I have the information that: $$ x^3 − x^2 −1 =0 $$ Has a "positive real root" of: $x \approx 1.4655\ldots$ My questions are, please: 1) What is a "positiv...

I want to know the real meaning of nth root of unity. I have searched various books , websites and videos but couldn't find a satisfying answer. Ever...

While reviewing improper integrals, a thought of the definition of logarithmic function came to me. $\ln(x) =\int_{1}^{x}\frac{1}{t}dt$ Looking at the def...

On the wikipedia site for the Kantorovich inequality, it is claimed ... the Kantorovich inequality is a particular case of the Cauchy–Schwarz inequality.....

Let $f(x) = \sum_{n=-\infty}^{\infty} \delta(x - n)$, where $\delta$ is the Dirac delta function. This function $f$ (a "comb function") is important in si...

We say that a graph $G=(V,E)$ has a $k$-coloring if each vertex can be assigned a color in $\{1,...,k\}$ so that no edge has two vertices of the same colo...

I'm trying my hand on these types of expressions. How to solve $x$ in $(x+1)^4+(x-1)^4=16$? Please write any idea you have, and try to keep it simple...

This is a GRE prep question: What's the derivative of $f(x)=\int_x^0 \frac{\cos xt}{t}\mathrm{d}t$? The answer is $\frac{1}{x}[1-2\cos x^2]$. I guess...

The Hilbert curve has always bugged me because it had no closed equation or function that I could find. What is its equation or function? For example, if ...

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...