I am starting reading about Hodge theory and while reading the definition of abstract Hodge structure a very basic question came to my mind... What is the...

We know that a rhombus is a parallelogram that has 1) equal sides and 2) diagonals that are perpendicular to each other. If, for instance, we are a told t...

Let $\hat p$ be the proportion of successes in $n$ independent Bernoulli trials each having probability $p$ of success. (a) Compute the expectation of $\h...

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Let $f(x)$ a polynomial with integer coefficients. If $r$ is an integral root of $f$, then prove that the polynomial $\frac{f(x)}{x-r}$ is also a polynomi...

i know to solve the question if it is given a+ib . but for this kind of question i can't solve it because it is only given 'ib' . for this ...

If this is obvious and a silly question, I'm sorry. As a part of an exercise, I had to see that the inverse of $(g\cdot h)$, with $g$ and $h$ in a gr...

I'm told that $\dfrac{(n+1)!}{(n+2)!}$ simplifies to $\dfrac{1}{n+2}$, but I dont understand how this works. Could someone explain the theory of how ...

A railroad track and a road cross at right angles. An observer stands on the road $70$ meters south of the crossing and watches an eastbound train traveli...

Parabola and a branch of hyperbola, visually looks similar. The only difference I find is that, when x tends to infinity, hyperbola approaches a straight ...