## 30 NovFundamental Theorem of Algebra using Galois theory

In this article we shall prove that \$\$\mathbb{C}\$\$ is algebraically closed. Here we consider \$\$\mathbb{C}\$\$ as a splitting field of the polynomial \$\$x^2+1\$\$. The proof uses very little analysis and most of it is Galois theory. The only facts from analysis which will be used in...

## 16 NovHow to Write Faster and Become More Productive in Science

The higher the productivity of a writer, the more projects he can complete and the more he earns. Working rationally, you can greatly reduce the time required to perform a single task. So how do you increase your writing efficiency and become more productive? It...

## 11 MayAutomorphisms of the Upper Half Plane

In this article we see that the automorphism group of biholomorphic functions of the upper half plane and the open unit ball in the complex plane is isomorphic to the second projective special linear group over the field of real numbers. [pdf-embedder url="http://gonitsora.mathematics.website/wp-content/uploads/2016/05/automorphisms-upper-half.pdf"] Click here to download. Image Source...

## 30 NovOccupation in 26 dimensions

In the previous antifeuilleton, Engels mentioned two interesting things through his criticism of Dühring: the 1+2+3+4+… series and the question of our world’s dimensionality. It is high time to connect these two questions in the spirit of our time and contemporary science. Final answer is not...

## 08 JulExceptional Embedding of S5 in S6

In this article we shall show a peculiar property of \$S_5\$. We first note that there are several subgroups of \$S_n\$ isomorphic to \$S_{n-1}\$. Infact there is one for each \$1leq ileq n\$ \$H_i={sigmain S_n |sigma(i) = i}\$ Let \$\$X={1,2,3,4,5,6}\$\$. All of the above subgroups have two orbits...

## 10 MayNorm Induced Topologies on Finite Dimensional Real Vector Spaces

In this article we show that the topology induced by a norm on a finite dimensional real vector space is an intrinsic topology irrespective of the norm. It is equivalent for all norms. Let V be a finite dimensional vector space over \$\$mathbb{R}\$\$ with dimension n....