All Questions

3 views

recursive automata, or recursion mod 2.

Consider the list of length $m$ $(1,0,\dots 0)$ we call this list $l_1$, we now define a sequence of lists recursively, where $l_1$ is the previous list, and if $l_n$ is the list $(a_1,a_2\dots a_n)$ ...
12 views

What algebra book to read after Artin's Algebra?

Could I directly go to Lang's Algebra? Or should I supplement some gaps by Dummit and Foote?
8 views

If $p(z)$ is an injective polynomial $\Longrightarrow$ $p(z)=az+b$

If $p(z)$ is an injective polynomial, how to prove that $p(z)=az+b$ with $a\neq 0$. $p(z)\in\mathbb{C}[z]$. Any hint would be appreciated.
4 views

A problem about martingale with filtration.

Is there something wrong with this statement? Why $\sigma(M_n)$ is a filtration instead of $\{\sigma(M_1,\cdots ,M_n)\}$?
2 views

22 views

Integrals of integer powers of dilogarithm function

I'm interested in evaluating integrals of positive integer powers of the dilogarithm function. I'd like to see the general case tackled if possible, or barring that then as many particular cases as ...
14 views

Alternative way of proving the subgroup of rotations is normal in $\mathbb D_4$

I've just solved a basic group theory exercise which is: decide if $\{1,r,r^2,r^3\}$ is a normal subgroup of $\mathbb D_4$ (I mean the dihedral group of $8$ elements, not the one of $4$). I've used ...
16 views

Proving that an equilateral triangle in the plane cannot have vertices on integer lattice points

I am hoping a few of you mathematicians more experienced with writing proofs might give me some guidance here and possibly give me some ideas about how to restructure the following into a more ...
17 views

26 views

Showing that a Unit Speed Curve is a Circle.

In my recent differential geometry tutorial, we were given the question: Given the unit speed curve, $$\boldsymbol{r}(s)=\left(\frac{4}{5}\cos(s),1-\sin(s),-\frac{3}{5}\cos(s)\right)$$ show that ...
74 views

Proof that odd + odd = even

In math class today we started talking about proofs that odd + odd is even. We went over the basic proof (using 2k+1 and equations etc) and I realized that the only reason that this property exists is ...
16 views

Upper bound on the covariance of two gamma processes?

Given two binary gamma processes, $X = \Gamma(t; \gamma_1, \lambda_1)$ and $Y = \Gamma(t; \gamma_2, \lambda_2)$, what is their maximum covariance? Applying this answer, it would seem that it is the ...