I have been in conflict with myself because of a confusion about the point convergence of sequences of functions and the uniform convergence over an arbit...

Sorry if this question isn't valid. I just need to know an equation/function for a graph which resembles something close to

I understand that for a system to behave chaotically, it needs to be "topologically mixing". However, I am not sure what that term really means. There are...

Find linear transformation $F$ in canonical bases given $ F: \Bbb R^4 \to \Bbb R^3 $ $ \ker F=\operatorname{span}\left\{\begin{bmatrix}1\\2\\3\\4\end{bmat...

The pmf of geometric distribution is given by $p(1-p)^{x-1}$. I want to generate the samples for a random variable which has geometric distribution. So, t...

Apparently, it can be shown that the Cauchy-Riemann equations can be written simply as, $df/dz^*=0$. I do not understand how it does not immediately follo...

Let $A = \{0,1,2,3,4\}$ and define a relation $R$ on $A$ as follows: $$R = \{(0,0),(0,4),(1,1),(1,3),(2,2),(3,1),(3,3),(4,0),(4,4)\}.$$ Find the distinct ...

Let $(\Omega,\mathcal{A})$ be a measurable space. (Hahn Decomposition Theorem) Let $\varphi\colon\mathcal{A}\to\mathbb{R}$ be a signed measure. Then there...

I am having problems understanding how to find the maximum value from a rate of change (derivative) function. The rate of change of Volume with respect to...

The sphere is $x^2+y^2+(z-1)^2=25$ with $0 \le z$ and i wanted to parametrize it with spherical coordinates. How does it change with the fact that it is n...