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I am currently taking graduate algebra as an undergraduate (junior) in University of Toronto Mathematics Specialist, and I just took a midterm today. Since I am an undergraduate, the grade matters. In order to get a good chance to go into graduate schools for Math in Canada and USA, do I need to get a A or A+ in graduate courses as an undergraduate? Or, is A– alright? (In my university, C and below are considered fail for graduate courses only) Or should I get at least an average grade on that course as an undergraduate competing with graduate students, instead of worrying about actual letter grade? (this is about absolute vs relative too)

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Not sure what type of answer you're looking for. You should do the best you can, the same as with any class you take. Why would the fact that it's a graduate-level class make a difference in your work ethic? – eykanal♦ Oct 23 '12 at 20:52
I am working hard, but then I typically so called "ace" (but not really) in undergraduate math (getting A+), but graduate courses have many smart people in class, and I do not think I got way above average grade for midterm in grad courses (as I am competing with masters and PhDs). Since I am undergraduate, all grades are important, instead of just aiming for A-s (this is all that is required for masters and PhDs), I am not sure how much grade is ideal as an undergraduate to get out of graduate course (also this will help me decide whether to drop course or not (but I prefer not dropping it)) – chhan92 Oct 23 '12 at 20:55
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You'd be surprised how many undergrads outperform the grads in my classes. – Suresh Oct 23 '12 at 21:01
If you are willing to share, can I ask which university/collge are you attending? – chhan92 Oct 23 '12 at 21:30
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Suresh is a prof. So am I; my experience is similar to his. – JeffE Oct 23 '12 at 23:08

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In order to get a good chance to go into graduate schools for Math in Canada and USA, do I need to get a A or A+ in graduate courses as an undergraduate?

I don't think anyone cares too much about the distinction between A and A+, since the standards for what merits an A+ vary so much between universities or even individual professors.

Or, is A– alright?

This is a little more meaningful, but it's not likely to be the deciding factor. If you have a great application otherwise, nobody will care about an A- or two. If your application is not so compelling, getting straight A's won't help much. This could make a difference, but it's really a low-order effect.

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Speaking as someone who regularly serves on admissions committees, I'd much rather see a B- in a graduate course than no graduate courses at all. – JeffE Oct 24 '12 at 1:06
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@JeffE: Hmm, I'm not sure. Not taking any grad classes is certainly a red flag, and I'd agree with you if you said B+, but B- is more questionable. The issue is that math grad students need a solid understanding of the core grad courses, and someone with a B- probably doesn't have that. The question then becomes whether they realize they need to learn this material better and have some likelihood of doing that. Someone mature and responsible enough can handle this, but what I don't want to see is someone saying "OK, I got my B-, so now I can move on and never think about topic X again." – Anonymous Mathematician Oct 24 '12 at 3:06
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someone with a B- probably doesn't have that — But at least they're willing to try, which is more than we can say for someone with no grad classes. Willingness to fail is crucial for good research, and it's much harder to learn than technical background. (Also, this all has to be calibrated by the relative strengths of the undergrad and grad programs at the applicant's school. There are many schools — Toronto is not one of them — where the grad classes are easier than the undergrad classes.) – JeffE Oct 24 '12 at 3:14
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Yeah, that's a good point about willingness to try. If someone enters with an unusually weak background, and they attend a school with a lot of challenging and interesting undergrad classes, then they might reasonably not get to grad classes within four years. However, a typical grad school applicant should have tried grad classes. – Anonymous Mathematician Oct 24 '12 at 3:23
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Just a quick note that the need for graduate courses as an undergraduate varies a lot by field. In math and maybe CS, it's nearly a prerequisite. In engineering, however, because of the relative inflexibility of the program, I don't think taking graduate-level courses is necessarily anticipated or required. It definitely helps, but it doesn't raise red flags if you don't have that experience. – aeismail♦ Oct 24 '12 at 6:18
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