35
votes
5answers
1k views

Understanding the Laplace operator conceptually

The Laplace operator: those of you who now understand it, how would you explain what it "does" conceptually? How do you wish you had been taught it? Any good essays (combining both history and ...
4
votes
2answers
244 views

What is elliptic bootstrapping?

While reading about elliptic differential operators, I have seen the phrase elliptic bootstrapping in several places, but none of them explain exactly what it means. I know it has something to do with ...
46
votes
5answers
4k views

Exterior Derivative vs. Covariant Derivative vs. Lie Derivative

In differential geometry, there are several notions of differentiation, namely: Exterior Derivative, $d$ Covariant Derivative/Connection, $\nabla$ Lie Derivative, $\mathcal{L}$. I have listed them ...
9
votes
3answers
894 views

Detailed diagram with mathematical fields of study

Some time ago, I was searching for a detailed diagram with mathematical fields of study the nearest one I could find is in this file, second page. I want something that shows information like: ...
25
votes
3answers
914 views

Rejecting infinity

I've heard about mathematicians who defend a strictly finite conception of mathematics, with no room for infinity. I wonder, how is it possible for these people to do this? Are there any concepts that ...