Livin' the SLOG Life

OH MY GOSH EVERYONE... this is my last post!! I hope that all of you had a nice semester and that maybe we'll be seeing each other in the future (236 and 263 anyone??). As a last post, I would just like to mention some other blog posts I've found interesting to read in these last months. If you have the time, take a look at how my fellow sloggers explain concepts, solve problems, or share their thoughts on the course! Here is a list below: http://sloggingthrough165.blogspot.ca/2014/11/problem-diagonals.html http://stuperfectionjih.blogspot.ca/2014/10/tractatus-logico-philosophicus.html http://ilikecakecsc165.blogspot.ca/2014/11/im-back-and-today-were-going-to-be.html This list isn't all the good ones out there! But I shall leave it as this for now. Toodeloo folks!! And good luck on your future endeavours! Lana :)

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...

Hello everybody! I am hoping all of you have had a nice Thanksgiving, and I hope you all aren't swamped by a huge wave of tests and assignments as I am! Today I would like to talk about floors. No, not the one you're standing on or the thing that's supporting your chair right now, I'm talking about mathematical floors! They are these magical things that sort of remove the decimals from any positive real numbers. The reason why I limit it to positive numbers in the previous statement is because they do something that looks different to negative numbers. Let's look at the definition of a floor that was given to us during class: At first glance, this looks preeeetty long and exhaustive, but really, all it's saying is that: 1. The floor of x is an integer 2. The floor of x is smaller than or equal to x and  3. For any integer that is smaller than x, it will be smaller than the floor of x (that is, the floor of x is the largest integer that is smal...

Hello readers!! Welcome to the end of Week 6 of classes and I hope that everyone has done well for the first term test. For me, this was quite the experience, as I've never felt so unsure about my own answers, but we shall see in probably a week or 2's time. I do apologize for not writing over the Thanksgiving break, but I assure you that I will be back on track for the rest of the semester! Today I'd like to talk about the different ways to prove things. I won't be going into all of them, as some are more self explanatory than others, but I will talk about the ones that I find rather confusing right now, just so I can use this post to help myself sort out some things. Proof by cases: When encountering a statement in which you feel that there is more sides to the statement to look at than what you can prove with just one line of thought, then we use proof by cases. We must, of course, think about all the different cases that are possible first, and then we prove...

Hello readers! Today I would like to talk to you about this week's newest topic: Proofs! (Because I'm sure you've all read enough about how easy or difficult the first assignment was). Since they have just been introduced to us, I am definitely no expert in the field, however I have to say that this is definitely an art, that is, a very accurate art. To create a proof for a statement takes true creativity and "out-of-the-box" thinking, while having to keep all the parts within it logically valid and true.  To me, making a proof is like making a burger: you have your standard buns (the outline of the proof) and then you're essentially free to put whatever you want between those buns, as long as it's edible and the flavours are coherent and harmonious. Further, just like how a BLT can't be missing any of those 3 ingredients that make it a BLT, you also can't just take out steps wherever you please. Creating cool new burgers is an art and ...

Hello readers! Today I'd like to talk about folding paper. Don't get too excited though, we didn't make or study any  hexaflexagons ; that would be way too complicated. We used a simple model and contemplated on the predictive power of its patterns. What I'm talking about is the interesting activity we did last class. It involved folding a simple strip of paper and the main point of the activity was to provide an opportunity to use the methods for approaching a problem. We were asked to fold a strip of paper in half as many times as possible, always folding the left end onto the right end. After each fold we would then unfold the strip to record the direction of the resulting crease, which either went up or down. The question was to find a way to predict the direction of the creases, in relation to how many folds were made. At first, the problem seemed very simple, until the actual results of the creases were recorded. Rather than a straightforward repeating pat...

Hi everyone! I hope all of you guys have had a nice week so far, today I'd like to write a short post on what we learned in class recently! Today I'd like to talk about this nifty thing we learned in class called vacuous truth . Sounds complicated or abstract at first right? How can a truth be empty? Vacuous truth is this interesting concept that in an implication, where A implies B, if A is never True, then you can never say that A doesn't imply B! Let's first look at a 'real-life' example: If a person were to say, "If your apple turns into a banana when submerged under water, then the apple must have grown upside down in the ancient tombs of the ancient Egyptian Pharaohs," you would have no means of proving that person wrong, since you would first have to find an apple that turned into a banana when submerged under water! Therefore what this person has said is vacuously true. Now let's look at an example dealing a little more with math:...

Hello readers! You have stumbled upon a small undergraduate student's (my) courSe LOG (SLOG), where, for the next few months, I will be posting about all things CSC165. The full name of this course is Mathematical Expression and Reasoning for Computer Science. Quite a mouthful, is it not? However, so far it's been very interesting, since I have always wanted to test to what extent my own logic is capable of. Since this is my first blog post, I will be just doing some first impressions on the course and the material we've covered so far. First off, I would like to say that I have never taken any course like this before, so this material is all very  foreign to me. From the emphasis on precise wording to the mystical venn diagrams that contained the universe, not to mention the new notation that I needed to learn, this seemed all very new and uncertain. After about a week of worrying about not being able to keep up with the coursework, I decided to buckle down and just en...