Hello all!
I am a current sophomore taking AP Calculus BC with an A+ average in the class, and I was wondering which of two math pathways would be preferable for my junior/senior years of high school? I will be dual enrolling with a college just 15 minutes away from my high school, and I only have the time to take one class per semester.
Option 1: Fall - Multivariable Calculus, Spring - Linear Algebra (with the idea of taking Differential Equations then Intro to Proofs Senior year)
OR
Option 2: Fall - Multivariable Calculus, Spring - Intro to Proofs (with the idea of taking Real Analysis I&II Senior year)
I want to delve into proof-based math courses as soon as possible (Option 2), but I was wondering if taking a more holistic approach to my math education would be more advisable (Option 1). For background, I have gone through Hammack’s Book of Proof and started working through Spivak’s Calculus.
Linear Algebra is a precursor to so much advanced math I would be reluctant to skip it. Indeed, I think it is usually required for Math majors. Diffy Q less so, although it is independently interesting.
My other thought is I think you might want to actually take what this college is calling the Intro to Proofs and Real Analysis sequence (what Ohio State calls Foundations of Higher Math and Intro Analysis) at whatever college you go to for a degree. Those will likely be very interesting classes, opportunities to get to know professors, and may be tailored to their own advanced math sequences.
Indeed, even with Option 1, I wonder if rather than Intro to Proofs you should just choose something you see as fun but off your main sequence. Combinatorics? Probability? Something like that.
Option 1.
I also second the idea of taking another type of math (calculus based statistics, discrete math, probability, combinatorics) and/or algorithmics rather than Diff Eqs.
You may want to look into the special math paths at Northwestern and Harvey Mudd. Email professors there.
Finally, do not neglect the other 4 core courses (English, Social Science, Science, Foreign Language) - every year we see kids who love math and are shut out from their top schools due to not having evidence of a solid enough academic background in other subjects. Obviously only Math is going to be that advanced for you but don’t neglect the rest. If necessary, look for patterns and symetry in foreign language and art, look at the logic in science…
This is so important! We see the same thing at our feederish HS. Our poor college counselors have to explain to some kids that MIT or Princeton or whatever might not be in the cards for them because those colleges are going to look closely at their non-Math credentials too.
Of course it is great if the OP can get through MVC and Linear Algebra plus some other advanced electives–that is exactly the Math profile of the kids we do send to those colleges for Math. But they also typically are A/A+ students with some advanced courses in all the other core areas too.
Is this referring to distance education opportunities?
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I’ll be taking the highest level of AP course offerings in all of these other subjects (namely AP Lit, APUSH, Physics C and French) so I think this shouldn’t pose that much of an academic conflict. I’ll probably just need to adjust to the new academic environment and workload at most.
Thanks for the response! The chart’s particularly insightful, as the college course registrar has a confusing network of prerequisites for math classes.
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So suggesting that my senior year mathematics should probably be more exploratory in nature?
No - both universities have special programs for very advanced math students. Emailing students from that program as well as professors who work with them would give you relevant insight as to what to choose/how to choose your senior year math classes.
Reaching AP physics C, AP French, plus having 1 AP English and a couple other APs would meet expectations at any college.
That would be my recommendation. People have different attitudes about this sort of thing, but I think even if you anticipate specializing in a certain field of math in the long run, I personally feel like exploring some of the more broadly-applicable classes outside your intended main sequence is well worth doing. In part that is just because you might find it interesting. But also, people do evolve in their personal and professional interests. With math in particular, some people eventually get more excited about actually doing things with their math talents and training. And a broader math education will tend to serve you well if you end up being the sort of person who is using math in the real world.
I agree, this looks like a great overall curriculum plan. So the choice of math courses at this point really isn’t about college admissions, it is more just about what might be interesting and what will make the most sense when you understand that you will also have lots of opportunities to explore these topics while getting an actual college degree.
