Sorry, I wasn’t trying to pile on; but I wasn’t going to read through a 250+ reply thread and just responded to your OP.
Eh, yeah, there have been a few of those comments scattered throughout. I’ve mostly just ignored them when they’re about things that have already been discussed. I’m not, like, bothered by them though. They definitely have some truth.
At this point the current conversation is more about the best path going forward between a few different schools (WSU and University of Tulsa) given their math departments and how grad school admissions work.
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Just not sure the Masters moves the needle much beyond undergrad if this student is able to accomplish in undergrad what we’re both suggesting. (I’m not talking about the sort of program you mentioned above, which would be funded and add prestige so probably would add value).
In any case, I think we’re agreeing that this student should squeeze every last drop of opportunity out of undergrad.
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Don’t any? Is Reed the only one?
It appears that OP knew UW wouldn’t be affordable. He has stated that WSU was affordable only because of additional merit $ that he wouldn’t have gotten at UDub.
Agreed that hindsight is 20/20, and he knows now that his list was flawed; but there was expertise needed to figure this out, and you don’t know what you don’t know.
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Not that it is advisable but outside of the box approach.
Can you go to WSU for a year and then transfer to UW? Would you get enough FA to afford the in-state tuition? You can carefully choose only classes that will transfer between WSU and UW (I bet there are databases between two schools that will show these.)
You can most likely be a TA for intro classes at UW to support yourself a bit. Then all your problems are solved. You are in good public with great Math classes and can complete PhD at UW.
BTW, you can always tutor HS students on the side with SAT to make some money.
Another option is GAP year with the goal of UW. It most likely will take most of your credits, so you possibly can graduate in 3 years there and catch up with everything.
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For direct admission to a top PhD program, two of the most important factors are 1) the quality of your research and/or publications, and 2) the strength of your recommendations. Which ever school you choose, you need to find professor(s) (at the college or outside) who can sponsor your research and who is relatively known and respected in the field in order for their recommendations to carry sufficient weight. The situation you find yourself in isn’t ideal, but you can still do it.
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Would changing the area of math I focused on between undergraduate and grad school be a reasonable possibility? I.e. studying analysis at Tulsa, and then if I don’t like it try to graduate a little early and study some other area of mathematics for my PhD?
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A friend’s son did his math undergrad at CMU and then headed to UCSD for their PhD program. In his first two years, he needed to pass qualifying exams in three different subject areas, and then proceed with his work in his chosen specialty area, which did not turn out to be quite what he anticipated going in. So yes, it not only seems possible to pivot in terms of focus, but actually encouraged by the program requirements - some exploration is built in. I can’t speak to how universal this is, but I suspect it’s pretty normal.
(The sequel to this story is that the student got poached by a tech company that made him an exciting offer-he-couldn’t refuse, so he ended up taking the Masters and leaving the PhD program to take the job. He was able to structure this as a leave of absence, so he can still go back within a certain amount of time if he changes his mind. So that’s another thing that can happen!)
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This is so typical situation. I know quite a few incredibly smart people who left PhD programs with Masters due to many different reasons. Actually friend of ours very recently got PhD in CS :). He already has a child in college. He finally completed his PhD just for fun of it during COVID time. He obviously does not need it for his job, since he has his own consulting business for years.
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For top PhD programs that attract a lot of applicants, you’ll be asked to identify the professors you’d like to work with and why on your applications. It’d be harder to justify why you want to pursue your interest in an area different from your prior research and coursework, but not impossible.
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For typical math majors, I’d say linear algebra serves as the gateway course into college-level mathematics.
My guess is - and I know little about math and you all are talking way above me - but my guess is that as a high schooler, even an advanced one, there’s likely an absolute ton to learn in the future - so no matter what OP decides, he will be challenged and exposed to so many things that he likely doesn’t even yet know exist.
OP - your interaction with everyone is awesome!!
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It was for me (if you don’t count the standard intro to proof sort of course that introduces you to cardinality and bijections and things), although I must say, in retrospect it feels like doing abstract algebra first would make more sense. As it is, I basically spent a whole semester working with vector spaces over generic fields, and then only afterwards got a formal definition of what a field is. During linear algebra, my best definition was “like the rational, real, or complex numbers.”
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If you do summer research on different topics (or independent study) that can support applying for a PhD in a different area. You could also take a year off to pursue paid research after undergrad while applying.
My son did both of those things. I don’t think his PhD program is a top one, but it’s in his area of interest with professors doing well in the field. His undergrad majors were math and physics at an LAC. His PhD will fall under engineering.
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The more I look into grad school applications for math, the more I’m wondering if taking a gap year actually does make the most sense. I’m not the most active person, but I could spend a year binging as much MIT OpenCourseWare as possible. I wouldn’t necessarily have to stop learning.
Tulsa has a lot of great qualities, but after sitting with the decision for a while, I don’t think I’d want to go there over WSU. There might be a way to make it work, but if I don’t go down the analysis route (and I kinda doubt I will), I don’t think I’ll end up being very happy with the research I’d be doing the last couple years, and I’d have to switch fields between undergraduate and graduate, which would be difficult.
Is taking a gap year as a math student reasonable? I’d be worried about losing the NMF aid though if I didn’t get into a non-safety school on the new round of applications.
You can ask but ultimately bird in hand.
Taking off to take open source isn’t worth it. Enroll in school now and learn.
You can’t predict your future with any certainty at 18.
In many ways this is over complicating.
You don’t know far more than you do. Not at 18.
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I’m not sure what you mean by that last statement. It seems self-evident regardless of age.
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My point is. U r super bright. U already know way more about math than I ever will.
And your passion is awesome.
But in the grand scheme of the subject and life, you’re still in the first inning.
Get in now. Wherever you feel best. Learn. Explore. A gap year isn’t likely for you.
My guess is either choice is fine and both will blow you away and both will support if you show the level of interest and effort that I’m sure you will.
Ps a gap year likely means, even if studying on your own, that you come back very rusty.
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Yes, I think the money is the biggest issue. A second issue would be connections.
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Money. If your father won’t contribute, then you are left with what your mother can pay, which I believe you said is low. There are a few schools that base financial aid only on the household income of the custodial parent, but you would need to find one that both has a good math department AND accepts you. Of course you could work to make money during your gap year, but realistically how much can you make?
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Connections. The students on CC who have taken gap years after disappointing results typically retooled their applications with the help of connections, e.g. prep school kids who were given internships, rich kids who did extensive service-travel or who immersed themselves in often expensive activities (intensive dive into music lessons etc.) Do you have that sort of connections and money?