How do graduate schools in Mathematics view advanced graduate courses taken at a less prestigious undergraduate institution?

Question

I am a junior undergraduate at a less prestigious school. I have the option of taking graduate courses. I am sure I won't run out of them. However I am skeptical of how committee especially top graduate schools in Mathematics view the courses taken at an unknown school. In my view these courses are as rigorous as a good school. I do hope to get few letters from instructors of these courses. Are graduate classes viewed equally irrespective of the institution or they won't do any good for my application as I am coming from a unknown school.?

Answer 1

For context: I am a relatively senior faculty member in a math dept at a fairly well-ranked state university in the U.S., ... and have been involved in graduate admissions, advising, etc., for 35+ years.

First, at nearly every (but not every...) U.S. university, the purely undergrad curriculum is a bit lightweight for people wanting to go to a serious graduate program. Thus, to have a more serious-looking undergrad transcript, it is highly desirable to have some "graduate-level courses".

Second, the content and demands of "graduate courses" vary widely. There is no enforcing authority, etc. But, at least, such things explicitly aim to address mathematics for future mathematicians, as opposed to just having some course-of-study for U.S. bachelor's-degree requirements. (Whose breadth is generally a good thing, but whose "major area" requirements are very thin by world-wide standards.)

So, no, taking grad courses at X versus Y are not automatically equivalent. But nevermind about that. Take as many, and as advanced, courses as you have available to you. And reading courses with faculty.