The brain is a very complex system composed of many interacting elements - proteins, neurons, and different anatomical regions. Understanding of how their interactions give rise to sophisticated functions often requires formal mathematical theory.
Computational neuroscience uses mathematical models to describe and explain the computations in single neurons, networks of neurons, or a whole system.
Close collaboration with experimental neuroscientists provides real biological data to constrain the models. In turn, formalizing theories of brain function by mathematical modelling generates predictions, which can then be tested in experiments.
This area of neuroscience provides a very powerful approach to studying the brain.
Techniques routinely in use include; dynamical systems theory, computer simulations, and machine learning.