How would I go about finding the inverse of a piecewise function? In this case the function is $$ f(x) = \left\{ \begin{array}{lr} x, & \text{if } 0\l...

Let $\phi$ be a smooth function on a Riemannian manifold $(M^n,g)$. Now, we could write $\nabla_g \phi$ as $$\nabla_g \phi = \sum^n_{i,j=1} g^{ij} \frac{\...

I want to prove that if we choose a positive real $a$ that has a terminating decimal representation, it has more than one decimal representation, and if a...

Does an equation containing infinity which is not equal to 0 or infinity exist? My math education stopped at poorly understanding trig so don't kill ...

Why is the derivative (d/dx) thought of as a linear operator instead of a function of functions? if we take the derivative of some function f(x) (d/dx(f(x...

Why is every positive integer the sum of at most 3 triangular numbers ?

What is the difference between the phrases "scalar line integral" and "line integral"? If the phrases are equivalent, what purpose does the adjective "sca...

Let $A = \left[ {\begin{array}{cc} 1 & 1 & 1 \\ 3 & -1 & 1 \\1 & 5 & 3\\ \end{array} } \right]$ and $V$ be the vector space of all...

I'm learning about the math invovled in PCA. For my purposes here, I'm just trying to understand a 90° rotation matrix. I get the concept of...

I have an equation for a cylinder as $x^2+(y-b)^2=a^2$ for some $a$ and $b$. so I just plugged in $b=2$ and $a=1$ and tried to plot it using wolfram alpha...