User okie

20 votes

2 answers

18k views

Upper Triangular Block Matrix Determinant by induction

asked Mar 11, 2015 at 3:42

20 votes

1 answer

2k views

How to fill my mathematical gaps?

asked May 3, 2015 at 8:04

16 votes

2 answers

16k views

Show that the Cantor set is nowhere dense

asked Oct 7, 2015 at 1:24

13 votes

1 answer

6k views

Let $f$ be a bounded measurable function on $E$. Show that there are sequences of simple functions converging uniformly on $E$.

asked Oct 28, 2015 at 22:54

11 votes

2 answers

10k views

Prove every prime ideal of a ring is a radical ideal.

asked Nov 22, 2014 at 22:39

10 votes

3 answers

14k views

Proof the Legendre polynomial $P_n$ has $n$ distinct real zeros

asked Oct 15, 2013 at 13:53

9 votes

1 answer

2k views

If $n\mid m$ prove that the canonical surjection $\pi: \mathbb Z_m \rightarrow \mathbb Z_n$ is also surjective on units

asked Nov 27, 2014 at 23:14

7 votes

2 answers

7k views

$3 \times 3$ matrices are similar if and only if they have the same characteristic and minimal polynomial

asked Apr 10, 2015 at 21:05

6 votes

0 answers

190 views

calculation of the determinant of a block matrix little help

asked Mar 11, 2015 at 6:49

6 votes

1 answer

1k views

Let $f$ be integrable over $\mathbb{R}$. Show that the following four assertions are equivalent:

asked Dec 6, 2015 at 20:35

5 votes

0 answers

3k views

Are these functions of bounded variations?

asked Dec 8, 2015 at 7:51

5 votes

1 answer

2k views

Use the Cauchy-Schwarz inequality to prove $||x||_1 \leq \sqrt{n}||x||_2$

asked Sep 8, 2016 at 19:25

5 votes

1 answer

429 views

algebra with topology homework problem

asked Nov 27, 2014 at 4:10

4 votes

2 answers

5k views

Prove that if $B$ is the set of rationals in $[0,1]$ with a finite subcover, then: $1 \leq \sum_{k=1}^n m^*(I_k)$

asked Sep 15, 2015 at 20:27

4 votes

1 answer

3k views

Prove that $\sigma$-algebra of subsets of $\mathbb{R}$ of the form $(a,\infty)$ contains all the intervals.

asked Sep 23, 2015 at 4:24

4 votes

0 answers

3k views

Let $f$ be Lipschitz and $g$ be absolutely continuous. Show that the composition $f\circ g$ is absolutely continuous.

asked Dec 6, 2015 at 20:21

4 votes

0 answers

172 views

If for each $\alpha, \beta$, the map $\psi_{\beta} \circ F \circ \phi_{\alpha}^{-1}$ is smooth, then $F$ is smooth.

asked Jun 10, 2016 at 20:10

4 votes

1 answer

2k views

"There are exactly two values of $x$ for which $P(x)$ is true" formula using logical symbols

asked Aug 5, 2015 at 15:19

4 votes

1 answer

304 views

Evaluate $\pi$ using $\arctan(\frac{\sqrt{3}}{3})$

asked Jan 30, 2015 at 22:43

4 votes

2 answers

4k views

Prove the $n$th Fibonacci number is the integer closest to $\frac{1}{\sqrt{5}}\left( \frac{1 + \sqrt{5}}{2} \right)^n$

asked Oct 27, 2014 at 2:52

4 votes

1 answer

2k views

Let $W$ be a Wiener process. Which of the following define a Wiener process?

asked Dec 1, 2016 at 21:23

3 votes

2 answers

191 views

what I am doing wrong in this probability problem?

asked Sep 16, 2016 at 3:10

3 votes

2 answers

689 views

voter paradox. Show that $\min\{a,b,c\} \leq 2/3$.

