# At what point in the curriculum should the tensor product be introduced?

I remember my linear algebra teacher mentioning tensor products as an advanced topic that would be covered in upper level algebra coursework. During undergraduate abstract algebra, tensor products were not mentioned. Later, my graduate algebra professor told me that the tensor product was required background knowledge that I should have learned in linear algebra. Ultimately, I ended up learning the tensor product in a special topics course in the physics department.

Several of my classmates who had attended different undergraduate institutions reported similar experiences. From my limited polling, this seems to imply that the tensor product has proven difficult to position within a conventional mathematics curriculum.

At what point during a mathematics degree should the tensor product be introduced?

• I've worked it into linear algebra once or twice. However, I have a proof prerequisite for my Junior level linear course. Even so, honestly, as much as I love $\otimes$, it is a bit much in linear. In a second course of theoretical linear algebra or Algebra II it makes more sense. Personally, I saw them concretely represented in my differential geometry and manifold theory coursework. They could be covered any time after abstract algebra has been covered. I would wager the vast majority of undergrad programs in the US fail to cover this topic. – James S. Cook Dec 19 '18 at 21:05