# All Questions

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### Rings and fields: any applications to science and technology?

While there are applications of Group Theory in Particle Physics and Cryptography in security systems, what about another very important part of Abstract Algebra: Rings and Fields? Are there any ...
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### Solving linear equations graphically

I have a pair of linear equations.i need to find two points from each of the equation.i have found points which are difficult to plot in the graph.help me to find two points from each of the equation ...
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### How many methods are available for finding this volume?

I wonder how many methods are available for finding the volume required by the question. Two spheres (of radii $r$ and $a$, with $r \lt 2a$) meet in such a way that the centre of the one of radius ...
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### A question regarding Grothendiek , topos and (adelic??) points

I am having a look at this conference: https://www.youtube.com/watch?v=yNgvvNx_P9w I am particularly interested in getting your feedback on 1:14:30 and the seconds thereafter. Could anyone expain me ...
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### First 10 digits after decimal point in the number $(1+\sqrt{3})^{2015}$

The question is how to find first 10 digits after decimal point in the number $(1+\sqrt{3})^{2015}$. I keep running into this kind of problems in a context of symmetric polynomials.
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### Proof structure validity: assume (a), (b), show (c). Then Permute.

I am given a collection of sets $\mathcal{E}$ and am trying to prove it is an elementary family. To show $\mathcal{E}$ is an elementary family I must show that it satisfies the following properties: ...
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### Real analysis using some key constraints

Let $\alpha>1$ and $M \geq 0$. Suppose $f:\mathbb{R}→\mathbb{R}$ satisfies $|f(x)-f(y)| \leq M|x-y|^\alpha$. Prove that $f$ is a constant function. I tried taking different values of $M$ and ...
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### 10th derivarive of a function

I want to find $f^{(10)}(0)$ where $f(x)=ln(2+x^2)$. I know that it can be done "by hand", but I believe there is a smarter way. I think I should use Taylor series and the fact that ...
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### Stable Marriage algorithms other than Gale-Shapely?

I've looked around lot and I haven't been able to find any algorithms for to the traditional stable marriage problem (I'm not talking about any of its variants like the roommate problem) besides the ...
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### Why do we need a Borel function in order to use this lemma?

Im trying to understand a proof for differentiably a.e for functions $F$ given by $$F(x)= \int_{-\infty}^{x}f\ \mathsf dt$$ for $f$ Lebesgue measurable and $L^{1}$. He defines a finite Borel measure ...
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### Two dimensional Lie Algebra - what do we know without knowing the Bracket?

I am having trouble understanding how Lie algebras act. I.e. if I am trying to work with a two dimensional Lie algebra, there isn't much I can do without knowing the Lie Bracket that is defined on the ...
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### Column Space/Row Space

I just have a small question. I was wondering if someone could explain to me the difference between "column space" and "basis for column space" as well as "row space" and "basis for row space". I've ...
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### Conditions for the existence of moments of the supremum of a random variable

let $\{x_i\}_{i=1}^\infty$ be a random variable with finite first $n$ moments. Under what conditions (if at all) do the first $n$ moments of the random variable $\sup_i x_i$ (i.e., the supremum of ...
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### When $\overline{(a,b)}$ does not equal $[a,b]$

Lee topological manifolds 2.13 c) says For any pair of points a,b in X show that $\overline{(a,b)}\subset[a,b]$. I have done that, but next: Give an example to show that equality need not ...
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### What is a good way to Google and obtain Math resources?

I'm having a great deal of difficulty finding math resources on Google and stackoverflow. Is there a scheme to search for MathJax equations? Any good ways to search the web via Wolfram Alpha?
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### SVD for square matrix

I already know the concept of SVD applyed on an mxn matrix. Eigen vectors can't exist for a non-square matrix, but singular-vectors can. My question is: does SVD on a square matrix relate to ...
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### a problem in gauss lemma

I was reading the Gauss Lemma from the do carmos Rienmannian geometry book which says that Let $p \in M$ and let $v \in T_pM$ such that $\exp _p v$ is defined Let $w\in T_pM$ is identified with ...
I came across this gem while discussing with my friends, If $X$ and $Y$ are two real valued random variables (not necessarily independent) that satisfy $$X =^d X+Y$$ (where $=^d$ means equal in ...