All of us know general equation for any conic section: $$Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$$ If we'll change of parameters of this equation we get ...

I work in computational chemistry, and I want make a simple Python program that rotates a molecular structure by some angle $\alpha$ around some axis defi...

I'm struggling to understand the basics of Galois theory. One of the things I don't understand is how to actually derive automorphisms of a fiel...

Please solve it and tell me the technique so that I can solve it in examination in multiple choice questions.

I just purchased the game Spot It. As per this site, the structure of the game is as follows: Game has 55 round playing cards. Each card has eight randoml...

I am setting up the problem to find the limit as delta x goes to zero, using the definition in the correct format. No matter what I've tried, I am st...

We know that if W(t) is a Brownian Motion, then the Ito Process is given by, X(t)= X(0) + $\int_0^t \Delta(u)dW(u)$ + $\int_0^t \Phi(u)du$ Could someone e...

Let $B$ be the solid tetrahedron bounded by $x = 0, y = 0, z = 0$, and $x+y+z = 1$. Assume that the density of $B$ is given by the function $y$. Compute t...

I want to calculate the following limit: $$\displaystyle{\lim_{x \to 0} \cfrac{\displaystyle{\int_1^{x^2+1} \cfrac{e^{-t}}{t} \; dt}}{3x^2}}$$ For that, I...

People make such a big deal of the number $e$. I do not get why it is so important, other than the fact that $\ln(x)=\log_e(x)$. People say it is used all...