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As a grad student (Computer Science), I always feel like I lack the tools needed to make progress with my research. One solution I thought might be helpful would be to take more courses, especially mathematics courses. However, I also feel like of all the courses I have done in undergrad and masters, very little sticks in my mind, and very little is relevant to my actual work. How to decide whether (and which) courses would be a worthwhile investment?

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    Ask your advisor. We have no idea about what you know and what you don't. What insights you have, or lack. Too personal for an answer here.
    – Buffy
    Nov 7 at 19:31
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    Nearly all graduate students have learned to learn outside courses. So courses are not so useful any more. Nov 7 at 19:37
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    @AnonymousPhysicist: I'm not sure I necessarily agree. I remember that I attended a course (more precisely: a lecture for one semester) even several years after I got my PhD, and I also know about experienced professors who sometimes do so when they want to learn about a specific topic. Of course, there are also other ways for experienced people to learn, but I think one shouldn't underestimate the efficiency and clarity of a good lecture compared to, say, self-studying a book. (Context: my field is maths, mostly functional analysis and operator theory.) Nov 7 at 20:00
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In my experience, in mathematics, in the U.S., a course's instructor matters enormously, probably decisively.

I was never a fan of going to sit on a hard chair at pre-ordained times to hear a monotone, flawed recapitulation of a small snippet of what was in a book that I'd already read. Yes, that sort of class can benefit people who would otherwise not read the book at all, passively absorbing something by sitting in the room.

In some cases a course/instructor covers material that is simply not available anywhere else, etc. If it's of interest, that can be great...

And, sometimes, an instructor's viewpoint on even seemingly mundane things can be very, very insightful, far beyond very-conventional textbooks. This can be not only profoundly informative but inspirational.

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