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I'm in my first year as a grad student in math at a large university in the US. For the moment I'm just taking classes, all of which have weekly problem sets which take a ton of time to complete in full. I have carried over the mentality from undergrad where I try to complete all the problems in the problem sets, and at least put in a significant amount of effort on each problem. However, this is taking up enough time that I haven't had much of an opportunity to do math things outside of the class (stuff like attending seminars, trying to read papers, pursuing interesting subjects brought up briefly in class in more depth, etc). Because of this, I've been contemplating taking less time on my problem sets, but I have a few questions about potentially receiving lower grades:

First, is it common for math programs in the US to kick out students for getting low (but not failing) grades? I can't find any official policy from my program and I don't feel comfortable asking anyone. A friend in a different subject said that his program regularly kicks out students in the first couple years even if they pass or are on track to pass their qualifying exams in time, but I'm not sure if this is done in math.

Also, aside from getting kicked out, what are the negative consequences to receiving a low grade? (in a class which is not particularly close to the area I think I want to do research in)

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    Many phd programs would require a GPA well above failing: a B- or a C. Aside from that, you risk not getting prepared well enough for your quals, and making a poor impression on possible future committee members, advisors, and letter writers. You learn a lot by solving problems, and I think it is better for you if you put in the work. Also, math is interconnected enough, that you should not brush off a strong background in the basic subjects. – Sasho Nikolov Oct 18 '14 at 0:56
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    What do you have in mind as a "low grade"? In my department, an A- is fine for a grad student, a B looks worrisome (so you'd better not get too many), and a C is a disaster. But this may vary between departments, so you'll need to calibrate for your own situation. – Anonymous Mathematician Oct 18 '14 at 1:06
  • It's a competitive environment. You don't want to be the weakest link. Receiving a low grade in a course is not the worst thing (but why is this happening?). Ideally, you are presenting yourself as someone that a faculty member wants to mentor. – David Hill Oct 18 '14 at 1:07
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    In my experience, each letter grade in a graduate class represents two letter grades in a comparable undergrad class. So a B in a grad-level class means the same thing as a C or D in an undergrad-level class: Acceptable, but below average. A C in a grad-level class is essentially failure. – JeffE Oct 18 '14 at 1:47
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    I definitely know of departments that would take action if you have a single C. You might be dismissed or put on some kind of probation (e.g. asked to retake the course with the condition that you must achieve a higher grade to continue in the program). – Sasho Nikolov Oct 18 '14 at 6:22
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In many (US, mathematics) graduate programs, there is quite significant grade inflation. A grade of B would raise significant concern about your progress (and maybe cause advisors to think twice about working with you), and a grade of C would create grave doubts about your ability to continue in the program. You may have a better sense if this is true in your program, but if so, it would be a really bad idea to reduce your efforts to the extent that your grades drop.

On the flip side, it is entirely possible that you could work a little less hard and still get A's (the standards for an A may be lower than you think). I hesitate to recommend this, though. The better you know this material, the easier your qualifying exams will be, and failing exams definitely gets students kicked out. Solving all the problems on all the problem sets is a really good idea in that direction - rather than worrying about how much time it takes you, you should perhaps rather be glad that you can do it at all (I bet many of your classmates cannot).

Mathematics is unlike some other fields in that (US, PhD) graduate programs place a strong emphasis on coursework for the first couple of years. A transition to research comes afterwards. In many cases you cannot meaningfully discuss a research topic with a potential advisor until you have mastered the material from a course. So it probably is in your long-term interest to prioritize your coursework now, even if some of your deeper mathematical interests are temporarily pushed to the back burner. (Don't worry, they'll still be there after you pass your exams.)

It is good to spend at least a little time on pursuits outside coursework, and you can probably find some combination giving maximum payoff for minimum commitment. For instance, attending seminars is good exposure to current research areas, and may require only an hour or two of your time per week. (Protip: try to go to dinner with the speaker. It's good networking, and your department may well pay for your meal (free food)).

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