Livin' the SLOG Life

Hello readers! I'm sure you're all hard at work trying to finish assignment 3. I just wanted to take a few minutes to share with you a video I found on the halting problem. It may be a tad overdramatic (especially with the music) and corny, but it does explain the problem quite well. Here's part 1 (which can be skipped if you want): And part 2, which is where the real explanation of the halting function starts (skip to 2:33 if you don't like corny dialogue): Hopefully this helps with your endeavors (or at least is a bit entertaining)! Good luck with the assignment! Lana :)

Hello readers!! I hope most of you have survived last week's cold weather and are enjoying this week's much more enjoyable temperatures! Last week we were introduced the Turing Machine, which sounds really cool (and it is), but it isn't exactly what it sounds like. For one, the Turing Machine isn't actually a machine. In fact, it isn't even a tangible object! It was something a thoughtful man named Alan Turing came up with, even before computing machines were even made (or were at least available to most people)!! Secondly, it doesn't exactly set out to 'do' anything. It is rather something that was made to prove what we can't do (or to be more specific, compute).  So what exactly was Turing trying to find out with his not-actually-real machine? He was trying to find the limits of what he thought mechanical machines or nowadays, computers could ever compute. "If you're thinking, oh man, computers can do everything!! Just look at thos...

Hello my good friends! This week is the coveted fall reading break, and I hope you all are doing something useful with your time, like me, who is currently writing my SLOG. Now that the course is nearing its end, I would like to take it back to the beginning and try to solve one of those logic puzzles, using the Polya method we learned in class. I am, afterall, an amateur logician now, am I not? So here is the puzzle I have found from the problem solving wiki page. So without further ado, I present to you: Walk Tilings Suppose you have tiles that are 1x2 rectangles, and you have to tile a walk that is 2x3 units long. You've got three choices: 3 vertical tiles, 1 vertical tile followed by two horizontal tiles, or two horizontal tiles followed by one vertical tiles. How many choices do you have in tiling a 2x4 walk? How about a 2xn walk, where n is some natural number? Do you have a procedure that works for any n? Understanding the Problem Ultimately ...

Greetings readers! I'm sure you're all super interested in learning about Big O, so without further ado, I shall share more of my (albeit limited) knowledge with you. Let me first present to you what it means to be bounded above by big O. Or more precisely: If the function f(n) which is a positive increasing function, is in the set of functions bounded above by the function listed in O, then beyond the breakpoint B, f(n) will be no bigger (or will be bounded above) than n^2 that is multiplied by some c that makes this statement true.  If we were to look at a graph, it would look something like this: In terms of coding and find the worst case in sorting methods, big O will help you find the maximum possible number of steps a function may take for any given input. Now that you know almost just as much about big O as I do! Isn't that something! (that something would be not much... but hey baby steps, baby steps) Thanks for stopping by and ...

Greetings my spooky readers!  I hope you all have had a wonderful Hallow's Eve munching on candies or partying it up and didn't have to think about all those assignments you haven't done yet!  So while you're still working on all those "leftover" candies that you bought so you could "give" them to the trick-o-treaters (but really we all know you saved the good ones for yourself) let's tackle a big topic: the BIG O. (cue spooky music here) Because I am a little short on time today, I would just like to introduce the concept of the big O. So, if we were to label, big O would be an asymptotic notation for a set of functions. It's kind of like giving the upper limit of a function. The notation O(f(x)) would be saying that the set of functions within O would never grow faster than f(x). This is helpful in computer programming for when we want to calculate the maximum number of steps that a function may take. In other words, big O tells us to...