/sci/ - Science & Math

It's hard to put the great feeling of discovering a new mathematical framework or tool-set, which often puts other learned topics in a new perspective. Arguably, I'd say it's more satisfying than sex. Learning new physics has a similar vibe to it, but sadly, I feel, it's easier to run out of physics aha-moments than it is with math. I also consider CS theory part of it, btw.

>>6365372
why are there so many programming languages when you can program anything* in Magic the Gathering?

*it's Turing complete

So you're saying
0 AND 0 = 1
?

a) equivalence relation has not to do with this question. that would mean reflexive and some more requirements
b) in an algebraic context, the name "binary relation" is sometimes implied to mean a relation on A times A, not two different sets A and B. But here I figure the standard definion as it being a subset of A times B is suitable.
c) the reflexivity propery is defined for a binary relation on A times A. So the answer is it doesn't make sense to ask for a general binary relation.
If you have A being a subset of B, as you say, then you can define the "inclused the diagonal" property for the relation, but it's not called reflexivity.
That new property isn't nice anyway, since it favours one side of the carterian product over the other.

If you have the coefficient for each frequency already, why do you want to compute the fourier transform of it? You can read it off from the data directly, no?
Also, why don't you just try it? The Mathematica help is good and I see now problem with it.

Cool, where you motivated by the thread yesterday?
Good to see some original content resulting from this here, no matter what it is.

>>6034641
>I can't even count I'm not even joking I get to maybe 12 and that's me I'm gone.
Grothendieck, most peoples favorite member of Bourbaki said that 57 is prime, so that's okay.

>I can't help but thinking 'has there ever been a deconstruction of the Bourbaki structures?'
Deconstruction in the sense of Derrida? It's not really my field, although I'd like to read some feminist theory and I know it's of relevance there.
I don't think that term is at all applicable here, but there is a structuralist dogma which is tangential to the idea of freeing the thing from all "unnecessary" interpretation, namely the concept of classifying things in terms of their essential relations
http://en.wikipedia.org/wiki/Universal_property
If you have a look at the people here

http://ncatlab.org/nlab/show/structural+set+theory

a page with modern algebraists focus, these people literally use the term "structuralists" and distance themselve from certain approaches to mathematics, many of which are quite philosophical in nature.

>>6034641
>I can't even count I'm not even joking I get to maybe 12 and that's me I'm gone.
Grothendieck, most peoples favorite member of Bourbaki said that 57 is prime, so that's okay.

>I can't help but thinking 'has there ever been a deconstruction of the Bourbaki structures?'
Deconstruction in the sense of Derrida? It's not really my field, although I'd like to read some feminist theory and I know it's of relevance there.
I don't think that term is at all applicable here, but there is a structuralist dogma which is tangential to the idea of freeing the thing from all "unnecessary" interpretation, namely the concept of classifying things in terms of their essential relations
http://en.wikipedia.org/wiki/Universal_property
If you have a look at the people here
http://ncatlab.org/nlab/show/structural+set+theory
a page with modern algebraists focus, these people literally distance themselves from mathematicans which they call "structuralists".

>>5787203
>tfw you named yourself after a Nazi

>>5691860
oh, and a third example, which is both related to ugly upper case naming as well as Hilbert space business

http://en.wikipedia.org/wiki/GNS_construction

this is something physicist needed (= just assumed to exists), which was proven only latter.

I have no idea of the field, but I assume the classification of 4-manifolds and analytic continuation of operator spaces involves some wild ad hoc maths, just because physicists (doing string theory) do it.
see e.g.
http://en.wikipedia.org/wiki/4-manifold

>>5649051
You can choose between any m and n, so there are more points (n,m) which give a length d(n,m):=sqrt(n^2+2*m^2), which could be close to r.
I guess one way to think of it is in terms of circles (elipses really) on a grid with points (n,m). There is an elipse for all (n,m) and if you consider bigger n,m (bigger values of d(n,m) really), the circles get closer.
Naively, I'd expect them to get closer and closer so that for bigger r, you always find a closer and closer ellipse making G(r) going against 0

I was thinking of this
http://mathworld.wolfram.com/GausssCircleProblem.html
and how the points between the r's get more and more. But since the quation says n^2+2*m^2, this is all just fuzzy talk.

choose any suitable metric and compute the minimal out of 4.

E.g. if
g=(n,m)
is any of the 16 green dots and the reds are
r(1)=(0,0),
r(2)=(4,0),
r(3)=(0,4),
r(4)=(4,4),
then
g-r(i)
is the vector connecting g a dn r(i) and the addition of it'scomponents gives a distance measure.
E.g.
if
g=(-1,5)
then
g-r(4)=(-1,5)-(4,4)=(-5,1)
is the vector from r(4) to g and the taxicab metric, which is given by addition of the absolute values of the componends, 5+1 gives the traveling distance 6.

http://en.wikipedia.org/wiki/Taxicab_metric

so the closes red point r(i) is the one with the i, for which
d(g-r(i))
is minimal

o is an index?
and I would shift everything not-o-dependend with its sum at the last place.
and usually
(A·B)_i^j = \sum_k A_i^k B_k^j
i.e. the summation indicess will be taken together.

the all 1's construction is strange, never seen that.

also the indicess of the derivatives definition would also need a mention, that's not too standard I think.

Hey /sci/, ring theory problem here. In the ring Q[X,Y], are there any *prime* ideals I such that (xy) is contained in I, and I is contained in (x)?

I haven't really read your request, but if it's anything near a serious question, don't ask /sci/ but rather StackExchangeAcademia or something like that..

http://the-book-of-shankman.tumblr.com/post/39441967276/descartes-rule-of-signs

When I was in high school, I tried (unsuccessfully) to discover why Descartes Rule worked. That's the rule that tells you that the number of positive roots of a polynomial is less than or equal to the number of sign changes by a multiple of two.

Most of the proofs I tried to read online were way too complicated for me. I just randomly found this one today, and most of it made sense. I didn't know math could be this easy.

What does /sci/ think of this proof? Should I consider going into maths if I can understand this proof? I've never been this interested in math before.

TL:DR freshman biology major understood Descartes Rule and now wants to be a math major. Discuss proof of Descartes Rule/math major specifics.

why not try an explicit example?

The board seems to be kinda dead today...

So lets talk about things that I find interesting.
For example...

Who knows something about non-equilibrium statistical mechanics?
What is a reasonable definition of a temperature quantity (one which reduces to the usual definition in the equilibrium case)

Also, what is the deal with type theory? It seems I don't get the main insight which leads to studying it.