User lithium barbie doll - Mathematics Stack Exchange

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4

9

votes

3

answers

261

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Prove or Disprove that $\left|\frac{e^{2i\theta} -2e^{i\theta} - 1}{e^{2i\theta} + 2e^{i\theta} -1}\right| = 1$

complex-analysis

apr 11 '12 at 20:20 bgins 6,010

3

7

votes

4

answers

177

views

Trying to prove $\frac{2}{n+\frac{1}{2}} \leq \int_{1/(n+1)}^{1/n}\sqrt{1+(\sin(\frac{\pi}{t}) -\frac{\pi}{t}\cos(\frac{\pi}{t}))^2}dt$

jul 12 at 18:18 Arturo Magidin 158k

1

7

votes

1

answer

228

views

Is it Possible to have Two Distinct Analytic Functions with the Same Real Part?

complex-analysis

apr 24 '12 at 8:53 Greg Martin 7,653

7

votes

2

answers

524

views

Show bounded harmonic function on $\mathbb{C}$ is constant.

homework complex-analysis

apr 20 '12 at 22:39 Nate Eldredge 22.4k

1

6

votes

3

answers

122

views

For $I,J$ ideals, show that $IJ\subseteq (I\cap J)(I+J)$

abstract-algebra ring-theory ideals

dec 21 at 4:11 Zev Chonoles 53.6k

6

votes

2

answers

283

views

What Topology does a Straight Line in the Plane Inherit as a Subspace of $\mathbb{R_l} \times \mathbb{R}$ and of $\mathbb{R_l} \times \mathbb{R_l}$

general-topology

jun 24 '12 at 21:18 tomasz 7,100

5

votes

1

answer

76

views

Showing that $\lim_{k\rightarrow 0}\int_0^1\frac{dx}{\sqrt{(1-x^2)(1-k^2x^2)}} = \int_0^1\frac{dx}{\sqrt{(1-x^2)}}$

real-analysis uniform-convergence

sep 26 at 5:15 Alex Becker♦ 28.1k

1

4

votes

4

answers

223

views

Using the Residue Theorem for a contour integral along the Riemann sphere

complex-analysis residue-calculus

may 7 at 17:27 John Dilinger 11

1

4

votes

2

answers

78

views

Prove that a random walk on $\mathbb{Z}_+\cup \{0\}$ is transient

probability stochastic-processes markov-chains random-walk

apr 27 at 12:56 Byron Schmuland 15.4k

1

4

votes

2

answers

74

views

Prove that $\displaystyle\prod_{q\in \mathbb{Q}^{\times}}|q|=1$

analysis infinite-product

feb 22 at 7:17 Zev Chonoles 53.6k

4

votes

5

answers

184

views

Help me prove the identity $\overline{f(0)} = \frac{1}{2\pi}\int_0^{2\pi}\frac{e^{i\phi}}{e^{i \phi}-z}\overline{f(e^{i\phi})}d\phi$

homework complex-analysis

dec 21 at 21:16 oen 7,468

4

votes

2

answers

79

views

Comparing the homomorphism $\mathbb{Z}[x]\rightarrow\mathbb{Z}_n[x]$ with the homomorphism $\mathbb{Z}[x]\rightarrow\mathbb{F}_p[x]$

abstract-algebra polynomials

oct 6 at 5:36 Community♦ 1

1

4

votes

4

answers

380

views

Let $M$ be a maximal ideal in $R$ such that for all $x\in M$, $x+1$ is a unit. Show that $R$ is a local ring with maximal ideal $M$

abstract-algebra commutative-algebra

aug 11 at 2:31 Community♦ 1

4

votes

2

answers

139

views

Why doesn't $2\pi\int_{-1}^1\sqrt{1-x^2}dx$ give the surface area of a sphere of radius $1$? [duplicate]

