Intereting Posts

How do I calculate the probability distribution of the percentage of a binary random variable?
Definite integral of arcsine over square-root of quadratic
Compute an integral containing a product of powers of logarithms.
Any periodic abelian group is the direct sum of its maximal p-subgroups
Surreal numbers without the axiom of infinity
What is $2^{7!}\bmod{2987}$
The conjecture that no triangle has rational sides, medians and altitudes
Why is the decimal representation of $\frac17$ “cyclical”?
Degree of splitting field less than n!
What are the main changes between ISO 31-11 and ISO 80000-2? (math notation standards)
Is the Collatz conjecture in $\Sigma_1 / \Pi_1$?
How to proof the following function is always constant which satisfies $f\left( x \right) + a\int_{x – 1}^x {f\left( t \right)\,dt} $?
Proving that product of two Cauchy sequences is Cauchy
Compute $e^{e^z}$, where z is a complex number
$f$ differentiable, $f(x)$ rational if $x$ rational; $f(x)$ irrational if $x$ irrational. Is $f$ a linear function?

For $a=\cos(2\pi/n)$, show that $[\mathbb{Q}(a):\mathbb{Q}] = \{1 \text{ for } n=1,2; (1/2)\phi(n) \text{ for } n>2\}$.

$\phi$ is the Euler totient function which gives the number of coprime elements.

We are new to abstract algebra. This is a question on a difficult project involving cyclotomic polynomials and their irreducibility.

- $F:G\to B$ is an isomorphism between groups implies $F^{-1}$ is an isomorphism
- If G is not commutative, then is there always a subgroup that is not a normal subgroup?
- Multiplication in Permutation Groups Written in Cyclic Notation
- Solve $f^n(x)=4^nx+\frac{4^n-1}{3}$ for $n$.
- Is there a purely algebraic proof of the Fundamental Theorem of Algebra?
- Does there exist a unital ring whose underlying abelian group is $\mathbb{Q}^*$?

We know that the degree of the cyclotomic extension is just $\phi(n)$, but obviously $a$ is just one piece of the roots of unity.

- Homomorphism from $\mathbb{Q}/ \mathbb{Z}\rightarrow \mathbb{Z}/n\mathbb{Z}$
- Logic for decomposing permutation into transpositions
- The product of all the elements of a finite abelian group
- Center of Heisenberg group- Dummit and Foote, pg 54, 2.2
- Finitely generated ideal in Boolean ring; how do we motivate the generator?
- Show that $\mathbb{Z}_{2} \times \mathbb{Z}_{4}$ is not a cyclic group
- Stuff which squares to $-1$ in the quaternions, thinking geometrically.
- $\mathbb S_n$ as semidirect product
- Multiplicative group of integers modulo n definition issues
- Finitely many prime ideals $\Rightarrow$ cartesian product of local rings

- Question on compactification
- Solution to least squares problem using Singular Value decomposition
- How does one prove that $(2\uparrow\uparrow16)+1$ is composite?
- Do there exist two primes $p<q$ such that $p^n-1\mid q^n-1$ for infinitely many $n$?
- What's the most efficient way to mow a lawn?
- Variance of the random sum of a Poisson?
- Identities for other coefficients of the characteristic polynomial
- Base and subbase of a topology
- Recast the scalar SPDE $du_t(Φ_t(x))=f_t(Φ_t(x))dt+∇ u_t(Φ_t(x))⋅ξ_t(Φ_t(x))dW_t$ into a SDE in an infinite dimensional function space.
- Special arrows for notation of morphisms
- Proving that isomorphic ideals are in the same ideal class
- Moebius band not homeomorphic to Cylinder.
- Regulators and uniqueness
- Bessel type function?
- What is (fundamentally) a coordinate system ?