I'm a high schooler and today my teacher taught us the implicit differentiation, in which he gave us a very brief explanation of implicit function. I...

For financial reasons, I dropped out my senior year of college as a piano performance major. I will be returning to college to dual major in mathematics a...

I'm reading a bit about the exponential function $e_k: \mathbb{R} \longrightarrow \mathbb{C}$ given by $$e_{k}: x \mapsto e^{i k x}=\cos k x+i \sin k...

What exactly is the physical interpretation of variance (in terms of a data set) and the difference between variance and co-variance matrices?

If \begin{align} A =\begin{bmatrix} 1 & 1 \\ -1 & 1 \\ \end{bmatrix} \end{align} and \begin{align}B = \begin{bmatrix} 1 & -1 \\ 1 & 0 \\ ...

I have a Markov chain with states {1,2,3,4,5} which has the following transition matrix: $$P= \begin{bmatrix} 0.3 & 0 & 0.7 & 0 & 0\\ 0 &a...

Find the $n$th term for the sequence of partial sums for the series $$\sum_{n=1}^{\infty} \frac{5}{n(n+3)} =\sum_{n=1}^{\infty} \left(\frac{5}{3n}-\frac{5...

I'm not sure why $$(-2^n)^{-2} + (2^{-n})^2=2^{-2n+1}$$ I have been going over this equation for a while now, noticing, and have successfully got qui...

I've been trying different methods but keep getting the same answer for the following question: Verify that Stokes’ Theorem is true for the given vec...

Solve the system below \begin{align} &\sqrt {3x} \left( 1+\frac {1}{x+y} \right) =2\\ &\sqrt {7y} \left( 1-\frac{1}{x+y} \right) =4\sqrt{2} \end{a...