Hello, my name is Alex Figueroa and I am currently a high school junior. I am highly motivated to learn math and wish to pursue a PHD in Applied Mathematics.
My question is: Would my hard work and motivation self-studying math be noticed by university admissions? If so, would it increase my chances of admission to Stanford, Princeton, or MIT? I have so much passion for mathematics (I want to learn everything there is to learn about it, and add to the plethora of mankind's mathematical knowledge), yet I fear that universities will fail to notice it.
I have began self studying calculus and am now ahead of my AP Calculus AB class. I plan to finish self studying Calculus II, Calculus III (Multivariable Calculus), and Linear Algebra before the start of my senior year. However, I searched online for opinions and perspectives on how universities would view this. The responses I read we generally along the lines of, " Colleges don't like self study. They want the student to fully grasp the concept, which is "not possible" through self study. They merely think 'This kid had nothing else to do with his time but read 1000s of pages of textbooks.'" However, I strongly disagree because mathematics is my passion. I love learning about it and think about it all the time, even when I'm supposed to be "hanging out" or "relaxing"; it stimulates my mind and is extremely pleasing to learn. I have a deep level of understanding for the mathematics that I have self studied so far and have put my mathematical skills to use by self studying even more intensively than as if I was in the class: assigning difficult exercises from multiple sources, taking notes from textbooks, videos, and online lectures, and occasionally, intuitively, discovering new (new to me) theorems before coming across them in my studies. I also plan on taking higher division classes at my local college. If possible, please contact me @email@example.com