How do you prove a number is prime?
I am a software engineer but try to keep up with maths as I really enjoyed the subject at school. I just saw a great TED talk: Why I fell in love with mon...
Published: Sep 06, 2026
Proving that the composition of relations are equal to each other
Please excuse my English if it's not understandable, exercises are translated so I don't know all the English terms in math. So I'm doing e...
Published: Sep 06, 2026
Finding the error of a Taylor Series
When calculating the error of a Taylor series, the formula is as follows: $$R_n(x)=\frac{f^{(n+1)}(z)(x-c)^{(n+1)}}{(n+1)!}$$ $z$ is the maximum value of ...
Published: Sep 06, 2026
two sides and angle between them triangle question.
is it possible to find the third side of a triangle if you know the lengths of the other two and the angle between the known sides? the triangle is not eq...
Published: Sep 06, 2026
What is a coordinate function $x^i$ of a manifold, given a chart $(U,x)$?
I am trying to understand the notes here: http://unapologetic.wordpress.com/2011/04/13/cotangent-vectors-differentials-and-the-cotangent-bundle/. Specific...
Published: Sep 06, 2026
If $e$ (Euler's constant) $= (1+\frac{1}{n})^n$ as $n$ approaches infinity, why is $e^x$ not equal to $e$? if x equals any number, real or not real.
If $e$ (Euler's constant) $= (1+\frac{1}{n})^n$ as $n$ approaches infinity, why is $e^x$ not equal to $e$ if x equals any number, real or not real. L...
Published: Sep 06, 2026
Local Max/Min, Critical points of integral
Given $$f(t) = \int_0^t \frac{x^2+14x+45}{1+\cos^2(x)}dx $$ I need to find the local max of f(t). Well here using the fundamental theorem of calculus, I k...
Published: Sep 06, 2026
Show that $\mathbb{R}$, when equipped with the standard topology, is not compact.
Proof: Let $\mathscr{U}$ := {$U_n$}$_{n \geq 1}$ = {$(n-1,n+1)$}$_{n \geq 1}$ be an open cover of $\mathbb{R}$. Consider finitely many of them, say: $U_{n...
Published: Sep 06, 2026
Is there a correct mathematical term for the inverse of the slope?
Linear graphs all have a slope that can be calculated by deviding the progress on the y-axis by the progress on the x-axis. Is there a correct term to ref...
Published: Sep 06, 2026
What is the affine connection, and what is the intuition behind/for affine connection?
Here is the definition of affine connection, as appears in Milnor's book Morse Theory. DEFINITION. An affine connection at a point $p \in \text{M}$ i...
Published: Sep 06, 2026
