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This may be a particularly specific question, but I am at a point where I can choose to take additional mathematics courses in the final year of my degree to strengthen my transcript for grad school applications to Computer Science, but I am also able to choose to do an 8 month supervised research/project course (essentially an undergrad capstone/thesis equivalent).

Of course it depends on the schools, but in terms of general grad school admissions, would a personal project that requires a large amount of independent work show more strength than a few additional (but still important, some schools I've looked into list these as preferred prerequisites) math classes?

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    This seems like an important question. I think the results would be the dictating factor (but you cant know it until you try). As in, does your supervised research use some of the math that you should learn in the class but have been able to figure out yourself, or does it result in a publication? Both of these would show to me that a student is capable of research and a fit for graduate school. *Assuming the graduate school you are applying to is for research and not a terminal engineering degree of applied skill.
    – user-2147482637
    Commented Apr 8, 2015 at 0:18
  • The goal of a PhD is to become a successful independent researcher. The admissions committee will be looking for evidence that you are likely to become a successful independent researcher. Actually doing successful independent research provides that evidence. Taking more classes may not.
    – JeffE
    Commented Apr 10, 2015 at 0:32
  • I should have mentioned that I am actually only considering my MSc./5 the moment, however I trust your logic applies the same in both scenarios
    – James
    Commented Apr 10, 2015 at 0:35

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The short answer, at least in my opinion, is definitely to do the independent project if you're considering graduate school. But an important consideration is making sure it contributes to a strong application package.

If you chose to take the additional classes, their grades would be reflected on your transcript and in your GPA, and so there would be an objective measure of how you had mastered their content and in so doing had become a better candidate for admission.

If you do the independent project, you want to consider carefully how its results will be communicated so as to strengthen your application package. You might at some point discuss this with the project supervisor. If publishable output is a possibility, that's great, but I'm assuming that's unlikely. But if things go well (AFTER it's established that things are going well), you should approach your supervisor about providing a reference letter that you can include with your applications. You don't want to just have that project listed in your application alongside all your other classes; you want to be able to demonstrate how doing independent research as an undergrad made you more likely to succeed as a graduate student (thereby making it easier for the admissions committees to justify offering you a place in their incoming class).

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