The goal of this class is to prove that category theory is a powerful language for understanding and formalizing common scientific models. The power of the language will be tested by its ability to penetrate into taken-for-granted ideas, either by exposing existing weaknesses or flaws in our understanding, or by highlighting hidden commonalities across scientific fields.

This is a collection of notes for a one-semester course in linear algebra taught at San Jacinto College (Houston, Texas). The notes are suited for a first course in linear algebra taken by students who have completed one year of single-variable calculus. Unlike most traditional linear algebra textbooks, these notes begin with the ideas of vector spaces and linear functions (transformations). Since functions play a central role in calculus, this approach should seem more natural to students. Systems of linear equations and matrix theory are presented afterward as consequences of the preceding material. The result is an economical (only 175 pages) treatment of the main themes of linear algebra along with a few applications of the theory to geometry, economics, and cryptography.