Interview: Gilbert Strang on Teaching Matrix Methods

What this lecture covers

This is an interview, not a lecture: Sarah Hansen asks Gilbert Strang about the origins of 18.065 and his decision to teach it through student projects instead of exams. He reflects on how the course differs from a conventional linear algebra class and what he learned from running it this way.

Watching gives you context for the course's structure and philosophy rather than mathematical content: why projects replaced exams, and what Strang sees as his role as an instructor.

Key ideas

• Deep learning's dependence on linear algebra motivated Strang to build a new course around it.
• Projects instead of exams: 18.065 has no final exam; students propose a project by email, work on it independently, and some present it in the final weeks.
• Students often know more than the instructor about their chosen application, which Strang treats as a feature of the format, not a problem.
• Presenting is part of the learning: writing up and presenting a project is treated as valuable as the technical work itself.
• Teaching over grading: Strang states his main job is to teach or learn alongside students, not to grade them.
• Advice for new instructors: don't rush, don't try to cover everything, and stay with the class.

Before you watch

• This video works best after or alongside the course introduction, since it explains why the course is structured around projects rather than exams.

Check your understanding

1. What led Strang to replace exams with a project-based structure in 18.065?
2. How does Strang describe his role as an instructor in relation to grading?
3. What logistical process did students follow to propose and complete their projects?
4. Why does Strang consider project presentations valuable for students?