The following are assumed to be familiar to the reader:

The symbols of set theory: ∈, ⊂, ⋃, ⋂. The Cartesian product of two sets: E × F = {(e,f):e ∈ E, f ∈ F}. The idea of a map, its source and target; injective, surjective, and bijective maps. Equivalence relations.

Elementary theorems of analysis: the notions of derivative, partial derivative, integral. Differentiation of the composition of functions. Taylor series. The existence and uniqueness of solutions of a system of differential equations.

The rudiments of linear and multilinear algebra: real vector space, linear map, rank of a linear map, determinant, linear functional, dual vector space, transpose of a map. Exterior derivative and exterior product.