Well, not really. It was the rest of the post that made me think that you're striving towards some romantic fiction. If you're going work in academia what you will be doing is probably something like working for 48 hours a day while not understanding things and failing to make important...
Any n-place relation R is just a subset of the cartesian product of some domain U, i.e., R\subseteqUx...xU. One of the first things you should've learned is that the empty set is a subset of every set, so it's trivial that there is an empty relation. I hope that helps.
Heheheheh... Sorry...
Ideally, what you should want is to do what Fs do, rather than to be an F. A lot of people, it seems to me, pursue careers or "interest" which they think will make them happy and satisfied, because they've created this romantic fiction in their head about how wonderful it is to be an F. Please...
There is some data suggesting that the performance on IQ tests can be increased by a few % by increasing working memory and related cognitive functions. Unless my memory is failing me, both Klingberg and Jaeggi have published on the subect, and probably others as well. But it seems that the...
There aren't any quantifiers in propositional calculus...? If you mean predicate calculus, then yes, the order matters. e.g.,
\existsx\forallyR(x, y)
\forally\existsxR(x, y)
The first case says that there exists something such that it stands in the relation R to everything. The second...
Most of the courses at the university I attend has this kind of scheduling. The main difference being that we do 8-10 courses/year, 1 course/month. Sometimes it's great, sometimes it's not so great. One potential problem is that if you get stuck or fall behind, chances are that you won't be able...
You most likely won't have time to try everything out, but that doesn't really matter. As long as you find something that interests you and that you enjoy doing you will probably end up fine. It's not possible to learn everything interesting, and you'll be facing the same problem in every field...
Hmh... The shortest lecture I've ever had was 2 hours. The standard time has been 3 hours so far, and the longest 4 hours. Most often there's a short break every hour though, so maybe it should count as 2 1hr lectures, 3 1hr lectures and 4 1hr lectures...?
But I have to say that I like the 3hr...
I don't think there's any such distinction where I'm at really.
Well, I'm not completely sure I'd be going into logic. The topics I've enjoyed the most so far are model theory and set theory, and I've also enjoyed categorical logic quite a bit. So maybe something similar. I don't know. I don't...
Well, maybe. The situation seems to to be pretty much the same from what you just said though. (I don't really care about "top programs" though...)
I'm not in the US. I also think that you somehow misunderstood something. First of all, I'm not going to take all the courses I listed in one...
Great. I wrote a really long reply and got logged out, and it was lost in the process... :mad:
Summary:
If I chose to do that extra year, I'll have at least the following math courses in addition to the ones I mentioned (Don't dis logic :frown: ):
Calculus I-III (Mandatory)
Linear Algebra...
Arguably, "creativity" plays an important role in all intellectual work, and is more important and easier to achieve the closer you get to the cutting edge of a subject. I don't think that there's anything special about creativity; It's just that the higher your expertise is in whatever it is...
\varphi\rightarrow\psi Is introduced as an abbreviation for or shown to be equivalent to \neg\varphi v \psi earlier in that chapter, and \varphi\leftrightarrow\psi for (\varphi\rightarrow\psi) ^ (\psi\rightarrow\varphi), so what you have to show is that
(\negP v Q) ^ (\negQ v R)...