I know a middle school math teacher looking for some suggestions for hands-on activities to teach the concept of real numbers. I'm new to this site, so this may be a little off to …

Let $\mathfrak{g}$ be a finite dimensional simple Lie algebra over $\mathbb{C}$. The polynomial current Lie algebra $\mathfrak{g}[t] = \mathfrak{g} \otimes \mathbb{C} [t]$ has the …

I am trying to factorize $sin(x)\over x$ which by Taylor series expansion and using the roots is $a \cdot \left(1 - \frac{x}{\pi} \right) \left(1 + \frac{x}{\pi} \right) \left(1 - …

In the defination of vertex algebra,we call the vertex operator state-field correspondence,does that mean that it is an injective map?? Are there some physical intepretations about …

A vertex operator is a linear map associating every state to a operator-valued distributions(quantum field) on a algebra curve,which is also called operator-state correspondence. C …

The fact that a commutative ring has a natural topological space associated with it is still a really interesting coincidence. The entire subject of Algebraic geometry is based on …

In his article where he stated what we know as Eisenstein's irreducibility criterion (which actually was first proved by Schönemann, as was Scholz's reciprocity law and Hensel …

Let's say I start with the polynomial ring in $n$ variables $R = \mathbb{Z}[x_1,...,x_n]$ (in the case at hand I had $\mathbb{C}$ in place of $\mathbb{Z}$). Now the symmetric group …

I wonder how modular property naturally arises in conformal theory. Is it obvious from physical viewpoint?

Everybody knows that polynomial rings over fields have unique factorization, and that if $R$ has unique factorization, then so does $R[X]$. And everybody knows who proved these res …

The classic handshake puzzle goes something like this: "Given that everyone has a different skin disease, how can you safely shake hands with 3 people when you have only 2 glove …

(I've edited this question) I'm searching for a continuously differentiable function $f:\mathbb R^2\to\mathbb R$ such that $f(x)+f(x+u+v)\neq f(x+u)+f(x+v)$ for all $x$ and all li …

Inspite of the fact that $C^{n \times n}$ is not a field, is it still possible to talk about it being 'algebraically closed' in the sense that $\forall f \in \mathbb{C}^{n \times n …

Forgive me for this naive question. We consider the following lemma and its proof in Lang's algebra, Third Ed., published 1999, Chap. 20, section 4, page 784. Every module is …

How can I compute the Galois group of the polynomial $fg\in K[x]$ assuming that I know the Galois groups of $f\in K[x]$ and $g\in K[x]$? Let's suppose for simplicity that the field …