User Max

19 votes

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Is the chart function of a smooth manifold a differomorphism, not just a homeomorphism

answered Dec 27, 2013 at 2:55

13 votes

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Do we always get the same dimension regardless of the manifold/topological structure?

answered Apr 26, 2021 at 5:39

13 votes

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Example of a surface where more than one coordinate patch is needed.

answered Jul 21, 2015 at 21:17

13 votes

Intuition behind variation of parameters method for solving differential equations

answered May 18, 2016 at 9:34

13 votes

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Why does the polynomial equation $1 + x + x^2 + \cdots + x^n = S$ have at most two solutions in $x$?

answered Nov 3, 2010 at 23:45

13 votes

Isometry in compact metric spaces

answered Nov 29, 2010 at 11:20

12 votes

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Lie Group Decomposition as Semidirect Product of Connected and Discrete Groups

answered Oct 1, 2014 at 21:06

10 votes

Is this definite integral really independent of a parameter? How can it be shown?

answered Dec 8, 2010 at 0:48

9 votes

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Local triviality of principal bundles

answered Feb 25, 2011 at 19:34

8 votes

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Maximizing the value of a determinant

answered Jun 12, 2019 at 7:09

7 votes

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How can a level set be convex?

answered Oct 8, 2021 at 2:03

7 votes

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Intuitive explanation for Why $0*a = 0$ in a field

answered Jun 29, 2022 at 0:15

7 votes

Intuitive explanation of $y' = y \implies y = Ce^x$

answered Mar 18, 2019 at 9:30

7 votes

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Why is symplectic geometry the natural setting for classical mechanics?

answered Apr 13, 2019 at 22:26

7 votes

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Are gradient flows the quickest way to minimize a function for a short time?

answered Oct 14, 2019 at 22:14

7 votes

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A set in the Borel $\sigma$-algebra over $[0,1]$ that isn't in the algebra generated by open sets

answered Nov 4, 2020 at 9:59

6 votes

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Process producing concatenations of two palindromes

answered Dec 21, 2019 at 7:48

6 votes

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How to prove that the Legendre symbol is multiplicative?

answered Jun 18, 2019 at 8:01

6 votes

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How does this image prove the identity $1+2+3+4\cdots + (n-1) = \binom{n}{2}$?

answered Oct 28, 2011 at 23:29

6 votes

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Why $T\mathbb{S}^{2}\otimes T\mathbb{S}^{2}$ is trivial?

answered Oct 29, 2011 at 0:21

6 votes

Polynomials, derivatives and repeated roots

answered Nov 15, 2010 at 16:02

6 votes

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Show a Cubic Polynomial over $\Bbb C$ can be factored as a product of linear terms

answered Jan 25, 2013 at 17:05

6 votes

Why does symplectic geometry have many applications in mathematics

answered Dec 7, 2010 at 23:29

5 votes

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Is a basin of attraction necessarily an open set?

answered Apr 3, 2018 at 17:55

5 votes

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Ext & Complexes

answered Dec 5, 2010 at 18:48

5 votes

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Proving $\lim_{n \to \infty} n[n^{1/n}-1] = +\infty$

answered Nov 10, 2012 at 17:44

5 votes

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Morse homology of $P^2$

answered Nov 11, 2012 at 22:43

5 votes

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Eigenvalues For the Laplacian Operator

answered May 24, 2011 at 9:11

5 votes

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Sphere eversion and Smale-Hirsch theorem

answered Jul 5, 2011 at 12:36

5 votes

Embedding of utility graph in two torus

answered Jun 14, 2019 at 9:34

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262 Answers

Is the chart function of a smooth manifold a differomorphism, not just a homeomorphism

Do we always get the same dimension regardless of the manifold/topological structure?

Example of a surface where more than one coordinate patch is needed.

Intuition behind variation of parameters method for solving differential equations

Why does the polynomial equation $1 + x + x^2 + \cdots + x^n = S$ have at most two solutions in $x$?

Isometry in compact metric spaces

Lie Group Decomposition as Semidirect Product of Connected and Discrete Groups

Is this definite integral really independent of a parameter? How can it be shown?

Local triviality of principal bundles

Maximizing the value of a determinant

How can a level set be convex?

Intuitive explanation for Why $0*a = 0$ in a field

Intuitive explanation of $y' = y \implies y = Ce^x$

Why is symplectic geometry the natural setting for classical mechanics?

Are gradient flows the quickest way to minimize a function for a short time?

A set in the Borel $\sigma$-algebra over $[0,1]$ that isn't in the algebra generated by open sets

Process producing concatenations of two palindromes

How to prove that the Legendre symbol is multiplicative?

How does this image prove the identity $1+2+3+4\cdots + (n-1) = \binom{n}{2}$?

Why $T\mathbb{S}^{2}\otimes T\mathbb{S}^{2}$ is trivial?

Polynomials, derivatives and repeated roots

Show a Cubic Polynomial over $\Bbb C$ can be factored as a product of linear terms

Why does symplectic geometry have many applications in mathematics

Is a basin of attraction necessarily an open set?

Ext & Complexes

Proving $\lim_{n \to \infty} n[n^{1/n}-1] = +\infty$

Morse homology of $P^2$

Eigenvalues For the Laplacian Operator

Sphere eversion and Smale-Hirsch theorem

Embedding of utility graph in two torus