Among other courses, I'm teaching a (basic) matrix algebra course for 1st year university students (they are studying Economics, and the cursus leads them to management, finance, or econometrics in 3rd univ year).
As it's quite common in France, these notions are taught in a rather abstract way, we teach them: matrix operations, determinants, rank, matrix equivalence, row echelon form, application to linear systems, optimum of functions, etc. (but not eigenvalues/vectors, this is done the next year).
It's a ~ 40-hour course in a semester, I have ~ 40 students per group, and I'm doing nearly 1/3 theory, 2/3 training exercises during these 40 hours.
The problem: even if 1) it works quite well after a few years teaching this course 2) noone complains 3) these notions are important for them for their following years (econometrics, they will also learn R, etc.), I feel the course is a bit "too abstract" / not enough connected to applications and not pro-active enough for them.
Idea: I would like to test something like that:
Do the usual 40 hours in ~ 34 hours (I can reduce the number of exercices of 20% more or less)
In the 6 remaining hours, I'd like to test something more active for them, more project based, example:
- First 1.5hr sequence: I present the project briefly, and give "topics", they start working in ~8 groups of 5 students
- Homework: they do some research on their "project"
- Second 1.5hr sequence: they continue their research, I help them / answer questions, give them directions if needed, they bring books from university library + their laptop to find additional resources
- Third 1.5hr sequence: half of the groups do a presentation of their "project"
- Fourth 1.5hr sequence: the other groups do the same
- Have you done such "project based" courses for university students? Any feedback?
The biggest question: what kind of math project could they work on? (using some matrix/linear algebra). I have a few ideas (see here for example, I used some of them for 3rd year students), but nearly all of these applications are too complex for students studying matrices for the first year.
What kind of setup would you use? Provided they are econ students, I was thinking about taking business-related examples.