Example of reduced ring which is not integral domain
So, a reduced ring has no nonzero nilpotent elements, while integral domain has no nonzero zero divisors. Of course, the latter is way stronger then the f...
19 Apr 2026 1 READS
Archive: General
Where does $xe^x$ solution come from when the characteristic polynomial is square?
When solving the differential equation $y'' + ay' + by = 0$ (with constant, real coefficients $a$ and $b$, although they could be complex i...
19 Apr 2026 1 READS
Congruence of quadrilaterals given the sides
Often while solving mensuration problems, I encounter situations where I need to establish the congruence of two quadrilaterals, mostly having been got al...
18 Apr 2026 1 READS
Semi-direct v.s. Direct products
What is the difference between a direct product and a semi-direct product in group theory? Based on what I can find, difference seems only to be the natur...
18 Apr 2026 1 READS
What shapes are described with $\rho = \cos{(\phi)}$ and $\rho = \cos{(2\theta)}$?
I have started an Multivariable course, and I'm learning about spherical coordinates. My problem now is learn how to graph this kind of shapes. This ...
18 Apr 2026 1 READS
Equation via matrix, having no solution, one solution and infinite solutions.
$$ \left[ \begin{array}{cc|c} 1&-2&4\\ a&4&5 \end{array} \right] $$ I came across this question on one of my course slides, and I am havin...
18 Apr 2026 1 READS
Differences between $L^p$ and $\ell^p$ spaces
Could someone explain some differences between the $L^p$ and $\ell^p$ spaces? Thanks a lot.
18 Apr 2026 1 READS
Find range of a reciprocal function given domain
I cannot find the range of this reciprocal function: 1/(x+1) whose domain is {x:x≥0, x a real number}. I could draw the graph of this function but my conf...
18 Apr 2026 1 READS
How to find the corner point of a non-function equation?
Consider the equation $$-242.0404+0.26639x-0.043941y+(5.9313\times10^{-5})\times xy-(3.9303\times{10^{-6}})\times y^2-7000=0$$ with $x,y>0$. If you plo...
18 Apr 2026 1 READS
Derivation of the formula for Ordinary Least Squares Linear Regression
How was the formula for Ordinary Least Squares Linear Regression arrived at? Note I am not only looking for the proof, but also the derivation. Where did ...
18 Apr 2026 1 READS
