What do we mean by a matrix is positive or negative definite? Does it have any analogy with a positive real number?

Original question: Is there any way to write $x!$ as a Pi notation? $$x!=\prod\text{?}$$ The answer should have been obvious $$x!=\prod_{r=1}^xr$$ Now I h...

Why is "material implication" called "material"? What does the word "material" imply or underline? It seems that the term "material condition" even prefer...

I was asked to show that the expression is constant in a circle : $\dfrac{\left[1+\left(\dfrac{\operatorname d \!y}{\operatorname d \!x}\right)^2\right]^{...

Here is a definition I have for an algebra: A family $f$ of subsets of the set $\Omega$ is called an algebra if it satisfies: $\emptyset, \Omega \in f$ If...

Possible Duplicate: Proof of a formula involving Euler's totient function. For positive integers $m$ and $n$ where $d=gcd(m,n)$, show that $$\phi(mn) ...

To become a better computer programmer I would like to take the time to learn discrete mathematics, but I am positive that I do not have the required exis...

I'm working on my Master's, in the field of computational fluid dynamics, where we have to solve the system $Ax = b$ a lot. As far as I can figu...

I am reading a textbook on complex manifolds and come across the Albanese map. For a compact Kähler manifold $X$, $$ T=H^0(X,\Omega_{X}^1)^*/H_1(M,\mathbb...

I have the following graph for a logarithmic function $f$: I don't know any thing about writing an equation for a logarithmic function by knowing it&...