While that may be true for some subjects, where you need to spend years gathering data, math and especially pure math is very much a test of (a particular kind of) intelligence.
Ah well. Perhaps I was just being optimistic.
I don’t remember ever dreaming in math. I had a dream a while back where I was a node traveling along a connected graph, and another where I was given magic powers related to the number 3, but I didn’t really reach any conclusions in either, so I’m not sure that counts. There were just some mathy things in the setting. Although, to be fair, I’m also yet to encounter a problem difficult enough that I’d need to ponder it for days on end (that I was trying to solve. I’m not counting the Riemann zeta hypothesis here). Although maybe it’s concerning I haven’t already started seeking out such problems? Not sure. I should also probably just get more sleep: I don’t remember dreaming much in general.
I used to seek out problems like that more often, but then once I started taking college classes that I could no longer just test out of I thought “studying things independently is just gonna make me more bored when those things come up in classes, so I should probably stop.”
There are a number of things that sound interesting to me at the moment - but analysis isn’t one of them. At the same time, I haven’t taken real analysis yet, so I can’t be sure.
I find differential geometry really interesting, probably because of me wanting to be able to understand what relativity saying space is bent actually means. Things like algebraic topology and knot theory also sound very cool. I did a little MIT OpenCourseWare on Theory of Computation and really liked the style of it, although I don’t really want to go into CS. Abstract algebra just sort of clicked for me right away. I liked linear algebra theory, right up until the point where I actually had to do things with specific matrices. I found weird things like the Poincare Disk really interesting in my Euclidean and non-Euclidean geometry course (although I was disappointed with how little non-Euclidean there was).
With the prestige thing, would you recommend I go to Tulsa and explore the areas I find interesting, and then just try to graduate early and not worry about their advanced offerings, and learn that stuff while getting a Masters?
I guess all people are different. I found myself solving problems while dreaming even in High School ( I was in some magnet program) and quite often in college. But that is not an indication of anything. It is more indication of how different brains work and possible persistent preoccupation with some Math problems that you want to crack.
I really believe that you are going to be successful at any college if you will continue to love what you study. You just need to find an area that is interesting for you.
That is another one that I wanted to ask too. However, if Tulsa is more advanced, repeating some Math classes (above Calc) may only help for possible future PhD student.
You probably don’t want to go for a Master’s, but instead enter a PhD program directly. PhD programs are usually funded (they pay your tuition and you get a stipend to live on). Master’s programs usually are not. (You may have to do some teaching in exchange for the PhD stipend).
In some disciplines, you can “pick up” a Master’s en route to a PhD – not sure if math is one of them.
If you are interested in PhD and need funding for grad school, you are better with PhD program. PhD students are almost always supported at least by public schools. Master programs are generally not funded. However, Math departments can be a bit different at different schools.
For example, GaTech 20+ years ago supported master’s Math students (I have no idea what is going there at the graduate level now). They needed a ton of TAs for all intro Math classes. I actually was teaching Calc recitation as a senior while I was doing BS in a pair with Math Statistics MS student who was teaching lectures. That support was given only by Math department. Many other students from other departments did not get tuition waivers and jobs and often had to pay even OOS tuition there as Master students.
I think the main idea with getting a Masters somewhere else is that it might provide a “prestige stepping-stone” of sorts. Go somewhere not that prestigious for undergrad, then somewhere more so for Masters, then more so for PhD.
Going to Tulsa would be considerably cheaper than WSU, so if a Masters program would be more expensive than directly going for a PhD, Tulsa might be better at accommodating that.
I don’t really have a great sense of how necessary such a stepping stone would be though.
Yes, you can always pick up Master’s on the way to Ph.D. (while in the Ph.D. program) for free if you are interested. You just need to satisfy the requirements for the program.
If Tulsa is going to be really cheap, then I would think about absorbing as much as you can. And working closely with a professor who will give you research experience and write your recommendation is very important. I’m not sure why graduating early makes sense, it certainly doesn’t if you want the best chance of getting into grad school. My S had finished almost everything for his degree after three years, so in his senior year he was doing research with professors, writing an honors thesis and participating in relevant ECs. He only took one or two taught courses total in three quarters.
A masters that is not part of a PhD program is hard to find funding for without something like a Churchill scholarship. And you need to demonstrate you can succeed in advanced courses before you can even get admitted to something like that. For comparison look at how much is covered in three years in a Cambridge undergrad math course:
So Tulsa gives you full ride as NMF, and WSU does not?
Then I would go with Tulsa but make sure that you are aware will registrar take some of your classes or not, so you will not be disappointed later.
Can you check with Tulsa professors, do they have some Math department partnerships with other schools? You can do some summer programs at other schools and participate in some research even while you are far away.
I think this is mistaken thinking. Best route is to do good work with profs as an undergrad, maybe some combo of thesis, independent study, some grad work, research. Build relationships with faculty as an undergrad. They will mentor you and their recommendations plus your body of work will get you into a good Ph.D program fully funded.
Unless Masters is a specialized program or some sort of funded, highly prestigious fellowship, it is not a useful steppingstone.
I’d go into undergrad thinking it’s my launching pad into Ph.D (or if I change my mind, lucrative quant job somewhere).
It will be challenging to get into a top math PhD program from a lower ranking undergrad institution. And it matters for subsequent academic appointments (I believe economics is similarly elitist). That’s why doing a masters as a stepping stone is AFAIK more common in math than in other STEM subjects. 250 students per year do the MMath at Cambridge with more than half coming from elsewhere.
But I would ask Tulsa about the paths followed by their graduating math majors.
I have no doubt you can get into a funded math PhD without a masters. But I wouldn’t assume that it’s a good career move to do a PhD at a low ranking institution. It’s not unlike considering the prospects from a T14 vs a T100 law school (though fortunately without the debt).
Very few data points are publicly available. According to Placement Outcomes & Statistics - The University of Tulsa, in 2021, one math graduate at Tulsa went to grad school, joining the Master’s program at UT Austin. In 2020, two went, one joining WUSTL (didn’t indicate Master’s or Ph.D.) and the other staying at Tulsa. In 2019, two went, but didn’t say where.
Most LACs would not have large enough math departments with enough depth and breadth of upper (and graduate) level math offerings for the OP, who is taking college junior level math courses while in high school. For example, here is Whitman’s math course list: https://www.whitman.edu/documents/Offices/Registrar/Catalog/Mathematics-and-Statistics.pdf , where there are likely only about three upper level pure math courses for the OP to take (real analysis I and II and complex variables).
UW was still a mistake though I think. It might’ve had worse financial aid than WSU, and Seattle isn’t exactly a cheap area to live, so I don’t know if it would’ve been viable, but I should’ve at least tried. As Tulsa illustrates, breadth at LACs varies considerably, yeah.