# All Questions

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### Solving Integral that includes radical expression

I need to solve this integral analytically. I used many methods but I can’t solve it. Please help me. Thank you $$\int\sqrt{x^4-c}\ dx$$ http://i62.tinypic.com/15heux1.png
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### Path-components of the general linear group using only elementary algebra

Let $E(c)$ be an elementary matrix of the type to add $c$ times a row to another row when applied to another matrix on the left (with $c$ in some off-diagonal position $(i, j)$), and, with the usual ...
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### Span the space of all polynomials of highest order?

I have 2 question in my homework I am not sure my answer. Can someone help me to solve it? Let $v_1 = t^2 + 2t + 1$ and $v_2 = t^2 + 2$ , where $t$ is a real number. Determine whether $v_1 , v_2$ ...
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### Mentioning Professors in math PhD applications

When applying to grad school, is it a good idea to mention professors you want to work with? For example, "I am applying to this program because University X has leading experts in the field Y, such ...
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### Greatest area using a string with the length of $l$

Suppose we have a string with length of $l$ what is the shape that has highest area? In other words,with a constant perimeter of $l$ what is the shape with the highest area? P.S:My own speculation ...
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### Chain rule version for partiel derivative?

Non-math student here so go easy on me. How do we calculate a partial derivative in terms of $x$ when dealing with a multivariable composite function, and what 'chain rule version', if any, could one ...
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### Finding elements in a set

Definitions You have a set $S$ with $n$ elements. Within these $n$ elements, we denote $2$ as "special numbers". Given a subset $T\subset S_n$ we say that the subset $T$ is "up" if it contains both ...
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### Galois group of the field of all constructible complex numbers

I am trying to understand infinite galois theory by self-made examples. First example I am struggling with is the field of all constructible (by compass and straightedge) complex numbers - let's call ...
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### $\Bbb R^n \times (0,\infty)$ what does this mean?

Just began to read about PDEs. There are a whole list of notations which I don't understand and the book isn't expecting a reader who is as inexperienced as me. Also don't understand what this ...
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### What is an example of a homomorphism of rings that doesn't preserve gcd's?

Given a commutative ring $R$, we say that $x$ is a gcd of $(y,z)$ iff the following conditions hold: $x \mid y,z$ For all $x' \in R$, if $x' \mid y,z$, then $x' \mid x$. This gives a ternary ...
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### T invariant subspace complement

Let $T$ be a linear operator on a linear space $V$ of finite dimension. How to prove that $\operatorname{ran} T$ has a complement T-invariant (i.e. a T-invariant subspace $W$ of $V$ such that ...
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### Examples of Non-Markov process with continuous time and finite set of states.

What is the best real world examples of non-Markov process with continuous time, but with finite set of states?
Let $A$ be a $n \times n$ real matrix whose entries $a_{i,j}(x)$ are continuous functions from $\mathbb{R^n} \to \mathbb{R}^n$. Suppose that $A$ is positive definite at $x = x^\star$. Then, is it ...