Spook
  • Member for 9 years, 10 months
  • Last seen more than 4 years ago
3 answers
27 votes
4k views
16 bookmarks
Existence of independent and identically distributed random variables.
3 answers
17 votes
7k views
10 bookmarks
If $A$ an integral domain contains a field $K$ and $A$ over $K$ is a finite-dimensional vector space, then $A$ is a field.
1 answers
15 votes
4k views
10 bookmarks
On every infinite-dimensional Banach space there exists a discontinuous linear functional.
3 answers
14 votes
414 views
3 bookmarks
For a graph $G$, why should one expect the ratio $\text{ex} (n;G)/ \binom n2$ to converge?
1 answers
12 votes
746 views
1 bookmarks
Factorize $(9+11\sqrt{-5})$ as a product of prime ideals in $\mathcal{O}_K$ where $K=\mathbb{Q}(\sqrt{-5})$
1 answers
10 votes
2k views
5 bookmarks
A Banach space is reflexive if a closed subspace and its quotient space are both reflexive
1 answers
10 votes
817 views
3 bookmarks
What is the probability that a random $n\times n$ bipartite graph has an isolated vertex?
2 answers
10 votes
2k views
5 bookmarks
Given a point $x$ and a closed subspace $Y$ of a normed space, must the distance from $x$ to $Y$ be achieved by some $y\in Y$?
1 answers
10 votes
820 views
Galois group of $X^5 - X^3 - 2X^2 - 2X - 1$ over $\mathbb{Q}$.
2 answers
10 votes
2k views
7 bookmarks
Borel $\sigma$ algebra on a topological subspace.
1 answers
9 votes
3k views
5 bookmarks
Find an integral basis of $\mathbb{Q}(\alpha)$ where $\alpha^3-\alpha-4=0$
1 answers
9 votes
8k views
5 bookmarks
What are the irreducible representations of the cyclic group $C_n$ over a real vector space $V$?
2 answers
9 votes
2k views
3 bookmarks
How to find all the ideals of a given norm?
3 answers
9 votes
619 views
4 bookmarks
Is there a pattern of the factorization of a polynomial modulo $p$ as $p$ varies
1 answers
8 votes
5k views
6 bookmarks
A finite field extension that is not simple
2 answers
8 votes
3k views
1 bookmarks
A holomorphic bijection from the open unit disc to the complex plane
3 answers
7 votes
2k views
2 bookmarks
The greatest common divisor of $a$ and $b$ is a linear combination of $a$ and $b$. In general, in what kind of ring does this hold?
1 answers
7 votes
1k views
4 bookmarks
Why is $PGL_2(5)\cong S_5$?
2 answers
7 votes
365 views
4 bookmarks
Let $p$ be an odd prime. $p$ and $(1-\zeta_p)^{p-1}$ are associates in $\mathbb{Z}[\zeta_p]$.
3 answers
7 votes
1k views
5 bookmarks
Does a red/blue coloring of the infinite subsets of $\mathbb{N}$ necessarily give an infinite monochromatic $M\subset \mathbb{N}$?
1 answers
6 votes
349 views
2 bookmarks
An infinite subset of the closed unit ball whose elements are more than distance 1 apart
0 answers
6 votes
1k views
3 bookmarks
What can be said about the number of connected components of $G(n,p)$ random graphs?
1 answers
6 votes
2k views
1 bookmarks
A Riemann integrable function $f$ on a bounded interval $[a, b]$ is measurable with respect to the Borel measure on $[a,b]$?
2 answers
6 votes
313 views
1 bookmarks
Evaluating $\int\frac{x^{1/2}}{1+x^2}\,dx.$
1 answers
5 votes
634 views
The matrix $J$(all of whose entries are 1) is a polynomial in the adjacency matrix $A$ of a graph $G$ ...
2 answers
5 votes
304 views
1 bookmarks
Show that the ideal of $k[X_1, X_2, X_3]$ generated by $X_1^3-X_3$ and $X_2^2-X_3$ is a prime ideal.
1 answers
5 votes
2k views
4 bookmarks
A stronger statement of Riesz's lemma
1 answers
4 votes
3k views
10 bookmarks
Ring of integers of a cubic number field
0 answers
4 votes
986 views
1 bookmarks
A domain on a sphere is simply connected if and only if its complement is connected
2 answers
4 votes
184 views
Soft question. Why do concrete problems motivate abstract theory?