User Diane Vanderwaif

22 votes

1 answer

22k views

Prove that the min and max of 2 continuous function are continuous

asked Oct 17, 2013 at 19:12

10 votes

3 answers

17k views

closed and open set - set $S$ is open if and only if its complement is closed?

asked Apr 23, 2013 at 17:18

9 votes

2 answers

5k views

Prove that if a function $f$ has a jump at an interior point of the interval $[a,b]$ then it cannot be the derivative of any function.

asked Nov 12, 2013 at 12:15

9 votes

1 answer

2k views

Use the divergent theorem to verify the volume of a circular cone

asked May 16, 2014 at 13:40

8 votes

1 answer

2k views

If $σ^2$ is the identity map from $G$ to $G$, prove that $G$ is abelian.

asked Jan 23, 2014 at 20:02

7 votes

3 answers

1k views

Increasing and bounded sequence proof

asked Sep 20, 2013 at 16:37

7 votes

2 answers

456 views

Limit superior inequalities proof: $\limsup_{n\to \infty} \left(\frac{a_1+a_{n+1}}{a_n}\right)^n\ge e$

asked Sep 28, 2013 at 13:20

7 votes

3 answers

18k views

Smooth function proof

asked Sep 19, 2014 at 21:39

7 votes

2 answers

2k views

Prove that if $S^k$ has a non vanishing vector field, then its antipodal map is homotopy to the identity if $k$ is even.

asked Oct 5, 2014 at 14:48

7 votes

3 answers

709 views

Find the error in following reason $(-z)^2=z^2 \implies \log(-z)^2=\log(z)^2 \implies2\log(-z)=2\log(z)\implies \log(-z)=\log(z)$

asked Feb 12, 2015 at 22:57

7 votes

2 answers

4k views

Suppose that $f$ is analytic on a close curve γ. Prove or disprove $\int_\gamma \overline{f(z)}f'(z)dz$ is purely imaginary.

asked Mar 21, 2015 at 18:01

6 votes

2 answers

2k views

Show that Möbius transformation $S$ commute with $T$ if $S$ and $T$ have the same fixed point.

asked Mar 1, 2015 at 14:10

6 votes

5 answers

1k views

Find an example of a regular triangle-free $4$-chromatic graph

asked Feb 13, 2015 at 2:48

6 votes

2 answers

2k views

Determine the set of points $z$ that satisfy the condition $|2z|>|1+z^2|$

asked Jan 30, 2015 at 20:11

6 votes

2 answers

854 views

Prove that there exists a smooth map $g\colon R\to R$ such that $f(\cos(t),\sin(t))=(\cos(g(t)),\sin(g(t)))$ and satisfying $g(2π)=g(0)+2\pi q$.

asked Oct 19, 2014 at 18:54

6 votes

1 answer

273 views

showing $a_n = \frac{\tan(1)}{2^1} + \frac{\tan(2)}{2^2} + \dots + \frac{\tan(n)}{2^n}$ is not Cauchy

asked Sep 22, 2013 at 12:42

6 votes

1 answer

166 views

How to prove that this recursively defined sequence converges to $e$?

asked Sep 18, 2013 at 17:02

6 votes

4 answers

211 views

Explain why $U_{44} \cong (\mathbb{Z}_{10} \oplus \mathbb{Z}_2) $.

asked Apr 17, 2013 at 23:58

6 votes

3 answers

6k views

Prove or disprove that if $f$ is continuous function and $A$ is closed, then $\,f[A]$ is closed.

asked Feb 23, 2014 at 18:14

5 votes

2 answers

252 views

For which $x$ does the series $∑_{n=1}^∞(1+\frac{1}{2}+ \frac{1}{3}+⋯+\frac{1}{n})\, x^n$ converge?

asked Feb 8, 2014 at 14:00

5 votes

2 answers

755 views

Evaluate $\int ^1 _0 x^2 \, dx$ without using the Fundamental Theorem of Calculus

asked Dec 2, 2013 at 14:41

5 votes

2 answers

2k views

Prove the third isomorphism theorem

asked Apr 19, 2013 at 12:50

5 votes

0 answers

212 views

Prove that there exists a diffeomorphism from an open neighborhood of $Z$ in $N(Z;Y)$ onto an open neighborhood of $Z$ in $Y$.

asked Oct 19, 2014 at 13:40

5 votes

3 answers

1k views

Prove that$ H_x (X)$ does not depend on the choice of local parametrization.

