How to prove its maximality of normal core?
For a group $G$, the normal core $H_G$ of a subgroup $H \le G$ is defined as the intersection of the conjugates of $H$, i.e., $$H_{G} = \bigcap_{a \in G} ...
22 Apr 2026 1 READS
Archive: News
Atypical definition of "regular ring"?
In my adventures I've finally come by a copy of Examples of Commutative Rings by Hutchins, and almost immediately read something that surprised me. O...
22 Apr 2026 1 READS
Logic, geometry, and graph theory
[Seven years later, I made an edit to this question, see below.] By delving into topos theory and sheaves one will eventually discover a "deep connec...
22 Apr 2026 1 READS
Motivation for Mirror-Descent
I am trying to wrap my head around why mirror descent is such a popular optimization algorithm. Based on my reading, it seems like the main reason is that...
22 Apr 2026 1 READS
How do I find a first order approximation?
I have a question on Calculus, where I have to find the "first order approximation", on a function where: sqrt[(C^2 + sin(h))], where C > 0, and h is s...
22 Apr 2026 1 READS
Four tetrahedron dice probability
We have four dice in the shape of a tetrahedron. Each dice has faces numbered 2, 0, 1, and 7. If we roll all four dice simultaneously, what is the probabi...
22 Apr 2026 1 READS
Definition of period of a decimal representation of a number
I need to define the period of a decimal representation of a number!! Thanks in advance!!
22 Apr 2026 1 READS
Calculating the shortest distance between n number of points on a scatter graph
This has been bugging me for about two weeks now.. I have a cartesian plane with n number of points randomly placed on it. You can get the coordinates of ...
22 Apr 2026 1 READS
How to calculate the area covered by any spherical rectangle?
Is there any analytic or generalized formula to calculate area covered by any rectangle having length $l$ & width $b$ each as a great circle arc on a ...
22 Apr 2026 1 READS
velocity and acceleration in a parabola
A particle moves with constant speed along a parabola of equation $y^{2}=2px$ with $p=constant$. I want to find its velocity and acceleration vector. Sinc...
22 Apr 2026 1 READS
