User Elias Costa

114 votes

0 answers

2k views

On the Constant Rank Theorem and the Frobenius Theorem for differential equations.

asked Jun 22, 2013 at 21:40

64 votes

5 answers

31k views

How to prove that a compact set in a Hausdorff topological space is closed?

asked Nov 18, 2011 at 12:46

31 votes

3 answers

3k views

A simple way to obtain $\prod_{p\in\mathbb{P}}\frac{1}{1-p^{-s}}=\sum_{n=1}^{\infty}\frac{1}{n^s}$.

asked Jun 24, 2013 at 0:11

25 votes

15 answers

2k views

Prove that $2018^{2019}> 2019^{2018}$ without induction, without Newton's binomial formula and without Calculus.

asked Feb 25, 2019 at 20:34

20 votes

1 answer

612 views

The problem of the most visited point.

asked Dec 24, 2013 at 13:24

20 votes

4 answers

5k views

What distinguishes measure theory and probability theory?

asked Mar 9, 2012 at 13:50

15 votes

1 answer

1k views

List videos of interesting courses at the doctoral level.

asked May 14, 2013 at 21:34

11 votes

1 answer

1k views

Why 'closed differential forms' are called 'closed'?

asked Feb 7, 2014 at 21:18

10 votes

1 answer

752 views

Minimax Theorems V.S. Fixed Point Theorems.

asked Mar 5, 2012 at 13:43

10 votes

1 answer

4k views

Intuitive explanation of Residue theorem in Complex Analysis [duplicate]

asked Dec 10, 2012 at 17:18

10 votes

1 answer

652 views

An accessible reference to proof of Nachbin's theorem

asked Feb 18, 2017 at 17:08

10 votes

1 answer

553 views

How do I prove that the second derivative of a function $f:M\to\mathbb{R}$ defined on a surface $M\subset\mathbb{R}^n$ is well defined?

asked Jan 31, 2019 at 17:02

9 votes

0 answers

792 views

A Lipschitz Implicit Function Theorem.

asked Nov 10, 2018 at 13:42

8 votes

1 answer

1k views

On convergence of nets in a topological space

asked Dec 18, 2012 at 11:48

8 votes

2 answers

536 views

It is possible to prove the existence of Gibbs measures using the Kolmogorov extension theorem?

asked Jun 16, 2012 at 19:26

8 votes

4 answers

4k views

On a topological proof of the infinitude of prime numbers.

asked Dec 20, 2011 at 15:58

8 votes

2 answers

1k views

A general definition of symmetry in mathematics

asked Dec 29, 2011 at 14:06

7 votes

0 answers

210 views

Percolation and number of phases in the 2D Ising model.

asked Oct 22, 2013 at 20:03

7 votes

2 answers

663 views

Proof of the infinitude of primes by probabilistic methods.

asked Jul 3, 2013 at 18:54

7 votes

0 answers

107 views

Number of circuits that surround the square.

asked Apr 2, 2015 at 14:58

7 votes

1 answer

338 views

Brouwer's fixed point theorem and continuous functional dependence on the fixed point.

asked Oct 17, 2019 at 20:07

7 votes

2 answers

408 views

Doubt about a passage on page 24 of the Evans Partial Differential Equations book

asked May 15, 2018 at 23:28

6 votes

2 answers

149 views

There are open sets $U$ and $V$ such that $U\cap V = \emptyset $ and $ U \cap \tau(V) =\emptyset $?

asked Jul 20, 2018 at 17:07

6 votes

0 answers

311 views

Calculating the convex conjugate of the function $f(x)=\lim_{n\to \infty}\left(-\frac{1}{n}\log \sum_{k=1}^n e^{a_k\cdot x+b_k}\right)$.

asked Jun 5, 2015 at 13:33

6 votes

0 answers

319 views

Algorithm to calculate multiple integral.

asked Apr 10, 2013 at 18:43

6 votes

2 answers

1k views

Product of two probability kernel is a probability kernel?

asked Nov 21, 2011 at 0:16

6 votes

4 answers

191 views

It is possible to prove that these two collections generate the same topology on $ \mathbb{X} $?

asked Oct 12, 2012 at 14:22

5 votes

2 answers

2k views

Puzzle on the triangle.

asked Nov 17, 2012 at 15:23

5 votes

2 answers

885 views

Two Dimensional Ising Model and Hamiltonian.

asked Mar 26, 2012 at 15:58

5 votes

0 answers

137 views

Legendre-Fenchel transformation for $\varphi\, \Big(\,x\, ,\, f\,\big(\,\Phi\,(\,x\,)\,\big)\,\Big)$.

asked Dec 29, 2016 at 20:38

Stack Exchange Network

117 Questions

On the Constant Rank Theorem and the Frobenius Theorem for differential equations.

How to prove that a compact set in a Hausdorff topological space is closed?

A simple way to obtain $\prod_{p\in\mathbb{P}}\frac{1}{1-p^{-s}}=\sum_{n=1}^{\infty}\frac{1}{n^s}$.

Prove that $2018^{2019}> 2019^{2018}$ without induction, without Newton's binomial formula and without Calculus.

The problem of the most visited point.

What distinguishes measure theory and probability theory?

List videos of interesting courses at the doctoral level.

Why 'closed differential forms' are called 'closed'?

Minimax Theorems V.S. Fixed Point Theorems.

Intuitive explanation of Residue theorem in Complex Analysis [duplicate]

An accessible reference to proof of Nachbin's theorem

How do I prove that the second derivative of a function $f:M\to\mathbb{R}$ defined on a surface $M\subset\mathbb{R}^n$ is well defined?

A Lipschitz Implicit Function Theorem.

On convergence of nets in a topological space

It is possible to prove the existence of Gibbs measures using the Kolmogorov extension theorem?

On a topological proof of the infinitude of prime numbers.

A general definition of symmetry in mathematics

Percolation and number of phases in the 2D Ising model.

Proof of the infinitude of primes by probabilistic methods.

Number of circuits that surround the square.

Brouwer's fixed point theorem and continuous functional dependence on the fixed point.

Doubt about a passage on page 24 of the Evans Partial Differential Equations book

There are open sets $U$ and $V$ such that $U\cap V = \emptyset $ and $ U \cap \tau(V) =\emptyset $?

Calculating the convex conjugate of the function $f(x)=\lim_{n\to \infty}\left(-\frac{1}{n}\log \sum_{k=1}^n e^{a_k\cdot x+b_k}\right)$.

Algorithm to calculate multiple integral.

Product of two probability kernel is a probability kernel?

It is possible to prove that these two collections generate the same topology on $ \mathbb{X} $?

Puzzle on the triangle.

Two Dimensional Ising Model and Hamiltonian.

Legendre-Fenchel transformation for $\varphi\, \Big(\,x\, ,\, f\,\big(\,\Phi\,(\,x\,)\,\big)\,\Big)$.