$(X_n), n \in \mathbb{N}$ is a stochastic process. I saw in one definition of Martingale that $$E [X_{n+1} |X_0 , X_1 , . . . , X_n ] = X_n \quad a.s., \f...

I want to take the inverse of a dot product, where both vectors have complex components. In other words, if $\textbf{A} \cdot \textbf{B} = d$, and I know ...

The following problem is from the 7th edition of the book "Calculus and Analytic Geometry Part II". It can be found in section 13.7. It is problem number ...

Below is the problem that I wanted to solve When there are $m$ balls and $n$ bins, balls are thrown into bins where each ball is thrown into a bin uniform...

I want to approximate the zeros of the following system of polynomial equations using the Newton-Raphson method: \begin{align} f(x,y) &= x + \frac13 y...

How would I solve this complex number equation? $$z^2=\bar z$$ basically I already solved it and got: $$z=-\frac{1}{2}\pm \sqrt {\frac {3}{4}}$$ BUT, they...

I have just started working through Pete Clark's elliptic curve notes, which are available here: http://math.uga.edu/~pete/EllipticCurves.pdf Early o...

Proposition: If the constant term is $1$ or $-1$, then we can't use the Eisenstein criterion to determine whether the polynomial is irreducible over ...

I am reading about right-inverse and left-inverse matrices. According to theory if a matrix $A_{m\times n}(\mathbb{R})$ is full row rank, then it has a ri...

How to represent 0 as rational number? $0/0$ is not legitimate, $0/\text{const}$ should be good enough, but what is the right value of const? $0/1$ works ...