For independent variables we have $E[XY]=E[X]E[Y]$. Now, since I could not find a statement that the converse is also true, I suspect that there are examp...

Let $(\Omega,\mathcal{A})$ be a measurable space. (Hahn Decomposition Theorem) Let $\varphi\colon\mathcal{A}\to\mathbb{R}$ be a signed measure. Then there...

Currently I'm studying differential geometry, and more specifically the Gauss map. I'm using the (in)famous Do Carmo Differential Geometry and S...

I don't think I fully understand the question. If I knew f(x) I would use the chain rule or product rule, but since I don't, how do I know what ...

I'm trying to solve this and when I add both of the different signs together I ended by a result of 2, but it's not one of the choices, any help...

For example in 2D space: It is possible to calculate unit normal, $\vec{n}$, using $\theta$ and a bit of the unit-circle application: $$\vec{n} = (\sin{\t...

The decimal number 371 equals the hexadecimal number 0x173. The part that is relevant to me is that 371 is simply 173 backwards. Is this the only multiple...

I have been wanting to learn about linear algebra (specifically about vector spaces) for a long time, but I am not sure what book to buy, any suggestions?

$$\log_2(x-5)=\log_5(2x+7)$$ Is there a way to solve this equation without drawing the graph and prove they "meet" in one point so the solution is unique?...

I'm reading Grothendieck's Tōhoku paper, and I was curious about the reasoning behind the terms "effaceable functor" and "injective efface...