I will be attending a top public university beginning this fall that houses a very reputable mathematics department. However, I will have to attend for one year before I apply to transfer into said dept.

For that year, I will be studying Philosophy. But having been a math major at my prior institute, I've already finished the Calc sequence and taken some upper division math courses (DiffEQ, Intro to Proofs, Intro to Real Analysis, Numerical Methods). The problem arises in that the important courses that my new math dept offers are usually restricted to math majors, and no one else.

Luckily, I did get into one open, upper-division course for the fall called Theory of Functions of a Complex Variable, but the other one I tried to get into, Linear Algebra and Matrix Theory, is one of the restricted courses. So, alternatively, I registered for a different courses called Matricies and Matrix Calculations which, judging by the description, sounds like a linear algebra course for non-math majors.

My question is, will the lack of the Matrix Theory course come back to bite me later on? I absolutely loved Intro to Proofs and Intro to Real while I was indifferent about Numerical, so my mind thus far has been shifted towards the pure math track. I do know that can change and I'm still brand new, but it's still a bit concerning.

Extra question to those involved in similar math departments - how would you react if a student from a different major in a different college approached you about joining a restricted mathematics course? Would I be an exception since I'm planning to transfer as soon as possible? Would that be a complete waste of time?

TL;DR: Overall, I am really just wondering if I will be fine if stick to the non-math majors Linear Algebra or if I should try like hell to get into the restricted Matrix Theory Linear Algebra (if possible).