I was on an accreditation visiting team for a K-12 Christian school once. First time I'd really been around that sort of instruction/institution. I'll admit: it was impressive in a lot of ways. I remember coming back to my school thinking "man, it'd be nice if we had any sort of institutional philosophy."
Hello I had a small question since Maths isnt my Forte. I have a original price, a sale price and I would like to calculate the percentage off that this represents. However I keep finding the formula for calculating what 30% off a certain number is which is not what im looking for
Would it be: (OriginalPrice - Current Price) / OriginalPrice * 100
Hi guys, are people familiar with differentiation under the integral sign formally the Leibnitz rule for integration with respect to a parameter. Sometimes you can create a new DE using this method. Does anyone know if it makes sense if your new DE contains the original integration variable?
So our friend with a funky name writes SvK as "this diagram is a pushout of groups", but I don't see how it that the same as SvK written in terms of presentations of groups, which gives an explicit description of $\pi_1$ of the space knowing those of the subspaces
Is there any chance to make sense out of the integral $\int \phi(x) dx$ where $x$ is a Banach space $V$ valued path with bounded variation and $\phi(x)$ a linear form on $V$.
What is meant by learning math historically (not learning math history only, but learning math with a historical development perspective)? I've seen some sources say that to learn a math topic X, you need to look at the historical development of the topic X and go over the famous questions by you...
BTW, given two sets (possibly infinite) $S, T$, is atleast one of this two statement true for sure ? 1. There's an injection from $S$ to $T$ 2. There's an injection from $T$ to $S$
If $S$ bijects into $T$, then the two has the same cardinality If $S$ injects but not surject into $T$, then $S$ has cardinality smaller than $T$ If $S$ surjects but not inject into $T$, then $S$ has cardinality not smaller or equal to $T$
Axiom of choice and generalised continuum hypothesis makes this easier as there will be an aleph cardinal biject to any given infinite set and said sleph cardinal is its cardinality
Given a set $A$ with cardinality $c$, there is a subset of $A$ having any cardinality less than $c$.
There is an injection from the subset $B$ to the set $A$, namely, the identity in which each element of $B$ maps to itself in $A$ (no axiom of choice needed; it is like choosing from pairs of s...
Also a weirdness that only appear when you reject the axiom of choice: If neither $S$ nor $T$ inject into each other, they are incomprable in cardinality
Axiom of choice destroys this case by forcing all unordered sets to be well orderable
as a choice function to well order them will always exist to do so
@AlexKChen: I even have some personal examples where reading historical texts helped me to better understand some maths topics. E.g. In reading Kleins lecture on the icosahedron I first got fully aware of the full significance of cosets and conjugation. He kind kind of really beautifully and concisely explains it. Even without loosing many words.
This is Theorem 1.5.3 from Scharlau's book Quadratic and Hermitian Forms
Let $(V, b)$ be a regular symmetric bilinear space.
Let $W$ be a subspace of $V$ and
$\sigma \colon W \to V$ an isometry.Then there exists
an isometry $\tau \colon V \to V$ which extends $\sigma $ i.e $\tau$ restricted t...
Hey everyone! Also hi @Leaky, sorry I didn't notice your ping earlier
@Balarka at least the hassle of moving will be mostly localized. I'm not sure how technical matters are gonna work there, but do you stuff along the lines of what classes you intend to do?
Sorry about that, well I think I'll concede the floor to someone else since I'm not quite qualified here (I originally thought that $\omega = e^{2\pi i/3}$
Well, continuing on though @Balarka, while it may very well be the case that you were going too fast up until now, I don't think the solution is to go extra slow for a while in order to "average" it out or anything. Boredom is a knife in the chest of enthusiasm, and that's something you should definitely try to keep alive and running
Hopefully it was maybe that the process of worrying about admission and whatnot, since that can take a toll on general cheerfulness. But yeah so, in case your professors are more okay with just showing up for the final, that might be good because it kinda leaves open the option of doing things on the side, either to just take a break from math for a bit entirely or to do your own thing
Anyway I'll be back later once the internet begins to return, this is a good opportunity to work because it's a lot harder to procrastinate :P
@BalarkaSen Gromov's h-principle gives you a metric of sectional curvature in any open interval on an open manifold. If that is negative curvature, can I modify it to be a negatively curved complete metric?
I think there are negative curvature metrics on noncompact manifolds which cannot be approximated by complete negatively curved metrics but I may be wrong
I am thinking of cusps
Like if I take $\Bbb H^2/SL_2(\Bbb Z)$ the points on the boundary with the $\Bbb Z/2$- and $\Bbb Z/3$-symmetry are points where geodesics diverge in finite time right?
I don't know how to perturb that metric to be complete while staying negatively curved
Considering the potential $\psi(r)$ of a sphere with density $\rho(\mathbf r')$,
connected by a small volume positioned in the $P'$ point as shown in the figure:
The $\psi(r)$ is:
$$\begin{align}
\psi(r)=-G\iiint_{\mathcal{V}} \frac{\rho(\mathbf r')dx'dy'dz'}{|\mathbf r - \mathbf r'|}=
-G\i...
@robjohn Sorry, I was away. No I don't. I believe that such a integral can be constructed in the same way as RS-Integral on $\Bbb R^d$. But I can't find anywhere such a notion of integration in the Literature. That made me bit unsure.
I found this degree sequencing problem interesting and tried to work it out but got stuck. I would like to find the graphs with the following degree sequence:
For $ N>4 $, the degree sequence of a set of graphs is defined as follows:
$ (N, N, N, N, 4, 4, 4, ... ) $,
where the number of $4's$ ...
Given a set $A$ with cardinality $c$, there is a subset of $A$ having any cardinality less than $c$.
There is an injection from the subset $B$ to the set $A$, namely, the identity in which each element of $B$ maps to itself in $A$ (no axiom of choice needed; it is like choosing from pairs of s...
This is Theorem 1.5.3 from Scharlau's book Quadratic and Hermitian Forms
Let $(V, b)$ be a regular symmetric bilinear space.
Let $W$ be a subspace of $V$ and
$\sigma \colon W \to V$ an isometry.Then there exists
an isometry $\tau \colon V \to V$ which extends $\sigma $ i.e $\tau$ restricted t...
Considering the potential $\psi(r)$ of a sphere with density $\rho(\mathbf r')$,
connected by a small volume positioned in the $P'$ point as shown in the figure:
The $\psi(r)$ is:
$$\begin{align}
\psi(r)=-G\iiint_{\mathcal{V}} \frac{\rho(\mathbf r')dx'dy'dz'}{|\mathbf r - \mathbf r'|}=
-G\i...
I found this degree sequencing problem interesting and tried to work it out but got stuck. I would like to find the graphs with the following degree sequence:
For $ N>4 $, the degree sequence of a set of graphs is defined as follows:
$ (N, N, N, N, 4, 4, 4, ... ) $,
where the number of $4's$ ...
