User Paul Siegel

44 votes

2 answers

856 views

Is there a naive proof that $x - \frac{x^3}{3!} + \frac{x^5}{5!} - \ldots$ has period $2\pi$?

calculus sequences-and-series

asked May 29, 2018 at 19:26

41 votes

2 answers

2k views

Which polynomials are characteristic polynomials of a symmetric matrix?

asked Nov 20, 2013 at 10:34

32 votes

1 answer

3k views

When is $C_0(X)$ separable?

general-topology functional-analysis separation-axioms second-countable separable-spaces

asked Aug 20, 2012 at 20:19

14 votes

1 answer

1k views

Coordinate free proof that curvature is the "square" of the connection

differential-geometry differential-forms

asked Jan 10, 2011 at 17:40

12 votes

1 answer

2k views

Elementary applications of Krein-Milman

functional-analysis convex-analysis locally-convex-spaces

asked May 2, 2012 at 5:07

10 votes

0 answers

1k views

Mayer-Vietoris implies Excision

algebraic-topology

asked May 19, 2012 at 20:13

9 votes

1 answer

1k views

Is the space of uniformly left continuous functions on [0,1] complete?

calculus real-analysis analysis banach-spaces

asked Sep 6, 2011 at 20:06

8 votes

2 answers

2k views

Modulus of Continuity

functional-analysis metric-spaces

asked Nov 16, 2011 at 21:03

8 votes

1 answer

1k views

An isomorphism in relative De Rham cohomology

algebraic-topology

asked Apr 26, 2012 at 23:18

7 votes

0 answers

132 views

Products in $C^*$-algebra $K$-theory

operator-algebras k-theory

asked May 8, 2012 at 4:00

7 votes

2 answers

988 views

Modulus of Continuity, Take 2

functional-analysis metric-spaces

asked Nov 17, 2011 at 21:27

7 votes

1 answer

383 views

Is there a statistical interpretation of Green's theorem, Stokes' theorem, or the divergence theorem?

probability multivariable-calculus

asked Jan 28, 2013 at 20:21

7 votes

5 answers

567 views

Complete and elementary proof that $(a^x - 1)/x $ converges as x goes to 0

calculus limits

asked Oct 11, 2013 at 1:09

6 votes

3 answers

1k views

A question related to Buffon's needle

probability geometry

asked Jan 25, 2013 at 21:44

6 votes

1 answer

215 views

Effect of permuting coordinates on K-theory

c-star-algebras k-theory

asked Jun 28, 2011 at 5:19

6 votes

3 answers

792 views

Can closed curves have small curvature?

differential-geometry plane-curves curvature

asked Jul 19, 2011 at 21:19

5 votes

1 answer

213 views

Operator K-theory and the unitary group

c-star-algebras k-theory

asked Apr 23, 2012 at 23:08

5 votes

2 answers

1k views

"Abstract nonsense" proof that the fundamental group of a topological group is abelian

general-topology

asked Dec 8, 2010 at 1:35

5 votes

2 answers

833 views

Are all critical points of energy geodesics?

riemannian-geometry calculus-of-variations

asked Apr 22, 2014 at 10:56

5 votes

1 answer

423 views

Is there such a thing as "cartesian closure" in category theory?

category-theory

asked Feb 3, 2018 at 17:51

4 votes

1 answer

716 views

Maurer-Cartan 1- form as a connection 1-form

differential-geometry

asked Jan 24, 2011 at 18:32

4 votes

1 answer

1k views

The (distributional) Fourier transform of the unit step function

distribution-theory

asked Jun 9, 2011 at 19:27

4 votes

2 answers

417 views

Yet another complex analysis problem

complex-analysis

asked Mar 1, 2012 at 22:19

4 votes

3 answers

603 views

An ignorant question about the incompleteness theorem

logic incompleteness

asked Jul 11, 2012 at 16:43

3 votes

1 answer

481 views

How do you prove that every curve of constant width is convex?

geometry

asked Feb 27, 2013 at 20:26

3 votes

0 answers

244 views

The magnetic monopole and the Hopf bundle

differential-geometry gauge-theory

asked Apr 18, 2014 at 16:58

3 votes

3 answers

271 views

More elementary proof that $\pi_n(S^n) \cong \mathbb{Z}$

algebraic-topology

asked Sep 2, 2014 at 17:08

3 votes

1 answer

235 views

Is a graph determined up to isomorphism by its path category?

graph-theory category-theory directed-graphs

asked May 4, 2017 at 16:00

2 votes

1 answer

76 views

Is a graph uniquely determined by its weighted 2-step graph?

graph-theory

asked Jul 23, 2014 at 21:38

2 votes

2 answers

451 views

A silly question about $C_0$

general-topology

asked Aug 26, 2010 at 16:39

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34 Questions

Is there a naive proof that $x - \frac{x^3}{3!} + \frac{x^5}{5!} - \ldots$ has period $2\pi$?

Which polynomials are characteristic polynomials of a symmetric matrix?

When is $C_0(X)$ separable?

Coordinate free proof that curvature is the "square" of the connection

Elementary applications of Krein-Milman

Mayer-Vietoris implies Excision

Is the space of uniformly left continuous functions on [0,1] complete?

Modulus of Continuity

An isomorphism in relative De Rham cohomology

Products in $C^*$-algebra $K$-theory

Modulus of Continuity, Take 2

Is there a statistical interpretation of Green's theorem, Stokes' theorem, or the divergence theorem?

Complete and elementary proof that $(a^x - 1)/x $ converges as x goes to 0

A question related to Buffon's needle

Effect of permuting coordinates on K-theory

Can closed curves have small curvature?

Operator K-theory and the unitary group

"Abstract nonsense" proof that the fundamental group of a topological group is abelian

Are all critical points of energy geodesics?

Is there such a thing as "cartesian closure" in category theory?

Maurer-Cartan 1- form as a connection 1-form

The (distributional) Fourier transform of the unit step function

Yet another complex analysis problem

An ignorant question about the incompleteness theorem

How do you prove that every curve of constant width is convex?

The magnetic monopole and the Hopf bundle

More elementary proof that $\pi_n(S^n) \cong \mathbb{Z}$

Is a graph determined up to isomorphism by its path category?

Is a graph uniquely determined by its weighted 2-step graph?

A silly question about $C_0$