties with induction

This is the first post in my CSC 236 Slog, and I welcome anyone who has given their time to read it.  Over the next few months, I will keep an active record of all the challenges that I face in CSC 236, as well as my plans on overcoming them, and my expressions of relief and happiness if or when I do overcome them.  So far, I've found the course to be fairly challenging and have spent a fair bit of time looking at the given proofs and then looking them over again.  I hope, and believe, that with time and effort they will eventually seep into my head and I will gain a greater understanding for the material.  I realize I am late to the game, and I should have started this blog a week ago, so this post might be quite long just to catch up. 

It's been a couple of years since I last took CSC 165, and unfortunately this course looks like it is heavily dependent upon it.  Thankfully, I began refreshing material, as well as looking at the past year's version of CSC 236 during the summer and I believe I am ready for this course.  I remember doing induction in high school, but of course the problems were nowhere near this level.  The preliminaries section at the beginning of the course notes helps immensely in learning and refreshing the basics of the set theory used in this course.  Many of the terms such as superset, proper superset/subset, and intensional/extensional I had never heard before.

So far, after week 1 and 2, we have gotten nearly through the first chapter on induction.  I feel as though we've gone through a lot material in the first 2 weeks, but I guess that might be expected from such a demanding course.  I'm currently at the point where I have a decent grasp of simple induction, and am currently getting a better understanding of complete induction, as well as its differences from simple induction.  I'm still a little unsure of when to use base cases (and how many), and when not to.  I think I will have a better understanding after problem set 2 and assignment 1.  I've started assignment 1, and have a pretty good idea of how to go about the first 3 questions.  To be honest, I'm finding it pretty easy, and am hoping that it will be enough to prepare everyone for the first test.  I will probably go to the help center or one of the office hours just to make sure that I'm on the right track.  There are also a few problems in the course notes that I'm unsure of why they took the approach they did.