Hello, I am currently a junior going to senior year high schooler and so far I have taken diff eq, lin alg, the calcs, and combinatorics. I have been doing research dealing with topology, aperiodic tilings, geometry, and algebra with a professor for about 6 months and we plan on publishing it (I will be co author). I plan on speaking at various colloquiums and likely the JMM in Denver (this is arranged with the help of profs). I will be taking abstract alg, topology (graduate material), probability (300 level), and lin alg 2 (400 level) in the fall and in the winter, logic (graduate level), abstract alg 2, complex variables , and a finance class (400 level). I will also be taking the first actuarial exam. I got a 770 in math and 650 in english for the sat but will be retaking it as well as taking the subject tests and the act in the coming months. I do highschool online (cuz I live in the middle of nowhere) I have all A+'s and will probably be valedictorian. I went through a medical crisis and was in and out of hospitals for the first ~2 years of high school ( was unable to do work during this period but caught up fast because highschool is easy lol ) but I will be graduating on time and I was not held back. My HS doesn’t offer any AP classes. I have a statewide leadership position for a mental health advocacy thing.
What universities should I think about applying to?
First thing is to talk to your parents about what they can contribute for your college education costs and run some net price calculators on some colleges (e.g. state flagship, private colleges of interest). For every other college you consider run the net price calculator.
As advanced as you are in math, you want a college with a good math graduate program, so that you have opportunities to take graduate courses and do graduate level research as an undergraduate.
I have some good scholarships from the advocacy work and a college fund set aside (both personal from research money, working and stock market as well as family). I don’t think cost is a big issue. I live in Michigan so Umich honors math looks interesting but, of course, big name universities are always intriguing but I have no idea what I’d have to do to get in to a place like that.
You need to talk to your parents about it rather than assuming and being disappointed in April of your senior year. Some universities have list prices over $70,000 per year, so you would need a lot of parental money and/or a lot of financial aid and scholarships to afford them.
University of Michigan is a highly respected school overall and in math.
Yes, you have a shot at Michigan. They are known for their math programs. World class university in your backyard and as much research then you can handle.
I would love to go to Oxford/Cambridge, though I doubt I could get in because I have no AP credits Also I have only been doing math for around 8 months since that is when I recovered.
Don’t assume that Oxford and Cambridge will automatically reject you without APs. University level courses are an adequate substitute (indeed they quite like students who have already done a year at a US university since APs aren’t as advanced as UK A levels).
I know someone whose highly gifted kid was completely unschooled, he just did college level math online for fun instead of attending high school, and got admitted to Cambridge (he got a first and is now doing a PhD back in the US). All they asked was for two S’s in the STEP 2 & 3 papers (which if you review them you will see would be a pretty challenging task for many US graduates with a math major).
If you got a tippy top (ie near perfect) score in the MAT then I suspect Oxford would invite you for an interview. Remember there is no financial aid, the total cost is around $140K-$150K for three years at current exchange rates (note it’s somewhat cheaper for single subject math than math+CS).
How would I go about taking tests such as the MAT and STEP 2+3? I would like to go into a pure math phd program so as an undergrad I’d like to be able to take at least 10 grad courses and have good opportunities for research with profs and summer RUE’s.
UMich has an amazing math department and you have a good chance. If you get your SAT scores up significantly, you might be in the running for the likes of MIT and Stanford. However, there is a danger of you appearing too one-sided. How much time does this leadership position take? Is there anything else you’re interested in?
I have 2 leadership positions I focus on, both statewide, one for mental health advocacy the other is helping with shelters (homeless, veterans, womens, etc) and together they usually take like ~5-10 hours a week but that goes way up when events come along. I have a gap of ~2 years where there’s nothing but medical records (this will be something in my essay, saying that not even 2 years gone can hold me back from achieving high and graduating on time with my friends y’know) but I still have like 500+ volunteer hours from before and after that. I love math but I also do a lot of learning outside of it for fun like studying psychology/neuro sci, physics, com sci(know a few programming languages), econ/finance, sociology (love Baudrillard), etc outside of HS. I will be taking a pretty hard finance class (4th year) in winter at the uni I take classes at which is slightly outside of math lol. I should be able to raise my SAT score to hopefully 1500+ (when I took it initially, it was in bad conditions)
Note that everyone does the same course, though there are more options in later years. But the level is pretty high (analysis is a first year course) and you just do math, nothing else, for three years so you would have much more depth than most math majors in the US.
However, summer research is not so much of a thing in the UK, instead students usually do a fourth year masters (the most famous is Cambridge Part 3 maths) as preparation for a PhD.
Hope you enjoy the beauty of complex variables. It’s so beautiful that some of the theorems will blow your mind. Some schools recommend Real Analysis first then Complex but you’ll be okay without it. If you know induction then you are set.
You need to review the details on UCAS applications and Oxford testing on their website. You need to spend plenty of time preparing for the test too. Deadlines are very early (Oct 15th) and the application format is very different. You also need an academic reference (normally a math teacher from your school but a math professor you’ve worked with will be OK) and to be prepared to go to the UK at short notice in December for an interview.
Generally Oxford is a better choice for Americans than Cambridge because MAT is in November whereas STEP isn’t until next June (with results not released until August). Once you’ve researched this yourself, ask questions in the UK forum if you have them.
In combinatorics and graph theory it’s been all proofs which is super fun, I am excited for complex var. I used things like the mobius transform when studying farey tessellations for the research I was working on in the spring, but we put that on the back-burner because we’re doing more official paid research right now involving topology and tilings. It’s wild how deep math goes, I love it.
With respect to your educational timeline, it seems you’ve experienced about ten months of schooling since eighth grade. In this compressed scenario, it’s unclear how your actual coursework and experiences could have reached the levels listed.
@merc81 I do highschool online so my hours I do the work are flexible, I tested out of all my english and math credits for highschool. I started calc 1+2 at norther Michigan university this past winter and I was able to do so because I talked with a professor there, who I am doing research with currently, and he said I could try. This summer I finished calc 3, combinatorics, diff eq and linear algebra (diff eq and linear algebra are online at a different university called Michigan technological university). That brings us to this fall and I am taking the classes previously listed, also like half the classes I am taking need an override which I get because I know the professors teaching the classes. If you’d like evidence I can give you it through email I guess lol.
If I had a kid with a serious medical condition, my interest in sending them from Michigan to the UK would be exactly zero.
OP- you need to have a sit down with your parents to discuss their financial limitations and expectations as well as everything else associated with the college search, before you get all excited about faraway options.
Also I have only been doing math for around 8 months since that is when I recovered.