When calculating the Euler Characteristic of any regular polyhedron the value is 2. Since a sphere is homoeomorphic to all regular polyhedrons, the sphere...

I am well familiar with the principle of mathematical induction. But while reading a paper by Roggenkamp, I encountered the Principle of Transfinite Induc...

I've been trying to understand how ${x^3-12x+9}$ factors to $(x-3) (x^2+3 x-3)$ What factoring rule does this follow? The net result seems to be simi...

I'm stuck and don't know what to do next to solve this equation for $y$ in terms of $x$. Any hints? $$ y(x_2−x_1)−y_1(x_2−x_1)=x(y_2−y_1)−x_1(y_...

Motivation: I have seen the interchange of limit/derivative and integral many times, but don't know how such operation makes sense. I've always ...

I don't know how it works, although I learn it by myself. I need to find the last three digit number 3^3^3^3.... power of 3 is reapeted 2016 times. F...

I'm in a Differential Equations class, and I'm having trouble solving a Laplace Transformation problem. This is the problem: Consider the functi...

Given equation is $$x^{2}p^{2}+py\left ( 2x+y \right )+y^{2}=0$$ Where $p=\frac{\mathrm{d} y}{\mathrm{d} x}$ I know about clairaut's form and if we p...

Let's focus on the following version of Cauchy's Mean Value Theorem: Cauchy's Mean Value Theorem: Let $f, g$ be functions defined on closed...

Define The algebraic multiplicity of $\lambda_{i}$ to be the degree of the root $\lambda_i$ in the polynomial $\det(A-\lambda I)$. The geometric multiplic...