Final Exam, About the Last Post

Final exam went well and was surprisingly pleasant. Most things were new and had to be figured out at the time we were writing the exam, so that was interesting. Not much else to talk about regarding the exam, other than computer science kids have the weirdest twitches.

I was thinking again about my last post not too long ago. I guess it was more of a nostalgia for a time that never actually existed. Which is actually a perfect definition of “nostalgia”, but I digress. Universities nowadays do very little to improve critical thinking, reasoning and most personal growth seem to happen outside of classrooms. I know that, I’m okay with universities serving only to form “specialized workers” in the most efficient form – not very different from a professional college, only using books instead of tools. With such a high number of people seeking higher education, I guess it couldn’t be different. I also doubt there was even a time when universities helped people think. Still, for some reason, I was expecting something like this from this course. I mean, I didn’t expect “Methods for Economic Analysis” to teach me individual thinking. Math courses could do something like that but honestly, nobody wants to learn it. It seemed logic would be a logical first step, but I guess I was wrong.

I feel this makes it seem like I’m complaining or didn’t like the course or something. No idea why I feel that way, of course. Again, I did like this course, or this semester, for that matter, and do not want it to leave this in a negative note. I don’t really know what to say to help this, though, so here’s a picture of a llama with a mohawk.

Diagonals, pt. 2, Final Remarks

Aaand I’m back! From New York, and from having to write exams. We didn’t win the competition, of course, but it was still fun. Plus, New York.

Classes ended about 10 days ago, so I don’t have a lot to report on that.Still waiting for marks on A3, which wasn’t too bad but was left for the last minute. Ooops. I did pretty well on quizzes, too, so I should do well on this course in the end. I should probably study for the exam though.

Anyway, back to the diagonal problem. At first I thought the formula would be m + n – 1. Then I realized some of them added up to m + n – 2. So then I thought that maybe one is for odd numbers, and the other for even numbers. But nope. Also, squares. If n = m, d = n.  What.

No point in drawing squares, though, since the formula for their diagonals is pretty simple. Also, I’m pretty sure white spaces are irrelevant. Or rather, they always just equal to m * n – d, and that’s it. I can’t find any other pattern for them.

So after this I went back to rectangle drawing. I was doing squares to see if I got anything interesting, but they always yield m + n – 1. It was when I started doing multiples, though, that I reached an interesting breakthrough.

3 x 9, to be precise. The diagonal passes through 9 squares. That’s m + n – 3, which is new. So the diagonal formula has to be related to a common denominator. I wasn’t sure if it’s the minimum or maximum denominator. (Besides 1, of course. I was actually just confused because I thought the formula would be m + n – (smallest prime), but let’s not get ahead of ourselves).

9 x 6, d = 12. 9 x 18, d = 18. So it is the maximum common denominator. This also explains squares, since the mcd when m = n is n, so the formula yields (n + n – n = n). Also, for numbers without a common denominator, the mcd is 1, which explains why most rectangles yielded m + n – 1.

So, d = m + n – mdc(m, n).

 

I guess this will be my last post here until the final exam, so I might as well make some remarks about the course.

First of all, I’m really glad this course is offered here and is mandatory for pretty much any CS related program. I think either this course or a similar, less CS focused course should be made mandatory for most other programs, too. I know there’s a Philosophy course in Logic, but as far as I know its only purpose is to help math kids fulfill their breadth requirements. No course like this is offered in Economics, at least not that I know of, and that is a shame because one would hope to be Logical as an Economist. (As a side note, most of them don’t seem to be. Damned thinking electrons).

That being said, though, I thought the course was pretty easy. Again, not that I’m getting 100s, but except for the problem solving we were asked to do in our blogs, the course was pretty self-contained. There wasn’t a lot of thinking in this course, mostly just trying to memorize and repeat what was done in front of us. I guess the whole school system is like this, but I was expecting something more from the course. I understand the reason this is done, as most people seem to prefer memorizing over theorizing. I’d rather this course pushed my reasoning ability by giving me a problem that I had to sleep on to solve. Kind of like actual CS problems we see. The assignments were solved mostly by looking at similar problems solved in the course notes. The midterms were 50 minutes long, for Christ’s sake. It wasn’t made to be solved on the spot, we were supposed to go there kind of already knowing the answer. Which, again, is usually better, since it’s more stable, secure, convenient, expected. Most of the time I spent on the assignment was typing (or making my partner type) everything according to the proof format for the course. Having a formalized proof structure is important, though, so I don’t hold that against anyone. I wished windows put arrows and math symbols in easier places, though. But I guess I can see why the wouldn’t. Anyways. In the sense of whether or not it made me a better thinker, the course was a disappointment to me.

