My son is a freshman math/CS major in one of the top schools. He wants to go to a top graduate program in math afterwards. His advisor is telling him to take more targeted math classes throughout undergrad, to concentrate on one area. This sounds counter-intuitive to me because even if he’s way more advanced than your average HS grad, he doesn’t know nearly enough math to be able to pick an area that he’ll enjoy most, and I’d think it’s best to gain general understanding of several different areas before picking one.
Also we are aware that undergraduate research is important for admissions. Again, should he try to stick with one area of research throughout his undergraduate years and maybe get more impressive results, or try different things? He has already found a professor to work with this summer, but he doesn’t necessarily want to stick with this area (applied math/stats) through graduate school. He says he wants to do more pure math but he’s not going to be able to do any meaningful research in pure math after his freshman year anyway.
I would love to hear from current T20 STEM grad students about their undergrad experiences.
Our system was different in the UK (9-10 math courses per year for 3 years), but students knew if they were pure or applied by the end of the first year and by the end of year two you knew more specifically what research you would want to do for a PhD.
The US system has so many fewer math courses as part of a degree (maybe 15 required though I guess a strong student might take more) that to get a decent level of preparation I think you’d want to have at least half of them (probably most courses beyond analysis if you are well ahead of the regular sequence) being increasingly specialized in one area.
First semester freshman year, most kids at most schools haven’t even officially declared a major let alone picked a field within a major to specialize in.
At most top math PhD programs, the “kids” have to finish their “qual” courses in the first year, and only then decide what courses to take in a particular field to continue their research specialization.
Expecting a kid to decide in freshman year undergrad, what they needn’t decide until the beginning of the second year of a PhD program sounds like remarkably dumb advice and a great way to drive someone away from the major entirely.
Well, usually I’d defer to a math professor, who has likely gotten dozens of students into graduate school and may even have some graduate students of his own depending on the kind of school your son attends. Your son may want to talk to other math professors at his college if he’s not sure if this is a matter of opinion vs. an actual requirement.
I’m not in math - and math is a bit different because the foundational knowledge required to do research is so much higher than in other fields - but generally speaking, it’s usually in the middle. Most U.S. college students looking to go to graduate school should take a wide range of foundational coursework in their area, but by the time they get to their junior or senior year, should be able to identify a specific area in which they are interested and concentrate a certain number of classes (3-5) in that area.
I am a prof in engineering, so the comparison not be perfectly one-to-one, but I’ve seen a fairly wide range in how specialized undergrads are when applying to and entering graduate school. Engineering curricula are so prescribed that there is limited opportunity for specialization anyway. What specialization does occur is due to a small number of elective courses and any undergraduate research experience. The former is usually limited and the latter is generally subject to the available openings in the student’s department at the time they are looking (i.e. luck).
So, as a PI looking for new graduate students, I am not fixated so much on specialization as much as I am on evidence that a student has the academic chops to handle the graduate program and the rest of the basic skills required to handle doing multiple years of research. This means I’d like to see a reasonably high GPA (doesn’t have to be perfect), especially in math and later coursework related to their proposed research area. I’d also like to see research experience (doesn’t matter what field, so much) and a good reference letter from the research advisor that can speak to that students’ ability in the lab.