So, I’m one of those freshmen taking Calculus BC that could’ve honestly taken it earlier if the school system had been more lenient and I’ve been studying up on Multivar and Linear Algebra lately, which I’ll be doing as Dual Enrollment next year. That part’s all fine and good, but the problem comes with the 2 years of highschool following that. Those are the highest level classes I can take through my school (no differential eqns.) and to be honest, I would much rather prefer to take Real Analysis or maybe introductory Complex Analysis, some things I’ve looked into a bit and want to study more. Is there a way I can somehow enroll in these at a local college without highschool credit, or maybe some other way to get credit for it, and how would I fit that into my highschool academics? (PS. my preferred area of study is pure mathematics - the likes of real analysis, number theory, set theory, etc.)
It’s unlikely anyone here can tell you how your high school will treat classes taken elsewhere or how they can fit in your high school schedule.
What did your high school guidance counselor say when you asked?
She said it’s something we could work out the details of later and that either way if I took classes it wouldn’t be anything credit-bearing. I just don’t know much else like what I’m actually allowed to take and how enrollment into a local college or something will work
Look into the dual enrollment rules in your school district. You’d likely want a 4-year university offering a math major that agrees on dual enrollment.
Are you preparing AIME, doing Art of problem solving?
I’ve looked into dual enrollment rules already and I can confirm that I can’t do anything for highschool credit but I do know that a local university here offers non-degree enrollment options so that’s my go-to atm. As for AIME, yes I am working on it and I just did the AIME I for the first time… let’s just say I’ve still got a while to go to get to USAMO (3/15 correct) lol… I haven’t really been focusing on competition type math as much as the pure mathematics I want to study
Usually, dual enrollment credits count toward HS graduation.
What does your HS offer for upper level credits to kids who have maxed out on the ath curriculum at your Hs?
Another option from you is to look into homeschooling rules and dual enrollment: after you’re recognized as homeschooled, typically your parents would then dual enroll you full time each semester (4-5 courses) where you would need 1 semester each, per year, enrolled in English, Math, Social science/history, Science, and Foreign language + rest of classes as you wish (in your case, each semester, you would likely take 1 math class + 2 from the mandatory list+ 1-2 other subjects.)
You need to consider a few things:
- High school graduation requirements. Do college courses taken while in high school but not officially dual enrollment count toward high school graduation requirements? Would you actually need the additional math courses to count toward high school graduation requirements, or could you fulfill them without needing them to be counted?
- College admission requirements. This may be less of an issue, since completion of calculus BC and beyond implies completion of lower level math, and you will show your college records to colleges you apply to anyway, even if the college courses are not dual enrollment.
- Transfer subject credit in college. Will the college you attend accept the advanced math courses for subject credit to equivalent math courses?
- Rigor and depth level of advanced math courses. If your local college is (for example) a state flagship with a strong research oriented math department, then courses like real analysis will likely have good rigor and depth. But if your local college’s math department does not have a lot of students going on to PhD study in math, its upper level math courses may be less rigorous or in-depth than at a state flagship with a strong research oriented math department.
- Real analysis is considered one of the more difficult upper level math courses. It is sometimes recommended for students to take other proof-heavy math courses first (e.g. honors lower level courses, upper level proof-oriented linear algebra, abstract algebra) before taking real analysis.
Yes, I’m aware, but my school stops dual enrollment at Multivar and linear algebra and offers nothing beyond that (2 years I won’t have math classes to take through school or dual enrollment)
- I’ve already planned out my graduation requirements and the only ones I need to have met following next year are English, social studies, and science (3 required classes per year since I already have all my language credits and elective/economics requirements). Of course I wouldn’t need the extra courses for fulfillment of requirements, but I want to start college with higher level classes since I already have a strong foundation and know what I want to pursue to some degree
- Having higher level courses is probably gonna be good on applications
- I would hope to go to a college with a mathematician in my preferred area of study, so even if credit doesn’t transfer, there are probably procedures to test out and/or exceptions that could be made with permission from the instructor
- The one I’m looking at applying to for those 2 years does seem to have a really advanced selection of courses for mathematics, at least from the ratings and course list on their website
- I know you’re right about this which is why I’ve been doing a bit of research into course sequencing for pure mathematics and working on my proof skills through simpler practice problems I’ve found and the earlier section of Terry Tao’s analysis 1 text
Depending on where you go to college eventually, the college may not recognize any college courses taken elsewhere. However, some of them have different levels of placement tests to place you into higher level courses if you pass their tests.
Again depending on the college, higher level courses generally don’t influence college admissions at most colleges. Doing well in competition math might.
1° you need to ask and MAKE SURE, IN WRITING that completing Multivariable and Linear Algebra at your HS will complete the math requirement for HS graduation. (It should, but you want to be sure).
Once you know that for sure, you’ll need a minimum of 1 math course per year for college admissions (you’ll probably want to take 1 each semester though). You’ll want to consult with the Math dept. or Undergraduate Chair at the nearby university and ask what they’d recommend as your first “proof based math”.
