User Alexei Averchenko

21 votes

Exterior Derivative vs. Covariant Derivative vs. Lie Derivative

answered Oct 9, 2012 at 23:59

20 votes

How can I prove that $xy\leq x^2+y^2$?

answered Apr 15, 2013 at 15:23

17 votes

What is the meaning of the third derivative of a function at a point

answered Dec 19, 2010 at 7:25

16 votes

Division by zero

answered Nov 17, 2012 at 8:28

14 votes

Intuitive explanation of why $\dim\operatorname{Im} T + \dim\operatorname{Ker} T = \dim V$

answered Oct 6, 2012 at 21:59

12 votes

Rigour in mathematics

answered Aug 11, 2013 at 17:05

9 votes

Defining a manifold without reference to the reals

answered Jul 22, 2011 at 11:44

8 votes

Functions which are Continuous, but not Bicontinuous

answered Oct 2, 2011 at 11:09

8 votes

Accepted

Isomorphism of rings implies isomorphism of vector spaces?

answered Jan 3, 2013 at 12:38

7 votes

Accepted

Geometric interpretation of the Kronecker product?

answered Nov 6, 2012 at 15:32

6 votes

Image of commutative diagram is commutative under functor?

answered Aug 6, 2012 at 6:48

5 votes

Accepted

Principal and fiber bundles as defined by Husemoller

answered Oct 2, 2011 at 9:03

4 votes

Which one result in mathematics has surprised you the most?

answered Feb 6, 2011 at 0:20

3 votes

Accepted

How come the columns of a matrix can form its nullspace?

answered Nov 24, 2011 at 17:26

3 votes

$\left( \begin{array}{cc} 1 & 1 \\ 0 & 1 \\ \end{array} \right)$ not diagonalizable

answered Oct 31, 2012 at 4:53

3 votes

Prove the isomorphism of cyclic groups $C_{mn}\cong C_m\times C_n$ via categorical considerations

answered Nov 30, 2012 at 1:51

3 votes

Why is there a constant of integration?

answered Jan 13, 2013 at 22:08

3 votes

Monoids. Disprove that $(a\cdot x=a) \Rightarrow (x=e)$

answered Mar 7, 2013 at 18:40

3 votes

Cardinality of the set of bijective functions on $\mathbb{N}$?

answered Apr 20, 2013 at 9:40

2 votes

Accepted

calculus gets challenged

answered Apr 26, 2013 at 19:48

2 votes

Is there a short proof for the Intermediate Value Theorem

answered Apr 10, 2013 at 15:46

2 votes

Linear Algebra: if $A$ spans $B$, does $B$ necessarily span $A$ if $\dim A = \dim B$?

answered Dec 12, 2012 at 9:43

2 votes

Curve of Equal SWR

answered Nov 20, 2012 at 9:00

2 votes

$S^n$ homeomorphic to $I^n/\partial(I^n)$

answered Oct 2, 2011 at 9:38

1 vote

Notation for fields

answered Mar 29, 2012 at 13:59

1 vote

Product of a monotone increasing function and a monotone decreasing function

answered Dec 14, 2010 at 5:48

1 vote

Concrete Example Illustrating the Interior Product

answered Jul 8, 2011 at 15:34

1 vote

Vector multiplication with scalars

answered Feb 27, 2011 at 17:07

1 vote

What is the intuitive meaning of the dual space of a tangent space?

answered May 3, 2011 at 9:33

1 vote

Showing $1,e^{x}$ and $\sin{x}$ are linearly independent in $\mathcal{C}[0,1]$

answered Dec 4, 2010 at 21:04

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43 Answers

Exterior Derivative vs. Covariant Derivative vs. Lie Derivative

How can I prove that $xy\leq x^2+y^2$?

What is the meaning of the third derivative of a function at a point

Division by zero

Intuitive explanation of why $\dim\operatorname{Im} T + \dim\operatorname{Ker} T = \dim V$

Rigour in mathematics

Defining a manifold without reference to the reals

Functions which are Continuous, but not Bicontinuous

Isomorphism of rings implies isomorphism of vector spaces?

Geometric interpretation of the Kronecker product?

Image of commutative diagram is commutative under functor?

Principal and fiber bundles as defined by Husemoller

Which one result in mathematics has surprised you the most?

How come the columns of a matrix can form its nullspace?

$\left( \begin{array}{cc} 1 & 1 \\ 0 & 1 \\ \end{array} \right)$ not diagonalizable

Prove the isomorphism of cyclic groups $C_{mn}\cong C_m\times C_n$ via categorical considerations

Why is there a constant of integration?

Monoids. Disprove that $(a\cdot x=a) \Rightarrow (x=e)$

Cardinality of the set of bijective functions on $\mathbb{N}$?

calculus gets challenged

Is there a short proof for the Intermediate Value Theorem

Linear Algebra: if $A$ spans $B$, does $B$ necessarily span $A$ if $\dim A = \dim B$?

Curve of Equal SWR

$S^n$ homeomorphic to $I^n/\partial(I^n)$

Notation for fields

Product of a monotone increasing function and a monotone decreasing function

Concrete Example Illustrating the Interior Product

Vector multiplication with scalars

What is the intuitive meaning of the dual space of a tangent space?

Showing $1,e^{x}$ and $\sin{x}$ are linearly independent in $\mathcal{C}[0,1]$