I know desktop hardware and I need to understand the differences in computing
power i.e.  between a Intel 1.7 centrino processor,a Pentium M- mobile
2.8 processor,AMD  M 3000 processor all compared performance wise to
an
an Intel Pentium 4 3.0 processor . The criteria should be
graphics,gaming,engineering and mathematical computation power

There is no Pentium M at 2.8 ghz,  there is only the Pentium 4 M at
2.8.  :)  I have a 1.7 Ghz Pentium M in my laptop with a ATI File GL
TL2.  I can play pretty much any game.  I'm also a aerospace engineer
graduate student, I would never dream of running anything
computational on this processor - it would just take to much time. 
I'm sure that some small simple engineering applications can run on
it.  As far as graphics - I would say that most important thing is
your GPU, not your Processor.

Just my two cent comment.

The Centrino processors have a larger than normal on-board cache and
use a improved speed technology - I think it's called Speedstep. This
make them quite fast and power saving but they can't out perform
desktop proccesors.

The P4 M is a bit of a mystery to me. I know that the Athlon mobiles
have built in technology to slow the clockspeed when not needed to
save battery power - perhaps the P4 M uses this as well ?

As said before the 3000+ M reduces clock speed when it's not needed.
That's the only difference from a desktop machine.

On a power skale the P4 and Athlon would be about equal, the P4 M a
close second and the Centrino a bit further behind.

As saem_aero-ga a GPU is the most important thing for games, and the
difference for a game when using the same graphics card and any one of
these processors will only be a couple of FPS. The Centrino is fine
for this but would fall behind on heavy maths work.