$\int_{\partial A}\left[ (x+y)\bar{i}-2xy\bar{j}+(y-z)\bar{k}\right]\times d\bar{a}$, can I use here somehow Green's formula or Stoke's rule? A is a ball so if I understand correctly $\partial A$ is its boundary or? (p1024, XV.1:4)
x on the denominator is like saying x^-1 in the numerator, so that's also written as x^.5*x^-1 all over 2, which is x^-.5/2, or 1/2x^.5, or 1 over 2sqrt(x)
It hadn't occurred to me that any part of math might be right or wrong, or even that math was full of ideas and was changing a the time. So I liked that it challenged my viewpoint
you see - I was busy thinking of how often we are 'lied to' or misled in school -
Write out the definition of the derivative using that function as the $f$. The 3's will cancel in the numerator and you will have to factor $a^3-b^3$ with $a=x+h$ and $b=x$ specifically.
@anon Definitely. Do any of you know how to prove to prove the volume of a cone is 1/3 of the cylinder without calculus? (I mean, I used the exhaustion principle to do so)
@MarianoSuárezAlvarez This is the kind of ideas of topology that interest me "A function $f:X→Y$ between two topological spaces is continuous if for every open set $U$ in $Y$, the preimage of $U$ under $f$ is open in $X$. "
@PeterTamaroff Putting my victory on the mantle. It means that I am going to show it off. I find it strange that you would need to ask what that means but know what an idiom is :P
@MarianoSuárezAlvarez Woah, woah, woah. General topology can be pretty interesting.
I read an analogy to greek cuisine recently: general topology is like parsley in greek cuisine: every greek dish requires a bit of parsely, but there are no "parsely recipes" one needs to know
@MarianoSuárezAlvarez Yes, that is the cliche response. That said, I feel that you could make the EXACT same argument about group cohomology--or, actually, most interesting mathematical subjects. They just aren't true.
I am working through the review sections of Stewart's Calc 7 book and I am at this question
$\frac{d}{dx} (tan^2 x) = \frac{d}{dx} (sec^2 x)$
It is true or false, I said false but the book says true and I do not understand why.
General topology started out trying to figure out geometrical properties of spaces--the exact same thing that any other topology does--we just don't go about it the same way anymore. So, if you think that studying the original type of combinatorial topology is cool/worth it you should say the same about point-set.
Yes, but originally people thought that many sorts of abstractions were useless/uninteresting, and then became interesting. What is currently interesting or not does not mean that it isn't interesting in the grand scheme of things.
if anyone asked me for guidance on a subject, I would emphatically tell him that topology is something that needs to be known, but that picking it as a subject is mostly a mistake
But, why should I care about them? Math is on tenuous enough grounds, about it being worth doing, as it is, that we don't need to say _____ is not worth doing. I don't know man. If you say that general topology is not worth doing, I don't understand why the Langland's program is worth doing.
Ok, so, this is fairly interesting. Let me ask you this. Suppose that I came to you and said that I am extremely interested in Model Theory. What would you say to me?
I understand where you are coming from, and most of the time I would make the same argument, but I just don't like the idea that we have some societally imposed notion of what is "interesting" and those who don't do work in this area are considered to be wasting their time.
@PeterTamaroff The two hottest subjects right now, in my extremely limited point of view, are low-dimensional topology/geometry and algebraic geometry.
Is there a way to check all of one's close votes, and which ones ended up being closed? Chaz seems well aware of his own stats, and Arturo of Chaz's too...
Anyways, Mariano my friend, I must go. It was, as always, very nice talking to you! I like useless arguments just as much as I like useless topology :)
@MarianoSuárezAlvarez As a minimal example, I find my proof of the sine and cosine series interesting, but they are if anything important. I think maths if rather an egotistic subject.
@AlexYoucis, another example is that he and his student Grothedieck defined most of the abstract fine concepts of functional spaces (barreled spaces, nuclear spaces, etc)
they solved huge problems, and then dropped it
that part of functional analysis is not unlike general topology now
@AlexYoucis Not really. He's in the main building so to speak. I'm in a dependence in the same province (state) which is for the first academic year, called Basic Common Course.
Alex, since it is still solving problems, old a new, for a while it will not be dropped, but the notions of quasi-hemi-barreled semi-spaces stopped solving problems not generated by themselves a long time ago
a good measure of the liveliness of a subject is: how many problems which can be stated without even mentioning it does it solve
Ok. So, I guess what I am looking for is this. You have continually said "as long as it keeps solving problems, it is useful". Which problems should a "lively" subject be able to solve? What is the measurement?
@AlexYoucis Basically, all those who will do a career in exact ciences have to study Chemistry, Physics, Analysis, Algebra and two more general courses Introduction to Sientific Thought and Society and State (basically Argentine history)
@AlexYoucis, Icannot tell you in general, because the question is pretty absurd; but this is one of the criteria the actual mathematical world uses to evaluate subjects
But, I think you can see my issue now. Being a man of mathematics I like precise definitions, and discounting a subjects worthiness (for doing) based on such imprecise definitions is maddening.
No, I am trying to get a semi-coherent definition for something that, in your opinion, governs whether or not someone is making good use of their time.
To not ask for such a definition is what seems silly to me.
So, if tomorrow everyone suddenly said "Hoschild cohomology is useless--we really screwed up there. Let's go elsewhere" you'd go "Oh, ok. Looking for a different subject now."
If being a mathematician is ENTIRELY (I understand that it is partially) just the process of pleasing a community of people who set (fairly) arbitrary standards of what is worth doing, then I think I am in the wrong subject. Thankfully, I don't think that is the case.
I am working through the review sections of Stewart's Calc 7 book and I am at this question
$\frac{d}{dx} (tan^2 x) = \frac{d}{dx} (sec^2 x)$
It is true or false, I said false but the book says true and I do not understand why.
