Sorry this sLOG post is a bit late, I was working on Assignment 1 for CSC148 for all of Friday and only just got around to doing this. I'm going to focus more on the first test this Wednesday than I am on the lectures for the week in this post, so here goes.
This was my first testing experience at University and the first thing I noticed - it's a big room. In High School the biggest test of the year was written in the Gym and that room is still smaller (floor area, not volume) than the Exam Centre writing room. The test itself was remarkably simple; I had expected to be using de Morgan's law or other laws of con/disjunction and I had written a ton of them down, but we only did stuff from around week 1-2 with translating between symbol and english. As I posted in week 1, I have a very effective strategy for that so I got a lot of good use out of it on the test (you can look at my test and see very clearly that I used it).
The only question I really had trouble with was the last question, which I tried a whole bunch of random solutions to, going about it through trial and error. However I soon realized that wasn't working and I switched methods. Instead I rewrote the statements that we were trying to verify/falsify from statements involving a lot of ands and ors into statements involving implication. That way, when I added a number to set D, I had a bunch of easy implications telling me what to do in order to make one statement true and the other false.
I hope that I did well on this test - I definitely feel that I did - and I look forward to the second half of the course!
Saturday, October 11, 2014
Friday, October 3, 2014
Week 3
Proofs! I love proofs! And apparently, so does everybody at University! I suppose proofs are fundamental to mathematics, so it makes sense that they're so popular in math streams.
Anyway, I'm going to start with positive opinions on proofs in this course. I really like how proofs are structured here; we have the assumption, then indent to indicate the universe where this assumption holds true and continue on. That is a lot more concise than many other forms where it is simply "write this up here and then continue on down the list". I think that the way proofs are structured here is going to be the way I write proofs in all situations from now on.
As for negative things I found about proofs, I really don't like the lack of examples because it is hard to conceptualize how these proofs will eventually look. An issue that comes up with that is the complicated notation used for proofs here, which I really need an example to fully understand. I really hope an example comes on Monday, otherwise I will be totally lost when trying to conduct a proof. Either way, proofs are a concept I hope to grasp fully this year and I think this course might be the number one contributor to that goal.
Anyway, I'm going to start with positive opinions on proofs in this course. I really like how proofs are structured here; we have the assumption, then indent to indicate the universe where this assumption holds true and continue on. That is a lot more concise than many other forms where it is simply "write this up here and then continue on down the list". I think that the way proofs are structured here is going to be the way I write proofs in all situations from now on.
As for negative things I found about proofs, I really don't like the lack of examples because it is hard to conceptualize how these proofs will eventually look. An issue that comes up with that is the complicated notation used for proofs here, which I really need an example to fully understand. I really hope an example comes on Monday, otherwise I will be totally lost when trying to conduct a proof. Either way, proofs are a concept I hope to grasp fully this year and I think this course might be the number one contributor to that goal.
Friday, September 26, 2014
Week 2
The last lecture today was incredibly interesting. Figuring out a puzzle for the entirety of a lecture is definitely not what one would expect to do at University, but we did it and it was really fun. To recap for anyone reading this that has no idea (or has forgotten) what I'm talking about, we worked on problem solving skills and applying them towards finding a pattern in the direction of the creases in a sheet of paper if you fold it n times. The main thing I learned from that is to always use a table because tables are amazing!
Other things we learned this week would be satisfiability, which I think is basic and straightforward and needs no talking about, and the properties of logical operators. I learned the properties of arithmetic operators in High School, but I had never thought to apply that to and or or (or both!), so having it brought up during lecture reminded me of having learned that way back then. I think it's pretty interesting how (relatively) advanced concepts like logical operators exhibit similar behaviors to (relatively) simple concepts like addition.
One thing that I particularly enjoyed from this week was the tutorial. Last week I thought the tutorial was pretty uneventful, but this week the tutorial exercise was actually fun to do. Creating statements with all and any is a fun way to exercise the mind. I'm not saying I'm going to start making games out of creating logical statements for a whole bunch of random things; but if I'm ever in a situation where I am creating logical statements, it won't be the worst thing in the world.
I'm looking forward to the lectures on proofs next week. Proofs are always fun, though I've associated with them before in many different ways. I'll make sure to mention in next week's post how I feel these lectures compared to my past experiences.
Other things we learned this week would be satisfiability, which I think is basic and straightforward and needs no talking about, and the properties of logical operators. I learned the properties of arithmetic operators in High School, but I had never thought to apply that to and or or (or both!), so having it brought up during lecture reminded me of having learned that way back then. I think it's pretty interesting how (relatively) advanced concepts like logical operators exhibit similar behaviors to (relatively) simple concepts like addition.
One thing that I particularly enjoyed from this week was the tutorial. Last week I thought the tutorial was pretty uneventful, but this week the tutorial exercise was actually fun to do. Creating statements with all and any is a fun way to exercise the mind. I'm not saying I'm going to start making games out of creating logical statements for a whole bunch of random things; but if I'm ever in a situation where I am creating logical statements, it won't be the worst thing in the world.
I'm looking forward to the lectures on proofs next week. Proofs are always fun, though I've associated with them before in many different ways. I'll make sure to mention in next week's post how I feel these lectures compared to my past experiences.
Friday, September 19, 2014
Week 1
First week of CSC165 is over! Well, technically two weeks, but first week of introducing concepts. Things we learned this week include: universal / existential statements, negation and (today) vacuous truth. I'll go over the first two in one paragraph and the third in a second.
Firstly, universal / existential statements and negation are really simple concepts. They can sometimes get a bit tricky when there are a lot of them combined together, but they are still not too complicated. One tip for anyone who actually reads this blog would be to write down every single statement in a line. The line doesn't have to make English sense, just translate universal (all) to "for every", translate existential (any) to "there exists" and translate "not" to "not". For example AxED, x > 4 translates to "for every x element of D, x is greater than 4". This strategy works wonders in difficult situations. I may make a dictionary of "symbols --> words" if I feel it would be useful to anyone.
Vacuous truth is a bit more complicated, but it's also pretty funny. For example, for every xE{}, x > ∞. Very interesting. Either way, the concept can get confusing but my trick with the writing sentences still works (I think, I haven't tested it). I think that the combination of these two things will prove to be very entertaining in the coming week(s).
Nothing too hard yet and nothing that I can't understand, but then again it's only the second week. I'm sure I'll have my mind blown by November, if not sooner. Until then, I'll post again next week!
Firstly, universal / existential statements and negation are really simple concepts. They can sometimes get a bit tricky when there are a lot of them combined together, but they are still not too complicated. One tip for anyone who actually reads this blog would be to write down every single statement in a line. The line doesn't have to make English sense, just translate universal (all) to "for every", translate existential (any) to "there exists" and translate "not" to "not". For example AxED, x > 4 translates to "for every x element of D, x is greater than 4". This strategy works wonders in difficult situations. I may make a dictionary of "symbols --> words" if I feel it would be useful to anyone.
Vacuous truth is a bit more complicated, but it's also pretty funny. For example, for every xE{}, x > ∞. Very interesting. Either way, the concept can get confusing but my trick with the writing sentences still works (I think, I haven't tested it). I think that the combination of these two things will prove to be very entertaining in the coming week(s).
Nothing too hard yet and nothing that I can't understand, but then again it's only the second week. I'm sure I'll have my mind blown by November, if not sooner. Until then, I'll post again next week!
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