A good overview, but could have used a bit more information. I had to look up some concepts for myself in order to really understand it.
Before getting into the course evaluation: James seems like a well-intentioned instructor and good person who put a lot of work into this course. As a former teacher myself, I know it can be hard to not take criticism personally. So please know that none of what is below is personal.
The course is a series of linear algebra drills with no connection to data science concepts or applications. A data scientist needs to develop a conceptual foundation that helps them **use linear algebra to solve data analysis problems** using programming languages or statistical packages. This is a lofty learning outcome and a big shift away from traditional math education practice, so it would be understandable if a course were to aim for this and come up short.
This course, however, is simply drill and kill math with no clear objective. There was no connection to data science, no demonstration of practical appliations, no focus on higher-level conceptual understandings. Memorizing procedures that in practice are always carried out by computers is only valuable to the people who either will will write code to implement the procedures from scratch or will develop new mathematical procedures entirely. I'm guessing neither of these groups are not the target for this course.
An analogy: Imagine somebody offered a "Thermodynamics for HVAC Technicians" course and then spent weeks on hand calculations of energy transfer or entropy in the abstract. Being able to calculate energy transfer by hand isn't necessary for learning to fix an air conditioner, and being able to calculate eigenvectors by hand isn't necessary for learning to use PCA. The concepts are the point: What data science problem does an eigenvector solve? Why does the eigenvector solve it? How can one make sure they're using the eigenvector effectively in real-world context (in which the eigenvector has been calculated by a computer). As a practicing data scientist who never took a formal linear algebra course before, I can say that I do not know the answer to those questions any more so than before I took this course. That is my biggest disappointment.
A more effective course would start with a data analysis problem, then walk through conceptually what solving it requires, then introduce just enough linear algebra concepts to help the student develop that "under the hood" understanding that allows them to recognize when to apply the solution to other problems and how to do so effectively. Quizzes would then give them an opportunity to do just that.
Perhaps subsequent courses in the series revisit the procedures drilled here and eventually illustrate their application, but it's the application that should be the focus up front, with linear algebra concepts introduced as needed to solve the problems. Hand calculations would be used sparingly if at all just to build conceptual-level understandings. Courses would build up with progressively more challenging data science problems to solve, with each introducing the relevant linear algebra concepts just-in-time to solve the problem.
