Let $\frak{g}$ be a simple complex Lie algebra with a choice of maximal torus. We denote the associated Cartan--Weyl presentation by $E_\alpha, F_\alpha, ...

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Grateful if somebody could help me have a look at the following — does it make sense? The derivative of the $f:=\Vert\cdot\Vert_\mathrm{eucl}$ for $...

The results are listed here: http://topospaces.subwiki.org/wiki/Homotopy_of_torus Is there an intuitive way to understand these results? In particular, wh...

For one of my homework questions we were given a 16-puzzle and we had to find out if it is solvable; and then solve it. My 16-puzzle is \begin{array}{|c|c...

I was reading a book on Calculus, by Michael Spivak. There they mention that points where the derivative is equal to zero are called critical points. They...

I understand that non-square matrices do not have an inverse, that is, both a left inverse and a right inverse. Yet, I am fairly certain that it is possib...

I am computing the Fourier series of $$f(x)=\sin\frac{\pi x}{L}.$$ The Fourier series of a piecewise smooth function $f(x)$ defined on the interval $-L\le...

I am having a hard time understanding the difference between classical, constructive, predicate, intuitionistic and propositional logic. I know that propo...

I think I have some good understanding of complex numbers. They are represented as a+ib where a,b are reals, and i² = -1. More precisely, multiplying a co...