The Coordinate Ring: Its Etymology
Well, to quote from Wolfram MathWorld directly, Given an affine variety $V$ in the $n$-dimensional affine space $K^n$, where $K$ is an algebraically close...
Apr 15, 2026 1 VIEWS
Topic: General
5104 Articles 
Zorn's lemma, every set can be well-ordered
My task is to prove the well-ordering theorem: Every non empty set $X$ can be well-ordered I want to do so in the following steps, which involve Zorn'...
Apr 15, 2026 1 VIEWS
Show that integral of Gaussian distribution is 1
Under a normal distribution, μ = 0 and σ = 1, but when then integrating this equation, I get an error function. Without using Riemann sums, how can I prov...
Apr 15, 2026 1 VIEWS
Finding the derivative of the integral using the Fundamental Theorem of Calculus.
(1 pt) Find the derivative of the following function $$F(x) = \int_{x^4}^{x^7} (2t - 1)^3 dt$$ using the Fundamental Theorem of Calculus. $F'(x) = \l...
Apr 15, 2026 1 VIEWS
Finding integrating factor for non-exact differential equation $(4y-10x)dx+(4x-6x^2y^{-1})dy=0$.
I am given this equation $$(4y-10x)dx+(4x-6x^2y^{-1})dy=0$$ where I must find an integrating factor to turn this into an exact differential. The integrati...
Apr 15, 2026 1 VIEWS
How can I formulate the 3-SAT problem as a 0-1 Linear integer program?
I understand the 3-Sat problem but I do not understand 0-1 Linear Integer Program. I know in a linear integer program I would have an indicator variable $...
Apr 15, 2026 1 VIEWS
What is "progressive" about progressively measurable processes?
So I have just started to learn about stochastic processes, and I got to learn about progressively measurable processes. Definition Let $(\Omega, \mathcal...
Apr 15, 2026 1 VIEWS
How to compute the pade approximation?
Like $\log(1+x)$? Is there any algorithms? I have read many materials but doesn't have an idea
Apr 15, 2026 1 VIEWS
Converting $(0, -6, 0)$ from rectangular coordinates to spherical. In particular, finding $\theta$
My homework asks me to convert the point $(0, -6, 0)$ from rectangular to spherical coordinates. I've found that $\rho = 6$ and $\phi = \frac{\pi}{2}...
Apr 15, 2026 1 VIEWS
Determinant of hermitian matrix
Let $M=A+iB$ be a complex $n \times n$ Hermitian matrix. First of all we know that $$(\det M)^2=\det \begin{pmatrix} A & -B \\ B & A \end{pmatrix}...
Apr 15, 2026 2 VIEWS
What does the inner product of two complex general vectors have to do with complex conjugation?
$ \newcommand{\qr}[1]{|#1 \rangle} \newcommand{\ql}[1]{\langle #1|} \newcommand{\q}[2]{\langle #1 | #2 \rangle} \newcommand{\v}[2]{\langle #1,#2\rangle} $...
Apr 15, 2026 1 VIEWS
Can calculus optimization problems be turned into linear programming problems?
I found a Linear Programming textbook somewhere, and I skimmed through the first few pages. While I am not nearly enough ready to go through it, the thing...
Apr 15, 2026 1 VIEWS