asked Sep 19, 2016 at 13:55

3 votes

1 answer

478 views

Prove that $M/\mathrm{Tor}(M)$ is an R-module with zero torsion

asked Feb 7, 2015 at 2:54

3 votes

0 answers

396 views

Tensor algebra becomes an R-algebra. Theorem, Proof, Dummit and Foote

asked Apr 27, 2015 at 6:08

3 votes

1 answer

2k views

Let $F,G$ to be distribution. Is the product $FG$ also a distribution?

asked Sep 3, 2016 at 22:57

3 votes

0 answers

50 views

Show that the following inequalities are satisfied.

asked Sep 8, 2016 at 5:17

3 votes

0 answers

67 views

If $\{T_n\} \to T$ and $\{u_n\} \to u$, then $\{T_n(u_n)\} \to T(u)$.

asked Apr 29, 2016 at 20:30

3 votes

1 answer

288 views

prove that $m(\emptyset) = 0$ where $m$ is countably additive over disjoint collection of sets of $\mathscr{A}$

asked Sep 11, 2015 at 21:09

2 votes

1 answer

4k views

Translate of $F_{\sigma}$, $G_{\delta}$ and a set of measure $0$

asked Sep 23, 2015 at 18:33

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97 Questions

Upper Triangular Block Matrix Determinant by induction

How to fill my mathematical gaps?

Show that the Cantor set is nowhere dense

Let $f$ be a bounded measurable function on $E$. Show that there are sequences of simple functions converging uniformly on $E$.

Prove every prime ideal of a ring is a radical ideal.

Proof the Legendre polynomial $P_n$ has $n$ distinct real zeros

If $n\mid m$ prove that the canonical surjection $\pi: \mathbb Z_m \rightarrow \mathbb Z_n$ is also surjective on units

$3 \times 3$ matrices are similar if and only if they have the same characteristic and minimal polynomial

calculation of the determinant of a block matrix little help

Let $f$ be integrable over $\mathbb{R}$. Show that the following four assertions are equivalent:

Are these functions of bounded variations?

Use the Cauchy-Schwarz inequality to prove $||x||_1 \leq \sqrt{n}||x||_2$

algebra with topology homework problem

Prove that if $B$ is the set of rationals in $[0,1]$ with a finite subcover, then: $1 \leq \sum_{k=1}^n m^*(I_k)$

Prove that $\sigma$-algebra of subsets of $\mathbb{R}$ of the form $(a,\infty)$ contains all the intervals.

Let $f$ be Lipschitz and $g$ be absolutely continuous. Show that the composition $f\circ g$ is absolutely continuous.

If for each $\alpha, \beta$, the map $\psi_{\beta} \circ F \circ \phi_{\alpha}^{-1}$ is smooth, then $F$ is smooth.

"There are exactly two values of $x$ for which $P(x)$ is true" formula using logical symbols

Evaluate $\pi$ using $\arctan(\frac{\sqrt{3}}{3})$

Prove the $n$th Fibonacci number is the integer closest to $\frac{1}{\sqrt{5}}\left( \frac{1 + \sqrt{5}}{2} \right)^n$

Let $W$ be a Wiener process. Which of the following define a Wiener process?

what I am doing wrong in this probability problem?

voter paradox. Show that $\min\{a,b,c\} \leq 2/3$.

Prove that $M/\mathrm{Tor}(M)$ is an R-module with zero torsion

Tensor algebra becomes an R-algebra. Theorem, Proof, Dummit and Foote

Let $F,G$ to be distribution. Is the product $FG$ also a distribution?

Show that the following inequalities are satisfied.

If $\{T_n\} \to T$ and $\{u_n\} \to u$, then $\{T_n(u_n)\} \to T(u)$.

prove that $m(\emptyset) = 0$ where $m$ is countably additive over disjoint collection of sets of $\mathscr{A}$

Translate of $F_{\sigma}$, $G_{\delta}$ and a set of measure $0$