calculus geometry

jul 14 at 22:13 Barun Dasgupta 286

1

4

votes

1

answer

74

views

Discrepancy in the Application of the Identity $\sum_{n=-\infty}^\infty f(n) = -\sum_{j=1}^l \operatorname{Res}(g;a_j)$

homework complex-analysis

jul 1 at 13:56 Eugene 3,728

4

votes

2

answers

456

views

Understanding the Analytic Continuation of the Gamma Function

complex-analysis gamma-function

jun 17 '12 at 6:15 user17762 76.2k

4

votes

1

answer

162

views

The Integral of a Harmonic Function

homework complex-analysis

apr 21 '12 at 1:39 Zarrax 19.7k

3

votes

1

answer

44

views

The semifinite portion of a measure $\mu$

measure-theory

may 17 at 20:22 Martin 3,688

3

votes

1

answer

63

views

Let $(X,\large\tau)$ be a normal topology, then show that the weak topology induced by the cont. real-valued functions on $X$ is $\large\tau$

real-analysis general-topology

apr 14 at 4:13 Arthur Fischer♦ 21.3k

3

votes

2

answers

59

views

Given that $(X_n)_{n\geq 0}$ is a Markov Chain, prove that $(X_{kn})_{n\geq 0}$ is a Markov Chain

probability markov-chains

apr 8 at 8:42 Donkey_2009 1,734

3

votes

0

answers

52

views

Why is the Euclidean metric called the prime at infinity?

soft-question notation p-adic-number-theory

mar 20 at 6:39 lithium barbie doll 1,291

2

3

votes

1

answer

81

views

Proving a group isomorphism from $(S,+)$ to $(S,+')$

abstract-algebra group-theory

jan 30 at 17:19 David Wheeler 1,180

3

votes

0

answers

87

views

The geometric intuition behind the fact that $y-x^3=0$ in $\mathbb{P}^2(\mathbb{R})$ has a singularity at infinity

geometry algebraic-geometry

dec 2 at 9:08 YACP 9,130

3

votes

1

answer

103

views

What does arithmetic actually mean (as an adjective)

soft-question terminology

oct 21 at 17:32 André Nicolas 161k

3

votes

1

answer

84

views

Prove that in $\mathbb{R}$, if $|a-b|>\alpha$ for all $a\in A$ and $b\in B$, then outer measure $m^(A\cup B)=m^(A)\cup m^*(B)$

real-analysis measure-theory

oct 13 at 4:16 Brian M. Scott 154k

3

votes

2

answers

475

views

Trying to prove that $p$ prime divides $\binom{p-1}{k} + \binom{p-2}{k-1} + \cdots +\binom{p-k}{1} + 1$

combinatorics number-theory elementary-number-theory binomial-coefficients divisibility

oct 1 at 13:49 Marc van Leeuwen 23.9k

3

votes

3

answers

99

views

Proving $\frac{-\theta + \theta^2}{2}$ is an algebraic integer in $K = \mathbb{Q}(\theta)$, given that $\theta^3 + 11\theta - 4 = 0$

polynomials algebraic-number-theory

jul 28 at 17:39 paul garrett 10.5k

3

votes

6

answers

223

views

How to prove that $\frac{10^{\frac{2}{3}}-1}{\sqrt{-3}}$ is an algebraic integer

polynomials algebraic-number-theory

jul 27 at 15:55 paul garrett 10.5k

3

votes

3

answers

297

views

Finding a splitting field of $x^3 + x +1$ over $\mathbb{Z}_2$

abstract-algebra field-theory

jul 6 at 9:53 Community♦ 1

1

3

votes

2

answers

233

views

If $K$ is an extension field of $\mathbb{Q}$ such that $[K:\mathbb{Q}]=2$, prove that $K=\mathbb{Q}(\sqrt{d})$ for some square free integer $d$

abstract-algebra field-theory

jul 2 at 1:01 BenjaLim 16.7k

lithium barbie doll

87 Questions