Question

If $f$ be non-negative, bounded and Riemann Integrable on $[a, b]$, then $\sqrt{f}$ is R- integrable.

score 720 · Answer 1 · 2026-03-27 04:18:43

720

Views

If $f$ be non-negative, bounded and Riemann Integrable on $[a, b]$, then $\sqrt{f}$ is R- integrable.

Published on 27 Mar 2026 - 4:18

score 242 · Answer 2 · 2018-12-26 22:06:15

242

Views

Show that if $K \subseteq M \subseteq L$, then the normal closure $N'$ of $L:M$ is contained in the normal closure $N$ of $L:K$.

Published on 26 Dec 2018 - 22:06

score 609 · Answer 3 · 2026-03-27 00:05:13

609

Views

Sufficiency for proof that if $P \in \mathcal{L}(V)$, such that $P^2 = P$ then $V = \text{null}(P) \oplus \text{range}(P).$

Published on 27 Mar 2026 - 0:05

score 228 · Answer 4 · 2018-12-27 19:08:23

228

Views

Is there a simpler proof of this fact in analysis?

Published on 27 Dec 2018 - 19:08

score 526 · Answer 5 · 2018-12-30 10:06:43

526

Views

Determinant of $n\times n$ matrix - two diagonals and a corner

Published on 30 Dec 2018 - 10:06

score 62 · Answer 6 · 2018-12-30 15:30:34

62

Views

Interesting way of determining that every integer is divisible by a prime?

Published on 30 Dec 2018 - 15:30

score 350 · Answer 7 · 2018-12-30 20:19:16

350

Views

If $x^3 = y^2$, why is $y/x$ transcendental?

Published on 30 Dec 2018 - 20:19

score 457 · Answer 8 · 2018-12-31 18:54:59

457

Views

Prove: $\lim_{n\to\infty}{\sum_{m=0}^{n}{\sum_{k=0}^{n-m}{\frac{2^{n-m-k}}{n-m+1}\,\frac{{{2k}\choose{k}}{{2m}\choose{m}}}{{{2n}\choose{n}}}}}}=\pi$

Published on 31 Dec 2018 - 18:54

score 290 · Answer 9 · 2019-01-01 12:25:22

290

Views

Rectangles in a $n \times n$ grid and the sum of the first $n$ cubes: a geometric connection?

Published on 01 Jan 2019 - 12:25

score 2.1k · Answer 10 · 2019-01-01 17:30:05

2.1k

Views

Integral $\int_0^\infty \frac{\ln x}{(\pi^2+\ln^2 x)(1+x)^2} \frac{dx}{\sqrt x}$

Published on 01 Jan 2019 - 17:30

score 94 · Answer 11 · 2026-03-25 20:36:07

94

Views

Find a group $G$ with $a\in G$ such that $|a|=6$ but $C_G(a)\neq C_G(a^3)$.

Published on 25 Mar 2026 - 20:36

score 136 · Answer 12 · 2026-03-25 22:03:42

136

Views

Special cases of Szemeredi's Theorem?

Published on 25 Mar 2026 - 22:03

score 148 · Answer 13 · 2026-03-25 05:59:41

148

Views

On $\sup|\varphi^{-1}(n)|=+\infty$

Published on 25 Mar 2026 - 5:59

score 1.4k · Answer 14 · 2026-03-25 06:06:51

1.4k

Views

Can you make the triviality of $\langle a,b,c \mid aba^{-1} = b^2, bcb^{-1} = c^2, cac^{-1} = a^2 \rangle$ more trivial?

Published on 25 Mar 2026 - 6:06

score 229 · Answer 15 · 2026-03-25 06:13:10

229

Views

Cayley-Hamilton says that evaluating an endomorphism's characteristic polynomial over that endomorphism gives zero. Isn't this true by substitution?

Published on 25 Mar 2026 - 6:13

List Question

If $f$ be non-negative, bounded and Riemann Integrable on $[a, b]$, then $\sqrt{f}$ is R- integrable.

Show that if $K \subseteq M \subseteq L$, then the normal closure $N'$ of $L:M$ is contained in the normal closure $N$ of $L:K$.

Sufficiency for proof that if $P \in \mathcal{L}(V)$, such that $P^2 = P$ then $V = \text{null}(P) \oplus \text{range}(P).$

Is there a simpler proof of this fact in analysis?

Determinant of $n\times n$ matrix - two diagonals and a corner

Interesting way of determining that every integer is divisible by a prime?

If $x^3 = y^2$, why is $y/x$ transcendental?

Prove: $\lim_{n\to\infty}{\sum_{m=0}^{n}{\sum_{k=0}^{n-m}{\frac{2^{n-m-k}}{n-m+1}\,\frac{{{2k}\choose{k}}{{2m}\choose{m}}}{{{2n}\choose{n}}}}}}=\pi$

Rectangles in a $n \times n$ grid and the sum of the first $n$ cubes: a geometric connection?

Integral $\int_0^\infty \frac{\ln x}{(\pi^2+\ln^2 x)(1+x)^2} \frac{dx}{\sqrt x}$

Find a group $G$ with $a\in G$ such that $|a|=6$ but $C_G(a)\neq C_G(a^3)$.

Special cases of Szemeredi's Theorem?

On $\sup|\varphi^{-1}(n)|=+\infty$

Can you make the triviality of $\langle a,b,c \mid aba^{-1} = b^2, bcb^{-1} = c^2, cac^{-1} = a^2 \rangle$ more trivial?

Cayley-Hamilton says that evaluating an endomorphism's characteristic polynomial over that endomorphism gives zero. Isn't this true by substitution?

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