Differential algebra is the study of differential equations and operators as algebraic objects, using polynomial algebras to study solution sets of systems of polynomial equations. It includes Weyl algebras and Lie algebras, and is based on the theory introduced by Joseph Ritt in 1950. Examples of differential fields include the field of rational functions in one variable over the complex numbers, where the derivation is differentiation with respect to the variable.

This course explores the relationship between algebra and computation, focusing on algorithms used for symbolic computation and modern algebra concepts. Subjects covered include proving combinatorial identities, Gröbner bases, symbolic integration, and experimental mathematics. Prerequisites suggest this is a mid-level course.