What is an OPERATOR?
I try to understand operator-valued kernels. For this purpose, first want to know what is an operator. I can see the definition of operator here, but I do...
Apr 17, 2026 1 VIEWS
Topic: General
5104 Articles 
Calculate height or width of rectangle given its area and height or width.
I guess this should be very easy, but I'm stuck. I have a rectangle: Area = $520\text{ cm}^2$ $x = 120\text{ cm}$ $y = ?$ So: Area = $x \cdot y$ $520...
Apr 17, 2026 1 VIEWS
Commutative/noncommutative algebra?
I know basic knowledge of undergraduate algebra till galois theory of finite extensions. I want to learn number theory, but also like algebra. This semest...
Apr 17, 2026 2 VIEWS
Why do we need polar coordinates?
So, I haven't formally started learning about polar coordinates or anything yet, I'm just curious about them. I'm saying this to convey tha...
Apr 17, 2026 1 VIEWS
Why doesn't this graph have a maximum value by the Extreme Value Theorem?
I was provided this graph and asked if it passed the Extreme Value Theorem. I thought yes. I can see that this function is discontinuous...however, I was ...
Apr 17, 2026 1 VIEWS
If $n$ is a positive integer such that $8n+1$ is a perfect square, then $2 n$ can't be a perfect square
If $n$ is a positive integer such that $8n+1$ is a perfect square, then (a) $n$ must be odd (b) $n$ cannot be a perfect square (c) $n$ must be a prime num...
Apr 17, 2026 1 VIEWS
Calculate the volume of a torus
I want calculate the volume of the solid obtained by rotating around the $z$-axis $$C=\{(x,y,z) \in \mathbb{R}^3\;:\; (x-R)^2+z^2\le r^2,y=0\}$$ with $0&l...
Apr 17, 2026 1 VIEWS
Degrees of Freedom in Affine Transformation and Homogeneous Transformation
I understand that a 2D Affine Transformation has 6 DOF and a 2D Homogeneous Transformation has 8 DOF. However, how can I identify what those independent p...
Apr 17, 2026 1 VIEWS
Two sides of a triangle are $\sqrt{3}+1$ and $\sqrt{3}-1$ and the included angle is $60^{\circ}$. Find other angles
Two sides of a triangle are $\sqrt{3}+1$ and $\sqrt{3}-1$ and the included angle is $60^{\circ}$. Then find the other angles My Attempt Let $a=\sqrt{3}+1$...
Apr 17, 2026 1 VIEWS
Number of rectangles to cover a circle
After searching around I found this is similiar to the Gauss Circle but different enough (for me anyway) that it doesn't translate well. I have a cir...
Apr 17, 2026 1 VIEWS
Different definitions of boundary
Wikipedia gives three apparently equivalent definitions of a boundary: the closure of S without the interior of $S: ∂S = \bar S$ \ $S^o$. the intersection...
Apr 17, 2026 1 VIEWS
What is the difference between an adapted process and a predictable process?
As the footnote on page 1 of this document mentions, even most experts in the field of stochastic processes don't seem to know rigorously what the di...
Apr 17, 2026 1 VIEWS