How to Remain Competitive at a Mediocre University? I am attending a university with a mediocre mathematics department. The courses at my school cover fewer topics and are less challenging than the same courses at top universities.


How can I avoid becoming behind in coursework compared to students at top universities?
How can I ensure that I am competitive when applying to mathematics graduate school?
Read as many mathematics books, lecture-notes, and published articles as possible. Not just "textbooks". Not just "undergraduate textbooks" as these contain very little substantive mathematics.

Even if your faculty people are not stellar mathematicians, they surely know some advanced mathematics and can give you guidance about what to read. Uninformed self-study can be a huge time-waster so you will want some direction to be productive and your mathematics faculty will be the best &amp; most available people to provide you with productive guidance.

Definitely talk to faculty to get guidance! This can be done officially through a "reading course" or "directed study." It can also be done informally through frequent check-ins with interesting questions. Either way this will enable those faculty members to write excellent letters of recommendation about your interest and motivation based on your capacity to appreciate the things you will have read and your perceptive questions.

It's not so much whether you (as a novice) can handle random questions, which novices rarely can, but whether your sensibilities are heading in the right direction, which would be manifest in your reaction to substantial mathematics.