For starters, torque is the number that directly correlates to acceleration (modulo gearing, which is explained well by furtive's link) . Shifting just when you reach your max torque means you're forgoing the region just above that when you're still getting good acceleration out of your car.

To an approximation, your car's velocity has a lot to do with the integral under the torque curve (as experienced by the wheels, not the engine). If you could plot the torque curves in each gear, where the X-axis is the car's velocity, the ideal shift point would be when the torque curves intersect. That would maximize the integral under the extended curve.

Of course, there are other tricks to getting a good 0-60 time that mostly involve destroying your transmission, clutch, and tires. From a lecture I saw recently on the mathematics of drag racing (an absolute blast, BTW), you get your maximum acceleration out of a tire when it's just starting to slip. To do that, you need lots of torque, which is hard to develop when your engine is still revving low. Solution? Rev high and slip the clutch.