Diane Vanderwaif's user avatar
Diane Vanderwaif's user avatar
Diane Vanderwaif's user avatar
Diane Vanderwaif
  • Member for 10 years, 8 months
  • Last seen more than 8 years ago
22 votes
1 answer
22k views

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

10 votes
3 answers
17k views

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

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.

9 votes
1 answer
2k views

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

8 votes
1 answer
2k views

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

7 votes
3 answers
1k views

Increasing and bounded sequence proof

7 votes
2 answers
456 views

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

7 votes
3 answers
18k views

Smooth function proof

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.

7 votes
3 answers
709 views

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

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.

6 votes
2 answers
2k views

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

6 votes
5 answers
1k views

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

6 votes
2 answers
2k views

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

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 $g(2π)=g(0)+2\pi q$.

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

6 votes
1 answer
166 views

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

6 votes
4 answers
211 views

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

6 votes
3 answers
6k views

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

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?

5 votes
2 answers
755 views

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

5 votes
2 answers
2k views

Prove the third isomorphism theorem

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 $Y$.

5 votes
3 answers
1k views

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

5 votes
2 answers
19k views

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

5 votes
2 answers
527 views

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

5 votes
2 answers
355 views

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

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 $w(0)=0$

4 votes
3 answers
3k views

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

4 votes
3 answers
196 views

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

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