Does anybody think it is worth starting a question thread on the meaning of "In mathematics you don't understand things. You just get used to them." ???
I understood start a question as "ask a question on the main site" where I'd vote to close as subjective and argumentative. Here I would vote to close as a duplicate.
@AsafKaragila "Waltzing Matilda" is Australia's most widely known bush ballad. A country folk song, the song has been referred to as "the unofficial national anthem of Australia"
We have a fantastic coffee machine in the department building, finally cheap coffee and good coffee are no longer disjoint sets. Also "very close coffee" is adjoined.
@tb Nah. There used to be a decent, but not very cheap, coffee stands around campus - not even far from the building. However the suppliers were shut down and some horrible company took over. They couldn't make coffee and everything was more expensive too.
So we got a deal with Lavazza. They supply the machine and service for free, we buy 500 capsules a month. For a whole department it's not a problem too - even for a small one like ours.
@Skullpatrol: the fun of that quote is that in its German original it is much better. Satz can mean "theorem" and "coffee grounds", but that's doomed get lost in translation.
I sometimes find it fascinating how people can write things like "This is a direct result of property X, and the implication requires no choice. I believe that property X requires choice for its proof, though".
This is like saying "This vegan food was organically bred, fed, and watered with tears of rich women with nothing better to do. We cook it in lard for the flavour though."
@Srivatsan Because there are too many Matts. I'll have to go back to "Matt" though once the marriage and dating proposals start. I'm getting enough in real life already.
Hmmpf. There are not AC questions to answer. All of them either have my answer, or someone already gave a complete and detailed answer that I have nothing to add on.
I'm taking the fact that I did this immensely tedious question and posted my answer on SE and got no reaction (apart from 3 up votes for the effort of typing it up) as proof that my homework was actually boring and not even people on SE want to look at it.
Fatou's lemma uses lim inf instead of lim. Lim inf is lim (inf )... I can imagine what it is (I take the set of all x_m where m > n if the limit is with respect to n). But what difference does it make?
2. This stood out a bit: when you break an equation into multiple lines, the equals sign comes in front of a new line. [Actually, in this particular question, the stackrels are upsetting the spacing. I do not know the solution to this. Perhaps I will ask JM or tb or robjohn later today.]
@Mattilda Oh, the difference is in the spacing between mod and the things surrounding it. For example, n a \bmod 1 looks better to me than n a \mod 1.
Yes. But considering how $\subseteq$ is much more frequently used than $\subsetneq$, I guess it makes sense to use the simpler symbol for the common case.
May someone answer my most recent three question since it have no full solution, i have evidence that those question is not my homework. Also i am unable to solve it even with the hint may someone give full solution
Click the room link (with a down arrow to the right). Click Create new bookmark. Then you will be presented with a cursor looking like a cross-hair. Click the start and end messages, and name the conversation.
What is the five most hard math subject for undergraduate you think, here is what i think(from most difficult to difficult): 1: Algebraic topology , 2:algebraic geometry , 3: differential algebra, 4:topology, 5:More advanced set theory . For those subject, less than 1 over a million of high school student know anything on any of those subject, do you people agree?
Which do you think is the hardest for a shoes salesman? 1: Nuclear weapon design; 2: Taking over the world; 3: Joining this chatroom and studying Chinese?
2
@Mattilda Yes. I studied rep. theory, set theory and could have taken alg. topology too during my undergrad. So what? These were grad level courses.
@AsafKaragila I'm still regretting that I ballsed up representation theory last term. I mean, I missed the first few weeks and then I couldn't manage to get the homework credits for exam admission : (
@Victor: Again, none of the indicated courses are "advanced" and in fact they are all defined as elementary or introductory. Mathematics is not complicated, it's just something you have to build one piece at a time.
@Victor: When I was just beginning with mathematics I wanted to take pretty much every possible course. After one year I already disliked geometry; another year and I disliked analysis too; I quickly realized that I want to settle into set theory. When you start studying you realize that some things you like and others you dislike.
@JonasTeuwen I don't know much about wine but I have been lectured many times that 1) decent wine doesn't have to be expensive and 2) expensive wine can be a rip off and disappointment.
@Victor Victor, almost everything in undergrad is going to be different. They are going to build on what you know, but they aren't going to be the same.
@AsafKaragila I think boring is in your imagination. I thought maths was boring until recently. You can't tell me that everything apart from set theory is boring.
@Victor, To explain myself a bit more: Between what you know and what you want to know eventually, there's real analysis, topology, abstract algebra (groups, rings, fields stuff), linear algebra.
My maths teacher would always tell us how he really had wanted to become a dentist. I think it's because he sees dentists as people who can torture other people and get away with.
@Mattilda Of course. I completely agree. However I also find certain topics to have more or less penchant for details of some sort. I don't like details.
I think I have to go to bed otherwise my partner will be upset. Anyway: I'll see you tomorrow. Less often though, need to transfer time spent here into time spent on work : )
In my view, there are three approaches to mathematics: There are those that cannot see the big picture, they are obsessed with the details and hardly ever understand the whole picture (either they can't or they don't grasp it unless figured out through details); there are those that see some details and some of the big picture. They usually require both to have an understanding; and lastly there are those that see the big picture but cannot handle much details.
The majority of people are of the second kind. I am of the third.
@Srivatsan: For example, I need to write a forcing proof in full details for my thesis. This is not the usual forcing proof, but involves symmetric extensions and forcing additional structure which is a less common thing to do (at least in what I did so far). I am having a hard time coming up with the details. I do know exactly what the proof needs to have, and that it is in fact correct. Even without verifying the details.
@JonasTeuwen Analysts are often of the first kind, and vice versa. Not always though.
