Earlier this year, I became bored and decided to begin learning math beyond my grade level. I soon discovered that I had greatly underestimated my abilities, and I could teach myself well into calculus (currently in grade 7). However, after losing my initial interest, I slowed down dramatically. The New Year has reminded me that, if I want to pursue my current interests, I first need to learn basic maths (calculus, ode, pde, etc.), and I have a limited amount of time to do so. This leads to my original question: How can I plan my self-teaching in a way such that I am proficient in partial differential equations by the end of high school?