asked Oct 12, 2014 at 14:34

5 votes

2 answers

19k views

Prove that every connected graph of all whose vertices have even degree contain no bridges.

asked Sep 27, 2014 at 13:20

5 votes

2 answers

527 views

Why this graph has automorphism group is isomorphic to the cyclic group of order 4?

asked Nov 27, 2014 at 13:52

5 votes

2 answers

355 views

Prove that the diagonal $∆$ in $S^2×S^2$ is not globally definable by $2$ independent function.

asked Nov 28, 2014 at 19:38

5 votes

2 answers

2k views

Find an analytic function that maps the angle $-\pi/4<\operatorname{arg}(z)<\pi/2$ onto the upper half plane so that $w(1-i)=2,w(i)=-1$, and $w(0)=0$

asked Mar 1, 2015 at 14:44

4 votes

3 answers

3k views

Describe the image of the set $\{z:|z|<1, Im(z)>0\}$ under the mapping $w =\frac{2z-i}{2+iz}$

asked Feb 21, 2015 at 16:10

4 votes

3 answers

196 views

Compute $\sum_{n=0}^\infty \frac {\sin ((2n+1)\phi)}{2n+1}$ for $0<\phi<\pi$

asked Mar 21, 2015 at 15:46

Stack Exchange Network

317 Questions

Prove that the min and max of 2 continuous function are continuous

closed and open set - set $S$ is open if and only if its complement is closed?

Prove that if a function $f$ has a jump at an interior point of the interval $[a,b]$ then it cannot be the derivative of any function.

Use the divergent theorem to verify the volume of a circular cone

If $σ^2$ is the identity map from $G$ to $G$, prove that $G$ is abelian.

Increasing and bounded sequence proof

Limit superior inequalities proof: $\limsup_{n\to \infty} \left(\frac{a_1+a_{n+1}}{a_n}\right)^n\ge e$

Smooth function proof

Prove that if $S^k$ has a non vanishing vector field, then its antipodal map is homotopy to the identity if $k$ is even.

Find the error in following reason $(-z)^2=z^2 \implies \log(-z)^2=\log(z)^2 \implies2\log(-z)=2\log(z)\implies \log(-z)=\log(z)$

Suppose that $f$ is analytic on a close curve γ. Prove or disprove $\int_\gamma \overline{f(z)}f'(z)dz$ is purely imaginary.

Show that Möbius transformation $S$ commute with $T$ if $S$ and $T$ have the same fixed point.

Find an example of a regular triangle-free $4$-chromatic graph

Determine the set of points $z$ that satisfy the condition $|2z|>|1+z^2|$

Prove that there exists a smooth map $g\colon R\to R$ such that $f(\cos(t),\sin(t))=(\cos(g(t)),\sin(g(t)))$ and satisfying $g(2π)=g(0)+2\pi q$.

showing $a_n = \frac{\tan(1)}{2^1} + \frac{\tan(2)}{2^2} + \dots + \frac{\tan(n)}{2^n}$ is not Cauchy

How to prove that this recursively defined sequence converges to $e$?

Explain why $U_{44} \cong (\mathbb{Z}_{10} \oplus \mathbb{Z}_2) $.

Prove or disprove that if $f$ is continuous function and $A$ is closed, then $\,f[A]$ is closed.

For which $x$ does the series $∑_{n=1}^∞(1+\frac{1}{2}+ \frac{1}{3}+⋯+\frac{1}{n})\, x^n$ converge?

Evaluate $\int ^1 _0 x^2 \, dx$ without using the Fundamental Theorem of Calculus

Prove the third isomorphism theorem

Prove that there exists a diffeomorphism from an open neighborhood of $Z$ in $N(Z;Y)$ onto an open neighborhood of $Z$ in $Y$.

Prove that$ H_x (X)$ does not depend on the choice of local parametrization.

Prove that every connected graph of all whose vertices have even degree contain no bridges.

Why this graph has automorphism group is isomorphic to the cyclic group of order 4?

Prove that the diagonal $∆$ in $S^2×S^2$ is not globally definable by $2$ independent function.

Find an analytic function that maps the angle $-\pi/4<\operatorname{arg}(z)<\pi/2$ onto the upper half plane so that $w(1-i)=2,w(i)=-1$, and $w(0)=0$

Describe the image of the set $\{z:|z|<1, Im(z)>0\}$ under the mapping $w =\frac{2z-i}{2+iz}$

Compute $\sum_{n=0}^\infty \frac {\sin ((2n+1)\phi)}{2n+1}$ for $0<\phi<\pi$