Hi, so I am a 16 year old who is a avid reader and loves math. What I love most about math is how it serves as a tool to view the world.
I might pursue a math degree when I go to uni (who knows, because a. my dreams change b. uni might not be worth it because of a.i.) but regardless of my choice I want to become mathematically proffecient by the end of two years. By mathematically proficient, I mean that I have the ability to write proofs at around the IMO level (a bit unrealistic perhaps) and know real analysis and linear algebra (cuz I want to build some stuff in a.i.). Basically, I want to be creative and also have good computational skills.
The thing is, I don't know how to achieve that. I have started IGCSE Additional mathematics (I think it's equivalent to AP precalc) but it's not really enough. It doesn't teach proof-based math either. I have been in an olympiad-training program for a year but to be honest I didn't pay much attention to it. It improved my problem-solving skills a lot though.
Now, I am faced with a choice. Continue with the olympiad training while learning the computational aspect OR learn the computational aspect and then use university textbooks on proof-based math. Or should I take a different path altogether?
What do you think? I would sincerely appreciate your advice.
Thank you. Have a wonderful day!
P.S. My classmate has finished the two year syllabus of IGCSE Add math within 2 weeks and I am so confused. Should I be trying to do that too? (And no, it doesn't seem like shallow working as he seems to be getting everything correct).