Comments on: “Fundamental” Theorems

By: Walt

Walt — Wed, 15 Aug 2007 14:54:45 +0000

I think the companies that write spamming software have rolled out new versions. The spamming strategies have changed in a way that lets more slip past Akismet.

By: John Armstrong

John Armstrong — Wed, 15 Aug 2007 12:01:24 +0000

hmm.. well that last spam just bombed.

By: sundar

sundar — Sat, 03 Mar 2007 12:05:54 +0000

Lebesgue dominated convergence theorem

By: Ars Mathematica » Blog Archive » Lax Attack

Ars Mathematica » Blog Archive » Lax Attack — Fri, 15 Jul 2005 18:44:59 +0000

[...] Last week, when Michael asked for a list of fundamental theorems in different branches of mathematics, “>Juan de Mairena suggested the Lax Equivalence Theorem as a candidate. Today on ArXiv I spotted a paper that makes the rather dramatic claim that the theorem is “wrong” — not that it is wrong in the strict mathematical sense, but that its conditions are not realistic for real-world problems. I’m not in a position to evaluate the claim (I never even heard of the result until Juan’s comment), but I thought it was interesting to see a paper on the subject so soon after we discussed it. [...]

By: demairena

demairena — Sun, 03 Jul 2005 15:43:04 +0000

I just found a different proof of Lax E.Thm., by using Fourier methods:
http://www.acm.caltech.edu/~acm210/2005/WINTER/week3.pdf

By: sigfpe

sigfpe — Sun, 03 Jul 2005 15:35:11 +0000

Theoretical Physics: Noether’s Theorem (symmetries give rise to conservation laws)

By: demairena

demairena — Sun, 03 Jul 2005 15:25:00 +0000

Lax Equiv. Thm: a consistent finite difference scheme for a well posed initial value problem is convergent if and only if it is stable.
Is a very deep theorem, which follows from the Uniform boundedness principle.

By the way, Lax won the Abel Prize this year: http://www.abelprisen.no/en/prisvinnere/2005/documents/abelprize_2005_EN.pdf , (previously, Jean-Pierre Serre in 2003, and MF Atiyah and IM Singer in 2004)

By: Megan

Megan — Sun, 03 Jul 2005 06:26:43 +0000

Graph Theory: Menger’s Theorem.

Let G be a graph and A, B be vertices in G. Then the minimum number of vertices separating A from B in G is equal to the maximum number of A-B disjoint paths in G.

There are three proofs available in Diestel.

Also Number Theory (and my favorite): There are infinitely many primes…

By: Walt

Walt — Sun, 03 Jul 2005 06:17:03 +0000

What is the Lax equivalence theorem?

By: demairena

demairena — Sat, 02 Jul 2005 13:18:51 +0000

Functional Analysis: Hanh- Banach’s Theorem.

Numerical Analysis (PDE): Lax equivalence Theorem.