Let $R$ and $S$ be rings with $R \subseteq S$, and let $_S M$ be a left $S$-module. If we restrict our scalars to $R$, we naturally have a left $R$-module...

I am currently reading Roger Penrose's The Road to Reality and in the book, the author poses various problems with three different levels of difficul...

According to Joyce' commentary, proposition 2 is only used in proposition 3 of Euclid's Elements, book I. As Euclid states himself (I-3, the len...

I'm taking a course on Modern Algebra at my university and my professor keeps asking us to look for examples of rings that may be interesting to disc...

I would like to show that $(\mathbf{A} \mathbf{B})^{-1} = \mathbf{B}^{-1} \mathbf{A}^{-1}$, where $\mathbf{A}$ and $\mathbf{B}$ are $N \times N$ square ma...

I have never been good at math. In my senior year I failed algebra 2 in the first semester because the teacher would refuse to show me how to solve proble...

What does it mean to take the gradient of a vector field? $\nabla \vec{v}(x,y,z)$? I only understand what it means to take the grad of a scalar field.

I have worked out the answers $45^\circ$, $135^\circ$, $225^\circ$, $315^\circ$; although some of these may be wrong. Where have I gone wrong (if I have)?...

Given a fair coin, what’s the p value of getting at least 14/20 heads. Am I correct in assuming Null hypothesis — P(heads)=0.5 Alternate hypothesis — P(he...

For some problem from my Galois Theory course, I need to prove that the polynomial $X^4-2X^2+4$ is irreducible in $\mathbb{Q}[X]$. I know it has no roots ...