User Diane Vanderwaif

22 votes

1 answer

21k views

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

asked Oct 17, 2013 at 19:12

10 votes

3 answers

16k 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

3 answers

17k 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

683 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

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

453 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

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

1 answer

268 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

165 views

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

asked Sep 18, 2013 at 17:02

6 votes

4 answers

208 views

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

asked Apr 17, 2013 at 23:58

6 votes

3 answers

5k 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

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

829 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

5 votes

0 answers

210 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

18k 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

349 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

515 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

251 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

738 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

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

193 views

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

asked Mar 21, 2015 at 15:46

4 votes

4 answers

1k views

Let $∑_{n=0}^∞c_n z^n $ be a representation for the function $\frac{1}{1-z-z^2 }$. Find the coefficient $c_n$

asked Mar 21, 2015 at 16:35

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

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 $(-z)^2=z^2 \implies \log(-z)^2=\log(z)^2 \implies2\log(-z)=2\log(z)\implies \log(-z)=\log(z)$

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

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.

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.

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 $g(2π)=g(0)+2\pi q$.

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.

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

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

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

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 $w(0)=0$

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

Let $∑_{n=0}^∞c_n z^n $ be a representation for the function $\frac{1}{1-z-z^2 }$. Find the coefficient $c_n$