maintaining atmosperic pressure on mars how would mankind be able to maintain an earth like atmospheric pressure on mars since mars only has 1/3rd the mass? I am not, nor have i ever attended college, but am very curious.
 A: The basic principle is clear - the extent of the atmosphere would just extend to a higher altitude.  
In order to treat this as a physics problem, let us contemplate a terraforming situation where the surface pressure of Mars is equal to the surface sea-level pressure on Earth.  This isn't actually necessary, and we would design it to be lower in order to conserve resources.
Compared to Earth, Mars has lower gravity.  This means that the pressure drops less over the same height.  I can write the relevant equation as such:
$$ \frac{ dP}{dh} = - \rho g $$
If we assume the atmosphere to be an ideal gas, constant composition, and constant temperature, then we can substitute with the ideal gas law.
$$ \rho \approx \frac{ P }{ R_{specific} T } \\
 \frac{ dP}{dh} = - P \frac{ g }{ R_{specific} T } $$
This tells us that atmospheric pressure decreases exponentially with increasing altitude.  This is the best general "toy" model for us to employ.  That also implies that all atmospheres have some non-zero leak rate in practice.  That means that the only relevant question is how much that rate will be.
Alternatively, we can put things in terms of gravitational potential.
$$ P(h) = P_0 e^{-h g / (R_{specific} T)} \\
P(h) = P_0 e^{-U(h) / (R_{specific} T)} $$
Where $U(h)=hg$ is normally an appropriate approximation for the potential difference, where h is the altitude relative to sea-level.  If you go from sea-level to space itself, the quantity is $GM/R$, from Newtonian gravity.
Plug the numbers in for the specific planets, and the parameters for our atmosphere, and you can get the "back pressure" needed from space in order to maintain the atmosphere... in the continuum model.
An accurate temperature would be more like 1,000 Kelvin for the exosphere, which is what matters.  Even with that number, you find that Mars' atmosphere almost completely terminates at the point that you leave its gravity well.  The pressure ratio calculated above is something like $10^{-20}$.  Accumulated over millions of years, however, that may still lead to loss of a good deal of atmosphere.
In practical terms, the mechanism is different.  Particles at the top of the atmosphere get hit by high-energy particles from the sun, and it "boils" off in this way.  Since those energies are much higher than the bulk atmosphere, this means that the above calculation is too conservative.
So it's not so-much about the gas continuum (although that is a part), but escape of individual particles.  A mathematical treatment more along those lines is given here:
http://terraformers.info/escape.html
You can see that Earth is just above the threshold for containing Hydrogen particles that get hit by space radiation over the long-term.  However, for mankind's purposes, millions of years is possibly sufficient, and Mars can clearly contain a breathable atmosphere over that time frame.
