Vector spaces are mathematical structures that allow for the manipulation of vectors. Examples of vector spaces include Euclidean space, polynomial space, and function space. Vector spaces are defined by a field, such as the real numbers, and a set of axioms. They can be used to represent linear transformations and solve linear equations.

This course provides an initial dive into complexity theory, exploring computations bound by resources like time, space, and energy. Emphasis is placed on low complexity classes.