updates
Order of general- and special linear groups over finite fields.
Let $\mathbb{F}_3$ be the field with three elements. Let $n\geq 1$. How many elements do the following groups have? $\text{GL}_n(\mathbb{F}_3)$ $\text{SL}...
Apr 14, 2026
Archive: Updates
updates
Integral with Tanh: $\int_{0}^{b} \tanh(x)/x \mathrm{d} x$ . What would be the solution when 'b' does not tends to infinity though a large one?
two integrals that got my attention because I really don't know how to solve them. They are a solution to the CDW equation below critical temperature...
Apr 14, 2026
updates
Saddle Points on Matrices
Let $n$, $m$ be positive integers. Suppose that $A$ is a $2$ x $n$ or an $m$ x $2$ matrix and that it has a saddle point. Show that among the saddle point...
Apr 14, 2026
![Why can't you have multiple domains in one function? [duplicate]](https://news.conceivablytech.com/uploads/why-can-039-t-you-have-multiple-domains-in-one-function-duplicate_720.jpg)
updates
Why can't you have multiple domains in one function? [duplicate]
Let's say we have function $y=\sqrt x$. For natural numbers it has two solutions. For example $\sqrt 4 = \pm2$. Wouldn't it make sense then to g...
Apr 14, 2026
updates
Integrating on open vs. closed intervals
What is one difference in the values of $$\int\limits_{\left[0,1\right]}y\, dx$$$$\int\limits_{\left(0,1\right)}y\, dx$$ and how would you calculate the v...
Apr 14, 2026
updates
Congruence of 2 fractions—how to properly rewrite in terms without modulo?
EDIT: Following Theo's comment, the equivalence holds since one can (must) rewrite $1/a$ as $(1+23k)/a$. Provided that $$\frac{1}{25} \equiv \frac{1}...
Apr 14, 2026
updates
Intuition behind $k$-algebra, $k$-algebra morphisms?
I will state the definition of a $k$-algebra and $k$-algebra morphisms. A ring $A$ equipped with a ring homomorphism $k \to Z(A)$ is called a $k$-algebra....
Apr 14, 2026
updates
Fourier transform of 1/cosh
How do you take the Fourier transform of $$ f(x) = \frac{1}{\cosh x} $$ This is for a complex class so I tried expanding the denominator and calculating a...
Apr 14, 2026
updates
Differentiate the Function $f(x) = \pi^2$
What does it mean to differentiate $\pi$? Is it similar to constant thus $0$?
Apr 14, 2026
updates
How to find magnitude of force based on graphs?
I don't get it. How do I get information from the graphs? How can it be solved?
Apr 14, 2026
