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I just finished my 3rd year in a combined pure/applied math program at a Canadian university. I have been leaning towards pure math, but I'm not sure if I'll have done enough to go to grad school for it. I've taken Real Analysis (single-variable, metric spaces, basic function spaces and topology), a standard course in complex analysis, and an introductory abstract algebra course (mostly rings and fields). I've also of course done the basics in single/multivariable calculus, linear algebra, probability, and ODES. Next year I was planning on taking measure theory, general topology, mathematical logic, and group theory, as well as some applied courses. In addition I'm planning on working through Munkres' Analysis on Manifolds this summer.

Will this suffice for grad school, or do I need more higher-level courses? Also, I've never written the Putnam or any other contests, or did research. I'm probably not going for top grad schools, but would an average school admit someone on the basis of coursework, or do they expect more evidence of research potential?

EDIT: My question is specifically about my math background and math grad school, I don't see how this is really answered by the other question.

Tim
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    Your backgound looks fine to me. It depends on how well you know this material and how much rigorous mathematics appeals to you. It's an important question for you, and it would be good to ask questions of your faculty on this. Letters of recommendation will be very important if you apply to a good school. –  May 02 '15 at 20:09
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    Regarding your request for a more personalized assessment: only somebody who knows very well both you, your situation, and the situation of the departments that you are applying to will be able to give you a more precise answer than the linked question. Such highly personalized assessments do not fit well with the SE model of reusable questions and answers. – jakebeal May 03 '15 at 19:43

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