# All Questions

75 views

### Understanding torsion from a presentation

Let $F_2 = \langle a,b \rangle$ be the free group on two generators, and for each word $w \in F_2$, let $G(w) = \langle a, b \ | \ w \rangle$. Is the following statement true? $G(w)$ is torsion free ...
39 views

### Which matrix operation should I use.

The title is quite vague, but I don't see how to phrase it. I'm new to MatLab and have very little experience with matrix calculation. Suppose a matrix "a" : ...
108 views

### Plotting a complex argument arc

I am having trouble sketching a complex argument arc $$\text{Sketch the following on an arcand diagram:}\\ \arg\left(\frac{w+1}{w}\right)=\frac{\pi}{6}$$ I've tried to devise a method on my own ...
89 views

### limit of derivatives of a function

I wanna show that for $f:(0,\infty)\rightarrow\mathbb R, x\mapsto\exp(-\frac1{x^2})$ the sum of the derivates of $f$, so $\sum\limits_{n=0}^\infty f^{(n)}(x)$, converges to $0$, so ...
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### Euclidean Geometry in Classical Thought - Used for Realization or Representation?

I posted this in the Physics.SE Forum but I figured I'd ask this here as well since it's relevant to the forum subject :] Taken from John J. Roche's "The Mathematics of Measurement: A Critical ...
3k views

### Probability a coin comes up heads more often than tails

I am told that a fair coin is flipped $2n$ times and I have to find the probability that it comes up heads more often that it comes up tails. Please, how do I find the required probability?
213 views

### Proof of smoothness of solution to a parabolic non-linear PDE (edited with images)

Edit: the images are from the paper by Sigurd Angenent called Parabolic Equations for Curves on Surfaces. You shouldn't need any more information to answer the question (I think..) They define the ...
358 views

### Primitive element of $\mathbb{Q}(\sqrt{2}+i,\sqrt{3}-i)/\mathbb{Q}$

Is there a clever way to determine a primitive element of the finite extension $$F=\mathbb{Q}(\sqrt{2}+i,\sqrt{3}-i)/\mathbb{Q} \text{ ?}$$ On simpler examples, I've been able to find one by ...
307 views

### Prove that a conic section is symmetrical with respect to its principal axis.

A Calculus book that I'm self-studying is asking me to prove the following theorem about conic sections: A conic section is symmetrical with respect to its principal axis. Here is my attempt at ...
414 views

### Why is the matrix representing a non-degenerate sesquilinear form invertible?

Let's consider a finite-dimensional vector space $E$ on the field $\mathbb{K}$ (where $\mathbb{K}=\mathbb{C} \ \text{or}\ \mathbb{R}$) and a sesquilinear (or bilinear if $\mathbb{K}=\mathbb{R}$) form ...
292 views

### Tensor product of sets

The cartesian product of two sets $A$ and $B$ can be seen as a tensor product. Are there examples for the tensor product of two sets $A$ and $B$ other than the usual cartesian product ? The context ...
922 views

### Countably Compact vs Compact vs Finite Intersection Property

There is this exercise: Show that countable compactness is equivalent to the following condition. If ${C_n}$ is a countable collection of closed sets in S satisfying the finite intersection ...
458 views

### How to find extrema on a triangle

Let $T\subset\mathbb{R}^2$ be the (closed) triangle bounded by the lines $x+y=4$, $x\ge-1$ and $y\ge-1$. I want to find and classify all the extrema of the function $f(x,y)=-x^2y(x+y-2)$ on the ...
40 views

### Is there any way to check if one graph is the result of identification and/or splitting on another graph?

Does some algorithm exist that can be used to check if graph $A$ and graph $B$ are related only by combining or separating vertices? Also, would this be possible if vertices had values (a vertex's ...