I guess this rant might make it seem like I disliked the course. But I didn’t, really. Some really interesting points were touched on, knowing how to do proofs is majorly important and we were given incentives to learn more on what was taught. Also props to Danny for his awesome dry humour. Simon, I hope you have a nice career in the Academia. It was a pleasure being on your first class.

I guess my main complaint is directed at the schooling system more than anything else. Regarding SLOGs, I would personally rather use them mostly for problem solving, but that goes back to my previous point. All in all, this was an enjoyable year. Now let’s get these exams out of the way so I can relax for a bit.

Start of problem solving

Just wrote the test. Didn’t have time to finish it. Damn it. I still need to work on being faster. Though that’s usually not an issue during the 3-hour finals.

I decided to try the diagonal problem Danny gave to us during class about a month ago. So let’s see. We have to figure a formula for how many squares of size 1 by 1 a diagonal of a given rectangle passes through. The only thing we know about the rectangle is that it is m by n in size. So whatever formula I have to find should only deal with these two variables. I’ll refer to the squares crossed by the diagonal as d. I don’t know if the number of squares the line doesn’t go through matters, but I’ll call it w, for whitespace. It’s easy to see that if either m = 0 or n = 0, d = 0. So d is a function of both m and n. Also, whenever m = n (ie whenever we have a square), d = m = n. Also, w = mn – d. So d = mn – w. Danny showed us an example on the handout. When m = 4, n = 6, d = 8, w = 16. The diagonal path is mirrored on the middle, so if m = 2, n = 3, d = 4, w = 2. I suppose if m = 6, n = 9, d = 12, w = 44, and so on. Doubling m and n doubles d, and something crazy happens to w. Maybe having w was not such a good idea.

Looked at some drawings I made. Possible values seem to be m + n – 1 or m + n – 2. Except for squares.

Simon: That’s true, I remember learning about different speeds in different languages. I guess I forgot about it 😛 glad to know we’ll be doing proofs, though! Problem solving is always enjoyable. I should be taking 209 next semester. I dropped it because I knew I wouldn’t have a lot of time this winter.. I’m only taking CS as a minor, though, so I won’t even have a chance of going deep into the theory, which is a shame, because it is the part I like the most about CS. But, as an economist-to-be, I figured I would maximize future revenue by focusing more on the applied side. I have also tried to learn the economist lingo so I can get more money. Anyway, I’ve been trying to learn more about the theory on the side, but it’s harder than I thought at first. Especially with school begging me for attention. But I digress.

OKAY so I started this post but didn’t have time to finish it. I’ll work on the problem and on the post I’ve missed later. I’m in NYC right now, working on the hackNY hackathon. Doing a beer related app. Good stuff. Anyways, I’ll update this later.

A sudden boom in my visitor stats

Why did we stop doing proofs? I liked proofs. Why are we studying sorting and big-oh? I remember doing sorts on 108 and 148 and half the class was interested and the other half just kept asking “But isn’t the python sort a lot faster than all that?”

My ex-roommate and his friends in computer science would spend time talking about Bogosort, which wasn’t as amusing as I expected it to be, based on their conversations.

I guess sorting is an interesting example and a decent thought experiment in efficiency. I liked talking about what constitutes a “step” on the tutorial. It was actually quite enlightening as I had never really thought about that before. Counting steps was just annoying though. I will probably look deeper into that later, if we don’t do it in class. Understanding how functions work would help me understand why function-calling is so slow, I guess.

Also people are reading this blog now. Special shout out to Maria, who went through a lot of trouble to find this blog. I acknowledge your efforts.
Simon, thank you for your comment! I wasn’t able to explain my results on the last quiz, so I guess you’re right about not underestimating problems too much. I’ll try my hand at solving one here next week.

