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I am struggling to understand the concept of rational maps. In Hartshorne, the definition of rational maps is as follows Let $X$ and $Y$ be varieties. A r...
I'm working with the following two concepts: Lipschitz Smoothness - a function $f$ is Lipschitz smooth with constant $L$ if its derivatives are Lipsc...
A sample of size $n = 22$ is drawn from a normal population. Find the critical value $t_{\alpha/2}$ needed to construct a $98\%$ confidence interval. I ha...
I've been learning conditional probability and encountered the problem statement given in the title. We roll the die only a single time: My method of...
Suppose $F$ is a field, a collection of subsets of a set $\Omega$. Define $\sigma(F)$ as the smallest $\sigma$-field containing the sets of $F$. My Questi...
Show $\operatorname{Aut}(C_2 \times C_2)$ is isomorphic to $D_6$ (the group with $x^3=1$, $y^2=1$ and $xy=yx^2$). I'm not really sure how to express ...
![Why sqrt(4) isn't equall to-2? [duplicate]](https://edu.smbbmcl.edu.pk/uploads/why-sqrt-4-isn-039-t-equall-to-2-duplicate_720.jpg)
Possible Duplicate: Square roots — positive and negative $\sqrt{4} = -2$. WolframAlpha says "false"! Now lets take a deeper look to my idea. Well...we kno...
This is quite simple. I know. I am having a problem when comparing my answer to online calculators like Symbolab and such. $$\begin{array}{rll} y &= *...
Most of the time I see matrix multiplication presented and defined, as a seemingly arbitrary sequence of operations. For example, the textbook I'm cu...
Show that the determinant of a matrix $A$ is equal to the product of its eigenvalues $\lambda_i$. So I'm having a tough time figuring this one out. I...
