User Aaron

61 votes

How to show that $\det(AB) =\det(A) \det(B)$?

answered Aug 28, 2011 at 7:13

56 votes

Accepted

Calculate distance in 3D space

answered Jun 1, 2011 at 20:03

54 votes

Accepted

Can Euler's identity be extended to quaternions?

answered May 27, 2011 at 1:55

40 votes

Accepted

Why is a covering space of a torus $T$ homeomorphic either to $\mathbb{R}^2$, $S^1\times\mathbb{R}$ or $T$?

answered Apr 21, 2011 at 11:04

38 votes

Accepted

How do people apply the Lebesgue integration theory?

answered Jul 22, 2011 at 17:54

27 votes

What are cohomology rings good for?

answered May 17, 2011 at 19:40

26 votes

Accepted

Why does the trivial representation have degree 1?

answered May 28, 2011 at 18:29

25 votes

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Covectors and Vectors

answered Jul 8, 2011 at 3:11

22 votes

Accepted

$\subset$ vs $\subseteq$ when not referring to strict inclusion

answered Jul 8, 2011 at 5:40

22 votes

Why do we write proofs "forward?"

answered Dec 31, 2011 at 23:28

19 votes

How to expand $\cos nx$ with $\cos x$?

answered Mar 29, 2012 at 13:35

18 votes

Is it possible for the Lagrange multiplier to be equal to zero?

answered May 26, 2011 at 18:38

18 votes

Under what conditions does a matrix $A$ have a square root?

answered Sep 20, 2011 at 19:18

17 votes

Why does topology rarely come up outside of topology?

answered Dec 29, 2015 at 9:50

17 votes

Show an integration equality without using $\int\frac{\mathrm dx}{x}=\ln|x|+c$

answered May 1, 2017 at 5:20

16 votes

Intuition of the meaning of homology groups

answered May 19, 2011 at 21:52

16 votes

Showing $\int_{0}^{2\pi}\cos(x)\cos(2x)\cos(3x)\,dx = \frac\pi2$

answered Jul 5, 2021 at 3:36

14 votes

Accepted

If $n\neq m$ then $\mathbb{R}^n$ is not homeomorphic to $\mathbb{R}^m$

answered Jun 5, 2011 at 20:27

13 votes

Advanced algebraic topology topics overview

answered Jul 23, 2011 at 19:09

13 votes

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The Mittag-Leffler condition and $\varprojlim^1$

answered May 13, 2011 at 20:56

13 votes

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Proving $\mathbb{Z}[\sqrt {10}]$ is not a UFD

answered Sep 24, 2015 at 2:18

13 votes

Dummit and Foote 4.3.13: Find all the finite groups which have exactly two conjugacy classes.

answered Nov 5, 2020 at 2:32

12 votes

Accepted

Signs in the natural map $\Lambda^k V \otimes \Lambda^k V^* \to \Bbbk$

answered Jun 8, 2011 at 22:05

12 votes

Accepted

Why is the pullback not just a cartesian product (modulo a relation)?

answered Jun 20, 2011 at 20:51

12 votes

If $\det A=1$ and the matrices $A^{2015}$ and $A^{2017}$ are integer, is $A$ an integer matrix?

answered May 27, 2015 at 7:25

12 votes

Accepted

If $G$ is an abelian group, then $H=\{g\in G \mid |g| \text{ divides }12\}$ is a subgroup of $G$

answered Sep 3, 2018 at 9:00

11 votes

Accepted

Are $\mathbb Q\times\mathbb Q$ and $\mathbb Q\times\mathbb Q\times\mathbb Q$ isomorphic?

answered Jun 11, 2019 at 8:35

10 votes

Accepted

Elucidating Tu's Definition of a Regular Submanifold

answered May 1, 2011 at 19:49

10 votes

What does it mean to integrate a Brownian motion with respect to time?

answered Jul 8, 2016 at 19:19

9 votes

Accepted

Definition of the quotient $G/H$

answered Jun 17, 2011 at 7:42

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533 Answers

How to show that $\det(AB) =\det(A) \det(B)$?

Calculate distance in 3D space

Can Euler's identity be extended to quaternions?

Why is a covering space of a torus $T$ homeomorphic either to $\mathbb{R}^2$, $S^1\times\mathbb{R}$ or $T$?

How do people apply the Lebesgue integration theory?

What are cohomology rings good for?

Why does the trivial representation have degree 1?

Covectors and Vectors

$\subset$ vs $\subseteq$ when not referring to strict inclusion

Why do we write proofs "forward?"

How to expand $\cos nx$ with $\cos x$?

Is it possible for the Lagrange multiplier to be equal to zero?

Under what conditions does a matrix $A$ have a square root?

Why does topology rarely come up outside of topology?

Show an integration equality without using $\int\frac{\mathrm dx}{x}=\ln|x|+c$

Intuition of the meaning of homology groups

Showing $\int_{0}^{2\pi}\cos(x)\cos(2x)\cos(3x)\,dx = \frac\pi2$

If $n\neq m$ then $\mathbb{R}^n$ is not homeomorphic to $\mathbb{R}^m$

Advanced algebraic topology topics overview

The Mittag-Leffler condition and $\varprojlim^1$

Proving $\mathbb{Z}[\sqrt {10}]$ is not a UFD

Dummit and Foote 4.3.13: Find all the finite groups which have exactly two conjugacy classes.

Signs in the natural map $\Lambda^k V \otimes \Lambda^k V^* \to \Bbbk$

Why is the pullback not just a cartesian product (modulo a relation)?

If $\det A=1$ and the matrices $A^{2015}$ and $A^{2017}$ are integer, is $A$ an integer matrix?

If $G$ is an abelian group, then $H=\{g\in G \mid |g| \text{ divides }12\}$ is a subgroup of $G$

Are $\mathbb Q\times\mathbb Q$ and $\mathbb Q\times\mathbb Q\times\mathbb Q$ isomorphic?

Elucidating Tu's Definition of a Regular Submanifold

What does it mean to integrate a Brownian motion with respect to time?

Definition of the quotient $G/H$