Advice for Grad School

• personal

Having been recently offered admission into some amazing math graduate programmes, I just returned from a two-week tour of some great schools all over the US.

Here is a list of advice (or warnings!) for incoming grad students, from current grad students and faculty.

• Learn about other fields: Even if you are interested only in geometry and topology, tools from other areas, such as analysis and algebraic geometry, are surprisingly useful. At some point, the distinction between different fields is unhelpful. Having a solid foundation in a wide variety of fields can reap benefits, which in many cases were only obvious in hindsight.
• But you can’t learn everything: There’s way too much math out there. This requires a change from the undergrad mindset: just because an area of math is there, or just because you’re taking a course on it, is not enough to justify spending time on it.
• Learn top-down: In undergrad, the norm is to build a theory from the ground up, starting with basics and building upwards systematically. To do research, this is not fast enough. A better approach is to begin with eg. a paper you want to understand, and to learn just enough to make it through the paper, filling in gaps along the way.
• Managing time and motivation: Many grad students feel that they could have spent their first year more wisely. Especially for schools with fewer or no required courses, there can be a sense of waking up in the morning not knowing what to do for the day. As such, it can be very helpful to set up a regular rhythm, say coming into office every day.