Linear algebra has become the most important subject in college mathematics in the 21st century. Mastery of linear algebra concepts and techniques is essential for advanced study in computing, engineering, sciences, and statistics. Linear algebra also introduces students to abstraction and simple proofs.

Since I’ve decided to convert my linear algebra course to the flipped model, this is a perfect opportunity to self-reflect and bring the course design to the best modern practices and expectations. Luckily, we can stand on the shoulders of giants. In 2015, MAA published an updated version of the CUPM Curriculum Guide to Majors in the Mathematical Sciences. Among other things, this guide includes specific recommendations on the linear algebra curriculum. It is these recommendations that I plan to implement in the redesigned linear algebra course.

On a macro level, a first course in linear algebra should allow students to link application and theory, use technology effectively both to solve problems and explore ideas, and compare analytical, visual, and numerical perspectives in exploring mathematics. Such a course should cover foundational topics in linear algebra with applications and integrate the use of software within the topics and applications

I have formulated three majors goals for my new linear algebra course:

- The students should be able to read, understand, and create (simple) mathematical proofs
- The student should be able to use the methods and techniques of linear algebra to solve applied problems
- The students should be able to use modern software to solve linear algebra problems numerically

In the next post, I will discuss what topics I’m planning to include in my linear algebra course. The list of recommended core topics is available in the 2015 CUPM Curriculum Guide to Majors in the Mathematical Sciences, but several topics are marked as optional because it might be difficult to cover everything in one semester.