Back to school

Came back from New York this week. It was an enjoyable, if not very academically productive, reading week.

There’s  again not much for me to report here. I got 85% on the test, which was kind of a disappointment. I’ve been getting quizzes right, so that’s okay. My assignment grade isn’t online, which makes me wonder if something went wrong. I do not know how well I did there. The new assignment is up and we should start working on it tomorrow.

I still find the course material pretty easy. I had more problems interpreting sentences on the test than with the actual material, though I suppose interpreting sentences is an important part in logic.

This blog hasn’t been read in a while, or received a comment. Danny said we should talk to our TA about it, but I keep forgetting. Oh well.

Proofs are interesting but the course has been very easy so far. Not that I’m getting 100s, but I often lose marks because of some distraction, and I’ve never seen a problem I couldn’t solve without a bit of thinking. I’d rather have weekly problem sets instead of quizzes and assignments, but that’s just me.

More proofs!

Proofs are fun! Especially since they’re really easy and no one else seems to get it, so I can have a nice break before having a reading week break. Most of the class seems to be lost on the simplest things, which is kind of baffling.

We’re getting our tests back tomorrow so I can report on whether or not I have reason to be acting like I know logic. Let’s hope I don’t have to go back on anything I said because that would be embarrassing.

I don’t understand why the quiz is easier than the tutorial exercises, either.

Not much more to say, really. I’ll report back after I receive my test.

First test

Missed the first class this week due to not sleeping enough at the Hackaton. Apparently there’s a limit to my body’s ability to stay awake.

Wrote the first test for the course. It really wasn’t hard. But then again, having only 50 minutes to write the test makes it hard to ask for anything very elaborate.

Also, apparently the right answer for the question on the assignment me and my partner spent the most timing arguing about was really the converse of the contrapositive. I still think that’s a weird answer, since we could just have said it’s the inverse. I’m glad we went with my partner’s suggestion, though, instead of my idea of answering “he-who-must-not-be-named”.

We started doing proofs. Proofs are fun.

Proofs

First of all, someone visited this blog. All right!

(Update: Also, Slog has been listed on the course webpage. Woo.)

Second of all, classes got more interesting. Actually doing something is better than just memorizing symbols. Looking forward to the next weeks.
Assignment was fairly straightforward, though me and my partner were unsure about some questions. Especially one where we were given the inverse of a statement, but could only list it as contrapositive or converse. So we called it the converse of the contrapositive, which made sense, but felt like cheating. I guess the hardest part on the assignment was saying “Every aphorism is catalytic unless it is dodecahedral, but are dodecahedral aphorisms catalytic?” I learned logic by talking about little Sue liking apples and oranges, but I guess Danny wants to make us feel in university now, where we have to use big words.

Missing class tomorrow to go to the Hackaton at the University of Michigan. I have no regrets. And might grow a neckbeard after coding for 30 hours nonstop.

A bit more work to do

Content has improved in this second week. Translating things from English to symbols and vice-versa is challenging enough, though it really is just a matter of practice, I think. I might have gotten the quiz wrong for writing something overly complex. I guess I should work on my simplifying skills. Doing the assignment should help. I hope me and my partner can finish it tomorrow.

Lectures are still the same as the past week, which is good. Tutorial is still too long, I think. Problems are never that hard.

Also, this Slog hasn’t been listed on the course website, which I guess makes me akin to the 52-hertz whale.

Introduction

First post on this SLOG for CSC165. Not really sure what do say. We’ve been covering the very basics of logic and though I like the professor so far, I find the class very boring. I guess it’s going to change in the future, when we get to material I haven’t learned somewhere else before, but until then, I can’t think of a lot to say about the course. I suppose the first weeks of classes are always like this, though, especially for first year courses. I really like logic, so I don’t expect this class to be boring, either. I think I’d learn better by sitting down and doing a bunch of exercises every week than by going to class. Or, at least, that was my impression for the first two weeks.

As for the tutorial, both the exercise and the quiz were really easy and I felt staying there for an hour was a waste of time. Nothing against the TA, I was just bored. I hope things get more interesting soon.