Q&A for people studying math at any level and professionals in related fields

I would like to know how to solve the following problem: Find the range of values of the parameter $m$ for which the equation $2x^2 - mx + m = 0$ has no r...

Question: Let $f(x)=x^6-2x^3-8$ and $g(x)=x^2+2x+4$. Let $a_1$ through $a_6$ be its roots. Find the value of $\displaystyle \prod_{n=1}^{6} (g(a_n))$ My p...

Let $A$, $B$, and $C$ denote vertices of a triangle in the plane. Let $O$ be some point in the plane. Prove that $OM = \frac{1}{3}(OA+OB+OC)$, where $M$ d...

Recently, I encountered a problem about infinite series. So my question is how to know whether the infinite series $\sum _{n=2}^{\infty } \frac{1}{n \log ...

In my Introductory Econometrics class we discussed a concept of "plim" or "probability limit. I'm not sure what this means though and my professor do...

What is an example of a Serre fibration that is not a Hurewicz fibration?

Lee's book defines the unit radial vector field in normal coordinates as $$ \partial_r:= \frac{x^i}{r(x)} \partial_i$$ and $r(x):=\sqrt{\sum_i (x^i)^...

I have been working through "Set theory for working mathematician" and near the end of chapter about real numbers there is a small bit of topology. Namely...

The concept of determinant is quite unmotivational topic to introduce. Textbooks use such "strung out" introductions like axiomatic definition, Laplace ex...