Are the symbols $d$ and $\delta$ equivalent in expressions like $dy/dx$? Or do they mean something different? Thanks

In An Invitation to Algebraic Geometry Karen Smith writes at the beginning of the book: The zero set of a single polynomial in arbitrary dimension is call...

The number $10^{19}+1035830$ is a $20$-digit number with $12$ distinct prime factors. I am not sure whether it is the smallest example because to save tim...

I am studying complex analysis and I have problem understanding the concept of branch cut. The lecturer draw this as some curve that starts from a point a...

The curve of the intersection of the surface $x^2+y^2-2z^2=1$ and the plane $y=2z+1$ is given by $\varphi(t)=(\sqrt2\cos t,2\sin t-1,\sin t-1), t\in [0,2\...

In general when considering an RKHS $\mathcal{H}$ over a set $X$ one has a kernel function $k:X\times X\rightarrow\mathbb{C}$. It is then not too hard to ...

In every geometry textbook it states that the shortest distance between two skew lines (lines that are not co-planar) is given by the unique line that run...

I know you can change to polar coordinates but then you still have to integrate $\sqrt{1+r^2}$ which is still non-trivial. I remember there being some tri...

Because the Hessian matrix is real and symmetric, we can decompose it into a set of real eigenvalues and an orthogonal basis of eigenvectors. The second d...

Note: Turns out this is a pretty tricky problem where we need to use techniques not developed in the chapter. We will go over this problem in class on Tue...