Noether's Theorem Explained: Symmetric Quantity & Conservation Laws

[unchained1978]

Can someone please explain this theorem to me? From my understanding (which is very limited), the theorem states that for every symmetric quantity, there exists a corresponding conservation law in physics.
First off, I don't entirely understand what constitutes a symmetric quantity. If someone could provide a general definition of what this means I would greatly appreciate it. Also, how is the conservation law derived from said symmetric quantity? i.e. how do you make the leap that because time is symmetric, energy is conserved?

And lastly, how would you prove this theorem? It seems entirely too abstract to be able to apply any mathematical rigor to it.

Any help would be appreciated.

 

[ZapperZ]

Try this:

http://xxx.lanl.gov/abs/physics/9807044

Zz.