The [Riemann curvature tensor](http://en.wikipedia.org/wiki/Riemann_curvature_tensor) can be expressed using the Christoffel symbols like this:

$R^m{}\_{jkl} = \partial\_k\Gamma^m{}\_{lj}
 - \partial\_l\Gamma^m{}\_{kj}
 + \Gamma^m{}\_{ki}\Gamma^i{}\_{lj}
 - \Gamma^m{}\_{li}\Gamma^i{}\_{kj}$

How did they come up with this? What was the idea?

I searched the web but the descriptions I found were too formal, and I was unable to decipher what the author tries to describe. 

So I'm looking for some thoughts or an easy paper I can start from and derive this formula myself.