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I just completed advanced linear algebra (fundamental theorem, isomorphisms, principal axis, shurs theorem, spectral theorems, gram schmidt, SVD, quadratic forms, etc), and got between 55-60. Now this course is known for being tough: it often has a 20-25% failure rate and a class average in the low, low 60s (which is barely a C by Canadian scales).

I didn't manage my time properly and didn't study for a big chapter on applications (SVD, linear regression, minimization). To my bad luck, 30% or more of the final exam was based on those bits. If I had ground out an hour or two of practice computation questions I would have had a 70 in the course at the very least.

Luckily, my gpa is measured by percentage: It will only go down by 1% this term by my current estimate since I got an 89 in quantum physics 1, and I have the ability to raise it to somewhere in the 80s by the time i am applying to grad schools (which is enough for the schools I'm interested in according to most professors and students I talk to).

My main question is: Should I retake lin alg next term and try to get an 80+? I understand the content of the course on the pure math side, and I can almost definitely succeed in the following math courses. I just don't know whether it will look better to retake a course, or to go on and take the next one regardless.

Thanks for any advice!