High School student wanting to learn more

[flebbyman]

Hey there,

I am high school student in South Africa, and I'm passionate about maths. I'm not too sure why, but it's fascinating.

In South Africa we don't do courses, we follow a set curriculum, and we have a program similar to the AP program in the US, which I take. I'm in grade 11, and last year I took the grade 11 AP exam, and I scored a 92%. I am doing my grade 12 exams this year, but it is a bit tedious. I'm so tired of the class doing quadratic equations when I'm figuring out Line Integrals. So I'm just about finished Stewart's Calculus book, except for the finer details of multivariable stuff, which I'll finish in university.

So I am now looking at my options of what to do. Linear Algebra is the most obvious choice, and I really like Calculus, so I might do Analysis after that, but what recommendations do you have?

 

[colin.mcenroe]

You could think about studying through a differential equations book and seeing if that satisfies your interests for a while. I am sure others will have better suggestions than I do. I figure that is the progression many make with math, first do all the calculus, then linear algebra/diff eq, and then from there whatever you want.

 

[stakehoagy]

read all the math books you can find. I'm a high school sophmore currently taking calculus, but i have plans to study lots of math over the summer. just don't have that much time to go all out on it now. subjects i think i will study are same as you mentioned but also number theory. you could maybe try combinatorics, probability, graph theory, analytic geometry, set theory. while i don't have any experience at all in the areas of mathematics that i just mentioned i have read about what they are and i think they look very interesting. probably ordinary differential equations after the multivariable calculus. as far as the analysis goes, two titles that i have heard are good but not read yet are rudin's principles of mathematical analysis; and spivak's calculus on manifolds.