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.
Friday, September 26, 2014
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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