Intereting Posts

Why $\bigwedge^{d-1}A=\bigwedge^{d-1}B \Rightarrow A= \pm B$
Prove that every positive integer $n$ is a unique product of a square and a squarefree number
Linear algebra to find EV of sort algorithm
the exact value of $\displaystyle\sum_{n=2}^\infty\arcsin{\left(\dfrac{\sqrt{n}-\sqrt{n-1}}{\sqrt{n^2-1}}\right)}$
How to prove this limit composition theorem?
Help with logarithmic definite integral: $\int_0^1\frac{1}{x}\ln{(x)}\ln^3{(1-x)}$
Evaluating $\int_0^\infty \frac{\log (1+x)}{1+x^2}dx$
which of the following is NOT a possible value of $(e^{f})''(0)$??
dA in polar coordinates?
Find an orthonormal basis for the subspace of $\mathbb R^4$
What are the technical reasons that we must define vectors as “arrows” and carefully distinguish them from a point?
taylor series of ln(1+x)?
Is there a reason why the number of non-isomorphic graphs with $v=4$ is odd?
New size of a rotated-then-cropped rectangle
Using the rules that prove the sum of all natural numbers is $-\frac{1}{12}$, how can you prove that the harmonic series diverges?

The problem: let $(x_1, x_2, …, x_r)$ be an r-cycle in $S_n$. Show that for every $h \in S_n$, $h \circ (x_1, x_2, \ldots, x_r) \circ h^{-1} = (h(x_1), h(x_2), \ldots, h(x_r))$

- Localisation isomorphic to a quotient of polynomial ring
- $R$ integral domain : $u\in R^*, a \text{ is prime} \iff au \text{ is prime}$
- Intermediate fields of cyclotomic splitting fields and the polynomials they split
- Localization of ideals at all primes
- ACC on principal ideals implies factorization into irreducibles. Does $R$ have to be a domain?
- If $x^3 =x$ then $6x=0$ in a ring
- Structure of $\mathbb{Z}]/(x-n)$
- Free groups and relations. Showing that $G\simeq FG^{(3)}/N$ for $N$ the normal subgroup generated by a set of relations.
- If $x^m=e$ has at most $m$ solutions for any $m\in \mathbb{N}$, then $G$ is cyclic
- There exists only two groups of order $p^2$ up to isomorphism.

For $i \notin \{h(x_1), \dots, h(x_r)\}$ you have

$$h \circ (x_1 \ \dots \ x_r) \circ h^{-1}(i)= h \circ h^{-1}(i)=i$$

And for $i =h(x_j) \in \{h(x_1), \dots, h(x_r)\}$ you have

$$h \circ (x_1 \ \dots \ x_r) \circ h^{-1}(i)= h \circ (x_1 \ \dots \ x_r)(x_j)=h (x_{j+1})$$

- Prove $( \lnot C \implies \lnot B) \implies (B \implies C)$ without the Deduction Theorem
- Neither provable nor disprovable theorem
- Supremum and union
- (Ito lemma proof): convergence of $\sum_{i=0}^{n-1}f(W(t_{i}))(W(t_{i+1})-W(t_{i}))^{2}.$
- Prove that $f(x) = x^3 -x $ is NOT Injective
- Norm-Euclidean rings?
- Let $G$ be a Lie group. Show that there is a diffeomorphism $TG \cong G \times T_e G$.
- How many subgroups does $\mathbb{Z}_6 \times\mathbb{Z}_6 \times\mathbb{Z}_6 \times\mathbb{Z}_6 $ have?
- Can a function that has uncountable many points of discontinuity be integrable?
- Correlation in Bernoulli trial
- mathematical maturity
- Showing that a level set is not a submanifold
- f is monotone and the integral is bounded. Prove that $\lim_{x→∞}xf(x)=0$
- Heisenberg uncertainty principle in $d$ dimensions.
- Is infinity an odd or even number?