What is the most motivating way to introduce continued fractions? Are there any real life applications of continued fractions?

I am wondering if there is a generally accepted definition of the term curve in mathematics. If one does exist, is there any requirement of continuity, be...

From the first page of this pdf on measurements of bandstructures it is written that: In the chain rule above, written again below for clarity: $$\frac{\p...

At the level of precalculus, there's a certain derivation of the equation of an ellipse that follows the same path. See this for example. Inevitably ...

In Wikipedia, there is Shannon's proof on Nyquist-Shannon sampling theorem. ( http://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem#S...

I'd like to prove that any orthogonal $2 \times 2$ matrix can be written $$\bigg(\begin{matrix} \cos x & -\sin x \\ \sin x & \cos x \end{matr...

Given the vector field $\vec{F}(x,y) = (x^2+y^2)^{-1}\begin{bmatrix} x \\ y \end{bmatrix}$, calculate the flux of $\vec{F}$ across the circle $C$ of radiu...

My book gives the following definition: Let $(M,d)$ be a metric space, and let $\mathcal{T}$ be the collection of all subsets of $M$ that are open in the ...

I am asked to find a $2 \times 2$ matrix with real and whole entries given it's characteristic polynomial: $$p^2 -5p +1.$$ This is what I have done t...

I have a question asking me why matrix multiplication isn't commutative. I'm not exactly sure what's the best way to explain this without s...