Week the Last: Some Definitions

So I've slacked a bit in this blogging business lately. In my defense, I had nothing to write about (still don't really, but I feel I've kind of got to write something at this point so here's hoping it's slightly more substantial than mere gibberish.)

So, what's been happening since last I wrote? (Good question, wish I knew.) Well, I do remember we had the second (and last, bar the final) test of the course, and the second assignment due as well. We got the marks back too, which goes to show just how absent I've been. Both went quite well (I'm being modest; I feel I deserve a pat on the head or something at this point.) so I'm (super) happy (ecstatic) with that.

In class we've been doing proofs with "Big-O", Omega and Theta. In lieu of recreating massively long-winded proofs here, I'll simply write the definitions for future reference:

Big-O:
formally, there exists a 'c' and 'B' such that for every 'n', if n >= B --> g(n) <= c*f(n)
in English, if g belongs to O(f), that means that g grows no faster than f. In other words, f is an upper bound of g.
Omega (aka the horseshoe):
formally, there exists a 'c' and 'B' such that for every 'n', if n >= B --> g(n) >= c*f(n)
in English, if g belongs to Omega(f), then g grows at least as fast as f; f is a lower bound for g. In other words, it's basically the opposite of the Big-O (yay opposites!!)
Theta (the halved egg):
formally, there exists a 'c1', 'c2' and 'B' such that for every 'n', if n >= B --> c1*f(n) <= g(n) <= c2*f(n)
in English, g grows at the same rate as f. f is both an upper and lower bound for g.

Boy, will I have fun with those tonight while working on assignment 3! All joking aside, while I do need more practice before I'm fully comfortable with them, they're not all that bad. They just look super funny (drawing horseshoes is harder than I thought).

All this aside, there is at least one more problem that I hope I'll get a chance to blog about before this course finishes and I lose the artificial excuse to do math for fun. Danny introduced the "Penny Piles" problem a few weeks back, which has proven quite fun to work on, but less fun to complete (and, being a bit of a perfectionist, I must say that it's part of the reason I've delayed writing for so long.) Perhaps I'll have time after this week finishes to sit down and write it nicely. Or, more likely, I'll get eaten alive by a mixture of exam season, alcoholism, sugar/caffeine overdose, and/or blatantly ignoring reality. Who knows.

At least Danny eased some of our worries a while back by saying "A&S arranges their exam schedules in such a way that most of my students are sleep deprived when they write the 3-hr exam, so I don't have to make it more gruesome than that." Small mercies.

Let's hope Robarts implements "puppies-and-kittens-stress-relief" one of these days (the procrastinating liars). Till then, here's a kitten to de-stress with:

(kitten is not mine, nor is the pic)

Cheers!