And Discrete Fourier Transform is pretty cool. There's a lot of stuff that I think I'm missing out on, and I guess I should pick up on it this semester.
So much intertwining - combinatorics with complex analysis, complex analysis with number theory, and so on.
suppose we have a polynnomial map between affine spaces....why I should look at its differential in order to know the dimension of the image? it sounds like rank-nullity theorem, but I'd like to have a clearer idea
Hi guys! I have a math related question which seems to be too broad for math.se, so I hope chat can be a suitable alternative.. In short, I'm looking for ideas regarding a suitable fitness function(s) for optimization and could really use the insights of somebody with a better understanding of spans, spaces etc. I have already explained it in "my home chatroom" (I don't want to spam this room seeing how I'm a newcomer...)
I'm considering a simple toy model. The spacetime is flat with $d$ space dimensions. Using cartesian coordinates, the spacetime metric is Minkowskian :
$$\tag{1}
ds^2 = dt^2 - dx_1^2 - dx_2^2 - dx_3^2 - \ldots - dx_d^2.
$$
A massless scalar field $\Phi$ is propagating in that spacetime accordin...
Consider the diophantine
$$ x^2 + t(n) \space y^2 = n $$
Where $x,y> 0$, $ n>1$ and $t(n) > -1$.
For a given $n$ we want to find the smallest possible integer $t(n)$.
Clearly when $n$ is a square then $t(n) = 0 $.
When $ n = a^2 \space b $ then $ t(n)$ is at most $t(b)$.
If $ n $ is a prime...
think about what this picture looks like - and then you'll learn more about this in ch5 of vakil, or when you read about associated primes in AM (which lacks the picture lol)
nothing really mathematically. writing some lie theory lectures for undergrads next semester. want to make it sufficiently physicsy to attract physics students. otherwise hanging out with friends and doing stupid stuff.
@BalarkaSen An alternate-timeline version of anakhronizein would tell future-present Alessandro that my message would be false, so give future-past @anakhronizein misleading instruction
I'm considering a simple toy model. The spacetime is flat with $d$ space dimensions. Using cartesian coordinates, the spacetime metric is Minkowskian :
$$\tag{1}
ds^2 = dt^2 - dx_1^2 - dx_2^2 - dx_3^2 - \ldots - dx_d^2.
$$
A massless scalar field $\Phi$ is propagating in that spacetime accordin...
Consider the diophantine
$$ x^2 + t(n) \space y^2 = n $$
Where $x,y> 0$, $ n>1$ and $t(n) > -1$.
For a given $n$ we want to find the smallest possible integer $t(n)$.
Clearly when $n$ is a square then $t(n) = 0 $.
When $ n = a^2 \space b $ then $ t(n)$ is at most $t(b)$.
If $ n $ is a prime...
