How is the relationship of acceleration to mass and force expressed mathematically

This is a case of Newton's Second Law of motion.

Mass is inversely proportional to the acceleration. And acceleration is inversely proportional to the mass of the object. The net force is the product of mass and acceleration.
Remember that your frame of reference must be an initial frame of reference which has no other accelerations acting on the object. For example the acceleration of our planet through the galaxy and therefore its acceleration through the universe. This is a reason we cannot prove Newton's second law of motion. Hope that it helped.