User Spook

36 votes

3 answers

6k views

Existence of independent and identically distributed random variables.

asked Nov 28, 2012 at 12:20

19 votes

1 answer

6k views

On every infinite-dimensional Banach space there exists a discontinuous linear functional.

asked Jan 27, 2013 at 14:02

17 votes

3 answers

9k views

If $A$ an integral domain contains a field $K$ and $A$ over $K$ is a finite-dimensional vector space, then $A$ is a field. [duplicate]

asked May 18, 2012 at 22:55

16 votes

2 answers

13k views

What are the irreducible representations of the cyclic group $C_n$ over a real vector space $V$?

asked Oct 23, 2012 at 13:25

14 votes

3 answers

621 views

For a graph $G$, why should one expect the ratio $\text{ex} (n;G)/ \binom n2$ to converge?

asked Dec 26, 2012 at 23:03

13 votes

2 answers

3k views

Borel $\sigma$ algebra on a topological subspace. [duplicate]

asked Oct 28, 2012 at 16:04

13 votes

2 answers

3k views

Given a point $x$ and a closed subspace $Y$ of a normed space, must the distance from $x$ to $Y$ be achieved by some $y\in Y$?

asked Feb 6, 2013 at 15:58

12 votes

1 answer

988 views

Factorize $(9+11\sqrt{-5})$ as a product of prime ideals in $\mathcal{O}_K$ where $K=\mathbb{Q}(\sqrt{-5})$

asked Mar 4, 2013 at 11:25

11 votes

1 answer

1k views

What is the probability that a random $n\times n$ bipartite graph has an isolated vertex?

asked Apr 22, 2013 at 23:27

11 votes

1 answer

7k views

A finite field extension that is not simple

asked Jan 12, 2013 at 23:44

11 votes

1 answer

3k views

A Banach space is reflexive if a closed subspace and its quotient space are both reflexive

asked Jan 16, 2014 at 20:36

10 votes

1 answer

937 views

Galois group of $X^5 - X^3 - 2X^2 - 2X - 1$ over $\mathbb{Q}$.

asked Apr 29, 2013 at 12:15

10 votes

3 answers

838 views

Is there a pattern of the factorization of a polynomial modulo $p$ as $p$ varies

asked Apr 29, 2013 at 21:50

10 votes

2 answers

3k views

How to find all the ideals of a given norm?

asked Mar 4, 2013 at 12:39

10 votes

1 answer

4k views

Find an integral basis of $\mathbb{Q}(\alpha)$ where $\alpha^3-\alpha-4=0$

asked Feb 7, 2013 at 21:09

9 votes

3 answers

2k views

Does a red/blue coloring of the infinite subsets of $\mathbb{N}$ necessarily give an infinite monochromatic $M\subset \mathbb{N}$?

asked Jan 20, 2013 at 16:37

8 votes

2 answers

4k views

A holomorphic bijection from the open unit disc to the complex plane

asked Feb 8, 2013 at 1:17

7 votes

1 answer

2k views

A stronger statement of Riesz's lemma

asked Feb 6, 2013 at 16:03

7 votes

3 answers

2k views

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?

asked Mar 30, 2013 at 13:14

7 votes

1 answer

2k views

Why is $PGL_2(5)\cong S_5$?

asked Apr 29, 2013 at 18:20

7 votes

2 answers

716 views

Let $p$ be an odd prime. $p$ and $(1-\zeta_p)^{p-1}$ are associates in $\mathbb{Z}[\zeta_p]$.

asked May 9, 2013 at 11:28

6 votes

0 answers

1k views

What can be said about the number of connected components of $G(n,p)$ random graphs?

asked Apr 12, 2013 at 1:00

6 votes

1 answer

483 views

An infinite subset of the closed unit ball whose elements are more than distance 1 apart

asked Feb 6, 2013 at 15:06

6 votes

1 answer

3k views

A Riemann integrable function $f$ on a bounded interval $[a, b]$ is measurable with respect to the Borel measure on $[a,b]$?

asked Oct 31, 2012 at 14:51

6 votes

2 answers

326 views

Evaluating $\int\frac{x^{1/2}}{1+x^2}\,dx.$

asked May 22, 2012 at 16:06

5 votes

1 answer

1k views

The matrix $J$(all of whose entries are 1) is a polynomial in the adjacency matrix $A$ of a graph $G$ ...

asked Nov 15, 2012 at 17:05

5 votes

3 answers

3k views

Convolution of an integrable function of compact support with a bump function.

asked Nov 23, 2012 at 15:52

5 votes

2 answers

379 views

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.

asked Feb 18, 2013 at 21:57

5 votes

0 answers

1k views

A domain on a sphere is simply connected if and only if its complement is connected

asked Jan 17, 2014 at 0:58

4 votes

2 answers

208 views

Soft question. Why do concrete problems motivate abstract theory?

asked Nov 29, 2013 at 22:42

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88 Questions

Existence of independent and identically distributed random variables.

On every infinite-dimensional Banach space there exists a discontinuous linear functional.

If $A$ an integral domain contains a field $K$ and $A$ over $K$ is a finite-dimensional vector space, then $A$ is a field. [duplicate]

What are the irreducible representations of the cyclic group $C_n$ over a real vector space $V$?

For a graph $G$, why should one expect the ratio $\text{ex} (n;G)/ \binom n2$ to converge?

Borel $\sigma$ algebra on a topological subspace. [duplicate]

Given a point $x$ and a closed subspace $Y$ of a normed space, must the distance from $x$ to $Y$ be achieved by some $y\in Y$?

Factorize $(9+11\sqrt{-5})$ as a product of prime ideals in $\mathcal{O}_K$ where $K=\mathbb{Q}(\sqrt{-5})$

What is the probability that a random $n\times n$ bipartite graph has an isolated vertex?

A finite field extension that is not simple

A Banach space is reflexive if a closed subspace and its quotient space are both reflexive

Galois group of $X^5 - X^3 - 2X^2 - 2X - 1$ over $\mathbb{Q}$.

Is there a pattern of the factorization of a polynomial modulo $p$ as $p$ varies

How to find all the ideals of a given norm?

Find an integral basis of $\mathbb{Q}(\alpha)$ where $\alpha^3-\alpha-4=0$

Does a red/blue coloring of the infinite subsets of $\mathbb{N}$ necessarily give an infinite monochromatic $M\subset \mathbb{N}$?

A holomorphic bijection from the open unit disc to the complex plane

A stronger statement of Riesz's lemma

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?

Why is $PGL_2(5)\cong S_5$?

Let $p$ be an odd prime. $p$ and $(1-\zeta_p)^{p-1}$ are associates in $\mathbb{Z}[\zeta_p]$.

What can be said about the number of connected components of $G(n,p)$ random graphs?

An infinite subset of the closed unit ball whose elements are more than distance 1 apart

A Riemann integrable function $f$ on a bounded interval $[a, b]$ is measurable with respect to the Borel measure on $[a,b]$?

Evaluating $\int\frac{x^{1/2}}{1+x^2}\,dx.$

The matrix $J$(all of whose entries are 1) is a polynomial in the adjacency matrix $A$ of a graph $G$ ...

Convolution of an integrable function of compact support with a bump function.

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.

A domain on a sphere is simply connected if and only if its complement is connected

Soft question. Why do concrete problems motivate abstract theory?