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For example, I am considering taking a proof-based linear algebra course that caters to math majors, when I could be doing a much lighter class focusing on applications rather than proofs.

Do graduate admissions look at your courses close enough to evaluate the difficulty of each one? To make things worse, not all more difficult classes explicitly say "honors" or emphasize that it is more difficult through the title.

Will graduate admissions care enough to look at it closely?

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    Based on what others have said, some universities ask which textbooks were used in your classes.
    – mkennedy
    Dec 5, 2016 at 3:38
  • @mkennedy Both classes use the same textbook at my school....
    – 123movies
    Dec 5, 2016 at 21:11

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When it comes to linear algebra, there are two basic types of course, proof-based and more cookbook, that just goes through the procedures, manipulating matrices, finding eigenvalues, and so on. (As you described in your question.) I can't say whether a graduate admissions committee would care which you took, because:

  1. It depends on what field you are applying for. For example, if you are pre-med, no one will care if you can write a proof.

  2. It depends on the approach of the university you are applying to.

However, I can answer a similar, related question:

How do colleges and universities evaluate the two types of linear algebra classes when making transfer credit decisions?

In this case, there is a clear distinction between the two. If you took your linear algebra at College A, the institution you are transferring into, call it College B, will look at A's course description carefully. If the course you took at A was primarily procedural, you won't get credit for B's proof-based course. And if they don't have a procedural version, it will just come in as an unspecified elective.

Please feel free to specify your field and a particular university you wish to apply to. No guarantees, but that might help you get a more useful answer.

Editorial notes (feel free to ignore): if you're interested in doing research in STEM, unless the proof-based course is very badly taught, you'd get much more out of taking that one -- even if you don't end up with an A. Proofs are like green leafy vegetables -- they're good for you! On the other hand, there are no prizes given out for completing a Bachelor's degree in record time. Linear algebra with proofs is an important foundational course and deserves to be savored.

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  • @A_Happy_Student First, you can study hard to get an A in an advanced class. Second, if you want to compete with other students applying MIT or other good schools, you better have an A in advanced linear algebra.
    – Nobody
    Dec 5, 2016 at 4:31
  • @scaaahu I am already studying hard and beginning to drown. I will do my best but I'm just curious of how it will be perceived... And of course there is the chance that I don't do well. Is it worth the risk or better to just do better in an easier applied class?
    – 123movies
    Dec 5, 2016 at 4:34
  • @A_Happy_Student If you just want to go to some mediocre schools, you don't need to take advanced class. But, I thought you want to apply to MIT, then, yes, advanced, proof based linear algebra is a must.
    – Nobody
    Dec 5, 2016 at 4:49
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    "I am already studying hard and beginning to drown" -- The last year is often the hardest. See if you can spread things out a bit. Consider taking something over winter term, consider summer study, and consider taking an extra semester to finish. Linear Algebra with proofs is a great course for increasing one's mathematical maturity. It's like Popeye building muscle fast with a can of spinach. It will stand you in good stead in the long run, in any STEM field of graduate study. But it's not a class to take when you have more than 12 OTHER credits in your schedule. In my opinion. Dec 5, 2016 at 17:38
  • You've heard two opinions -- now it's time to reflect, on your own. At the end of the day, it's a very personal decision. Dec 5, 2016 at 17:39

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