updates
Modular arithmetic in Montgomery form
I am trying to apply an algorithm that requires significant modular arithmetic, but in such a way as to avoid as many costly mod or division operations as...
Read Journal Category
Updates
updates
Why is the complex projective line homeomorphic to a $2$-sphere?
Define an equivalence relation $\sim$ on $X={\bf C}^2\setminus \{(0,0)\}$ by $(x_1,y_1)\sim(x_2,y_2)$ if and only if there exists $t \in C\setminus\{0\}$ ...
Read Journal
updates
Can an undirected graph strongly connected?
From various books and online resources, I've come to know a directed graph is said to be strongly connected if, all of its vertices reachable from e...
Read Journal
updates
Percentage greater than 2 standard deviations from the mean
A question reads: "The weights of $910$ young deer tagged and weighed in a research study are normally distributed with a mean of $86$ pounds and a standa...
Read Journal
updates
Generalizing the 290 theorem.
I have only just come across the remarkable theorem of Conway about universal quadratic forms over $\mathbb{Z}$; namely that in determining whether a inte...
Read Journal
updates
Solving $\displaystyle py+xq+pq=0$
To Solve: $\displaystyle py+xq+pq=0$, where $\displaystyle p=\frac{\partial z}{\partial x}, q=\frac{\partial z}{\partial y}$ My Attempt: $\displaystyle p(...
Read Journal
updates
How many different ways can you solve the cracker barrel peg game? And is there an optimal starting arrangement of pegs?
The cracker barrel peg game is a strategical table game that is mockingly cocky with its confidence that the player won't win. Let me explain... Here...
Read Journal
updates
Deductive proof - need help, explanation how to
I am working on assignment for school where the task asks to give a deductive proof. However, I have never used this technique (nor that I am very good in...
Read Journal
updates
Why isn't the derivative of $e^x$ equal to $xe^{(x-1)}$?
When we take a derivative of a function where the power rule applies, e.g. $x^3$, we multiply the function by the exponent and subtract the current expone...
Read Journal
updates
Multidimensional chain rule, online calculator
I would like to check my solutions for the derivative with the multidimensional chain rule, and I would like to do that online with a calculator. But I ca...
Read Journal