The branch of mechanics dealing with mathematically describing motion is called kinematics.

Here's a breakdown:

* Mechanics is the study of motion and its causes.

* Kinematics focuses specifically on the *description* of motion, without considering the forces that cause it. It deals with concepts like:

* Displacement: The change in position of an object.

* Velocity: The rate of change of displacement (speed with direction).

* Acceleration: The rate of change of velocity.

* Time: The duration of motion.

In contrast, dynamics is the branch of mechanics that deals with the forces that cause motion.

So, kinematics provides the mathematical framework for understanding *how* things move, while dynamics explains *why* they move.