Graduate coursework for graduate admissions I’m a rising senior in a mathematics program, and I’m planning to apply to top US schools in maths in the fall. I’ve completed most of my undergrad coursework requirements, and I’m looking into what I should take for the fall.
I have a choice between Graduate Analysis I or Undergraduate Complex Analysis. Now, I find both of these to be very interesting, but what do graduate schools think when they look at my transcript? Will it be more advantageous to have the graduate course listed on there?
If I take the graduate course, it’ll also open up the sequel Graduate Analysis II in the winter.
The answer strongly depends on the programs you apply for. As a very general statement, I would say that getting a good grade on a more advanced/challenging graduate class is better than getting a good grade on an undergraduate class.
Grad classes carry several benefits in terms of the signal they send to prospective admission committees. First of all, they show that you are ready to handle independent studies and the advanced material that is given in these classes. Moreover, graduate classes tend to be smaller and offer more intimate interaction with the lecturer on a topic that they care deeply about (they probably involve their own research papers in the class) - this means you get the opportunity to receive a good reference letter from someone who can personally attest to your capability to handle graduate level material.
All of this is premised on the assumption that you can get a similar grade on both - failing (or barely passing) a graduate class sends a very bad signal to admission committees, as opposed to doing well on an undergraduate class.
So - be sure that you are indeed ready for the class, and the types of materials covered there. Good luck!