Last Post!

04/12/12  I think I actually did end up posting every other week.  Oh well.  On assignment 3:  I ended up having to rush through it in order to have enough time to write an essay due the following Monday and do the 207 assignment due the Sunday.  The first assignment question had me stumped for a while, so I had to go back and read more about DFSAs to figure it out.  I guess the exam is next week, but I think it should go over well.

    Now, for the problem solving bit.  I ended up trying the "negative coconuts" problem.  I started it right after making my last post, gave it about an hour, and well... forgot about it until recently.  My first strategy was to let the original pile of coconuts be a number x, then step through the event after each man wakes up.  After each man, x has 1/5 removed and an extra 1 removed for the monkey.
    I decided to scrap that plan after getting to about the 3rd man, since all the substitution was going to create a giant mess.  My next attempt at the problem involved a similar plan of starting with x as the number of coconuts each man receives in the morning, then working backwards.  Again, that was going to create a big, slightly more complicated mess.
   Looking over the problem, there are some simple facts:  The monkey received 5 coconuts before the morning, since each man gave him 1.  The number of coconuts in the pile as a man wakes up always has a remainder of 1 when divided by 5.  The number of coconuts after the last man wakes up is divisible by 5.
    So, I then wrote out the amount of coconuts after each man wakes up like so:
man 1(x2) : x - x/5 - 1
man 2(x3) : x2 -x2/5 - 1
And so forth, until x6 is also equal to 5y, where y is the amount each man gets in the morning.
    I attempted to work backwards again, stating that each step is 4/5 the previous one.  I ended up with x = (5^5)/(4^5)y.
    Since the original question doesn't actually provide any numbers besides that there are > 5 coconuts (since the monkey gets 5), the initial amount will depend on the amount each man gets in the end.

     Now, I sort of assumed that the subtraction of 1 coconut after each man would sort itself out to make my life easier.

After looking up the answer:  I was close.  The provided answer did each step opposite the way I did, and  it worked out better.  The solution also discussed the idea of starting with negative coconuts (as hinted by the title), which I figured was probably a solution, but dismissed since I think it's not really a "fair" way out if having a negative number of coconuts is impossible.  The answer is dependent on what you say each man got in the end, but it doesn't quite work out to what I got.  But at least I tried, right?

Fourth Post!

20/11/12  I guess my memory has turned this thing into a bi-weekly thing.  Oh well, my loss.  Now... what's happened since my last post...?  I think there was the test.  Again, it was simpler than I had expected, so it went pretty well.

With multiple extensions in my courses, things are finally starting to relax which means I'm able to get a start on assignment 3 today.  This is a good thing, since after reading over it I'm going to have to do some learning.  Since what we're learning now is largely new material (I think), assignment 3 requires more than just stepping through an ordinary proof structure.

Not much else I can say.  I guess I still have to blog about a proof or something, but that can happen next week.

Third post!

07/11/12  I think I forgot to post again last week?  Maybe not.  Anyway, I think things have been gong well in terms of 236 (maybe not so much for everything else. 207 is a time sink).  Assignment 2 was fairly short and easy, so maybe my proofs weren't elaborate enough.
    The second test is tomorrow, but I've had very little time to prepare for it.  I think I'm learning most of the material from tutorials since I have work from ~7am - 3pm every Thursday, so the exhaustion makes it a little difficult to follow what Danny is saying in lecture.  That being said, I think I've decided that 236 is my favorite course this semester because of the nature of the material.  Once you have a good understanding of proofs (thanks, 165) then it's not so bad picking up new material.  The progression of material is also at a nice pace, and doesn't get overwhelming like some other "mathy" courses.
    Hopefully my tired brain can pull its weight on tomorrow's test like it did the last time.  I can't overstate how pleased I am that there's a break after this weekend though -- it should give me enough time to learn three week's worth of linear algebra after writing up a STA assignment.

Second post!

28/10/12  Forgot to post last week.  Oops.  Test and assignment 1 went well, but unfortunately I haven't even read the questions for assignment 2 at this point.  Not sure if two questions makes the assignment look more intimidating or if I should be looking forward to less work.  At least I can devote my whole week to finishing the assignment.  Not sure what else to say -- having a hard time thinking after working 26 hours in 4 morning shifts since Thursday.  I guess that's it.

First post!

14/10/12.  Finally getting around to posting this.  What time I have left after working tends to be dominated by whichever subject I have a test or assignment coming up.  This week ending was full of 236 with the assignment due last Friday and the test 4 days ago.

The assignment was interesting.  It was the first real mathematical induction I've done since CSC165 in last year's fall semester (the first tutorial quiz I found to be simple, considering it was only slightly different from the example done 5 minutes beforehand).  Complete induction, on the other hand, was a new experience.  I was surprised to find it no harder than "simple" induction (hopefully I wasn't just doing it wrong).  The last two assignment questions I found to be the type where you keep thinking and working out a system until finally it clicks (although I'm not sure Id' have figured out the Q3 method had Danny not given the tip about subsets).  Overall: a good way to relearn how to do proofs.

The test:  Went much better than expected.  Going into the test, all my knowledge about well ordering and structural induction came from the text and lectures.  Even the day before the test (prior to studying)  I wouldn't have been able to describe either if someone asked me to.  When it was actually time to write the test, my biggest concern was doing 3 proofs in 50 minutes.  But after looking it over, I thought I was missing something.  The questions seemed deceptively easy (hopefully that's not the case).  Even after working from 7:00 - 15:00 prior to the test, all 3 poofs were downed no problem.  I guess actually putting time into 165 paid off (too bad I didn't put that much effort into calculus).

With the test and assignment out of the way, I guess this next week will be spent almost entirely on !236.