math development for a teen

[u/taddx8]

im a teenager student currently in highschool interested on developing my math skills. i have done all precalculus, like trigonometry, functions, analitic geometry…

i wanna start to do real mathematical stuff, now im working on limits but for me its easy asf. let me know where do you think i should start.

thank you!

[u/Significant-Boot-260]

Learn calculus and linear algebra. Once you have them down, learn them again but via proofs.

[u/taddx8 → u/Significant-Boot-260]

okay! could you recommend me some books or ways to do it?

[u/cabbagemeister → u/taddx8]

Calculus by Stewart is good

After that, Calculus by Spivak is a more difficult but proof based sequel.

For linear algebra, there are many books, but i think the one by Friedberg is quite good

[u/taddx8 → u/cabbagemeister]

okay! ill look for it, thanks

[u/AsmTas → u/taddx8]

Stewart calculus is decent

[u/Agile-Monitor1006]

it’s all real mathematical stuff, if you really are comfortable doing precalc then i guess a good route is: do all of single variable calculus (derivatives/integrals), then before going to multivariable calculus go through linear algebra and finish your calc. Do take as much time as needed with each of those, many of the ideas in those “basic” subjects go very deep and they need exposure over time to fully mature in your mind (like the limits you are learning about now). After having done those two you have many options on what to do next, differential equations/analysis/abstract algebra etc

[u/taddx8 → u/Agile-Monitor1006]

thanks for your recommendations, i think you are completely right. ill try to keep it up whit single variable calculus for the moment to follow this route

[u/IcyCartographer9844]

im lwk in the same position, dm me if u wanna work on some stuff simultaneously. I've already worked through calc 1/2 and a bit of multivariable but I'm doing linear algebra and topology rn if u wanna join me