User Galois - Mathematics Stack Exchange

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2

10

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217

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$\sum a_n$ converges absolutely, does $\sum (a_n + \cdots + a_n^n)$ converge

sequences-and-series analysis

jul 26 at 6:59 Giuseppe 2,664

8

votes

3

answers

276

views

Showing a homomorphism of a field algebraic over $\mathbb{Q}$ to itself is an isomorphism.

abstract-algebra field-theory

jun 1 '12 at 15:47 rschwieb 20.7k

2

8

votes

2

answers

278

views

Showing a UFD which is not a PID must have a nonprincipal maximal ideal.

commutative-algebra ring-theory

may 7 '12 at 23:14 Community♦ 1

3

6

votes

1

answer

380

views

Showing a subset of $C([0,1])$ is compact.

real-analysis functional-analysis

jun 7 '12 at 19:05 checkmath 1,759

1

6

votes

2

answers

229

views

Can $ABA-BAB=I$?

linear-algebra

may 21 '12 at 22:42 Henry T. Horton 7,429

6

votes

1

answer

105

views

Showing $f\left(A\right)=e^{A^{2}}$ is differentiable.

real-analysis analysis

may 13 '12 at 21:50 Did 102k

6

votes

1

answer

126

views

Automorphism of $\mathbb{Q}^*$

abstract-algebra

feb 6 '12 at 6:52 Bruno 6,971

5

votes

4

answers

463

views

For $f$ Riemann integrable prove $\lim_{n\to\infty} \int_0^1x^nf(x)dx=0.$

real-analysis

oct 8 at 6:54 Peter Tamaroff 25.4k

2

5

votes

1

answer

96

views

Proving $\int_{1}^{\infty}\frac{\sin x}{\left(\log x\right)^{\frac{1}{2}}}dx$ converges

real-analysis analysis

jul 23 at 0:26 alex.jordan 8,739

5

votes

3

answers

199

views

Show $\int_0^\infty x^{-\alpha}\sin x dx$ exists for $\alpha \in (0,2)$.

real-analysis

mar 30 '12 at 20:32 Salech Alhasov 1,962

1

4

votes

2

answers

93

views

Finding $f\in L^{p}\left(\mathbb{R}\right)\setminus L^{q}\left(\mathbb{R}\right)$

real-analysis measure-theory lp-spaces

jan 12 at 16:18 Davide Giraudo 56k

4

votes

4

answers

237

views

Convergence of the sequence $f_{1}\left(x\right)=\sqrt{x} $ and $f_{n+1}\left(x\right)=\sqrt{x+f_{n}\left(x\right)} $

real-analysis sequences-and-series

nov 28 at 6:39 Did 102k

4

votes

1

answer

104

views

Elements of $\mathbb{F}_p$ having cube roots in $\mathbb{F}_p$

finite-fields

jul 22 at 0:04 DonAntonio 46.3k

4

votes

1

answer

150

views

Finding quadratic extensions in $\mathbb{Q}\left(\sqrt{i+2}\right)$

abstract-algebra field-theory

jul 19 at 18:38 Lubin 5,796

1

4

votes

1

answer

122

views

Showing $V_a^b\alpha = \sup \left\{\int_a^bfd\alpha:\|f\|_\infty\leq 1\right\}$

analysis

mar 6 '12 at 15:48 Byron Schmuland 15.4k

3

votes

2

answers

165

views

Counterexample to Fubini?

real-analysis analysis

dec 9 at 9:59 Christian Blatter 32.3k

1

3

votes

2

answers

76

views

Find all monic polynomials $f\left(x\right)\in F\left[x\right]$ with distinct roots closed under multiplication.

abstract-algebra field-theory

jun 4 '12 at 2:14 Patrick Da Silva 13.3k

3

votes

3

answers

185

views

Finding points of continuity

real-analysis

feb 20 '12 at 2:11 JavaMan 8,270

1

2

votes

3

answers

159

views

Where is $f(z)=\Re (z)$ differentiable?

complex-analysis

feb 6 at 22:48 Community♦ 1

1

2

votes

2

answers

56

views

How to compute $\int_{\partial D\left(0,1\right)}\frac{\overline{z}}{z-w}dz$.

complex-analysis

oct 27 at 18:07 Valentin 2,812

2

votes

1

answer

290

views

Proving $\sup\left\{ r\in\mathbb{Q}:r^{2}<3\right\}=\sqrt{3}$

analysis

jun 28 at 14:38 Peter Tamaroff 25.4k

2

votes

1

answer

317

views

Prove $\sum a_n^2$ converges.

real-analysis sequences-and-series

may 27 '12 at 16:03 Joel Cohen 3,669

2

votes

2

answers

142

views

Want f differentiable at the origin but discontinuous everywhere else!

analysis

may 6 '12 at 22:11 draks ... 6,323

1

2

votes

3

answers

149

views

Showing the intersection of maximal ideals is not prime.

ring-theory

apr 30 '12 at 15:52 Community♦ 1

2

votes

2

answers

198

views

$f_1,f_2,\ldots$ continuous on $[0,1]$ s.t $f_1 \geq f_2 \geq \ldots$ and $\lim_{n\to\infty}f_n(x)=0$ .

real-analysis

mar 19 '12 at 2:29 Michael Hardy 47.9k

2

votes

1

answer

268

views

If monotone decreasing and $\int_0^\infty f(x)dx <\infty$ then $\lim_{x\to\infty} xf(x)=0.$

real-analysis

mar 12 '12 at 21:11 William DeMeo 1,430

2

votes

3

answers

382

views

Applying Arzelà–Ascoli Theorem

real-analysis

feb 21 '12 at 7:34 Galois 748

2

votes

1

answer

133

views

Is the sequence of continuous functions such that $\left\Vert f_{n}(x) -f_{m}(x) \right\Vert _{\infty}=1$ equicontinuous?

real-analysis

feb 21 '12 at 4:03 David Mitra 41k

1

vote

3

answers

104

views

Why $\lim_{R\to\infty} \int_{C_R}\frac{e^{iz}}{z}dz=0$?

complex-analysis

dec 14 at 14:10 robjohn♦ 59.2k

1

vote

2

answers

64

views

Showing $\sum_{n=1}^{\infty}\left\Vert x\right\Vert ^{n} $ does not converge uniformly.

real-analysis sequences-and-series

jul 27 at 0:02 Henning Makholm 53.5k

Galois

36 Questions