On the benefits of retaking advanced linear algebra

[mcabbage]

I'm a physics student who has the option to take some advanced math courses (Real analysis through Rudin and beyond, functional analysis if I have time, as well as algebra through Artin). I'm only just going into my second year this term, and will either be retaking linear algebra 2, or taking group theory.

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!

 

[FactChecker]

My two cents: Learn the material you were weak on by self-study and move on. But do not cut corners in understanding linear algebra. It is fundamental.

 

[fresh_42]

All are important for physicists:

• real analysis
• functional analysis
• linear algebra 2

Group theory is a bit different. Beside the easy examples $\mathbb{Z}\; , \;\mathbb{Z}_2\; , \;(\mathbb{R},+)\; , \;\mathcal{Sym}(n)$ it are mainly the linear groups which are used in physics. But group theory often means theory of finite groups, and detailed knowledge about them is rarely required for a physicist. So if it was a lecture about linear group, geometric groups, algebraic groups or how ever the subgroups of $GL(n,\mathbb{F})$ are called, I would answer: good idea. But the few occasions you really need classical group theory in physics can be learned on demand (IMO) - orbit-stabilizer formula, normal subgroups, center, isomorphism theorems.