Real analysis: inequalities, the continuum property, induction, sequences, functions and limits, continuity, contraction mappings and fixed points, differentiation, mean value theorems and Taylor's ...

Properties of the real numbers, infimum and supremum of sets. Numerical sequences and series. Limits of functions, continuous functions, intermediate value theorem, uniform continuity. Differentiation ...

Linear algebra: matrices and vectors; eigenvalue problems; matrix diagonalisation; vector spaces; transformation of basis; rotation matrices; tensors; Lie groups ...