This course is designed to enhance the undergraduate study of linear algebra as the theory of vector spaces. In this course we view vector spaces as a specific part of the more general theory of R-modules. The course begins with a treatment of the basic properties and characteristics of these structures, and introduces the beginnings of category theory. We then consider vector spaces and introduce K-algebras – specifically the tensor, symmetric and exterior algebras. The course culminates in a proof of the fundamental theorem of finitely generated PIDs, and we consider the applications of this theorem to both group theory and to linear transformations.
- Teacher: Ramanuja Rao