I'm trying to solve a problem where I have to create a DFA for the intersection of two languages. These are: $$\{s \in \{{\tt a}, {\tt b},{\tt c}\}^\...

Let $x,y\in \mathbb R$. A common definition of Euclidean line segment $xy$ on $\mathbb R$ - real line - going from $x$ to $y$ is the set ${\{s:s=tx+(1-t)y...

The answer: 6, 670, 903, 752, 021, 072, 936, 960, according to this site: https://www.technologyreview.com/2012/01/06/188520/mathematicians-solve-minimum-...

this question says only three of the below are topology. So,according to me,$\tau_2$ is topology it is satisfying all three definition for topology. And I...

I am trying to differentiate with respect to $x$, $y = \cos^2{x}$ Using the chain rule and my working out is this: \begin{align*}\frac{dy}{dx} &= 2 \c...

If $H$ is an orthogonal matrix, then $||H||=1$ and $||HA||=||A||, \forall A$-matrix (such that we can writ $H \cdot A$). What norm is this about?

I am reading this text: and I'm confused at this part: If all x-coordinates of the points are distinct, then there is precisely one polynomial functi...

The taylor series expansion about point $a$ for function $f(x)$ is given by $$f(x) \approx f(a) + f'(a)(x-a) + \frac{1}{2!}f''(a)(x-a)^2 +....

Let's say an ordinary linear DE is separable. Then $$\frac{dy}{dx} = P(y)Q(x) \Leftrightarrow \frac{1}{P(y)}dy = Q(x)dx \Leftrightarrow Q(x)dx + R(y)...

I search on the Internet for what a proper function is but cannot find anything very related. Wikipedia has definitions about proper convex function and p...