If you already have several advanced math courses (w/ good grades) on your transcript, then B would be the most useful. Though, you should know the material from Axler very well if you intend on doing anything that requires advanced econometrics.
I have a couple of choices of linear algebra courses to take.
- A is standard linear algebra course, uses Strang's Intro to Linear Algebra (should give context on the material)
- B is computational linear algebra, ie it has a focus on computational applications, MATLAB programming, etc. It covers the same material as course A in a sense, but probably with less focus on the theory.
- C is proof-based, abstract linear algebra, uses Linear Algebra Done Right as a textbook (for context on the material). Known to be the hardest of the three.
B seems more helpful towards possible research work, as it provides experience with computational methods that could be useful in doing RA work (and also in applying to pre-doctoral RA positions, which I'm considering). C seems the most helpful for signalling, but I don't know how valuable linear algebra is as a signal compared to other math courses (I've heard it's not) and the potential grade hit/opportunity cost may not be worth it. A is probably the least work and maximizes probability of a good grade while giving me time to focus on other math courses. Which should I take?
Of course you do. The highlights of Axler's book will be taught in most econometrics sequences. What I meant is that you should take the advanced linear algebra course if your anticipated research area requires knowledge of theoretical econometrics, for example financial econometrics or structural IO. If you are interested in mostly reduced-form micro (development, health, labor, public, etc.), then a less advanced linear algebra course would probably be fine preparation.
I guess A would be fine. You could (should?) learn the content in B in a separate numerical analysis course. I'm not sure what the value added of taking C is over A, considering adcoms may not be familiar with the fact that it is more proof-based than A (unless the name of the course is something like "Honors Linear Algebra").
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