Module I - Calculus Basic calculus, Euclidean space, implicit functions and their derivatives, ordinary differential equations.
 

Module II - Linear Algebra Systems of linear equations, vector spaces and subspaces, linear transformations and matrix representation.
 

Module III - Probability Covering probability spaces, random variables, independence and conditioning, conditional expectation as best estimator, law of large number, central limit theorem.

Module IV - Optimisation Covering quadratic forms and their signs, unconstrained optimisation, constrained optimisation.