2° High school graduation requirements are totally different from selective college entrance requirements.
Look at Cornell, MIT, Williams, HarveyMudd and Northwestern 's academic requirement. Keep in mind that these are the bare minima.
No matter what your HS requires, you’ll need one each of English, Social Science/history, science, and foreign language*, every year of high school + at least 1 other class that reflects your skills and interests.
You can mix-and-match them through dual enrollment or AP if that’s allowed by your HS, as this will increase overall rigor.
3° * since you want to work in math, your choice should be French or Russian as those are the most commonly recommended/required language for math graduate study.
My recommendation would be for you to try and get through the highest level you can in one of these two languages, as well as CS and Philosophy - showing different ways in which your mind handles abstraction.
As a result, your schedule (assuming DE) would look like this
Semester1: Math, English, French/Russian, Social Science/History, CS
S2: Math, Science, Philosophy, French/Russian, elective
S3: Math, English, French/Russian, Science or CS, Social Science
S4: Math, Philosophy, Science or CS, French/Russian, elective/math
You’d need to ensure you have US History as well as European or World History, all three from Bio, Chem, Physics+1 of those at a more advanced level, foreign language through the intermediate/Upper intermediate level, English: Composition+ some form of communication or literature class.
4° you’ll need something else: competition math or anything else in terms of EC’s. A part time job can be a solid EC.
- Fortunately, I already got verification that I met the math requirement before starting highschool
- Getting in contact with the undergraduate admissions people is honestly not something I’ve thought of yet, so thanks for the info
- Quite coincidentally, I’m fluent in Russian and my grandma teaches French so I know a bit and I can actually continue with that with my her help. As for CS and philosophy, I already took AP CS A and I’m taking several other dual Enrollment CS related classes during my next few years in highschool and I plan on taking both philosophy and AP philosophy
I’ve never had difficulty with abstraction and ideas, more with trying to fit those into the restrictions of writing and other literature forms. My preferred method of idea communication is through music and math, patterns and such. - I’m starting training for AIME since I already qualified this year but I messed up on my calculations and got 3/15 ;-; if I’m lucky, I might even qualify to USAMO by senior year. As for extracurriculars and jobs, I’ve actually been working at a local Russian School of Mathematics branch as a student tutor the past few years (plan to stay throughout highschool) and I’m in a youth orchestra, I hope that’s enough in terms of extracurriculars?
The main problem I see here that I’m gonna struggle with is English and history courses, which I’ve always struggled with
In that case, if it’s affordable, you should at least consider applying to the UK where they don’t care about anything other than how good you are at math.
It’s really excellent you’re fluent in Russian and you could get a headstart on French. Get a placement test for Russian at the university and see if you can place into the Upper Intermediate or Advanced level. In that case, you could be considered “done” for that level in 1 semester, unless you wanted to take more, and if you can take Intermediate French1&2 (201-202) you would already be well on your way so that in college you can focus on advanced classes if you wish, or simply conversation clubs and language tables to keep your language at sufficient level. I suppose you’ve heard of the Budapest Math semester and you can contact mathematicians in their language if you have queries worthy of their time (Cedric Villani has social media, not sure for others; in addition to math research, he’s also active in math education reform.) I don’t know whether Polytechnique has an exchange program but Russian universities certainly would.
If you’re very advanced at math, I wouldn’t think you have difficulty with abstraction and ideas, but your knowing it is one thing: by showing clearly that you don’t -through higher level foreign language, higher level math, philosophy, and CS - you demonstrate it to adcoms, which is an entirely different hurdle to clear. Music is another way, too. All together these would create a very consistent, compelling portrait for the adcom.
Yes, your EC’s are solid.
Do you know what your parents can afford for college? I know it’s very early for you to be thinking about that but you may, indeed, have a better profile for Oxbridge than a typical US college, although Northwestern, HarveyMudd etc. have pathways for accelerated math students. Knowing what is affordable would matter.
Thank you for all the ideas and suggestions, all of this is really helpful! Unfortunately, our financial situation for college isn’t great so my best choices are either Ivy League financial aid + decent scholarships or an in-state university. UK does seem great but of course it’s international and it’s harder
If some of your in-state public universities have strong research-oriented math departments, then that can be very helpful to you, especially if a local one is such a school (where you can take math courses while in high school). Which state, if you do not mind answering?
Here are some examples of upper level course requirements and recommendations for pure math majors at some state flagship universities:
https://math.berkeley.edu/programs/undergraduate/major/pure
https://catalog.utexas.edu/undergraduate/natural-sciences/degrees-and-programs/bs-mathematics/
I live in Northern Virginia and UVA seems to have a rather decent pure math department, I looked a bit into the courses but I’m not sure about the course rigor for any of them
Run the NPC on all the colleges I listed, then come back with reactions (ok, too high, better than you feared, etc.)
Are you Pell Grant eligible? (if you don’t know, look up Fafsa forecaster).
Uva is very good but it’s not a safety at all.